diff --git a/src/raymath.h b/src/raymath.h index f246f26d9..d3c8b9697 100644 --- a/src/raymath.h +++ b/src/raymath.h @@ -2552,65 +2552,91 @@ RMAPI int QuaternionEquals(Quaternion p, Quaternion q) return result; } -// Decompose a transformation matrix into its rotational, translational and scaling components +// Decompose a transformation matrix into its rotational, translational and scaling components and remove shear RMAPI void MatrixDecompose(Matrix mat, Vector3 *translation, Quaternion *rotation, Vector3 *scale) { - // Extract translation. + float eps = 1e-9; + + // Extract Translation translation->x = mat.m12; translation->y = mat.m13; translation->z = mat.m14; - // Extract upper-left for determinant computation - const float a = mat.m0; - const float b = mat.m4; - const float c = mat.m8; - const float d = mat.m1; - const float e = mat.m5; - const float f = mat.m9; - const float g = mat.m2; - const float h = mat.m6; - const float i = mat.m10; - const float A = e*i - f*h; - const float B = f*g - d*i; - const float C = d*h - e*g; - - // Extract scale - const float det = a*A + b*B + c*C; - Vector3 abc = { a, b, c }; - Vector3 def = { d, e, f }; - Vector3 ghi = { g, h, i }; - - float scalex = Vector3Length(abc); - float scaley = Vector3Length(def); - float scalez = Vector3Length(ghi); - Vector3 s = { scalex, scaley, scalez }; - - if (det < 0) s = Vector3Negate(s); - - *scale = s; - - // Remove scale from the matrix if it is not close to zero - Matrix clone = mat; - if (!FloatEquals(det, 0)) + // Matrix Columns - Rotation will be extracted into here. + Vector3 matColumns[3] = { { mat.m0, mat.m4, mat.m8 }, + { mat.m1, mat.m5, mat.m9 }, + { mat.m2, mat.m6, mat.m10 } }; + + // Shear Parameters XY, XZ, and YZ (extract and ignored) + float shear[3] = { 0 }; + + // Normalized Scale Parameters + Vector3 scl = { 0 }; + + // Max-Normalizing helps numerical stability + float stabilizer = eps; + for (int i = 0; i < 3; i++) + { + stabilizer = fmaxf(stabilizer, fabsf(matColumns[i].x)); + stabilizer = fmaxf(stabilizer, fabsf(matColumns[i].y)); + stabilizer = fmaxf(stabilizer, fabsf(matColumns[i].z)); + }; + matColumns[0] = Vector3Scale(matColumns[0], 1.0f / stabilizer); + matColumns[1] = Vector3Scale(matColumns[1], 1.0f / stabilizer); + matColumns[2] = Vector3Scale(matColumns[2], 1.0f / stabilizer); + + // X Scale + scl.x = Vector3Length(matColumns[0]); + if (scl.x > eps) { - clone.m0 /= s.x; - clone.m4 /= s.x; - clone.m8 /= s.x; - clone.m1 /= s.y; - clone.m5 /= s.y; - clone.m9 /= s.y; - clone.m2 /= s.z; - clone.m6 /= s.z; - clone.m10 /= s.z; - - // Extract rotation - *rotation = QuaternionFromMatrix(clone); + matColumns[0] = Vector3Scale(matColumns[0], 1.0f / scl.x); } - else + + // Compute XY shear and make col2 orthogonal + shear[0] = Vector3DotProduct(matColumns[0], matColumns[1]); + matColumns[1] = Vector3Subtract(matColumns[1], Vector3Scale(matColumns[0], shear[0])); + + // Y Scale + scl.y = Vector3Length(matColumns[1]); + if (scl.y > eps) { - // Set to identity if close to zero - *rotation = QuaternionIdentity(); + matColumns[1] = Vector3Scale(matColumns[1], 1.0f / scl.y); + shear[0] /= scl.y; // Correct XY shear } + + // Compute XZ and YZ shears and make col3 orthogonal + shear[1] = Vector3DotProduct(matColumns[0], matColumns[2]); + matColumns[2] = Vector3Subtract(matColumns[2], Vector3Scale(matColumns[0], shear[1])); + shear[2] = Vector3DotProduct(matColumns[1], matColumns[2]); + matColumns[2] = Vector3Subtract(matColumns[2], Vector3Scale(matColumns[1], shear[2])); + + // Z Scale + scl.z = Vector3Length(matColumns[2]); + if (scl.z > eps) + { + matColumns[2] = Vector3Scale(matColumns[2], 1.0f / scl.z); + shear[1] /= scl.z; // Correct XZ shear + shear[2] /= scl.z; // Correct YZ shear + } + + // matColumns are now orthonormal in O(3). Now ensure its in SO(3) by enforcing det = 1. + if (Vector3DotProduct(matColumns[0], Vector3CrossProduct(matColumns[1], matColumns[2])) < 0) + { + scl = Vector3Negate(scl); + matColumns[0] = Vector3Negate(matColumns[0]); + matColumns[1] = Vector3Negate(matColumns[1]); + matColumns[2] = Vector3Negate(matColumns[2]); + } + + // Set Scale + *scale = Vector3Scale(scl, stabilizer); + + // Extract Rotation + Matrix rotationMatrix = { matColumns[0].x, matColumns[0].y, matColumns[0].z, 0, + matColumns[1].x, matColumns[1].y, matColumns[1].z, 0, + matColumns[2].x, matColumns[2].y, matColumns[2].z, 0, + 0, 0, 0, 1 }; + *rotation = QuaternionFromMatrix(rotationMatrix); } #if defined(__cplusplus) && !defined(RAYMATH_DISABLE_CPP_OPERATORS)