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目錄樹: 0d0f306fc2
raylib-src/src/external/OculusSDK/LibOVR/Include/Extras/OVR_Math.h

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/********************************************************************************//**
\file OVR_Math.h
\brief Implementation of 3D primitives such as vectors, matrices.
\copyright Copyright 2014-2016 Oculus VR, LLC All Rights reserved.
*************************************************************************************/
#ifndef OVR_Math_h
#define OVR_Math_h
// This file is intended to be independent of the rest of LibOVR and LibOVRKernel and thus
// has no #include dependencies on either.
#include <math.h>
#include <stdint.h>
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <float.h>
#include "../OVR_CAPI.h" // Currently required due to a dependence on the ovrFovPort_ declaration.
#if defined(_MSC_VER)
#pragma warning(push)
#pragma warning(disable: 4127) // conditional expression is constant
#endif
#if defined(_MSC_VER)
#define OVRMath_sprintf sprintf_s
#else
#define OVRMath_sprintf snprintf
#endif
//-------------------------------------------------------------------------------------
// ***** OVR_MATH_ASSERT
//
// Independent debug break implementation for OVR_Math.h.
#if !defined(OVR_MATH_DEBUG_BREAK)
#if defined(_DEBUG)
#if defined(_MSC_VER)
#define OVR_MATH_DEBUG_BREAK __debugbreak()
#else
#define OVR_MATH_DEBUG_BREAK __builtin_trap()
#endif
#else
#define OVR_MATH_DEBUG_BREAK ((void)0)
#endif
#endif
//-------------------------------------------------------------------------------------
// ***** OVR_MATH_ASSERT
//
// Independent OVR_MATH_ASSERT implementation for OVR_Math.h.
#if !defined(OVR_MATH_ASSERT)
#if defined(_DEBUG)
#define OVR_MATH_ASSERT(p) if (!(p)) { OVR_MATH_DEBUG_BREAK; }
#else
#define OVR_MATH_ASSERT(p) ((void)0)
#endif
#endif
//-------------------------------------------------------------------------------------
// ***** OVR_MATH_STATIC_ASSERT
//
// Independent OVR_MATH_ASSERT implementation for OVR_Math.h.
#if !defined(OVR_MATH_STATIC_ASSERT)
#if defined(__cplusplus) && ((defined(_MSC_VER) && (defined(_MSC_VER) >= 1600)) || defined(__GXX_EXPERIMENTAL_CXX0X__) || (__cplusplus >= 201103L))
#define OVR_MATH_STATIC_ASSERT static_assert
#else
#if !defined(OVR_SA_UNUSED)
#if defined(__GNUC__) || defined(__clang__)
#define OVR_SA_UNUSED __attribute__((unused))
#else
#define OVR_SA_UNUSED
#endif
#define OVR_SA_PASTE(a,b) a##b
#define OVR_SA_HELP(a,b) OVR_SA_PASTE(a,b)
#endif
#define OVR_MATH_STATIC_ASSERT(expression, msg) typedef char OVR_SA_HELP(compileTimeAssert, __LINE__) [((expression) != 0) ? 1 : -1] OVR_SA_UNUSED
#endif
#endif
namespace OVR {
template<class T>
const T OVRMath_Min(const T a, const T b)
{ return (a < b) ? a : b; }
template<class T>
const T OVRMath_Max(const T a, const T b)
{ return (b < a) ? a : b; }
template<class T>
void OVRMath_Swap(T& a, T& b)
{ T temp(a); a = b; b = temp; }
//-------------------------------------------------------------------------------------
// ***** Constants for 3D world/axis definitions.
// Definitions of axes for coordinate and rotation conversions.
enum Axis
{
Axis_X = 0, Axis_Y = 1, Axis_Z = 2
};
// RotateDirection describes the rotation direction around an axis, interpreted as follows:
// CW - Clockwise while looking "down" from positive axis towards the origin.
// CCW - Counter-clockwise while looking from the positive axis towards the origin,
// which is in the negative axis direction.
// CCW is the default for the RHS coordinate system. Oculus standard RHS coordinate
// system defines Y up, X right, and Z back (pointing out from the screen). In this
// system Rotate_CCW around Z will specifies counter-clockwise rotation in XY plane.
enum RotateDirection
{
Rotate_CCW = 1,
Rotate_CW = -1
};
// Constants for right handed and left handed coordinate systems
enum HandedSystem
{
Handed_R = 1, Handed_L = -1
};
// AxisDirection describes which way the coordinate axis points. Used by WorldAxes.
enum AxisDirection
{
Axis_Up = 2,
Axis_Down = -2,
Axis_Right = 1,
Axis_Left = -1,
Axis_In = 3,
Axis_Out = -3
};
struct WorldAxes
{
AxisDirection XAxis, YAxis, ZAxis;
WorldAxes(AxisDirection x, AxisDirection y, AxisDirection z)
: XAxis(x), YAxis(y), ZAxis(z)
{ OVR_MATH_ASSERT(abs(x) != abs(y) && abs(y) != abs(z) && abs(z) != abs(x));}
};
} // namespace OVR
//------------------------------------------------------------------------------------//
// ***** C Compatibility Types
// These declarations are used to support conversion between C types used in
// LibOVR C interfaces and their C++ versions. As an example, they allow passing
// Vector3f into a function that expects ovrVector3f.
typedef struct ovrQuatf_ ovrQuatf;
typedef struct ovrQuatd_ ovrQuatd;
typedef struct ovrSizei_ ovrSizei;
typedef struct ovrSizef_ ovrSizef;
typedef struct ovrSized_ ovrSized;
typedef struct ovrRecti_ ovrRecti;
typedef struct ovrVector2i_ ovrVector2i;
typedef struct ovrVector2f_ ovrVector2f;
typedef struct ovrVector2d_ ovrVector2d;
typedef struct ovrVector3f_ ovrVector3f;
typedef struct ovrVector3d_ ovrVector3d;
typedef struct ovrVector4f_ ovrVector4f;
typedef struct ovrVector4d_ ovrVector4d;
typedef struct ovrMatrix2f_ ovrMatrix2f;
typedef struct ovrMatrix2d_ ovrMatrix2d;
typedef struct ovrMatrix3f_ ovrMatrix3f;
typedef struct ovrMatrix3d_ ovrMatrix3d;
typedef struct ovrMatrix4f_ ovrMatrix4f;
typedef struct ovrMatrix4d_ ovrMatrix4d;
typedef struct ovrPosef_ ovrPosef;
typedef struct ovrPosed_ ovrPosed;
typedef struct ovrPoseStatef_ ovrPoseStatef;
typedef struct ovrPoseStated_ ovrPoseStated;
namespace OVR {
// Forward-declare our templates.
template<class T> class Quat;
template<class T> class Size;
template<class T> class Rect;
template<class T> class Vector2;
template<class T> class Vector3;
template<class T> class Vector4;
template<class T> class Matrix2;
template<class T> class Matrix3;
template<class T> class Matrix4;
template<class T> class Pose;
template<class T> class PoseState;
// CompatibleTypes::Type is used to lookup a compatible C-version of a C++ class.
template<class C>
struct CompatibleTypes
{
// Declaration here seems necessary for MSVC; specializations are
// used instead.
typedef struct {} Type;
};
// Specializations providing CompatibleTypes::Type value.
template<> struct CompatibleTypes<Quat<float> > { typedef ovrQuatf Type; };
template<> struct CompatibleTypes<Quat<double> > { typedef ovrQuatd Type; };
template<> struct CompatibleTypes<Matrix2<float> > { typedef ovrMatrix2f Type; };
template<> struct CompatibleTypes<Matrix2<double> > { typedef ovrMatrix2d Type; };
template<> struct CompatibleTypes<Matrix3<float> > { typedef ovrMatrix3f Type; };
template<> struct CompatibleTypes<Matrix3<double> > { typedef ovrMatrix3d Type; };
template<> struct CompatibleTypes<Matrix4<float> > { typedef ovrMatrix4f Type; };
template<> struct CompatibleTypes<Matrix4<double> > { typedef ovrMatrix4d Type; };
template<> struct CompatibleTypes<Size<int> > { typedef ovrSizei Type; };
template<> struct CompatibleTypes<Size<float> > { typedef ovrSizef Type; };
template<> struct CompatibleTypes<Size<double> > { typedef ovrSized Type; };
template<> struct CompatibleTypes<Rect<int> > { typedef ovrRecti Type; };
template<> struct CompatibleTypes<Vector2<int> > { typedef ovrVector2i Type; };
template<> struct CompatibleTypes<Vector2<float> > { typedef ovrVector2f Type; };
template<> struct CompatibleTypes<Vector2<double> > { typedef ovrVector2d Type; };
template<> struct CompatibleTypes<Vector3<float> > { typedef ovrVector3f Type; };
template<> struct CompatibleTypes<Vector3<double> > { typedef ovrVector3d Type; };
template<> struct CompatibleTypes<Vector4<float> > { typedef ovrVector4f Type; };
template<> struct CompatibleTypes<Vector4<double> > { typedef ovrVector4d Type; };
template<> struct CompatibleTypes<Pose<float> > { typedef ovrPosef Type; };
template<> struct CompatibleTypes<Pose<double> > { typedef ovrPosed Type; };
//------------------------------------------------------------------------------------//
// ***** Math
//
// Math class contains constants and functions. This class is a template specialized
// per type, with Math<float> and Math<double> being distinct.
template<class T>
class Math
{
public:
// By default, support explicit conversion to float. This allows Vector2<int> to
// compile, for example.
typedef float OtherFloatType;
static int Tolerance() { return 0; } // Default value so integer types compile
};
//------------------------------------------------------------------------------------//
// ***** double constants
#define MATH_DOUBLE_PI 3.14159265358979323846
#define MATH_DOUBLE_TWOPI (2*MATH_DOUBLE_PI)
#define MATH_DOUBLE_PIOVER2 (0.5*MATH_DOUBLE_PI)
#define MATH_DOUBLE_PIOVER4 (0.25*MATH_DOUBLE_PI)
#define MATH_FLOAT_MAXVALUE (FLT_MAX)
#define MATH_DOUBLE_RADTODEGREEFACTOR (360.0 / MATH_DOUBLE_TWOPI)
#define MATH_DOUBLE_DEGREETORADFACTOR (MATH_DOUBLE_TWOPI / 360.0)
#define MATH_DOUBLE_E 2.71828182845904523536
#define MATH_DOUBLE_LOG2E 1.44269504088896340736
#define MATH_DOUBLE_LOG10E 0.434294481903251827651
#define MATH_DOUBLE_LN2 0.693147180559945309417
#define MATH_DOUBLE_LN10 2.30258509299404568402
#define MATH_DOUBLE_SQRT2 1.41421356237309504880
#define MATH_DOUBLE_SQRT1_2 0.707106781186547524401
#define MATH_DOUBLE_TOLERANCE 1e-12 // a default number for value equality tolerance: about 4500*Epsilon;
#define MATH_DOUBLE_SINGULARITYRADIUS 1e-12 // about 1-cos(.0001 degree), for gimbal lock numerical problems
//------------------------------------------------------------------------------------//
// ***** float constants
#define MATH_FLOAT_PI float(MATH_DOUBLE_PI)
#define MATH_FLOAT_TWOPI float(MATH_DOUBLE_TWOPI)
#define MATH_FLOAT_PIOVER2 float(MATH_DOUBLE_PIOVER2)
#define MATH_FLOAT_PIOVER4 float(MATH_DOUBLE_PIOVER4)
#define MATH_FLOAT_RADTODEGREEFACTOR float(MATH_DOUBLE_RADTODEGREEFACTOR)
#define MATH_FLOAT_DEGREETORADFACTOR float(MATH_DOUBLE_DEGREETORADFACTOR)
#define MATH_FLOAT_E float(MATH_DOUBLE_E)
#define MATH_FLOAT_LOG2E float(MATH_DOUBLE_LOG2E)
#define MATH_FLOAT_LOG10E float(MATH_DOUBLE_LOG10E)
#define MATH_FLOAT_LN2 float(MATH_DOUBLE_LN2)
#define MATH_FLOAT_LN10 float(MATH_DOUBLE_LN10)
#define MATH_FLOAT_SQRT2 float(MATH_DOUBLE_SQRT2)
#define MATH_FLOAT_SQRT1_2 float(MATH_DOUBLE_SQRT1_2)
#define MATH_FLOAT_TOLERANCE 1e-5f // a default number for value equality tolerance: 1e-5, about 84*EPSILON;
#define MATH_FLOAT_SINGULARITYRADIUS 1e-7f // about 1-cos(.025 degree), for gimbal lock numerical problems
// Single-precision Math constants class.
template<>
class Math<float>
{
public:
typedef double OtherFloatType;
static inline float Tolerance() { return MATH_FLOAT_TOLERANCE; }; // a default number for value equality tolerance
static inline float SingularityRadius() { return MATH_FLOAT_SINGULARITYRADIUS; }; // for gimbal lock numerical problems
};
// Double-precision Math constants class
template<>
class Math<double>
{
public:
typedef float OtherFloatType;
static inline double Tolerance() { return MATH_DOUBLE_TOLERANCE; }; // a default number for value equality tolerance
static inline double SingularityRadius() { return MATH_DOUBLE_SINGULARITYRADIUS; }; // for gimbal lock numerical problems
};
typedef Math<float> Mathf;
typedef Math<double> Mathd;
// Conversion functions between degrees and radians
// (non-templated to ensure passing int arguments causes warning)
inline float RadToDegree(float rad) { return rad * MATH_FLOAT_RADTODEGREEFACTOR; }
inline double RadToDegree(double rad) { return rad * MATH_DOUBLE_RADTODEGREEFACTOR; }
inline float DegreeToRad(float deg) { return deg * MATH_FLOAT_DEGREETORADFACTOR; }
inline double DegreeToRad(double deg) { return deg * MATH_DOUBLE_DEGREETORADFACTOR; }
// Square function
template<class T>
inline T Sqr(T x) { return x*x; }
// Sign: returns 0 if x == 0, -1 if x < 0, and 1 if x > 0
template<class T>
inline T Sign(T x) { return (x != T(0)) ? (x < T(0) ? T(-1) : T(1)) : T(0); }
// Numerically stable acos function
inline float Acos(float x) { return (x > 1.0f) ? 0.0f : (x < -1.0f) ? MATH_FLOAT_PI : acosf(x); }
inline double Acos(double x) { return (x > 1.0) ? 0.0 : (x < -1.0) ? MATH_DOUBLE_PI : acos(x); }
// Numerically stable asin function
inline float Asin(float x) { return (x > 1.0f) ? MATH_FLOAT_PIOVER2 : (x < -1.0f) ? -MATH_FLOAT_PIOVER2 : asinf(x); }
inline double Asin(double x) { return (x > 1.0) ? MATH_DOUBLE_PIOVER2 : (x < -1.0) ? -MATH_DOUBLE_PIOVER2 : asin(x); }
#if defined(_MSC_VER)
inline int isnan(double x) { return ::_isnan(x); }
#elif !defined(isnan) // Some libraries #define isnan.
inline int isnan(double x) { return ::isnan(x); }
#endif
template<class T>
class Quat;
//-------------------------------------------------------------------------------------
// ***** Vector2<>
// Vector2f (Vector2d) represents a 2-dimensional vector or point in space,
// consisting of coordinates x and y
template<class T>
class Vector2
{
public:
typedef T ElementType;
static const size_t ElementCount = 2;
T x, y;
Vector2() : x(0), y(0) { }
Vector2(T x_, T y_) : x(x_), y(y_) { }
explicit Vector2(T s) : x(s), y(s) { }
explicit Vector2(const Vector2<typename Math<T>::OtherFloatType> &src)
: x((T)src.x), y((T)src.y) { }
static Vector2 Zero() { return Vector2(0, 0); }
// C-interop support.
typedef typename CompatibleTypes<Vector2<T> >::Type CompatibleType;
Vector2(const CompatibleType& s) : x(s.x), y(s.y) { }
operator const CompatibleType& () const
{
OVR_MATH_STATIC_ASSERT(sizeof(Vector2<T>) == sizeof(CompatibleType), "sizeof(Vector2<T>) failure");
return reinterpret_cast<const CompatibleType&>(*this);
}
bool operator== (const Vector2& b) const { return x == b.x && y == b.y; }
bool operator!= (const Vector2& b) const { return x != b.x || y != b.y; }
Vector2 operator+ (const Vector2& b) const { return Vector2(x + b.x, y + b.y); }
Vector2& operator+= (const Vector2& b) { x += b.x; y += b.y; return *this; }
Vector2 operator- (const Vector2& b) const { return Vector2(x - b.x, y - b.y); }
Vector2& operator-= (const Vector2& b) { x -= b.x; y -= b.y; return *this; }
Vector2 operator- () const { return Vector2(-x, -y); }
// Scalar multiplication/division scales vector.
