Improve Vector3RotateByAxisAngle() function

src/rcamera.h

@@ -202,9 +202,55 @@ Matrix GetCameraProjectionMatrix(Camera3D* camera, float aspect);
 
 // Rotates the given vector around the given axis
 // Note: angle must be provided in radians
-Vector3 Vector3RotateAxis(Vector3 v, Vector3 axis, float angle) { // TODO there is a better way without the intermediate matrix
+Vector3 Vector3RotateByAxisAngle(Vector3 v, Vector3 axis, float angle)
-    Matrix rot = MatrixRotate(axis, angle);
+{
-    return Vector3Transform(v, rot);
+    // Using Euler-Rodrigues Formula
+    // Ref.: https://en.wikipedia.org/w/index.php?title=Euler%E2%80%93Rodrigues_formula
+
+    Vector3 result = v;
+
+    // Vector3Normalize(axis);
+    float length = sqrtf(axis.x * axis.x + axis.y * axis.y + axis.z * axis.z);
+    if (length == 0.0f) length = 1.0f;
+    float ilength = 1.0f / length;
+    axis.x *= ilength;
+    axis.y *= ilength;
+    axis.z *= ilength;
+
+    angle /= 2.0f;
+    float a = sinf(angle);
+    float b = axis.x * a;
+    float c = axis.y * a;
+    float d = axis.z * a;
+    a = cosf(angle);
+    Vector3 w = { b, c, d };
+
+    // Vector3CrossProduct(w, v)
+    Vector3 wv = { w.y * v.z - w.z * v.y, w.z * v.x - w.x * v.z, w.x * v.y - w.y * v.x };
+
+    // Vector3CrossProduct(w, wv)
+    Vector3 wwv = { w.y * wv.z - w.z * wv.y, w.z * wv.x - w.x * wv.z, w.x * wv.y - w.y * wv.x };
+
+    // Vector3Scale(wv, 2 * a)
+    a *= 2;
+    wv.x *= a;
+    wv.y *= a;
+    wv.z *= a;
+
+    // Vector3Scale(wwv, 2)
+    wwv.x *= 2;
+    wwv.y *= 2;
+    wwv.z *= 2;
+
+    result.x += wv.x;
+    result.y += wv.y;
+    result.z += wv.z;
+
+    result.x += wwv.x;
+    result.y += wwv.y;
+    result.z += wwv.z;
+
+    return result;
 }
 
 //----------------------------------------------------------------------------------
@@ -340,7 +386,7 @@ void CameraYaw(Camera3D *camera, float angle)
     Vector3 target_position = Vector3Subtract(camera->target, camera->position);
 
     // Rotate view vector around up axis
-    target_position = Vector3RotateAxis(target_position, up, angle);
+    target_position = Vector3RotateByAxisAngle(target_position, up, angle);
 
     if (camera->mode == CAMERA_FREE ||
         camera->mode == CAMERA_FIRST_PERSON)
@@ -390,7 +436,7 @@ void CameraPitch(Camera3D *camera, float angle)
     Vector3 right = GetCameraRight(camera);
 
     // Rotate view vector around right axis
-    target_position = Vector3RotateAxis(target_position, right, angle);
+    target_position = Vector3RotateByAxisAngle(target_position, right, angle);
 
     if (camera->mode == CAMERA_FREE)
     {
@@ -398,7 +444,7 @@ void CameraPitch(Camera3D *camera, float angle)
         camera->target = Vector3Add(camera->position, target_position);
 
         // Rotate up direction around right axis
-        camera->up = Vector3RotateAxis(camera->up, right, angle);
+        camera->up = Vector3RotateByAxisAngle(camera->up, right, angle);
     }
     else if (camera->mode == CAMERA_FIRST_PERSON)
     {
@@ -422,7 +468,7 @@ void CameraRoll(Camera3D *camera, float angle)
     Vector3 forward = GetCameraForward(camera);
 
     // Rotate up direction around forward axis
-    camera->up = Vector3RotateAxis(camera->up, forward, angle);
+    camera->up = Vector3RotateByAxisAngle(camera->up, forward, angle);
 }
 
 // Moves camera slightly to simulate a walking motion