[rmodels] `DrawSphereEx()` optimization (#4106)

* Optimize DrawSphereEx()

Precalculates sin/cos to eliminate unnecessary calls.

* Formatting correction to previous commit

* Bugfix to optimized DrawSphereEx()

OBO error -- added 1 additional precalculated cos/sin value to each array to complete the 360-degree wraparound. Technically the value of these last elements will always be the same as the first element due to 360-degree wraparound, but this is the simplest solution.

* Corrected missing free()

* Formatting correction

* New DrawSphereEx() algorithm

src/rmodels.c

@@ -432,30 +432,36 @@ void DrawSphereEx(Vector3 centerPos, float radius, int rings, int slices, Color
         rlBegin(RL_TRIANGLES);
             rlColor4ub(color.r, color.g, color.b, color.a);
 
-            for (int i = 0; i < (rings + 2); i++)
+            float ringangle = DEG2RAD*(180.0f/(rings + 1)); // Angle between latitudinal parallels
-            {
+            float sliceangle = DEG2RAD*(360.0f/slices); // Angle between longitudinal meridians
-                for (int j = 0; j < slices; j++)
+            float cosring = cosf(ringangle);
-                {
+            float sinring = sinf(ringangle);
-                    rlVertex3f(cosf(DEG2RAD*(270 + (180.0f/(rings + 1))*i))*sinf(DEG2RAD*(360.0f*j/slices)),
+            float cosslice = cosf(sliceangle);
-                               sinf(DEG2RAD*(270 + (180.0f/(rings + 1))*i)),
+            float sinslice = sinf(sliceangle);
-                               cosf(DEG2RAD*(270 + (180.0f/(rings + 1))*i))*cosf(DEG2RAD*(360.0f*j/slices)));
+            Vector3 vertices[4]; // Store face vertices
-                    rlVertex3f(cosf(DEG2RAD*(270 + (180.0f/(rings + 1))*(i + 1)))*sinf(DEG2RAD*(360.0f*(j + 1)/slices)),
+            vertices[2] = (Vector3){0,1,0};
-                               sinf(DEG2RAD*(270 + (180.0f/(rings + 1))*(i + 1))),
+            vertices[3] = (Vector3){sinring, cosring, 0};
-                               cosf(DEG2RAD*(270 + (180.0f/(rings + 1))*(i + 1)))*cosf(DEG2RAD*(360.0f*(j + 1)/slices)));
+            for (int i = 0; i < rings + 1; i++) {
-                    rlVertex3f(cosf(DEG2RAD*(270 + (180.0f/(rings + 1))*(i + 1)))*sinf(DEG2RAD*(360.0f*j/slices)),
+                for (int j = 0; j < slices; j++) {
-                               sinf(DEG2RAD*(270 + (180.0f/(rings + 1))*(i + 1))),
+                    vertices[0] = vertices[2]; // Rotate around y axis to set up vertices for next face
-                               cosf(DEG2RAD*(270 + (180.0f/(rings + 1))*(i + 1)))*cosf(DEG2RAD*(360.0f*j/slices)));
+                    vertices[1] = vertices[3];
-
+                    vertices[2] = (Vector3){cosslice*vertices[2].x - sinslice*vertices[2].z, vertices[2].y, sinslice*vertices[2].x + cosslice*vertices[2].z}; // Rotation matrix around y axis
-                    rlVertex3f(cosf(DEG2RAD*(270 + (180.0f/(rings + 1))*i))*sinf(DEG2RAD*(360.0f*j/slices)),
+                    vertices[3] = (Vector3){cosslice*vertices[3].x - sinslice*vertices[3].z, vertices[3].y, sinslice*vertices[3].x + cosslice*vertices[3].z};
-                               sinf(DEG2RAD*(270 + (180.0f/(rings + 1))*i)),
+                    rlVertex3f(vertices[0].x, vertices[0].y, vertices[0].z);
-                               cosf(DEG2RAD*(270 + (180.0f/(rings + 1))*i))*cosf(DEG2RAD*(360.0f*j/slices)));
+                    rlVertex3f(vertices[3].x, vertices[3].y, vertices[3].z);
-                    rlVertex3f(cosf(DEG2RAD*(270 + (180.0f/(rings + 1))*(i)))*sinf(DEG2RAD*(360.0f*(j + 1)/slices)),
+                    rlVertex3f(vertices[1].x, vertices[1].y, vertices[1].z);
-                               sinf(DEG2RAD*(270 + (180.0f/(rings + 1))*(i))),
+                    rlVertex3f(vertices[0].x, vertices[0].y, vertices[0].z);
-                               cosf(DEG2RAD*(270 + (180.0f/(rings + 1))*(i)))*cosf(DEG2RAD*(360.0f*(j + 1)/slices)));
+                    rlVertex3f(vertices[2].x, vertices[2].y, vertices[2].z);
-                    rlVertex3f(cosf(DEG2RAD*(270 + (180.0f/(rings + 1))*(i + 1)))*sinf(DEG2RAD*(360.0f*(j + 1)/slices)),
+                    rlVertex3f(vertices[3].x, vertices[3].y, vertices[3].z);
-                               sinf(DEG2RAD*(270 + (180.0f/(rings + 1))*(i + 1))),
-                               cosf(DEG2RAD*(270 + (180.0f/(rings + 1))*(i + 1)))*cosf(DEG2RAD*(360.0f*(j + 1)/slices)));
                 }
+
+                vertices[2] = vertices[3]; // Rotate around z axis to set up  starting vertices for next ring
+                vertices[3] = (Vector3){cosring*vertices[3].x + sinring*vertices[3].y, -sinring*vertices[3].x + cosring*vertices[3].y, vertices[3].z}; // Rotation matrix around z axis
             }
         rlEnd();
     rlPopMatrix();