Vector2 operator* (T s) const { return Vector2(x*s, y*s); }
Vector2& operator*= (T s) { x *= s; y *= s; return *this; }
Vector2 operator/ (T s) const { T rcp = T(1)/s;
return Vector2(x*rcp, y*rcp); }
Vector2& operator/= (T s) { T rcp = T(1)/s;
x *= rcp; y *= rcp;
return *this; }
static Vector2 Min(const Vector2& a, const Vector2& b) { return Vector2((a.x < b.x) ? a.x : b.x,
(a.y < b.y) ? a.y : b.y); }
static Vector2 Max(const Vector2& a, const Vector2& b) { return Vector2((a.x > b.x) ? a.x : b.x,
(a.y > b.y) ? a.y : b.y); }
Vector2 Clamped(T maxMag) const
{
T magSquared = LengthSq();
if (magSquared <= Sqr(maxMag))
return *this;
else
return *this * (maxMag / sqrt(magSquared));
}
// Compare two vectors for equality with tolerance. Returns true if vectors match withing tolerance.
bool IsEqual(const Vector2& b, T tolerance =Math<T>::Tolerance()) const
{
return (fabs(b.x-x) <= tolerance) &&
(fabs(b.y-y) <= tolerance);
}
bool Compare(const Vector2& b, T tolerance = Math<T>::Tolerance()) const
{
return IsEqual(b, tolerance);
}
// Access element by index
T& operator[] (int idx)
{
OVR_MATH_ASSERT(0 <= idx && idx < 2);
return *(&x + idx);
}
const T& operator[] (int idx) const
{
OVR_MATH_ASSERT(0 <= idx && idx < 2);
return *(&x + idx);
}
// Entry-wise product of two vectors
Vector2 EntrywiseMultiply(const Vector2& b) const { return Vector2(x * b.x, y * b.y);}
// Multiply and divide operators do entry-wise math. Used Dot() for dot product.
Vector2 operator* (const Vector2& b) const { return Vector2(x * b.x, y * b.y); }
Vector2 operator/ (const Vector2& b) const { return Vector2(x / b.x, y / b.y); }
// Dot product
// Used to calculate angle q between two vectors among other things,
// as (A dot B) = |a||b|cos(q).
T Dot(const Vector2& b) const { return x*b.x + y*b.y; }
// Returns the angle from this vector to b, in radians.
T Angle(const Vector2& b) const
{
T div = LengthSq()*b.LengthSq();
OVR_MATH_ASSERT(div != T(0));
T result = Acos((this->Dot(b))/sqrt(div));
return result;
}
// Return Length of the vector squared.
T LengthSq() const { return (x * x + y * y); }
// Return vector length.
T Length() const { return sqrt(LengthSq()); }
// Returns squared distance between two points represented by vectors.
T DistanceSq(const Vector2& b) const { return (*this - b).LengthSq(); }
// Returns distance between two points represented by vectors.
T Distance(const Vector2& b) const { return (*this - b).Length(); }
// Determine if this a unit vector.
bool IsNormalized() const { return fabs(LengthSq() - T(1)) < Math<T>::Tolerance(); }
// Normalize, convention vector length to 1.
void Normalize()
{
T s = Length();
if (s != T(0))
s = T(1) / s;
*this *= s;
}
// Returns normalized (unit) version of the vector without modifying itself.
Vector2 Normalized() const
{
T s = Length();
if (s != T(0))
s = T(1) / s;
return *this * s;
}
// Linearly interpolates from this vector to another.
// Factor should be between 0.0 and 1.0, with 0 giving full value to this.
Vector2 Lerp(const Vector2& b, T f) const { return *this*(T(1) - f) + b*f; }
// Projects this vector onto the argument; in other words,
// A.Project(B) returns projection of vector A onto B.
Vector2 ProjectTo(const Vector2& b) const
{
T l2 = b.LengthSq();
OVR_MATH_ASSERT(l2 != T(0));
return b * ( Dot(b) / l2 );
}
// returns true if vector b is clockwise from this vector
bool IsClockwise(const Vector2& b) const
{
return (x * b.y - y * b.x) < 0;
}
};
typedef Vector2<float> Vector2f;
typedef Vector2<double> Vector2d;
typedef Vector2<int> Vector2i;
typedef Vector2<float> Point2f;
typedef Vector2<double> Point2d;
typedef Vector2<int> Point2i;
//-------------------------------------------------------------------------------------
// ***** Vector3<> - 3D vector of {x, y, z}
//
// Vector3f (Vector3d) represents a 3-dimensional vector or point in space,
// consisting of coordinates x, y and z.
template<class T>
class Vector3
{
public:
typedef T ElementType;
static const size_t ElementCount = 3;
T x, y, z;
// FIXME: default initialization of a vector class can be very expensive in a full-blown
// application. A few hundred thousand vector constructions is not unlikely and can add
// up to milliseconds of time on processors like the PS3 PPU.
Vector3() : x(0), y(0), z(0) { }
Vector3(T x_, T y_, T z_ = 0) : x(x_), y(y_), z(z_) { }
explicit Vector3(T s) : x(s), y(s), z(s) { }
explicit Vector3(const Vector3<typename Math<T>::OtherFloatType> &src)
: x((T)src.x), y((T)src.y), z((T)src.z) { }
static Vector3 Zero() { return Vector3(0, 0, 0); }
// C-interop support.
typedef typename CompatibleTypes<Vector3<T> >::Type CompatibleType;
Vector3(const CompatibleType& s) : x(s.x), y(s.y), z(s.z) { }
operator const CompatibleType& () const
{
OVR_MATH_STATIC_ASSERT(sizeof(Vector3<T>) == sizeof(CompatibleType), "sizeof(Vector3<T>) failure");
return reinterpret_cast<const CompatibleType&>(*this);
}
bool operator== (const Vector3& b) const { return x == b.x && y == b.y && z == b.z; }
bool operator!= (const Vector3& b) const { return x != b.x || y != b.y || z != b.z; }
Vector3 operator+ (const Vector3& b) const { return Vector3(x + b.x, y + b.y, z + b.z); }
Vector3& operator+= (const Vector3& b) { x += b.x; y += b.y; z += b.z; return *this; }
Vector3 operator- (const Vector3& b) const { return Vector3(x - b.x, y - b.y, z - b.z); }
Vector3& operator-= (const Vector3& b) { x -= b.x; y -= b.y; z -= b.z; return *this; }
Vector3 operator- () const { return Vector3(-x, -y, -z); }
// Scalar multiplication/division scales vector.
Vector3 operator* (T s) const { return Vector3(x*s, y*s, z*s); }
Vector3& operator*= (T s) { x *= s; y *= s; z *= s; return *this; }
Vector3 operator/ (T s) const { T rcp = T(1)/s;
return Vector3(x*rcp, y*rcp, z*rcp); }
Vector3& operator/= (T s) { T rcp = T(1)/s;
x *= rcp; y *= rcp; z *= rcp;
return *this; }
static Vector3 Min(const Vector3& a, const Vector3& b)
{
return Vector3((a.x < b.x) ? a.x : b.x,
(a.y < b.y) ? a.y : b.y,
(a.z < b.z) ? a.z : b.z);
}
static Vector3 Max(const Vector3& a, const Vector3& b)
{
return Vector3((a.x > b.x) ? a.x : b.x,
(a.y > b.y) ? a.y : b.y,
(a.z > b.z) ? a.z : b.z);
}
Vector3 Clamped(T maxMag) const
{
T magSquared = LengthSq();
if (magSquared <= Sqr(maxMag))
return *this;
else
return *this * (maxMag / sqrt(magSquared));
}
// Compare two vectors for equality with tolerance. Returns true if vectors match withing tolerance.
bool IsEqual(const Vector3& b, T tolerance = Math<T>::Tolerance()) const
{
return (fabs(b.x-x) <= tolerance) &&
(fabs(b.y-y) <= tolerance) &&
(fabs(b.z-z) <= tolerance);
}
bool Compare(const Vector3& b, T tolerance = Math<T>::Tolerance()) const
{
return IsEqual(b, tolerance);
}
T& operator[] (int idx)
{
OVR_MATH_ASSERT(0 <= idx && idx < 3);
return *(&x + idx);
}
const T& operator[] (int idx) const
{
OVR_MATH_ASSERT(0 <= idx && idx < 3);
return *(&x + idx);
}
// Entrywise product of two vectors
Vector3 EntrywiseMultiply(const Vector3& b) const { return Vector3(x * b.x,
y * b.y,
z * b.z);}
// Multiply and divide operators do entry-wise math
Vector3 operator* (const Vector3& b) const { return Vector3(x * b.x,
y * b.y,
z * b.z); }
Vector3 operator/ (const Vector3& b) const { return Vector3(x / b.x,
y / b.y,
z / b.z); }
// Dot product
// Used to calculate angle q between two vectors among other things,
// as (A dot B) = |a||b|cos(q).
T Dot(const Vector3& b) const { return x*b.x + y*b.y + z*b.z; }
// Compute cross product, which generates a normal vector.
// Direction vector can be determined by right-hand rule: Pointing index finder in
// direction a and middle finger in direction b, thumb will point in a.Cross(b).
Vector3 Cross(const Vector3& b) const { return Vector3(y*b.z - z*b.y,
z*b.x - x*b.z,
x*b.y - y*b.x); }
// Returns the angle from this vector to b, in radians.
T Angle(const Vector3& b) const
{
T div = LengthSq()*b.LengthSq();
OVR_MATH_ASSERT(div != T(0));
T result = Acos((this->Dot(b))/sqrt(div));
return result;
}
// Return Length of the vector squared.
T LengthSq() const { return (x * x + y * y + z * z); }
// Return vector length.
T Length() const { return (T)sqrt(LengthSq()); }
// Returns squared distance between two points represented by vectors.
T DistanceSq(Vector3 const& b) const { return (*this - b).LengthSq(); }
// Returns distance between two points represented by vectors.
T Distance(Vector3 const& b) const { return (*this - b).Length(); }
bool IsNormalized() const { return fabs(LengthSq() - T(1)) < Math<T>::Tolerance(); }
// Normalize, convention vector length to 1.
void Normalize()
{
T s = Length();
if (s != T(0))
s = T(1) / s;
*this *= s;
}
// Returns normalized (unit) version of the vector without modifying itself.
Vector3 Normalized() const
{
T s = Length();
if (s != T(0))
s = T(1) / s;
return *this * s;
}
// Linearly interpolates from this vector to another.
// Factor should be between 0.0 and 1.0, with 0 giving full value to this.
Vector3 Lerp(const Vector3& b, T f) const { return *this*(T(1) - f) + b*f; }
// Projects this vector onto the argument; in other words,
// A.Project(B) returns projection of vector A onto B.
Vector3 ProjectTo(const Vector3& b) const
{
T l2 = b.LengthSq();
OVR_MATH_ASSERT(l2 != T(0));
return b * ( Dot(b) / l2 );
}
// Projects this vector onto a plane defined by a normal vector
Vector3 ProjectToPlane(const Vector3& normal) const { return *this - this->ProjectTo(normal); }
};
typedef Vector3<float> Vector3f;
typedef Vector3<double> Vector3d;
typedef Vector3<int32_t> Vector3i;
OVR_MATH_STATIC_ASSERT((sizeof(Vector3f) == 3*sizeof(float)), "sizeof(Vector3f) failure");
OVR_MATH_STATIC_ASSERT((sizeof(Vector3d) == 3*sizeof(double)), "sizeof(Vector3d) failure");
OVR_MATH_STATIC_ASSERT((sizeof(Vector3i) == 3*sizeof(int32_t)), "sizeof(Vector3i) failure");
typedef Vector3<float> Point3f;
typedef Vector3<double> Point3d;
typedef Vector3<int32_t> Point3i;
//-------------------------------------------------------------------------------------
// ***** Vector4<> - 4D vector of {x, y, z, w}
//
// Vector4f (Vector4d) represents a 3-dimensional vector or point in space,
// consisting of coordinates x, y, z and w.
template<class T>
class Vector4
{
public:
typedef T ElementType;
static const size_t ElementCount = 4;
T x, y, z, w;
// FIXME: default initialization of a vector class can be very expensive in a full-blown
// application. A few hundred thousand vector constructions is not unlikely and can add
// up to milliseconds of time on processors like the PS3 PPU.
Vector4() : x(0), y(0), z(0), w(0) { }
Vector4(T x_, T y_, T z_, T w_) : x(x_), y(y_), z(z_), w(w_) { }
explicit Vector4(T s) : x(s), y(s), z(s), w(s) { }
explicit Vector4(const Vector3<T>& v, const T w_=T(1)) : x(v.x), y(v.y), z(v.z), w(w_) { }
explicit Vector4(const Vector4<typename Math<T>::OtherFloatType> &src)
: x((T)src.x), y((T)src.y), z((T)src.z), w((T)src.w) { }
static Vector4 Zero() { return Vector4(0, 0, 0, 0); }
// C-interop support.
typedef typename CompatibleTypes< Vector4<T> >::Type CompatibleType;
Vector4(const CompatibleType& s) : x(s.x), y(s.y), z(s.z), w(s.w) { }
operator const CompatibleType& () const
{
OVR_MATH_STATIC_ASSERT(sizeof(Vector4<T>) == sizeof(CompatibleType), "sizeof(Vector4<T>) failure");
return reinterpret_cast<const CompatibleType&>(*this);
}
Vector4& operator= (const Vector3<T>& other) { x=other.x; y=other.y; z=other.z; w=1; return *this; }
bool operator== (const Vector4& b) const { return x == b.x && y == b.y && z == b.z && w == b.w; }
bool operator!= (const Vector4& b) const { return x != b.x || y != b.y || z != b.z || w != b.w; }
Vector4 operator+ (const Vector4& b) const { return Vector4(x + b.x, y + b.y, z + b.z, w + b.w); }
Vector4& operator+= (const Vector4& b) { x += b.x; y += b.y; z += b.z; w += b.w; return *this; }
Vector4 operator- (const Vector4& b) const { return Vector4(x - b.x, y - b.y, z - b.z, w - b.w); }
Vector4& operator-= (const Vector4& b) { x -= b.x; y -= b.y; z -= b.z; w -= b.w; return *this; }
Vector4 operator- () const { return Vector4(-x, -y, -z, -w); }
// Scalar multiplication/division scales vector.
Vector4 operator* (T s) const { return Vector4(x*s, y*s, z*s, w*s); }
Vector4& operator*= (T s) { x *= s; y *= s; z *= s; w *= s;return *this; }
Vector4 operator/ (T s) const { T rcp = T(1)/s;
return Vector4(x*rcp, y*rcp, z*rcp, w*rcp); }
Vector4& operator/= (T s) { T rcp = T(1)/s;
x *= rcp; y *= rcp; z *= rcp; w *= rcp;
return *this; }
static Vector4 Min(const Vector4& a, const Vector4& b)
{
return Vector4((a.x < b.x) ? a.x : b.x,
(a.y < b.y) ? a.y : b.y,
(a.z < b.z) ? a.z : b.z,
(a.w < b.w) ? a.w : b.w);
}
static Vector4 Max(const Vector4& a, const Vector4& b)
{
return Vector4((a.x > b.x) ? a.x : b.x,
(a.y > b.y) ? a.y : b.y,
(a.z > b.z) ? a.z : b.z,
(a.w > b.w) ? a.w : b.w);
}
Vector4 Clamped(T maxMag) const
{
T magSquared = LengthSq();
if (magSquared <= Sqr(maxMag))
return *this;
else
return *this * (maxMag / sqrt(magSquared));
}
// Compare two vectors for equality with tolerance. Returns true if vectors match withing tolerance.
bool IsEqual(const Vector4& b, T tolerance = Math<T>::Tolerance()) const
{
return (fabs(b.x-x) <= tolerance) &&
(fabs(b.y-y) <= tolerance) &&
(fabs(b.z-z) <= tolerance) &&
(fabs(b.w-w) <= tolerance);
}
bool Compare(const Vector4& b, T tolerance = Math<T>::Tolerance()) const
{
return IsEqual(b, tolerance);
}
T& operator[] (int idx)
{
OVR_MATH_ASSERT(0 <= idx && idx < 4);
return *(&x + idx);
}
const T& operator[] (int idx) const
{
OVR_MATH_ASSERT(0 <= idx && idx < 4);
return *(&x + idx);
}
// Entry wise product of two vectors
Vector4 EntrywiseMultiply(const Vector4& b) const { return Vector4(x * b.x,
y * b.y,
z * b.z,
w * b.w);}
// Multiply and divide operators do entry-wise math
Vector4 operator* (const Vector4& b) const { return Vector4(x * b.x,
y * b.y,
z * b.z,
w * b.w); }
Vector4 operator/ (const Vector4& b) const { return Vector4(x / b.x,
y / b.y,
z / b.z,
w / b.w); }
// Dot product
T Dot(const Vector4& b) const { return x*b.x + y*b.y + z*b.z + w*b.w; }
// Return Length of the vector squared.
T LengthSq() const { return (x * x + y * y + z * z + w * w); }
// Return vector length.
T Length() const { return sqrt(LengthSq()); }
bool IsNormalized() const { return fabs(LengthSq() - T(1)) < Math<T>::Tolerance(); }
// Normalize, convention vector length to 1.
void Normalize()
{
T s = Length();
if (s != T(0))
s = T(1) / s;
*this *= s;
}
// Returns normalized (unit) version of the vector without modifying itself.
Vector4 Normalized() const
{
T s = Length();
if (s != T(0))
s = T(1) / s;
return *this * s;
}
// Linearly interpolates from this vector to another.
// Factor should be between 0.0 and 1.0, with 0 giving full value to this.
Vector4 Lerp(const Vector4& b, T f) const { return *this*(T(1) - f) + b*f; }
};
typedef Vector4<float> Vector4f;
typedef Vector4<double> Vector4d;
typedef Vector4<int> Vector4i;
//-------------------------------------------------------------------------------------
// ***** Bounds3
// Bounds class used to describe a 3D axis aligned bounding box.
template<class T>
class Bounds3
{
public:
Vector3<T> b[2];
Bounds3()
{
}
Bounds3( const Vector3<T> & mins, const Vector3<T> & maxs )
{
b[0] = mins;
b[1] = maxs;
}
void Clear()
{
b[0].x = b[0].y = b[0].z = Math<T>::MaxValue;
b[1].x = b[1].y = b[1].z = -Math<T>::MaxValue;
}
void AddPoint( const Vector3<T> & v )
{
b[0].x = (b[0].x < v.x ? b[0].x : v.x);
b[0].y = (b[0].y < v.y ? b[0].y : v.y);
b[0].z = (b[0].z < v.z ? b[0].z : v.z);
b[1].x = (v.x < b[1].x ? b[1].x : v.x);
b[1].y = (v.y < b[1].y ? b[1].y : v.y);
b[1].z = (v.z < b[1].z ? b[1].z : v.z);
}
const Vector3<T> & GetMins() const { return b[0]; }
const Vector3<T> & GetMaxs() const { return b[1]; }
Vector3<T> & GetMins() { return b[0]; }
Vector3<T> & GetMaxs() { return b[1]; }
};
typedef Bounds3<float> Bounds3f;
typedef Bounds3<double> Bounds3d;
//-------------------------------------------------------------------------------------
// ***** Size
// Size class represents 2D size with Width, Height components.
// Used to describe distentions of render targets, etc.
template<class T>
class Size
{
public:
T w, h;
Size() : w(0), h(0) { }
Size(T w_, T h_) : w(w_), h(h_) { }
explicit Size(T s) : w(s), h(s) { }
explicit Size(const Size<typename Math<T>::OtherFloatType> &src)
: w((T)src.w), h((T)src.h) { }
// C-interop support.
typedef typename CompatibleTypes<Size<T> >::Type CompatibleType;
Size(const CompatibleType& s) : w(s.w), h(s.h) { }
operator const CompatibleType& () const
{
OVR_MATH_STATIC_ASSERT(sizeof(Size<T>) == sizeof(CompatibleType), "sizeof(Size<T>) failure");
return reinterpret_cast<const CompatibleType&>(*this);
}
bool operator== (const Size& b) const { return w == b.w && h == b.h; }
bool operator!= (const Size& b) const { return w != b.w || h != b.h; }
Size operator+ (const Size& b) const { return Size(w + b.w, h + b.h); }
Size& operator+= (const Size& b) { w += b.w; h += b.h; return *this; }
Size operator- (const Size& b) const { return Size(w - b.w, h - b.h); }
Size& operator-= (const Size& b) { w -= b.w; h -= b.h; return *this; }
Size operator- () const { return Size(-w, -h); }
Size operator* (const Size& b) const { return Size(w * b.w, h * b.h); }
Size& operator*= (const Size& b) { w *= b.w; h *= b.h; return *this; }
Size operator/ (const Size& b) const { return Size(w / b.w, h / b.h); }
Size& operator/= (const Size& b) { w /= b.w; h /= b.h; return *this; }
// Scalar multiplication/division scales both components.
Size operator* (T s) const { return Size(w*s, h*s); }
Size& operator*= (T s) { w *= s; h *= s; return *this; }
Size operator/ (T s) const { return Size(w/s, h/s); }
Size& operator/= (T s) { w /= s; h /= s; return *this; }
static Size Min(const Size& a, const Size& b) { return Size((a.w < b.w) ? a.w : b.w,
(a.h < b.h) ? a.h : b.h); }
static Size Max(const Size& a, const Size& b) { return Size((a.w > b.w) ? a.w : b.w,
(a.h > b.h) ? a.h : b.h); }
T Area() const { return w * h; }
inline Vector2<T> ToVector() const { return Vector2<T>(w, h); }
};
typedef Size<int> Sizei;
typedef Size<unsigned> Sizeu;
typedef Size<float> Sizef;
typedef Size<double> Sized;
//-----------------------------------------------------------------------------------
// ***** Rect
// Rect describes a rectangular area for rendering, that includes position and size.
template<class T>
class Rect
{
public:
T x, y;
T w, h;
Rect() { }
Rect(T x1, T y1, T w1, T h1) : x(x1), y(y1), w(w1), h(h1) { }
Rect(const Vector2<T>& pos, const Size<T>& sz) : x(pos.x), y(pos.y), w(sz.w), h(sz.h) { }
Rect(const Size<T>& sz) : x(0), y(0), w(sz.w), h(sz.h) { }
// C-interop support.
typedef typename CompatibleTypes<Rect<T> >::Type CompatibleType;
Rect(const CompatibleType& s) : x(s.Pos.x), y(s.Pos.y), w(s.Size.w), h(s.Size.h) { }
operator const CompatibleType& () const
{
OVR_MATH_STATIC_ASSERT(sizeof(Rect<T>) == sizeof(CompatibleType), "sizeof(Rect<T>) failure");
return reinterpret_cast<const CompatibleType&>(*this);
}
Vector2<T> GetPos() const { return Vector2<T>(x, y); }
Size<T> GetSize() const { return Size<T>(w, h); }
void SetPos(const Vector2<T>& pos) { x = pos.x; y = pos.y; }
void SetSize(const Size<T>& sz) { w = sz.w; h = sz.h; }
bool operator == (const Rect& vp) const
{ return (x == vp.x) && (y == vp.y) && (w == vp.w) && (h == vp.h); }
bool operator != (const Rect& vp) const
{ return !operator == (vp); }
};
typedef Rect<int> Recti;
//-------------------------------------------------------------------------------------//
// ***** Quat
//
// Quatf represents a quaternion class used for rotations.
//
// Quaternion multiplications are done in right-to-left order, to match the
// behavior of matrices.
template<class T>
class Quat
{
public:
typedef T ElementType;
static const size_t ElementCount = 4;
// x,y,z = axis*sin(angle), w = cos(angle)
T x, y, z, w;
Quat() : x(0), y(0), z(0), w(1) { }
Quat(T x_, T y_, T z_, T w_) : x(x_), y(y_), z(z_), w(w_) { }
explicit Quat(const Quat<typename Math<T>::OtherFloatType> &src)
: x((T)src.x), y((T)src.y), z((T)src.z), w((T)src.w)
{
// NOTE: Converting a normalized Quat<float> to Quat<double>
// will generally result in an un-normalized quaternion.
// But we don't normalize here in case the quaternion
// being converted is not a normalized rotation quaternion.
}
typedef typename CompatibleTypes<Quat<T> >::Type CompatibleType;
// C-interop support.
Quat(const CompatibleType& s) : x(s.x), y(s.y), z(s.z), w(s.w) { }
operator CompatibleType () const
{
CompatibleType result;
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
}
// Constructs quaternion for rotation around the axis by an angle.
Quat(const Vector3<T>& axis, T angle)
{
// Make sure we don't divide by zero.
if (axis.LengthSq() == T(0))
{
// Assert if the axis is zero, but the angle isn't
OVR_MATH_ASSERT(angle == T(0));
x = y = z = T(0); w = T(1);
return;
}
Vector3<T> unitAxis = axis.Normalized();
T sinHalfAngle = sin(angle * T(0.5));
w = cos(angle * T(0.5));
x = unitAxis.x * sinHalfAngle;
y = unitAxis.y * sinHalfAngle;
z = unitAxis.z * sinHalfAngle;
}
// Constructs quaternion for rotation around one of the coordinate axis by an angle.
Quat(Axis A, T angle, RotateDirection d = Rotate_CCW, HandedSystem s = Handed_R)
{
T sinHalfAngle = s * d *sin(angle * T(0.5));
T v[3];
v[0] = v[1] = v[2] = T(0);
v[A] = sinHalfAngle;
w = cos(angle * T(0.5));
x = v[0];
y = v[1];
z = v[2];
}
Quat operator-() { return Quat(-x, -y, -z, -w); } // unary minus
static Quat Identity() { return Quat(0, 0, 0, 1); }
// Compute axis and angle from quaternion
void GetAxisAngle(Vector3<T>* axis, T* angle) const
{
if ( x*x + y*y + z*z > Math<T>::Tolerance() * Math<T>::Tolerance() ) {
*axis = Vector3<T>(x, y, z).Normalized();
*angle = 2 * Acos(w);
if (*angle > ((T)MATH_DOUBLE_PI)) // Reduce the magnitude of the angle, if necessary
{
*angle = ((T)MATH_DOUBLE_TWOPI) - *angle;
*axis = *axis * (-1);
}
}
else
{
*axis = Vector3<T>(1, 0, 0);
*angle= T(0);
}
}
// Convert a quaternion to a rotation vector, also known as
// Rodrigues vector, AxisAngle vector, SORA vector, exponential map.
// A rotation vector describes a rotation about an axis:
// the axis of rotation is the vector normalized,
// the angle of rotation is the magnitude of the vector.
Vector3<T> ToRotationVector() const
{
OVR_MATH_ASSERT(IsNormalized() || LengthSq() == 0);
T s = T(0);
T sinHalfAngle = sqrt(x*x + y*y + z*z);
if (sinHalfAngle > T(0))
{
T cosHalfAngle = w;
T halfAngle = atan2(sinHalfAngle, cosHalfAngle);
// Ensure minimum rotation magnitude
if (cosHalfAngle < 0)
halfAngle -= T(MATH_DOUBLE_PI);
s = T(2) * halfAngle / sinHalfAngle;
}
return Vector3<T>(x*s, y*s, z*s);
}
// Faster version of the above, optimized for use with small rotations, where rotation angle ~= sin(angle)
inline OVR::Vector3<T> FastToRotationVector() const
{
OVR_MATH_ASSERT(IsNormalized());
T s;
T sinHalfSquared = x*x + y*y + z*z;
if (sinHalfSquared < T(.0037)) // =~ sin(7/2 degrees)^2
{
// Max rotation magnitude error is about .062% at 7 degrees rotation, or about .0043 degrees
s = T(2) * Sign(w);
}
else
{
T sinHalfAngle = sqrt(sinHalfSquared);
T cosHalfAngle = w;
T halfAngle = atan2(sinHalfAngle, cosHalfAngle);
// Ensure minimum rotation magnitude
if (cosHalfAngle < 0)
halfAngle -= T(MATH_DOUBLE_PI);
s = T(2) * halfAngle / sinHalfAngle;
}
return Vector3<T>(x*s, y*s, z*s);
}
// Given a rotation vector of form unitRotationAxis * angle,
// returns the equivalent quaternion (unitRotationAxis * sin(angle), cos(Angle)).
static Quat FromRotationVector(const Vector3<T>& v)
{
T angleSquared = v.LengthSq();
T s = T(0);
T c = T(1);
if (angleSquared > T(0))
{
T angle = sqrt(angleSquared);
s = sin(angle * T(0.5)) / angle; // normalize
c = cos(angle * T(0.5));
}
return Quat(s*v.x, s*v.y, s*v.z, c);
}
// Faster version of above, optimized for use with small rotation magnitudes, where rotation angle =~ sin(angle).
// If normalize is false, small-angle quaternions are returned un-normalized.
inline static Quat FastFromRotationVector(const OVR::Vector3<T>& v, bool normalize = true)
{
T s, c;
T angleSquared = v.LengthSq();
if (angleSquared < T(0.0076)) // =~ (5 degrees*pi/180)^2
{
s = T(0.5);
c = T(1.0);
// Max rotation magnitude error (after normalization) is about .064% at 5 degrees rotation, or .0032 degrees
if (normalize && angleSquared > 0)
{
// sin(angle/2)^2 ~= (angle/2)^2 and cos(angle/2)^2 ~= 1
T invLen = T(1) / sqrt(angleSquared * T(0.25) + T(1)); // normalize
s = s * invLen;
c = c * invLen;
}
}
else
{
T angle = sqrt(angleSquared);
s = sin(angle * T(0.5)) / angle;
c = cos(angle * T(0.5));
}
return Quat(s*v.x, s*v.y, s*v.z, c);
}
// Constructs the quaternion from a rotation matrix
explicit Quat(const Matrix4<T>& m)
{
T trace = m.M[0][0] + m.M[1][1] + m.M[2][2];
// In almost all cases, the first part is executed.
// However, if the trace is not positive, the other
// cases arise.
if (trace > T(0))
{
T s = sqrt(trace + T(1)) * T(2); // s=4*qw
w = T(0.25) * s;
x = (m.M[2][1] - m.M[1][2]) / s;
y = (m.M[0][2] - m.M[2][0]) / s;
z = (m.M[1][0] - m.M[0][1]) / s;
}
else if ((m.M[0][0] > m.M[1][1])&&(m.M[0][0] > m.M[2][2]))
{
T s = sqrt(T(1) + m.M[0][0] - m.M[1][1] - m.M[2][2]) * T(2);
w = (m.M[2][1] - m.M[1][2]) / s;
x = T(0.25) * s;
y = (m.M[0][1] + m.M[1][0]) / s;
z = (m.M[2][0] + m.M[0][2]) / s;
}
else if (m.M[1][1] > m.M[2][2])
{
T s = sqrt(T(1) + m.M[1][1] - m.M[0][0] - m.M[2][2]) * T(2); // S=4*qy
w = (m.M[0][2] - m.M[2][0]) / s;
x = (m.M[0][1] + m.M[1][0]) / s;
y = T(0.25) * s;
z = (m.M[1][2] + m.M[2][1]) / s;
}
else
{
T s = sqrt(T(1) + m.M[2][2] - m.M[0][0] - m.M[1][1]) * T(2); // S=4*qz
w = (m.M[1][0] - m.M[0][1]) / s;
x = (m.M[0][2] + m.M[2][0]) / s;
y = (m.M[1][2] + m.M[2][1]) / s;
z = T(0.25) * s;
}
OVR_MATH_ASSERT(IsNormalized()); // Ensure input matrix is orthogonal
}
// Constructs the quaternion from a rotation matrix
explicit Quat(const Matrix3<T>& m)
{
T trace = m.M[0][0] + m.M[1][1] + m.M[2][2];
// In almost all cases, the first part is executed.
// However, if the trace is not positive, the other
// cases arise.
if (trace > T(0))
{
T s = sqrt(trace + T(1)) * T(2); // s=4*qw
w = T(0.25) * s;
x = (m.M[2][1] - m.M[1][2]) / s;
y = (m.M[0][2] - m.M[2][0]) / s;
z = (m.M[1][0] - m.M[0][1]) / s;
}
else if ((m.M[0][0] > m.M[1][1])&&(m.M[0][0] > m.M[2][2]))
{
T s = sqrt(T(1) + m.M[0][0] - m.M[1][1] - m.M[2][2]) * T(2);
w = (m.M[2][1] - m.M[1][2]) / s;
x = T(0.25) * s;
y = (m.M[0][1] + m.M[1][0]) / s;
z = (m.M[2][0] + m.M[0][2]) / s;
}
else if (m.M[1][1] > m.M[2][2])
{
T s = sqrt(T(1) + m.M[1][1] - m.M[0][0] - m.M[2][2]) * T(2); // S=4*qy
w = (m.M[0][2] - m.M[2][0]) / s;
x = (m.M[0][1] + m.M[1][0]) / s;
y = T(0.25) * s;
z = (m.M[1][2] + m.M[2][1]) / s;
}
else
{
T s = sqrt(T(1) + m.M[2][2] - m.M[0][0] - m.M[1][1]) * T(2); // S=4*qz
w = (m.M[1][0] - m.M[0][1]) / s;
x = (m.M[0][2] + m.M[2][0]) / s;
y = (m.M[1][2] + m.M[2][1]) / s;
z = T(0.25) * s;
}
OVR_MATH_ASSERT(IsNormalized()); // Ensure input matrix is orthogonal
}
bool operator== (const Quat& b) const { return x == b.x && y == b.y && z == b.z && w == b.w; }
bool operator!= (const Quat& b) const { return x != b.x || y != b.y || z != b.z || w != b.w; }
Quat operator+ (const Quat& b) const { return Quat(x + b.x, y + b.y, z + b.z, w + b.w); }
Quat& operator+= (const Quat& b) { w += b.w; x += b.x; y += b.y; z += b.z; return *this; }
Quat operator- (const Quat& b) const { return Quat(x - b.x, y - b.y, z - b.z, w - b.w); }
Quat& operator-= (const Quat& b) { w -= b.w; x -= b.x; y -= b.y; z -= b.z; return *this; }
Quat operator* (T s) const { return Quat(x * s, y * s, z * s, w * s); }
Quat& operator*= (T s) { w *= s; x *= s; y *= s; z *= s; return *this; }
Quat operator/ (T s) const { T rcp = T(1)/s; return Quat(x * rcp, y * rcp, z * rcp, w *rcp); }
Quat& operator/= (T s) { T rcp = T(1)/s; w *= rcp; x *= rcp; y *= rcp; z *= rcp; return *this; }
// Compare two quats for equality within tolerance. Returns true if quats match withing tolerance.
bool IsEqual(const Quat& b, T tolerance = Math<T>::Tolerance()) const
{
return Abs(Dot(b)) >= T(1) - tolerance;
}
static T Abs(const T v) { return (v >= 0) ? v : -v; }
// Get Imaginary part vector
Vector3<T> Imag() const { return Vector3<T>(x,y,z); }
// Get quaternion length.
T Length() const { return sqrt(LengthSq()); }
// Get quaternion length squared.
T LengthSq() const { return (x * x + y * y + z * z + w * w); }
// Simple Euclidean distance in R^4 (not SLERP distance, but at least respects Haar measure)
T Distance(const Quat& q) const
{
T d1 = (*this - q).Length();
T d2 = (*this + q).Length(); // Antipodal point check
return (d1 < d2) ? d1 : d2;
}
T DistanceSq(const Quat& q) const
{
T d1 = (*this - q).LengthSq();
T d2 = (*this + q).LengthSq(); // Antipodal point check
return (d1 < d2) ? d1 : d2;
}
T Dot(const Quat& q) const
{
return x * q.x + y * q.y + z * q.z + w * q.w;
}
// Angle between two quaternions in radians
T Angle(const Quat& q) const
{
return T(2) * Acos(Abs(Dot(q)));
}
// Angle of quaternion
T Angle() const
{
return T(2) * Acos(Abs(w));
}
// Normalize
bool IsNormalized() const { return fabs(LengthSq() - T(1)) < Math<T>::Tolerance(); }
void Normalize()
{
T s = Length();
if (s != T(0))
s = T(1) / s;
*this *= s;
}
Quat Normalized() const
{
T s = Length();
if (s != T(0))
s = T(1) / s;
return *this * s;
}
inline void EnsureSameHemisphere(const Quat& o)
{
if (Dot(o) < T(0))
{
x = -x;
y = -y;
z = -z;
w = -w;
}
}
// Returns conjugate of the quaternion. Produces inverse rotation if quaternion is normalized.
Quat Conj() const { return Quat(-x, -y, -z, w); }
// Quaternion multiplication. Combines quaternion rotations, performing the one on the
// right hand side first.
Quat operator* (const Quat& b) const { return Quat(w * b.x + x * b.w + y * b.z - z * b.y,
w * b.y - x * b.z + y * b.w + z * b.x,
w * b.z + x * b.y - y * b.x + z * b.w,
w * b.w - x * b.x - y * b.y - z * b.z); }
const Quat& operator*= (const Quat& b) { *this = *this * b; return *this; }
//
// this^p normalized; same as rotating by this p times.
Quat PowNormalized(T p) const
{
Vector3<T> v;
T a;
GetAxisAngle(&v, &a);
return Quat(v, a * p);
}
// Compute quaternion that rotates v into alignTo: alignTo = Quat::Align(alignTo, v).Rotate(v).
// NOTE: alignTo and v must be normalized.
static Quat Align(const Vector3<T>& alignTo, const Vector3<T>& v)
{
OVR_MATH_ASSERT(alignTo.IsNormalized() && v.IsNormalized());
Vector3<T> bisector = (v + alignTo);
bisector.Normalize();
T cosHalfAngle = v.Dot(bisector); // 0..1
if (cosHalfAngle > T(0))
{
Vector3<T> imag = v.Cross(bisector);
return Quat(imag.x, imag.y, imag.z, cosHalfAngle);
}
else
{
// cosHalfAngle == 0: a 180 degree rotation.
// sinHalfAngle == 1, rotation axis is any axis perpendicular
// to alignTo. Choose axis to include largest magnitude components
if (fabs(v.x) > fabs(v.y))
{
// x or z is max magnitude component
// = Cross(v, (0,1,0)).Normalized();
T invLen = sqrt(v.x*v.x + v.z*v.z);
if (invLen > T(0))
invLen = T(1) / invLen;
return Quat(-v.z*invLen, 0, v.x*invLen, 0);
}
else
{
// y or z is max magnitude component
// = Cross(v, (1,0,0)).Normalized();
T invLen = sqrt(v.y*v.y + v.z*v.z);
if (invLen > T(0))
invLen = T(1) / invLen;
return Quat(0, v.z*invLen, -v.y*invLen, 0);
}
}
}
// Normalized linear interpolation of quaternions
// NOTE: This function is a bad approximation of Slerp()
// when the angle between the *this and b is large.
// Use FastSlerp() or Slerp() instead.
Quat Lerp(const Quat& b, T s) const
{
return (*this * (T(1) - s) + b * (Dot(b) < 0 ? -s : s)).Normalized();
}
// Spherical linear interpolation between rotations
Quat Slerp(const Quat& b, T s) const
{
Vector3<T> delta = (b * this->Inverted()).ToRotationVector();
return FromRotationVector(delta * s) * *this;
}
// Spherical linear interpolation: much faster for small rotations, accurate for large rotations. See FastTo/FromRotationVector
Quat FastSlerp(const Quat& b, T s) const
{
Vector3<T> delta = (b * this->Inverted()).FastToRotationVector();
return (FastFromRotationVector(delta * s, false) * *this).Normalized();
}
// Rotate transforms vector in a manner that matches Matrix rotations (counter-clockwise,
// assuming negative direction of the axis). Standard formula: q(t) * V * q(t)^-1.
Vector3<T> Rotate(const Vector3<T>& v) const
{
OVR_MATH_ASSERT(isnan(w) || IsNormalized());
// rv = q * (v,0) * q'
// Same as rv = v + real * cross(imag,v)*2 + cross(imag, cross(imag,v)*2);
// uv = 2 * Imag().Cross(v);
T uvx = T(2) * (y*v.z - z*v.y);
T uvy = T(2) * (z*v.x - x*v.z);
T uvz = T(2) * (x*v.y - y*v.x);
// return v + Real()*uv + Imag().Cross(uv);
return Vector3<T>(v.x + w*uvx + y*uvz - z*uvy,
v.y + w*uvy + z*uvx - x*uvz,
v.z + w*uvz + x*uvy - y*uvx);
}
// Rotation by inverse of *this
Vector3<T> InverseRotate(const Vector3<T>& v) const
{
OVR_MATH_ASSERT(IsNormalized());
// rv = q' * (v,0) * q
// Same as rv = v + real * cross(-imag,v)*2 + cross(-imag, cross(-imag,v)*2);
// or rv = v - real * cross(imag,v)*2 + cross(imag, cross(imag,v)*2);
// uv = 2 * Imag().Cross(v);
T uvx = T(2) * (y*v.z - z*v.y);
T uvy = T(2) * (z*v.x - x*v.z);
T uvz = T(2) * (x*v.y - y*v.x);
// return v - Real()*uv + Imag().Cross(uv);
return Vector3<T>(v.x - w*uvx + y*uvz - z*uvy,
v.y - w*uvy + z*uvx - x*uvz,
v.z - w*uvz + x*uvy - y*uvx);
}
// Inversed quaternion rotates in the opposite direction.
Quat Inverted() const
{
return Quat(-x, -y, -z, w);
}
Quat Inverse() const
{
return Quat(-x, -y, -z, w);
}
// Sets this quaternion to the one rotates in the opposite direction.
void Invert()
{
*this = Quat(-x, -y, -z, w);
}
// Time integration of constant angular velocity over dt
Quat TimeIntegrate(Vector3<T> angularVelocity, T dt) const
{
// solution is: this * exp( omega*dt/2 ); FromRotationVector(v) gives exp(v*.5).
return (*this * FastFromRotationVector(angularVelocity * dt, false)).Normalized();
}
// Time integration of constant angular acceleration and velocity over dt
// These are the first two terms of the "Magnus expansion" of the solution
//
// o = o * exp( W=(W1 + W2 + W3+...) * 0.5 );
//
// omega1 = (omega + omegaDot*dt)
// W1 = (omega + omega1)*dt/2
// W2 = cross(omega, omega1)/12*dt^2 % (= -cross(omega_dot, omega)/12*dt^3)
// Terms 3 and beyond are vanishingly small:
// W3 = cross(omega_dot, cross(omega_dot, omega))/240*dt^5
//
Quat TimeIntegrate(Vector3<T> angularVelocity, Vector3<T> angularAcceleration, T dt) const
{
const Vector3<T>& omega = angularVelocity;
const Vector3<T>& omegaDot = angularAcceleration;
Vector3<T> omega1 = (omega + omegaDot * dt);
Vector3<T> W = ( (omega + omega1) + omega.Cross(omega1) * (dt/T(6)) ) * (dt/T(2));
// FromRotationVector(v) is exp(v*.5)
return (*this * FastFromRotationVector(W, false)).Normalized();
}
// Decompose rotation into three rotations:
// roll radians about Z axis, then pitch radians about X axis, then yaw radians about Y axis.
// Call with nullptr if a return value is not needed.
void GetYawPitchRoll(T* yaw, T* pitch, T* roll) const
{
return GetEulerAngles<Axis_Y, Axis_X, Axis_Z, Rotate_CCW, Handed_R>(yaw, pitch, roll);
}
// GetEulerAngles extracts Euler angles from the quaternion, in the specified order of
// axis rotations and the specified coordinate system. Right-handed coordinate system
// is the default, with CCW rotations while looking in the negative axis direction.
// Here a,b,c, are the Yaw/Pitch/Roll angles to be returned.
// Rotation order is c, b, a:
// rotation c around axis A3
// is followed by rotation b around axis A2
// is followed by rotation a around axis A1
// rotations are CCW or CW (D) in LH or RH coordinate system (S)
//
template <Axis A1, Axis A2, Axis A3, RotateDirection D, HandedSystem S>
void GetEulerAngles(T *a, T *b, T *c) const
{
OVR_MATH_ASSERT(IsNormalized());
OVR_MATH_STATIC_ASSERT((A1 != A2) && (A2 != A3) && (A1 != A3), "(A1 != A2) && (A2 != A3) && (A1 != A3)");
T Q[3] = { x, y, z }; //Quaternion components x,y,z
T ww = w*w;
T Q11 = Q[A1]*Q[A1];
T Q22 = Q[A2]*Q[A2];
T Q33 = Q[A3]*Q[A3];
T psign = T(-1);
// Determine whether even permutation
if (((A1 + 1) % 3 == A2) && ((A2 + 1) % 3 == A3))
psign = T(1);
T s2 = psign * T(2) * (psign*w*Q[A2] + Q[A1]*Q[A3]);
T singularityRadius = Math<T>::SingularityRadius();
if (s2 < T(-1) + singularityRadius)
{ // South pole singularity
if (a) *a = T(0);
if (b) *b = -S*D*((T)MATH_DOUBLE_PIOVER2);
if (c) *c = S*D*atan2(T(2)*(psign*Q[A1] * Q[A2] + w*Q[A3]), ww + Q22 - Q11 - Q33 );
}
else if (s2 > T(1) - singularityRadius)
{ // North pole singularity
if (a) *a = T(0);
if (b) *b = S*D*((T)MATH_DOUBLE_PIOVER2);
if (c) *c = S*D*atan2(T(2)*(psign*Q[A1] * Q[A2] + w*Q[A3]), ww + Q22 - Q11 - Q33);
}
else
{
if (a) *a = -S*D*atan2(T(-2)*(w*Q[A1] - psign*Q[A2] * Q[A3]), ww + Q33 - Q11 - Q22);
if (b) *b = S*D*asin(s2);
if (c) *c = S*D*atan2(T(2)*(w*Q[A3] - psign*Q[A1] * Q[A2]), ww + Q11 - Q22 - Q33);
}
}
template <Axis A1, Axis A2, Axis A3, RotateDirection D>
void GetEulerAngles(T *a, T *b, T *c) const
{ GetEulerAngles<A1, A2, A3, D, Handed_R>(a, b, c); }
template <Axis A1, Axis A2, Axis A3>
void GetEulerAngles(T *a, T *b, T *c) const
{ GetEulerAngles<A1, A2, A3, Rotate_CCW, Handed_R>(a, b, c); }
// GetEulerAnglesABA extracts Euler angles from the quaternion, in the specified order of
// axis rotations and the specified coordinate system. Right-handed coordinate system
// is the default, with CCW rotations while looking in the negative axis direction.
// Here a,b,c, are the Yaw/Pitch/Roll angles to be returned.
// rotation a around axis A1
// is followed by rotation b around axis A2
// is followed by rotation c around axis A1
// Rotations are CCW or CW (D) in LH or RH coordinate system (S)
template <Axis A1, Axis A2, RotateDirection D, HandedSystem S>
void GetEulerAnglesABA(T *a, T *b, T *c) const
{
OVR_MATH_ASSERT(IsNormalized());
OVR_MATH_STATIC_ASSERT(A1 != A2, "A1 != A2");
T Q[3] = {x, y, z}; // Quaternion components
// Determine the missing axis that was not supplied
int m = 3 - A1 - A2;
T ww = w*w;
T Q11 = Q[A1]*Q[A1];
T Q22 = Q[A2]*Q[A2];
T Qmm = Q[m]*Q[m];
T psign = T(-1);
if ((A1 + 1) % 3 == A2) // Determine whether even permutation
{
psign = T(1);
}
T c2 = ww + Q11 - Q22 - Qmm;
T singularityRadius = Math<T>::SingularityRadius();
if (c2 < T(-1) + singularityRadius)
{ // South pole singularity
if (a) *a = T(0);
if (b) *b = S*D*((T)MATH_DOUBLE_PI);
if (c) *c = S*D*atan2(T(2)*(w*Q[A1] - psign*Q[A2] * Q[m]),
ww + Q22 - Q11 - Qmm);
}
else if (c2 > T(1) - singularityRadius)
{ // North pole singularity
if (a) *a = T(0);
if (b) *b = T(0);
if (c) *c = S*D*atan2(T(2)*(w*Q[A1] - psign*Q[A2] * Q[m]),
ww + Q22 - Q11 - Qmm);
}
else
{
if (a) *a = S*D*atan2(psign*w*Q[m] + Q[A1] * Q[A2],
w*Q[A2] -psign*Q[A1]*Q[m]);
if (b) *b = S*D*acos(c2);
if (c) *c = S*D*atan2(-psign*w*Q[m] + Q[A1] * Q[A2],
w*Q[A2] + psign*Q[A1]*Q[m]);
}
}
};
typedef Quat<float> Quatf;
typedef Quat<double> Quatd;
OVR_MATH_STATIC_ASSERT((sizeof(Quatf) == 4*sizeof(float)), "sizeof(Quatf) failure");
OVR_MATH_STATIC_ASSERT((sizeof(Quatd) == 4*sizeof(double)), "sizeof(Quatd) failure");
//-------------------------------------------------------------------------------------
// ***** Pose
//
// Position and orientation combined.
//
// This structure needs to be the same size and layout on 32-bit and 64-bit arch.
// Update OVR_PadCheck.cpp when updating this object.
template<class T>
class Pose
{
public:
typedef typename CompatibleTypes<Pose<T> >::Type CompatibleType;
Pose() { }
Pose(const Quat<T>& orientation, const Vector3<T>& pos)
: Rotation(orientation), Translation(pos) { }
Pose(const Pose& s)
: Rotation(s.Rotation), Translation(s.Translation) { }
Pose(const Matrix3<T>& R, const Vector3<T>& t)
: Rotation((Quat<T>)R), Translation(t) { }
Pose(const CompatibleType& s)
: Rotation(s.Orientation), Translation(s.Position) { }
explicit Pose(const Pose<typename Math<T>::OtherFloatType> &s)
: Rotation(s.Rotation), Translation(s.Translation)
{
// Ensure normalized rotation if converting from float to double
if (sizeof(T) > sizeof(typename Math<T>::OtherFloatType))
Rotation.Normalize();
}
static Pose Identity() { return Pose(Quat<T>(0, 0, 0, 1), Vector3<T>(0, 0, 0)); }
void SetIdentity() { Rotation = Quat<T>(0, 0, 0, 1); Translation = Vector3<T>(0, 0, 0); }
// used to make things obviously broken if someone tries to use the value
void SetInvalid() { Rotation = Quat<T>(NAN, NAN, NAN, NAN); Translation = Vector3<T>(NAN, NAN, NAN); }
bool IsEqual(const Pose&b, T tolerance = Math<T>::Tolerance()) const
{
return Translation.IsEqual(b.Translation, tolerance) && Rotation.IsEqual(b.Rotation, tolerance);
}
operator typename CompatibleTypes<Pose<T> >::Type () const
{
typename CompatibleTypes<Pose<T> >::Type result;
result.Orientation = Rotation;
result.Position = Translation;
return result;
}
Quat<T> Rotation;
Vector3<T> Translation;
OVR_MATH_STATIC_ASSERT((sizeof(T) == sizeof(double) || sizeof(T) == sizeof(float)), "(sizeof(T) == sizeof(double) || sizeof(T) == sizeof(float))");
void ToArray(T* arr) const
{
T temp[7] = { Rotation.x, Rotation.y, Rotation.z, Rotation.w, Translation.x, Translation.y, Translation.z };
for (int i = 0; i < 7; i++) arr[i] = temp[i];
}
static Pose<T> FromArray(const T* v)
{
Quat<T> rotation(v[0], v[1], v[2], v[3]);
Vector3<T> translation(v[4], v[5], v[6]);
// Ensure rotation is normalized, in case it was originally a float, stored in a .json file, etc.
return Pose<T>(rotation.Normalized(), translation);
}
Vector3<T> Rotate(const Vector3<T>& v) const
{
return Rotation.Rotate(v);
}
Vector3<T> InverseRotate(const Vector3<T>& v) const
{
return Rotation.InverseRotate(v);
}
Vector3<T> Translate(const Vector3<T>& v) const
{
return v + Translation;
}
Vector3<T> Transform(const Vector3<T>& v) const
{
return Rotate(v) + Translation;
}
Vector3<T> InverseTransform(const Vector3<T>& v) const
{
return InverseRotate(v - Translation);
}
Vector3<T> Apply(const Vector3<T>& v) const
{
return Transform(v);
}
Pose operator*(const Pose& other) const
{
return Pose(Rotation * other.Rotation, Apply(other.Translation));
}
Pose Inverted() const
{
Quat<T> inv = Rotation.Inverted();
return Pose(inv, inv.Rotate(-Translation));
}
// Interpolation between two poses: translation is interpolated with Lerp(),
// and rotations are interpolated with Slerp().
Pose Lerp(const Pose& b, T s)
{
return Pose(Rotation.Slerp(b.Rotation, s), Translation.Lerp(b.Translation, s));
}
// Similar to Lerp above, except faster in case of small rotation differences. See Quat<T>::FastSlerp.
Pose FastLerp(const Pose& b, T s)
{
return Pose(Rotation.FastSlerp(b.Rotation, s), Translation.Lerp(b.Translation, s));
}
Pose TimeIntegrate(const Vector3<T>& linearVelocity, const Vector3<T>& angularVelocity, T dt) const
{
return Pose(
(Rotation * Quat<T>::FastFromRotationVector(angularVelocity * dt, false)).Normalized(),
Translation + linearVelocity * dt);
}
Pose TimeIntegrate(const Vector3<T>& linearVelocity, const Vector3<T>& linearAcceleration,
const Vector3<T>& angularVelocity, const Vector3<T>& angularAcceleration,
T dt) const
{
return Pose(Rotation.TimeIntegrate(angularVelocity, angularAcceleration, dt),
Translation + linearVelocity*dt + linearAcceleration*dt*dt * T(0.5));
}
};
typedef Pose<float> Posef;
typedef Pose<double> Posed;
OVR_MATH_STATIC_ASSERT((sizeof(Posed) == sizeof(Quatd) + sizeof(Vector3d)), "sizeof(Posed) failure");
OVR_MATH_STATIC_ASSERT((sizeof(Posef) == sizeof(Quatf) + sizeof(Vector3f)), "sizeof(Posef) failure");
//-------------------------------------------------------------------------------------
// ***** Matrix4
//
// Matrix4 is a 4x4 matrix used for 3d transformations and projections.
// Translation stored in the last column.
// The matrix is stored in row-major order in memory, meaning that values
// of the first row are stored before the next one.
//
// The arrangement of the matrix is chosen to be in Right-Handed
// coordinate system and counterclockwise rotations when looking down
// the axis
//
// Transformation Order:
// - Transformations are applied from right to left, so the expression
// M1 * M2 * M3 * V means that the vector V is transformed by M3 first,
// followed by M2 and M1.
//
// Coordinate system: Right Handed
//
// Rotations: Counterclockwise when looking down the axis. All angles are in radians.
//
// | sx 01 02 tx | // First column (sx, 10, 20): Axis X basis vector.
// | 10 sy 12 ty | // Second column (01, sy, 21): Axis Y basis vector.
// | 20 21 sz tz | // Third columnt (02, 12, sz): Axis Z basis vector.
// | 30 31 32 33 |
//
// The basis vectors are first three columns.
template<class T>
class Matrix4
{
public:
typedef T ElementType;
static const size_t Dimension = 4;
T M[4][4];
enum NoInitType { NoInit };
// Construct with no memory initialization.
Matrix4(NoInitType) { }
// By default, we construct identity matrix.
Matrix4()
{
M[0][0] = M[1][1] = M[2][2] = M[3][3] = T(1);
M[0][1] = M[1][0] = M[2][3] = M[3][1] = T(0);
M[0][2] = M[1][2] = M[2][0] = M[3][2] = T(0);
M[0][3] = M[1][3] = M[2][1] = M[3][0] = T(0);
}
Matrix4(T m11, T m12, T m13, T m14,
T m21, T m22, T m23, T m24,
T m31, T m32, T m33, T m34,
T m41, T m42, T m43, T m44)
{
M[0][0] = m11; M[0][1] = m12; M[0][2] = m13; M[0][3] = m14;
M[1][0] = m21; M[1][1] = m22; M[1][2] = m23; M[1][3] = m24;
M[2][0] = m31; M[2][1] = m32; M[2][2] = m33; M[2][3] = m34;
M[3][0] = m41; M[3][1] = m42; M[3][2] = m43; M[3][3] = m44;
}
Matrix4(T m11, T m12, T m13,
T m21, T m22, T m23,
T m31, T m32, T m33)
{
M[0][0] = m11; M[0][1] = m12; M[0][2] = m13; M[0][3] = T(0);
M[1][0] = m21; M[1][1] = m22; M[1][2] = m23; M[1][3] = T(0);
M[2][0] = m31; M[2][1] = m32; M[2][2] = m33; M[2][3] = T(0);
M[3][0] = T(0); M[3][1] = T(0); M[3][2] = T(0); M[3][3] = T(1);
}
explicit Matrix4(const Matrix3<T>& m)
{
M[0][0] = m.M[0][0]; M[0][1] = m.M[0][1]; M[0][2] = m.M[0][2]; M[0][3] = T(0);
M[1][0] = m.M[1][0]; M[1][1] = m.M[1][1]; M[1][2] = m.M[1][2]; M[1][3] = T(0);
M[2][0] = m.M[2][0]; M[2][1] = m.M[2][1]; M[2][2] = m.M[2][2]; M[2][3] = T(0);
M[3][0] = T(0); M[3][1] = T(0); M[3][2] = T(0); M[3][3] = T(1);
}
explicit Matrix4(const Quat<T>& q)
{
OVR_MATH_ASSERT(q.IsNormalized());
T ww = q.w*q.w;
T xx = q.x*q.x;
T yy = q.y*q.y;
T zz = q.z*q.z;
M[0][0] = ww + xx - yy - zz; M[0][1] = 2 * (q.x*q.y - q.w*q.z); M[0][2] = 2 * (q.x*q.z + q.w*q.y); M[0][3] = T(0);
M[1][0] = 2 * (q.x*q.y + q.w*q.z); M[1][1] = ww - xx + yy - zz; M[1][2] = 2 * (q.y*q.z - q.w*q.x); M[1][3] = T(0);
M[2][0] = 2 * (q.x*q.z - q.w*q.y); M[2][1] = 2 * (q.y*q.z + q.w*q.x); M[2][2] = ww - xx - yy + zz; M[2][3] = T(0);
M[3][0] = T(0); M[3][1] = T(0); M[3][2] = T(0); M[3][3] = T(1);
}
explicit Matrix4(const Pose<T>& p)
{
Matrix4 result(p.Rotation);
result.SetTranslation(p.Translation);
*this = result;
}
// C-interop support
explicit Matrix4(const Matrix4<typename Math<T>::OtherFloatType> &src)
{
for (int i = 0; i < 4; i++)
for (int j = 0; j < 4; j++)
M[i][j] = (T)src.M[i][j];
}
// C-interop support.
Matrix4(const typename CompatibleTypes<Matrix4<T> >::Type& s)
{
OVR_MATH_STATIC_ASSERT(sizeof(s) == sizeof(Matrix4), "sizeof(s) == sizeof(Matrix4)");
memcpy(M, s.M, sizeof(M));
}
operator typename CompatibleTypes<Matrix4<T> >::Type () const
{
typename CompatibleTypes<Matrix4<T> >::Type result;
OVR_MATH_STATIC_ASSERT(sizeof(result) == sizeof(Matrix4), "sizeof(result) == sizeof(Matrix4)");
memcpy(result.M, M, sizeof(M));
return result;
}
void ToString(char* dest, size_t destsize) const
{
size_t pos = 0;
for (int r=0; r<4; r++)
{
for (int c=0; c<4; c++)
{
pos += OVRMath_sprintf(dest+pos, destsize-pos, "%g ", M[r][c]);
}
}
}
static Matrix4 FromString(const char* src)
{
Matrix4 result;
if (src)
{
for (int r = 0; r < 4; r++)
{
for (int c = 0; c < 4; c++)
{
result.M[r][c] = (T)atof(src);
while (*src && *src != ' ')
{
src++;
}
while (*src && *src == ' ')
{
src++;
}
}
}
}
return result;
}
static Matrix4 Identity() { return Matrix4(); }
void SetIdentity()
{
M[0][0] = M[1][1] = M[2][2] = M[3][3] = T(1);
M[0][1] = M[1][0] = M[2][3] = M[3][1] = T(0);
M[0][2] = M[1][2] = M[2][0] = M[3][2] = T(0);
M[0][3] = M[1][3] = M[2][1] = M[3][0] = T(0);
}
void SetXBasis(const Vector3<T>& v)
{
M[0][0] = v.x;
M[1][0] = v.y;
M[2][0] = v.z;
}
Vector3<T> GetXBasis() const
{
return Vector3<T>(M[0][0], M[1][0], M[2][0]);
}
void SetYBasis(const Vector3<T> & v)
{
M[0][1] = v.x;
M[1][1] = v.y;
M[2][1] = v.z;
}
Vector3<T> GetYBasis() const
{
return Vector3<T>(M[0][1], M[1][1], M[2][1]);
}
void SetZBasis(const Vector3<T> & v)
{
M[0][2] = v.x;
M[1][2] = v.y;
M[2][2] = v.z;
}
Vector3<T> GetZBasis() const
{
return Vector3<T>(M[0][2], M[1][2], M[2][2]);
}
bool operator== (const Matrix4& b) const
{
bool isEqual = true;
for (int i = 0; i < 4; i++)
for (int j = 0; j < 4; j++)
isEqual &= (M[i][j] == b.M[i][j]);
return isEqual;
}
Matrix4 operator+ (const Matrix4& b) const
{
Matrix4 result(*this);
result += b;
return result;
}
Matrix4& operator+= (const Matrix4& b)
{
for (int i = 0; i < 4; i++)
for (int j = 0; j < 4; j++)
M[i][j] += b.M[i][j];
return *this;
}
Matrix4 operator- (const Matrix4& b) const
{
Matrix4 result(*this);
result -= b;
return result;
}
Matrix4& operator-= (const Matrix4& b)
{
for (int i = 0; i < 4; i++)
for (int j = 0; j < 4; j++)
M[i][j] -= b.M[i][j];
return *this;
}
// Multiplies two matrices into destination with minimum copying.
static Matrix4& Multiply(Matrix4* d, const Matrix4& a, const Matrix4& b)
{
OVR_MATH_ASSERT((d != &a) && (d != &b));
int i = 0;
do {
d->M[i][0] = a.M[i][0] * b.M[0][0] + a.M[i][1] * b.M[1][0] + a.M[i][2] * b.M[2][0] + a.M[i][3] * b.M[3][0];
d->M[i][1] = a.M[i][0] * b.M[0][1] + a.M[i][1] * b.M[1][1] + a.M[i][2] * b.M[2][1] + a.M[i][3] * b.M[3][1];
d->M[i][2] = a.M[i][0] * b.M[0][2] + a.M[i][1] * b.M[1][2] + a.M[i][2] * b.M[2][2] + a.M[i][3] * b.M[3][2];
d->M[i][3] = a.M[i][0] * b.M[0][3] + a.M[i][1] * b.M[1][3] + a.M[i][2] * b.M[2][3] + a.M[i][3] * b.M[3][3];
} while((++i) < 4);
return *d;
}
Matrix4 operator* (const Matrix4& b) const
{
Matrix4 result(Matrix4::NoInit);
Multiply(&result, *this, b);
return result;
}
Matrix4& operator*= (const Matrix4& b)
{
return Multiply(this, Matrix4(*this), b);
}
Matrix4 operator* (T s) const
{
Matrix4 result(*this);
result *= s;
return result;
}
Matrix4& operator*= (T s)
{
for (int i = 0; i < 4; i++)
for (int j = 0; j < 4; j++)
M[i][j] *= s;
return *this;
}
Matrix4 operator/ (T s) const
{
Matrix4 result(*this);
result /= s;
return result;
}
Matrix4& operator/= (T s)
{
for (int i = 0; i < 4; i++)
for (int j = 0; j < 4; j++)
M[i][j] /= s;
return *this;
}
Vector3<T> Transform(const Vector3<T>& v) const
{
const T rcpW = T(1) / (M[3][0] * v.x + M[3][1] * v.y + M[3][2] * v.z + M[3][3]);
return Vector3<T>((M[0][0] * v.x + M[0][1] * v.y + M[0][2] * v.z + M[0][3]) * rcpW,
(M[1][0] * v.x + M[1][1] * v.y + M[1][2] * v.z + M[1][3]) * rcpW,
(M[2][0] * v.x + M[2][1] * v.y + M[2][2] * v.z + M[2][3]) * rcpW);
}
Vector4<T> Transform(const Vector4<T>& v) const
{
return Vector4<T>(M[0][0] * v.x + M[0][1] * v.y + M[0][2] * v.z + M[0][3] * v.w,
M[1][0] * v.x + M[1][1] * v.y + M[1][2] * v.z + M[1][3] * v.w,
M[2][0] * v.x + M[2][1] * v.y + M[2][2] * v.z + M[2][3] * v.w,
M[3][0] * v.x + M[3][1] * v.y + M[3][2] * v.z + M[3][3] * v.w);
}
Matrix4 Transposed() const
{
return Matrix4(M[0][0], M[1][0], M[2][0], M[3][0],
M[0][1], M[1][1], M[2][1], M[3][1],
M[0][2], M[1][2], M[2][2], M[3][2],
M[0][3], M[1][3], M[2][3], M[3][3]);
}
void Transpose()
{
*this = Transposed();
}
T SubDet (const size_t* rows, const size_t* cols) const
{
return M[rows[0]][cols[0]] * (M[rows[1]][cols[1]] * M[rows[2]][cols[2]] - M[rows[1]][cols[2]] * M[rows[2]][cols[1]])
- M[rows[0]][cols[1]] * (M[rows[1]][cols[0]] * M[rows[2]][cols[2]] - M[rows[1]][cols[2]] * M[rows[2]][cols[0]])
+ M[rows[0]][cols[2]] * (M[rows[1]][cols[0]] * M[rows[2]][cols[1]] - M[rows[1]][cols[1]] * M[rows[2]][cols[0]]);
}
T Cofactor(size_t I, size_t J) const
{
const size_t indices[4][3] = {{1,2,3},{0,2,3},{0,1,3},{0,1,2}};
return ((I+J)&1) ? -SubDet(indices[I],indices[J]) : SubDet(indices[I],indices[J]);
}
T Determinant() const
{
return M[0][0] * Cofactor(0,0) + M[0][1] * Cofactor(0,1) + M[0][2] * Cofactor(0,2) + M[0][3] * Cofactor(0,3);
}
Matrix4 Adjugated() const
{
return Matrix4(Cofactor(0,0), Cofactor(1,0), Cofactor(2,0), Cofactor(3,0),
Cofactor(0,1), Cofactor(1,1), Cofactor(2,1), Cofactor(3,1),
Cofactor(0,2), Cofactor(1,2), Cofactor(2,2), Cofactor(3,2),
Cofactor(0,3), Cofactor(1,3), Cofactor(2,3), Cofactor(3,3));
}
Matrix4 Inverted() const
{
T det = Determinant();
OVR_MATH_ASSERT(det != 0);
return Adjugated() * (T(1)/det);
}
void Invert()
{
*this = Inverted();
}
// This is more efficient than general inverse, but ONLY works
// correctly if it is a homogeneous transform matrix (rot + trans)
Matrix4 InvertedHomogeneousTransform() const
{
// Make the inverse rotation matrix
Matrix4 rinv = this->Transposed();
rinv.M[3][0] = rinv.M[3][1] = rinv.M[3][2] = T(0);
// Make the inverse translation matrix
Vector3<T> tvinv(-M[0][3],-M[1][3],-M[2][3]);
Matrix4 tinv = Matrix4::Translation(tvinv);
return rinv * tinv; // "untranslate", then "unrotate"
}
// This is more efficient than general inverse, but ONLY works
// correctly if it is a homogeneous transform matrix (rot + trans)
void InvertHomogeneousTransform()
{
*this = InvertedHomogeneousTransform();
}
// Matrix to Euler Angles conversion
// a,b,c, are the YawPitchRoll angles to be returned
// rotation a around axis A1
// is followed by rotation b around axis A2
// is followed by rotation c around axis A3
// rotations are CCW or CW (D) in LH or RH coordinate system (S)
template <Axis A1, Axis A2, Axis A3, RotateDirection D, HandedSystem S>
void ToEulerAngles(T *a, T *b, T *c) const
{
OVR_MATH_STATIC_ASSERT((A1 != A2) && (A2 != A3) && (A1 != A3), "(A1 != A2) && (A2 != A3) && (A1 != A3)");
T psign = T(-1);
if (((A1 + 1) % 3 == A2) && ((A2 + 1) % 3 == A3)) // Determine whether even permutation
psign = T(1);
T pm = psign*M[A1][A3];
T singularityRadius = Math<T>::SingularityRadius();
if (pm < T(-1) + singularityRadius)
{ // South pole singularity
*a = T(0);
*b = -S*D*((T)MATH_DOUBLE_PIOVER2);
*c = S*D*atan2( psign*M[A2][A1], M[A2][A2] );
}
else if (pm > T(1) - singularityRadius)
{ // North pole singularity
*a = T(0);
*b = S*D*((T)MATH_DOUBLE_PIOVER2);
*c = S*D*atan2( psign*M[A2][A1], M[A2][A2] );
}
else
{ // Normal case (nonsingular)
*a = S*D*atan2( -psign*M[A2][A3], M[A3][A3] );
*b = S*D*asin(pm);
*c = S*D*atan2( -psign*M[A1][A2], M[A1][A1] );
}
}
// Matrix to Euler Angles conversion
// a,b,c, are the YawPitchRoll angles to be returned
// rotation a around axis A1
// is followed by rotation b around axis A2
// is followed by rotation c around axis A1
// rotations are CCW or CW (D) in LH or RH coordinate system (S)
template <Axis A1, Axis A2, RotateDirection D, HandedSystem S>
void ToEulerAnglesABA(T *a, T *b, T *c) const
{
OVR_MATH_STATIC_ASSERT(A1 != A2, "A1 != A2");
// Determine the axis that was not supplied
int m = 3 - A1 - A2;
T psign = T(-1);
if ((A1 + 1) % 3 == A2) // Determine whether even permutation
psign = T(1);
T c2 = M[A1][A1];
T singularityRadius = Math<T>::SingularityRadius();
if (c2 < T(-1) + singularityRadius)
{ // South pole singularity
*a = T(0);
*b = S*D*((T)MATH_DOUBLE_PI);
*c = S*D*atan2( -psign*M[A2][m],M[A2][A2]);
}
else if (c2 > T(1) - singularityRadius)
{ // North pole singularity
*a = T(0);
*b = T(0);
*c = S*D*atan2( -psign*M[A2][m],M[A2][A2]);
}
else
{ // Normal case (nonsingular)
*a = S*D*atan2( M[A2][A1],-psign*M[m][A1]);
*b = S*D*acos(c2);
*c = S*D*atan2( M[A1][A2],psign*M[A1][m]);
}
}
// Creates a matrix that converts the vertices from one coordinate system
// to another.
static Matrix4 AxisConversion(const WorldAxes& to, const WorldAxes& from)
{
// Holds axis values from the 'to' structure
int toArray[3] = { to.XAxis, to.YAxis, to.ZAxis };
// The inverse of the toArray
int inv[4];
inv[0] = inv[abs(to.XAxis)] = 0;
inv[abs(to.YAxis)] = 1;
inv[abs(to.ZAxis)] = 2;
Matrix4 m(0, 0, 0,
0, 0, 0,
0, 0, 0);
// Only three values in the matrix need to be changed to 1 or -1.
m.M[inv[abs(from.XAxis)]][0] = T(from.XAxis/toArray[inv[abs(from.XAxis)]]);
m.M[inv[abs(from.YAxis)]][1] = T(from.YAxis/toArray[inv[abs(from.YAxis)]]);
m.M[inv[abs(from.ZAxis)]][2] = T(from.ZAxis/toArray[inv[abs(from.ZAxis)]]);
return m;
}
// Creates a matrix for translation by vector
static Matrix4 Translation(const Vector3<T>& v)
{
Matrix4 t;
t.M[0][3] = v.x;
t.M[1][3] = v.y;
t.M[2][3] = v.z;
return t;
}
// Creates a matrix for translation by vector
static Matrix4 Translation(T x, T y, T z = T(0))
{
Matrix4 t;
t.M[0][3] = x;
t.M[1][3] = y;
t.M[2][3] = z;
return t;
}
// Sets the translation part
void SetTranslation(const Vector3<T>& v)
{
M[0][3] = v.x;
M[1][3] = v.y;
M[2][3] = v.z;
}
Vector3<T> GetTranslation() const
{
return Vector3<T>( M[0][3], M[1][3], M[2][3] );
}
// Creates a matrix for scaling by vector
static Matrix4 Scaling(const Vector3<T>& v)
{
Matrix4 t;
t.M[0][0] = v.x;
t.M[1][1] = v.y;
t.M[2][2] = v.z;
return t;
}
// Creates a matrix for scaling by vector
static Matrix4 Scaling(T x, T y, T z)
{
Matrix4 t;
t.M[0][0] = x;
t.M[1][1] = y;
t.M[2][2] = z;
return t;
}
// Creates a matrix for scaling by constant
static Matrix4 Scaling(T s)
{
Matrix4 t;
t.M[0][0] = s;
t.M[1][1] = s;
t.M[2][2] = s;
return t;
}
// Simple L1 distance in R^12
T Distance(const Matrix4& m2) const
{
T d = fabs(M[0][0] - m2.M[0][0]) + fabs(M[0][1] - m2.M[0][1]);
d += fabs(M[0][2] - m2.M[0][2]) + fabs(M[0][3] - m2.M[0][3]);
d += fabs(M[1][0] - m2.M[1][0]) + fabs(M[1][1] - m2.M[1][1]);
d += fabs(M[1][2] - m2.M[1][2]) + fabs(M[1][3] - m2.M[1][3]);
d += fabs(M[2][0] - m2.M[2][0]) + fabs(M[2][1] - m2.M[2][1]);
d += fabs(M[2][2] - m2.M[2][2]) + fabs(M[2][3] - m2.M[2][3]);
d += fabs(M[3][0] - m2.M[3][0]) + fabs(M[3][1] - m2.M[3][1]);
d += fabs(M[3][2] - m2.M[3][2]) + fabs(M[3][3] - m2.M[3][3]);
return d;
}
// Creates a rotation matrix rotating around the X axis by 'angle' radians.
// Just for quick testing. Not for final API. Need to remove case.
static Matrix4 RotationAxis(Axis A, T angle, RotateDirection d, HandedSystem s)
{
T sina = s * d *sin(angle);
T cosa = cos(angle);
switch(A)
{
case Axis_X:
return Matrix4(1, 0, 0,
0, cosa, -sina,
0, sina, cosa);
case Axis_Y:
return Matrix4(cosa, 0, sina,
0, 1, 0,
-sina, 0, cosa);
case Axis_Z:
return Matrix4(cosa, -sina, 0,
sina, cosa, 0,
0, 0, 1);
default:
return Matrix4();
}
}
// Creates a rotation matrix rotating around the X axis by 'angle' radians.
// Rotation direction is depends on the coordinate system:
// RHS (Oculus default): Positive angle values rotate Counter-clockwise (CCW),
// while looking in the negative axis direction. This is the
// same as looking down from positive axis values towards origin.
// LHS: Positive angle values rotate clock-wise (CW), while looking in the
// negative axis direction.
static Matrix4 RotationX(T angle)
{
T sina = sin(angle);
T cosa = cos(angle);
return Matrix4(1, 0, 0,
0, cosa, -sina,
0, sina, cosa);
}
// Creates a rotation matrix rotating around the Y axis by 'angle' radians.
// Rotation direction is depends on the coordinate system:
// RHS (Oculus default): Positive angle values rotate Counter-clockwise (CCW),
// while looking in the negative axis direction. This is the
// same as looking down from positive axis values towards origin.
// LHS: Positive angle values rotate clock-wise (CW), while looking in the
// negative axis direction.
static Matrix4 RotationY(T angle)
{
T sina = (T)sin(angle);
T cosa = (T)cos(angle);
return Matrix4(cosa, 0, sina,
0, 1, 0,
-sina, 0, cosa);
}
// Creates a rotation matrix rotating around the Z axis by 'angle' radians.
// Rotation direction is depends on the coordinate system:
// RHS (Oculus default): Positive angle values rotate Counter-clockwise (CCW),
// while looking in the negative axis direction. This is the
// same as looking down from positive axis values towards origin.
// LHS: Positive angle values rotate clock-wise (CW), while looking in the
// negative axis direction.
static Matrix4 RotationZ(T angle)
{
T sina = sin(angle);
T cosa = cos(angle);
return Matrix4(cosa, -sina, 0,
sina, cosa, 0,
0, 0, 1);
}
// LookAtRH creates a View transformation matrix for right-handed coordinate system.
// The resulting matrix points camera from 'eye' towards 'at' direction, with 'up'
// specifying the up vector. The resulting matrix should be used with PerspectiveRH
// projection.
static Matrix4 LookAtRH(const Vector3<T>& eye, const Vector3<T>& at, const Vector3<T>& up)
{
Vector3<T> z = (eye - at).Normalized(); // Forward
Vector3<T> x = up.Cross(z).Normalized(); // Right
Vector3<T> y = z.Cross(x);
Matrix4 m(x.x, x.y, x.z, -(x.Dot(eye)),
y.x, y.y, y.z, -(y.Dot(eye)),
z.x, z.y, z.z, -(z.Dot(eye)),
0, 0, 0, 1 );
return m;
}
// LookAtLH creates a View transformation matrix for left-handed coordinate system.
// The resulting matrix points camera from 'eye' towards 'at' direction, with 'up'
// specifying the up vector.
static Matrix4 LookAtLH(const Vector3<T>& eye, const Vector3<T>& at, const Vector3<T>& up)
{
Vector3<T> z = (at - eye).Normalized(); // Forward
Vector3<T> x = up.Cross(z).Normalized(); // Right
Vector3<T> y = z.Cross(x);
Matrix4 m(x.x, x.y, x.z, -(x.Dot(eye)),
y.x, y.y, y.z, -(y.Dot(eye)),
z.x, z.y, z.z, -(z.Dot(eye)),
0, 0, 0, 1 );
return m;
}
// PerspectiveRH creates a right-handed perspective projection matrix that can be
// used with the Oculus sample renderer.
// yfov - Specifies vertical field of view in radians.
// aspect - Screen aspect ration, which is usually width/height for square pixels.
// Note that xfov = yfov * aspect.
// znear - Absolute value of near Z clipping clipping range.
// zfar - Absolute value of far Z clipping clipping range (larger then near).
// Even though RHS usually looks in the direction of negative Z, positive values
// are expected for znear and zfar.
static Matrix4 PerspectiveRH(T yfov, T aspect, T znear, T zfar)
{
Matrix4 m;
T tanHalfFov = tan(yfov * T(0.5));
m.M[0][0] = T(1) / (aspect * tanHalfFov);
m.M[1][1] = T(1) / tanHalfFov;
m.M[2][2] = zfar / (znear - zfar);
m.M[3][2] = T(-1);
m.M[2][3] = (zfar * znear) / (znear - zfar);
m.M[3][3] = T(0);
// Note: Post-projection matrix result assumes Left-Handed coordinate system,
// with Y up, X right and Z forward. This supports positive z-buffer values.
// This is the case even for RHS coordinate input.
return m;
}
// PerspectiveLH creates a left-handed perspective projection matrix that can be
// used with the Oculus sample renderer.
// yfov - Specifies vertical field of view in radians.
// aspect - Screen aspect ration, which is usually width/height for square pixels.
// Note that xfov = yfov * aspect.
// znear - Absolute value of near Z clipping clipping range.
// zfar - Absolute value of far Z clipping clipping range (larger then near).
static Matrix4 PerspectiveLH(T yfov, T aspect, T znear, T zfar)
{
Matrix4 m;
T tanHalfFov = tan(yfov * T(0.5));
m.M[0][0] = T(1) / (aspect * tanHalfFov);
m.M[1][1] = T(1) / tanHalfFov;
//m.M[2][2] = zfar / (znear - zfar);
m.M[2][2] = zfar / (zfar - znear);
m.M[3][2] = T(-1);
m.M[2][3] = (zfar * znear) / (znear - zfar);
m.M[3][3] = T(0);
// Note: Post-projection matrix result assumes Left-Handed coordinate system,
// with Y up, X right and Z forward. This supports positive z-buffer values.
// This is the case even for RHS coordinate input.
return m;
}
static Matrix4 Ortho2D(T w, T h)
{
Matrix4 m;
m.M[0][0] = T(2.0)/w;
m.M[1][1] = T(-2.0)/h;
m.M[0][3] = T(-1.0);
m.M[1][3] = T(1.0);
m.M[2][2] = T(0);
return m;
}
};
typedef Matrix4<float> Matrix4f;
typedef Matrix4<double> Matrix4d;
//-------------------------------------------------------------------------------------
// ***** Matrix3
//
// Matrix3 is a 3x3 matrix used for representing a rotation matrix.
// The matrix is stored in row-major order in memory, meaning that values
// of the first row are stored before the next one.
//
// The arrangement of the matrix is chosen to be in Right-Handed
// coordinate system and counterclockwise rotations when looking down
// the axis
//
// Transformation Order:
// - Transformations are applied from right to left, so the expression
// M1 * M2 * M3 * V means that the vector V is transformed by M3 first,
// followed by M2 and M1.
//
// Coordinate system: Right Handed
//
// Rotations: Counterclockwise when looking down the axis. All angles are in radians.
template<class T>
class Matrix3
{
public:
typedef T ElementType;
static const size_t Dimension = 3;
T M[3][3];
enum NoInitType { NoInit };
// Construct with no memory initialization.
Matrix3(NoInitType) { }
// By default, we construct identity matrix.
Matrix3()
{
M[0][0] = M[1][1] = M[2][2] = T(1);
M[0][1] = M[1][0] = M[2][0] = T(0);
M[0][2] = M[1][2] = M[2][1] = T(0);
}
Matrix3(T m11, T m12, T m13,
T m21, T m22, T m23,
T m31, T m32, T m33)
{
M[0][0] = m11; M[0][1] = m12; M[0][2] = m13;
M[1][0] = m21; M[1][1] = m22; M[1][2] = m23;
M[2][0] = m31; M[2][1] = m32; M[2][2] = m33;
}
// Construction from X, Y, Z basis vectors
Matrix3(const Vector3<T>& xBasis, const Vector3<T>& yBasis, const Vector3<T>& zBasis)
{
M[0][0] = xBasis.x; M[0][1] = yBasis.x; M[0][2] = zBasis.x;
M[1][0] = xBasis.y; M[1][1] = yBasis.y; M[1][2] = zBasis.y;
M[2][0] = xBasis.z; M[2][1] = yBasis.z; M[2][2] = zBasis.z;
}
explicit Matrix3(const Quat<T>& q)
{
OVR_MATH_ASSERT(q.IsNormalized());
const T tx = q.x+q.x, ty = q.y+q.y, tz = q.z+q.z;
const T twx = q.w*tx, twy = q.w*ty, twz = q.w*tz;
const T txx = q.x*tx, txy = q.x*ty, txz = q.x*tz;
const T tyy = q.y*ty, tyz = q.y*tz, tzz = q.z*tz;
M[0][0] = T(1) - (tyy + tzz); M[0][1] = txy - twz; M[0][2] = txz + twy;
M[1][0] = txy + twz; M[1][1] = T(1) - (txx + tzz); M[1][2] = tyz - twx;
M[2][0] = txz - twy; M[2][1] = tyz + twx; M[2][2] = T(1) - (txx + tyy);
}
inline explicit Matrix3(T s)
{
M[0][0] = M[1][1] = M[2][2] = s;
M[0][1] = M[0][2] = M[1][0] = M[1][2] = M[2][0] = M[2][1] = T(0);
}
Matrix3(T m11, T m22, T m33)
{
M[0][0] = m11; M[0][1] = T(0); M[0][2] = T(0);
M[1][0] = T(0); M[1][1] = m22; M[1][2] = T(0);
M[2][0] = T(0); M[2][1] = T(0); M[2][2] = m33;
}
explicit Matrix3(const Matrix3<typename Math<T>::OtherFloatType> &src)
{
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
M[i][j] = (T)src.M[i][j];
}
// C-interop support.
Matrix3(const typename CompatibleTypes<Matrix3<T> >::Type& s)
{
OVR_MATH_STATIC_ASSERT(sizeof(s) == sizeof(Matrix3), "sizeof(s) == sizeof(Matrix3)");
memcpy(M, s.M, sizeof(M));
}
operator const typename CompatibleTypes<Matrix3<T> >::Type () const
{
typename CompatibleTypes<Matrix3<T> >::Type result;
OVR_MATH_STATIC_ASSERT(sizeof(result) == sizeof(Matrix3), "sizeof(result) == sizeof(Matrix3)");
memcpy(result.M, M, sizeof(M));
return result;
}
T operator()(int i, int j) const { return M[i][j]; }
T& operator()(int i, int j) { return M[i][j]; }
void ToString(char* dest, size_t destsize) const
{
size_t pos = 0;
for (int r=0; r<3; r++)
{
for (int c=0; c<3; c++)
pos += OVRMath_sprintf(dest+pos, destsize-pos, "%g ", M[r][c]);
}
}
static Matrix3 FromString(const char* src)
{
Matrix3 result;
if (src)
{
for (int r=0; r<3; r++)
{
for (int c=0; c<3; c++)
{
result.M[r][c] = (T)atof(src);
while (*src && *src != ' ')
src++;
while (*src && *src == ' ')
src++;
}
}
}
return result;
}
static Matrix3 Identity() { return Matrix3(); }
void SetIdentity()
{
M[0][0] = M[1][1] = M[2][2] = T(1);
M[0][1] = M[1][0] = M[2][0] = T(0);
M[0][2] = M[1][2] = M[2][1] = T(0);
}
static Matrix3 Diagonal(T m00, T m11, T m22)
{
return Matrix3(m00, 0, 0,
0, m11, 0,
0, 0, m22);
}
static Matrix3 Diagonal(const Vector3<T>& v) { return Diagonal(v.x, v.y, v.z); }
T Trace() const { return M[0][0] + M[1][1] + M[2][2]; }
bool operator== (const Matrix3& b) const
{
bool isEqual = true;
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
isEqual &= (M[i][j] == b.M[i][j]);
}
return isEqual;
}
Matrix3 operator+ (const Matrix3& b) const
{
Matrix3<T> result(*this);
result += b;
return result;
}
Matrix3& operator+= (const Matrix3& b)
{
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
M[i][j] += b.M[i][j];
return *this;
}
void operator= (const Matrix3& b)
{
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
M[i][j] = b.M[i][j];
}
Matrix3 operator- (const Matrix3& b) const
{
Matrix3 result(*this);
result -= b;
return result;
}
Matrix3& operator-= (const Matrix3& b)
{
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
M[i][j] -= b.M[i][j];
}
return *this;
}
// Multiplies two matrices into destination with minimum copying.
static Matrix3& Multiply(Matrix3* d, const Matrix3& a, const Matrix3& b)
{
OVR_MATH_ASSERT((d != &a) && (d != &b));
int i = 0;
do {
d->M[i][0] = a.M[i][0] * b.M[0][0] + a.M[i][1] * b.M[1][0] + a.M[i][2] * b.M[2][0];
d->M[i][1] = a.M[i][0] * b.M[0][1] + a.M[i][1] * b.M[1][1] + a.M[i][2] * b.M[2][1];
d->M[i][2] = a.M[i][0] * b.M[0][2] + a.M[i][1] * b.M[1][2] + a.M[i][2] * b.M[2][2];
} while((++i) < 3);
return *d;
}
Matrix3 operator* (const Matrix3& b) const
{
Matrix3 result(Matrix3::NoInit);
Multiply(&result, *this, b);
return result;
}
Matrix3& operator*= (const Matrix3& b)
{
return Multiply(this, Matrix3(*this), b);
}
Matrix3 operator* (T s) const
{
Matrix3 result(*this);
result *= s;
return result;
}
Matrix3& operator*= (T s)
{
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
M[i][j] *= s;
}
return *this;
}
Vector3<T> operator* (const Vector3<T> &b) const
{
Vector3<T> result;
result.x = M[0][0]*b.x + M[0][1]*b.y + M[0][2]*b.z;
result.y = M[1][0]*b.x + M[1][1]*b.y + M[1][2]*b.z;
result.z = M[2][0]*b.x + M[2][1]*b.y + M[2][2]*b.z;
return result;
}
Matrix3 operator/ (T s) const
{
Matrix3 result(*this);
result /= s;
return result;
}
Matrix3& operator/= (T s)
{
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
M[i][j] /= s;
}
return *this;
}
Vector2<T> Transform(const Vector2<T>& v) const
{
const T rcpZ = T(1) / (M[2][0] * v.x + M[2][1] * v.y + M[2][2]);
return Vector2<T>((M[0][0] * v.x + M[0][1] * v.y + M[0][2]) * rcpZ,
(M[1][0] * v.x + M[1][1] * v.y + M[1][2]) * rcpZ);
}
Vector3<T> Transform(const Vector3<T>& v) const
{
return Vector3<T>(M[0][0] * v.x + M[0][1] * v.y + M[0][2] * v.z,
M[1][0] * v.x + M[1][1] * v.y + M[1][2] * v.z,
M[2][0] * v.x + M[2][1] * v.y + M[2][2] * v.z);
}
Matrix3 Transposed() const
{
return Matrix3(M[0][0], M[1][0], M[2][0],
M[0][1], M[1][1], M[2][1],
M[0][2], M[1][2], M[2][2]);
}
void Transpose()
{
*this = Transposed();
}
T SubDet (const size_t* rows, const size_t* cols) const
{
return M[rows[0]][cols[0]] * (M[rows[1]][cols[1]] * M[rows[2]][cols[2]] - M[rows[1]][cols[2]] * M[rows[2]][cols[1]])
- M[rows[0]][cols[1]] * (M[rows[1]][cols[0]] * M[rows[2]][cols[2]] - M[rows[1]][cols[2]] * M[rows[2]][cols[0]])
+ M[rows[0]][cols[2]] * (M[rows[1]][cols[0]] * M[rows[2]][cols[1]] - M[rows[1]][cols[1]] * M[rows[2]][cols[0]]);
}
// M += a*b.t()
inline void Rank1Add(const Vector3<T> &a, const Vector3<T> &b)
{
M[0][0] += a.x*b.x; M[0][1] += a.x*b.y; M[0][2] += a.x*b.z;
M[1][0] += a.y*b.x; M[1][1] += a.y*b.y; M[1][2] += a.y*b.z;
M[2][0] += a.z*b.x; M[2][1] += a.z*b.y; M[2][2] += a.z*b.z;
}
// M -= a*b.t()
inline void Rank1Sub(const Vector3<T> &a, const Vector3<T> &b)
{
M[0][0] -= a.x*b.x; M[0][1] -= a.x*b.y; M[0][2] -= a.x*b.z;
M[1][0] -= a.y*b.x; M[1][1] -= a.y*b.y; M[1][2] -= a.y*b.z;
M[2][0] -= a.z*b.x; M[2][1] -= a.z*b.y; M[2][2] -= a.z*b.z;
}
inline Vector3<T> Col(int c) const
{
return Vector3<T>(M[0][c], M[1][c], M[2][c]);
}
inline Vector3<T> Row(int r) const
{
return Vector3<T>(M[r][0], M[r][1], M[r][2]);
}
inline Vector3<T> GetColumn(int c) const
{
return Vector3<T>(M[0][c], M[1][c], M[2][c]);
}
inline Vector3<T> GetRow(int r) const
{
return Vector3<T>(M[r][0], M[r][1], M[r][2]);
}
inline void SetColumn(int c, const Vector3<T>& v)
{
M[0][c] = v.x;
M[1][c] = v.y;
M[2][c] = v.z;
}
inline void SetRow(int r, const Vector3<T>& v)
{
M[r][0] = v.x;
M[r][1] = v.y;
M[r][2] = v.z;
}
inline T Determinant() const
{
const Matrix3<T>& m = *this;
T d;
d = m.M[0][0] * (m.M[1][1]*m.M[2][2] - m.M[1][2] * m.M[2][1]);
d -= m.M[0][1] * (m.M[1][0]*m.M[2][2] - m.M[1][2] * m.M[2][0]);
d += m.M[0][2] * (m.M[1][0]*m.M[2][1] - m.M[1][1] * m.M[2][0]);
return d;
}
inline Matrix3<T> Inverse() const
{
Matrix3<T> a;
const Matrix3<T>& m = *this;
T d = Determinant();
OVR_MATH_ASSERT(d != 0);
T s = T(1)/d;
a.M[0][0] = s * (m.M[1][1] * m.M[2][2] - m.M[1][2] * m.M[2][1]);
a.M[1][0] = s * (m.M[1][2] * m.M[2][0] - m.M[1][0] * m.M[2][2]);
a.M[2][0] = s * (m.M[1][0] * m.M[2][1] - m.M[1][1] * m.M[2][0]);
a.M[0][1] = s * (m.M[0][2] * m.M[2][1] - m.M[0][1] * m.M[2][2]);
a.M[1][1] = s * (m.M[0][0] * m.M[2][2] - m.M[0][2] * m.M[2][0]);
a.M[2][1] = s * (m.M[0][1] * m.M[2][0] - m.M[0][0] * m.M[2][1]);
a.M[0][2] = s * (m.M[0][1] * m.M[1][2] - m.M[0][2] * m.M[1][1]);
a.M[1][2] = s * (m.M[0][2] * m.M[1][0] - m.M[0][0] * m.M[1][2]);
a.M[2][2] = s * (m.M[0][0] * m.M[1][1] - m.M[0][1] * m.M[1][0]);
return a;
}
// Outer Product of two column vectors: a * b.Transpose()
static Matrix3 OuterProduct(const Vector3<T>& a, const Vector3<T>& b)
{
return Matrix3(a.x*b.x, a.x*b.y, a.x*b.z,
a.y*b.x, a.y*b.y, a.y*b.z,
a.z*b.x, a.z*b.y, a.z*b.z);
}
// Vector cross product as a premultiply matrix:
// L.Cross(R) = LeftCrossAsMatrix(L) * R
static Matrix3 LeftCrossAsMatrix(const Vector3<T>& L)
{
return Matrix3(
T(0), -L.z, +L.y,
+L.z, T(0), -L.x,
-L.y, +L.x, T(0));
}
// Vector cross product as a premultiply matrix:
// L.Cross(R) = RightCrossAsMatrix(R) * L
static Matrix3 RightCrossAsMatrix(const Vector3<T>& R)
{
return Matrix3(
T(0), +R.z, -R.y,
-R.z, T(0), +R.x,
+R.y, -R.x, T(0));
}
// Angle in radians of a rotation matrix
// Uses identity trace(a) = 2*cos(theta) + 1
T Angle() const
{
return Acos((Trace() - T(1)) * T(0.5));
}
// Angle in radians between two rotation matrices
T Angle(const Matrix3& b) const
{
// Compute trace of (this->Transposed() * b)
// This works out to sum of products of elements.
T trace = T(0);
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
trace += M[i][j] * b.M[i][j];
}
}
return Acos((trace - T(1)) * T(0.5));
}
};
typedef Matrix3<float> Matrix3f;
typedef Matrix3<double> Matrix3d;
//-------------------------------------------------------------------------------------
// ***** Matrix2
template<class T>
class Matrix2
{
public:
typedef T ElementType;
static const size_t Dimension = 2;
T M[2][2];
enum NoInitType { NoInit };
// Construct with no memory initialization.
Matrix2(NoInitType) { }
// By default, we construct identity matrix.
Matrix2()
{
M[0][0] = M[1][1] = T(1);
M[0][1] = M[1][0] = T(0);
}
Matrix2(T m11, T m12,
T m21, T m22)
{
M[0][0] = m11; M[0][1] = m12;
M[1][0] = m21; M[1][1] = m22;
}
// Construction from X, Y basis vectors
Matrix2(const Vector2<T>& xBasis, const Vector2<T>& yBasis)
{
M[0][0] = xBasis.x; M[0][1] = yBasis.x;
M[1][0] = xBasis.y; M[1][1] = yBasis.y;
}
explicit Matrix2(T s)
{
M[0][0] = M[1][1] = s;
M[0][1] = M[1][0] = T(0);
}
Matrix2(T m11, T m22)
{
M[0][0] = m11; M[0][1] = T(0);
M[1][0] = T(0); M[1][1] = m22;
}
explicit Matrix2(const Matrix2<typename Math<T>::OtherFloatType> &src)
{
M[0][0] = T(src.M[0][0]); M[0][1] = T(src.M[0][1]);
M[1][0] = T(src.M[1][0]); M[1][1] = T(src.M[1][1]);
}
// C-interop support
Matrix2(const typename CompatibleTypes<Matrix2<T> >::Type& s)
{
OVR_MATH_STATIC_ASSERT(sizeof(s) == sizeof(Matrix2), "sizeof(s) == sizeof(Matrix2)");
memcpy(M, s.M, sizeof(M));
}
operator const typename CompatibleTypes<Matrix2<T> >::Type() const
{
typename CompatibleTypes<Matrix2<T> >::Type result;
OVR_MATH_STATIC_ASSERT(sizeof(result) == sizeof(Matrix2), "sizeof(result) == sizeof(Matrix2)");
memcpy(result.M, M, sizeof(M));
return result;
}
T operator()(int i, int j) const { return M[i][j]; }
T& operator()(int i, int j) { return M[i][j]; }
const T* operator[](int i) const { return M[i]; }
T* operator[](int i) { return M[i]; }
static Matrix2 Identity() { return Matrix2(); }
void SetIdentity()
{
M[0][0] = M[1][1] = T(1);
M[0][1] = M[1][0] = T(0);
}
static Matrix2 Diagonal(T m00, T m11)
{
return Matrix2(m00, m11);
}
static Matrix2 Diagonal(const Vector2<T>& v) { return Matrix2(v.x, v.y); }
T Trace() const { return M[0][0] + M[1][1]; }
bool operator== (const Matrix2& b) const
{
return M[0][0] == b.M[0][0] && M[0][1] == b.M[0][1] &&
M[1][0] == b.M[1][0] && M[1][1] == b.M[1][1];
}
Matrix2 operator+ (const Matrix2& b) const
{
return Matrix2(M[0][0] + b.M[0][0], M[0][1] + b.M[0][1],
M[1][0] + b.M[1][0], M[1][1] + b.M[1][1]);
}
Matrix2& operator+= (const Matrix2& b)
{
M[0][0] += b.M[0][0]; M[0][1] += b.M[0][1];
M[1][0] += b.M[1][0]; M[1][1] += b.M[1][1];
return *this;
}
void operator= (const Matrix2& b)
{
M[0][0] = b.M[0][0]; M[0][1] = b.M[0][1];
M[1][0] = b.M[1][0]; M[1][1] = b.M[1][1];
}
Matrix2 operator- (const Matrix2& b) const
{
return Matrix2(M[0][0] - b.M[0][0], M[0][1] - b.M[0][1],
M[1][0] - b.M[1][0], M[1][1] - b.M[1][1]);
}
Matrix2& operator-= (const Matrix2& b)
{
M[0][0] -= b.M[0][0]; M[0][1] -= b.M[0][1];
M[1][0] -= b.M[1][0]; M[1][1] -= b.M[1][1];
return *this;
}
Matrix2 operator* (const Matrix2& b) const
{
return Matrix2(M[0][0] * b.M[0][0] + M[0][1] * b.M[1][0], M[0][0] * b.M[0][1] + M[0][1] * b.M[1][1],
M[1][0] * b.M[0][0] + M[1][1] * b.M[1][0], M[1][0] * b.M[0][1] + M[1][1] * b.M[1][1]);
}
Matrix2& operator*= (const Matrix2& b)
{
*this = *this * b;
return *this;
}
Matrix2 operator* (T s) const
{
return Matrix2(M[0][0] * s, M[0][1] * s,
M[1][0] * s, M[1][1] * s);
}
Matrix2& operator*= (T s)
{
M[0][0] *= s; M[0][1] *= s;
M[1][0] *= s; M[1][1] *= s;
return *this;
}
Matrix2 operator/ (T s) const
{
return *this * (T(1) / s);
}
Matrix2& operator/= (T s)
{
return *this *= (T(1) / s);
}
Vector2<T> operator* (const Vector2<T> &b) const
{
return Vector2<T>(M[0][0] * b.x + M[0][1] * b.y,
M[1][0] * b.x + M[1][1] * b.y);
}
Vector2<T> Transform(const Vector2<T>& v) const
{
return Vector2<T>(M[0][0] * v.x + M[0][1] * v.y,
M[1][0] * v.x + M[1][1] * v.y);
}
Matrix2 Transposed() const
{
return Matrix2(M[0][0], M[1][0],
M[0][1], M[1][1]);
}
void Transpose()
{
OVRMath_Swap(M[1][0], M[0][1]);
}
Vector2<T> GetColumn(int c) const
{
return Vector2<T>(M[0][c], M[1][c]);
}
Vector2<T> GetRow(int r) const
{
return Vector2<T>(M[r][0], M[r][1]);
}
void SetColumn(int c, const Vector2<T>& v)
{
M[0][c] = v.x;
M[1][c] = v.y;
}
void SetRow(int r, const Vector2<T>& v)
{
M[r][0] = v.x;
M[r][1] = v.y;
}
T Determinant() const
{
return M[0][0] * M[1][1] - M[0][1] * M[1][0];
}
Matrix2 Inverse() const
{
T rcpDet = T(1) / Determinant();
return Matrix2( M[1][1] * rcpDet, -M[0][1] * rcpDet,
-M[1][0] * rcpDet, M[0][0] * rcpDet);
}
// Outer Product of two column vectors: a * b.Transpose()
static Matrix2 OuterProduct(const Vector2<T>& a, const Vector2<T>& b)
{
return Matrix2(a.x*b.x, a.x*b.y,
a.y*b.x, a.y*b.y);
}
// Angle in radians between two rotation matrices
T Angle(const Matrix2& b) const
{
const Matrix2& a = *this;
return Acos(a(0, 0)*b(0, 0) + a(1, 0)*b(1, 0));
}
};
typedef Matrix2<float> Matrix2f;
typedef Matrix2<double> Matrix2d;
//-------------------------------------------------------------------------------------
template<class T>
class SymMat3
{
private:
typedef SymMat3<T> this_type;
public:
typedef T Value_t;
// Upper symmetric
T v[6]; // _00 _01 _02 _11 _12 _22
inline SymMat3() {}
inline explicit SymMat3(T s)
{
v[0] = v[3] = v[5] = s;
v[1] = v[2] = v[4] = T(0);
}
inline explicit SymMat3(T a00, T a01, T a02, T a11, T a12, T a22)
{
v[0] = a00; v[1] = a01; v[2] = a02;
v[3] = a11; v[4] = a12;
v[5] = a22;
}
// Cast to symmetric Matrix3
operator Matrix3<T>() const
{
return Matrix3<T>(v[0], v[1], v[2],
v[1], v[3], v[4],
v[2], v[4], v[5]);
}
static inline int Index(unsigned int i, unsigned int j)
{
return (i <= j) ? (3*i - i*(i+1)/2 + j) : (3*j - j*(j+1)/2 + i);
}
inline T operator()(int i, int j) const { return v[Index(i,j)]; }
inline T &operator()(int i, int j) { return v[Index(i,j)]; }
inline this_type& operator+=(const this_type& b)
{
v[0]+=b.v[0];
v[1]+=b.v[1];
v[2]+=b.v[2];
v[3]+=b.v[3];
v[4]+=b.v[4];
v[5]+=b.v[5];
return *this;
}
inline this_type& operator-=(const this_type& b)
{
v[0]-=b.v[0];
v[1]-=b.v[1];
v[2]-=b.v[2];
v[3]-=b.v[3];
v[4]-=b.v[4];
v[5]-=b.v[5];
return *this;
}
inline this_type& operator*=(T s)
{
v[0]*=s;
v[1]*=s;
v[2]*=s;
v[3]*=s;
v[4]*=s;
v[5]*=s;
return *this;
}
inline SymMat3 operator*(T s) const
{
SymMat3 d;
d.v[0] = v[0]*s;
d.v[1] = v[1]*s;
d.v[2] = v[2]*s;
d.v[3] = v[3]*s;
d.v[4] = v[4]*s;
d.v[5] = v[5]*s;
return d;
}
// Multiplies two matrices into destination with minimum copying.
static SymMat3& Multiply(SymMat3* d, const SymMat3& a, const SymMat3& b)
{
// _00 _01 _02 _11 _12 _22
d->v[0] = a.v[0] * b.v[0];
d->v[1] = a.v[0] * b.v[1] + a.v[1] * b.v[3];
d->v[2] = a.v[0] * b.v[2] + a.v[1] * b.v[4];
d->v[3] = a.v[3] * b.v[3];
d->v[4] = a.v[3] * b.v[4] + a.v[4] * b.v[5];
d->v[5] = a.v[5] * b.v[5];
return *d;
}
inline T Determinant() const
{
const this_type& m = *this;
T d;
d = m(0,0) * (m(1,1)*m(2,2) - m(1,2) * m(2,1));
d -= m(0,1) * (m(1,0)*m(2,2) - m(1,2) * m(2,0));
d += m(0,2) * (m(1,0)*m(2,1) - m(1,1) * m(2,0));
return d;
}
inline this_type Inverse() const
{
this_type a;
const this_type& m = *this;
T d = Determinant();
OVR_MATH_ASSERT(d != 0);
T s = T(1)/d;
a(0,0) = s * (m(1,1) * m(2,2) - m(1,2) * m(2,1));
a(0,1) = s * (m(0,2) * m(2,1) - m(0,1) * m(2,2));
a(1,1) = s * (m(0,0) * m(2,2) - m(0,2) * m(2,0));
a(0,2) = s * (m(0,1) * m(1,2) - m(0,2) * m(1,1));
a(1,2) = s * (m(0,2) * m(1,0) - m(0,0) * m(1,2));
a(2,2) = s * (m(0,0) * m(1,1) - m(0,1) * m(1,0));
return a;
}
inline T Trace() const { return v[0] + v[3] + v[5]; }
// M = a*a.t()
inline void Rank1(const Vector3<T> &a)
{
v[0] = a.x*a.x; v[1] = a.x*a.y; v[2] = a.x*a.z;
v[3] = a.y*a.y; v[4] = a.y*a.z;
v[5] = a.z*a.z;
}
// M += a*a.t()
inline void Rank1Add(const Vector3<T> &a)
{
v[0] += a.x*a.x; v[1] += a.x*a.y; v[2] += a.x*a.z;
v[3] += a.y*a.y; v[4] += a.y*a.z;
v[5] += a.z*a.z;
}
// M -= a*a.t()
inline void Rank1Sub(const Vector3<T> &a)
{
v[0] -= a.x*a.x; v[1] -= a.x*a.y; v[2] -= a.x*a.z;
v[3] -= a.y*a.y; v[4] -= a.y*a.z;
v[5] -= a.z*a.z;
}
};
typedef SymMat3<float> SymMat3f;
typedef SymMat3<double> SymMat3d;
template<class T>
inline Matrix3<T> operator*(const SymMat3<T>& a, const SymMat3<T>& b)
{
#define AJB_ARBC(r,c) (a(r,0)*b(0,c)+a(r,1)*b(1,c)+a(r,2)*b(2,c))
return Matrix3<T>(
AJB_ARBC(0,0), AJB_ARBC(0,1), AJB_ARBC(0,2),
AJB_ARBC(1,0), AJB_ARBC(1,1), AJB_ARBC(1,2),
AJB_ARBC(2,0), AJB_ARBC(2,1), AJB_ARBC(2,2));
#undef AJB_ARBC
}
template<class T>
inline Matrix3<T> operator*(const Matrix3<T>& a, const SymMat3<T>& b)
{
#define AJB_ARBC(r,c) (a(r,0)*b(0,c)+a(r,1)*b(1,c)+a(r,2)*b(2,c))
return Matrix3<T>(
AJB_ARBC(0,0), AJB_ARBC(0,1), AJB_ARBC(0,2),
AJB_ARBC(1,0), AJB_ARBC(1,1), AJB_ARBC(1,2),
AJB_ARBC(2,0), AJB_ARBC(2,1), AJB_ARBC(2,2));
#undef AJB_ARBC
}
//-------------------------------------------------------------------------------------
// ***** Angle
// Cleanly representing the algebra of 2D rotations.
// The operations maintain the angle between -Pi and Pi, the same range as atan2.
template<class T>
class Angle
{
public:
enum AngularUnits
{
Radians = 0,
Degrees = 1
};
Angle() : a(0) {}
// Fix the range to be between -Pi and Pi
Angle(T a_, AngularUnits u = Radians) : a((u == Radians) ? a_ : a_*((T)MATH_DOUBLE_DEGREETORADFACTOR)) { FixRange(); }
T Get(AngularUnits u = Radians) const { return (u == Radians) ? a : a*((T)MATH_DOUBLE_RADTODEGREEFACTOR); }
void Set(const T& x, AngularUnits u = Radians) { a = (u == Radians) ? x : x*((T)MATH_DOUBLE_DEGREETORADFACTOR); FixRange(); }
int Sign() const { if (a == 0) return 0; else return (a > 0) ? 1 : -1; }
T Abs() const { return (a >= 0) ? a : -a; }
bool operator== (const Angle& b) const { return a == b.a; }
bool operator!= (const Angle& b) const { return a != b.a; }
// bool operator< (const Angle& b) const { return a < a.b; }
// bool operator> (const Angle& b) const { return a > a.b; }
// bool operator<= (const Angle& b) const { return a <= a.b; }
// bool operator>= (const Angle& b) const { return a >= a.b; }
// bool operator= (const T& x) { a = x; FixRange(); }
// These operations assume a is already between -Pi and Pi.
Angle& operator+= (const Angle& b) { a = a + b.a; FastFixRange(); return *this; }
Angle& operator+= (const T& x) { a = a + x; FixRange(); return *this; }
Angle operator+ (const Angle& b) const { Angle res = *this; res += b; return res; }
Angle operator+ (const T& x) const { Angle res = *this; res += x; return res; }
Angle& operator-= (const Angle& b) { a = a - b.a; FastFixRange(); return *this; }
Angle& operator-= (const T& x) { a = a - x; FixRange(); return *this; }
Angle operator- (const Angle& b) const { Angle res = *this; res -= b; return res; }
Angle operator- (const T& x) const { Angle res = *this; res -= x; return res; }
T Distance(const Angle& b) { T c = fabs(a - b.a); return (c <= ((T)MATH_DOUBLE_PI)) ? c : ((T)MATH_DOUBLE_TWOPI) - c; }
private:
// The stored angle, which should be maintained between -Pi and Pi
T a;
// Fixes the angle range to [-Pi,Pi], but assumes no more than 2Pi away on either side
inline void FastFixRange()
{
if (a < -((T)MATH_DOUBLE_PI))
a += ((T)MATH_DOUBLE_TWOPI);
else if (a > ((T)MATH_DOUBLE_PI))
a -= ((T)MATH_DOUBLE_TWOPI);
}
// Fixes the angle range to [-Pi,Pi] for any given range, but slower then the fast method
inline void FixRange()
{
// do nothing if the value is already in the correct range, since fmod call is expensive
if (a >= -((T)MATH_DOUBLE_PI) && a <= ((T)MATH_DOUBLE_PI))
return;
a = fmod(a,((T)MATH_DOUBLE_TWOPI));
if (a < -((T)MATH_DOUBLE_PI))
a += ((T)MATH_DOUBLE_TWOPI);
else if (a > ((T)MATH_DOUBLE_PI))
a -= ((T)MATH_DOUBLE_TWOPI);
}
};
typedef Angle<float> Anglef;
typedef Angle<double> Angled;
//-------------------------------------------------------------------------------------
// ***** Plane
// Consists of a normal vector and distance from the origin where the plane is located.
template<class T>
class Plane
{
public:
Vector3<T> N;
T D;
Plane() : D(0) {}
// Normals must already be normalized
Plane(const Vector3<T>& n, T d) : N(n), D(d) {}
Plane(T x, T y, T z, T d) : N(x,y,z), D(d) {}
// construct from a point on the plane and the normal
Plane(const Vector3<T>& p, const Vector3<T>& n) : N(n), D(-(p * n)) {}
// Find the point to plane distance. The sign indicates what side of the plane the point is on (0 = point on plane).
T TestSide(const Vector3<T>& p) const
{
return (N.Dot(p)) + D;
}
Plane<T> Flipped() const
{
return Plane(-N, -D);
}
void Flip()
{
N = -N;
D = -D;
}
bool operator==(const Plane<T>& rhs) const
{
return (this->D == rhs.D && this->N == rhs.N);
}
};
typedef Plane<float> Planef;
typedef Plane<double> Planed;
//-----------------------------------------------------------------------------------
// ***** ScaleAndOffset2D
struct ScaleAndOffset2D
{
Vector2f Scale;
Vector2f Offset;
ScaleAndOffset2D(float sx = 0.0f, float sy = 0.0f, float ox = 0.0f, float oy = 0.0f)
: Scale(sx, sy), Offset(ox, oy)
{ }
};
//-----------------------------------------------------------------------------------
// ***** FovPort
// FovPort describes Field Of View (FOV) of a viewport.
// This class has values for up, down, left and right, stored in
// tangent of the angle units to simplify calculations.
//
// As an example, for a standard 90 degree vertical FOV, we would
// have: { UpTan = tan(90 degrees / 2), DownTan = tan(90 degrees / 2) }.
//
// CreateFromRadians/Degrees helper functions can be used to
// access FOV in different units.
// ***** FovPort
struct FovPort
{
float UpTan;
float DownTan;
float LeftTan;
float RightTan;
FovPort ( float sideTan = 0.0f ) :
UpTan(sideTan), DownTan(sideTan), LeftTan(sideTan), RightTan(sideTan) { }
FovPort ( float u, float d, float l, float r ) :
UpTan(u), DownTan(d), LeftTan(l), RightTan(r) { }
// C-interop support: FovPort <-> ovrFovPort (implementation in OVR_CAPI.cpp).
FovPort(const ovrFovPort &src)
: UpTan(src.UpTan), DownTan(src.DownTan), LeftTan(src.LeftTan), RightTan(src.RightTan)
{ }
operator ovrFovPort () const
{
ovrFovPort result;
result.LeftTan = LeftTan;
result.RightTan = RightTan;
result.UpTan = UpTan;
result.DownTan = DownTan;
return result;
}
static FovPort CreateFromRadians(float horizontalFov, float verticalFov)
{
FovPort result;
result.UpTan = tanf ( verticalFov * 0.5f );
result.DownTan = tanf ( verticalFov * 0.5f );
result.LeftTan = tanf ( horizontalFov * 0.5f );
result.RightTan = tanf ( horizontalFov * 0.5f );
return result;
}
static FovPort CreateFromDegrees(float horizontalFovDegrees,
float verticalFovDegrees)
{
return CreateFromRadians(DegreeToRad(horizontalFovDegrees),
DegreeToRad(verticalFovDegrees));
}
// Get Horizontal/Vertical components of Fov in radians.
float GetVerticalFovRadians() const { return atanf(UpTan) + atanf(DownTan); }
float GetHorizontalFovRadians() const { return atanf(LeftTan) + atanf(RightTan); }
// Get Horizontal/Vertical components of Fov in degrees.
float GetVerticalFovDegrees() const { return RadToDegree(GetVerticalFovRadians()); }
float GetHorizontalFovDegrees() const { return RadToDegree(GetHorizontalFovRadians()); }
// Compute maximum tangent value among all four sides.
float GetMaxSideTan() const
{
return OVRMath_Max(OVRMath_Max(UpTan, DownTan), OVRMath_Max(LeftTan, RightTan));
}
static ScaleAndOffset2D CreateNDCScaleAndOffsetFromFov ( FovPort tanHalfFov )
{
float projXScale = 2.0f / ( tanHalfFov.LeftTan + tanHalfFov.RightTan );
float projXOffset = ( tanHalfFov.LeftTan - tanHalfFov.RightTan ) * projXScale * 0.5f;
float projYScale = 2.0f / ( tanHalfFov.UpTan + tanHalfFov.DownTan );
float projYOffset = ( tanHalfFov.UpTan - tanHalfFov.DownTan ) * projYScale * 0.5f;
ScaleAndOffset2D result;
result.Scale = Vector2f(projXScale, projYScale);
result.Offset = Vector2f(projXOffset, projYOffset);
// Hey - why is that Y.Offset negated?
// It's because a projection matrix transforms from world coords with Y=up,
// whereas this is from NDC which is Y=down.
return result;
}
// Converts Fov Tan angle units to [-1,1] render target NDC space
Vector2f TanAngleToRendertargetNDC(Vector2f const &tanEyeAngle)
{
ScaleAndOffset2D eyeToSourceNDC = CreateNDCScaleAndOffsetFromFov(*this);
return tanEyeAngle * eyeToSourceNDC.Scale + eyeToSourceNDC.Offset;
}
// Compute per-channel minimum and maximum of Fov.
static FovPort Min(const FovPort& a, const FovPort& b)
{
FovPort fov( OVRMath_Min( a.UpTan , b.UpTan ),
OVRMath_Min( a.DownTan , b.DownTan ),
OVRMath_Min( a.LeftTan , b.LeftTan ),
OVRMath_Min( a.RightTan, b.RightTan ) );
return fov;
}
static FovPort Max(const FovPort& a, const FovPort& b)
{
FovPort fov( OVRMath_Max( a.UpTan , b.UpTan ),
OVRMath_Max( a.DownTan , b.DownTan ),
OVRMath_Max( a.LeftTan , b.LeftTan ),
OVRMath_Max( a.RightTan, b.RightTan ) );
return fov;
}
};
} // Namespace OVR
#if defined(_MSC_VER)
#pragma warning(pop)
#endif
#endif