honor closest distance in quaternion slerp

Fix the quaternion spherical linear interpolation
to make it choose the shortest linear path, which
is the intended behavior in graphical animations.

GitHub-Pull-Request: #90

Author: nitrix

mgl32/quat.go

@@ -210,14 +210,20 @@ func (q1 Quat) OrientationEqualThreshold(q2 Quat, epsilon float32) bool {
 }
 
 // QuatSlerp is *S*pherical *L*inear Int*erp*olation, a method of interpolating
-// between two quaternions. This always takes the straightest path on the sphere between
+// between two quaternions. This always takes the straightest and shortest path on the sphere between
 // the two quaternions, and maintains constant velocity.
 //
 // However, it's expensive and QuatSlerp(q1,q2) is not the same as QuatSlerp(q2,q1)
 func QuatSlerp(q1, q2 Quat, amount float32) Quat {
 	q1, q2 = q1.Normalize(), q2.Normalize()
 	dot := q1.Dot(q2)
 
+	// Make sure we take the shortest path in case dot product is negative.
+	if dot < 0.0 {
+		q2 = q2.Scale(-1)
+		dot = -dot
+	}
+
 	// If the inputs are too close for comfort, linearly interpolate and normalize the result.
 	if dot > 0.9995 {
 		return QuatNlerp(q1, q2, amount)

mgl32/quat_test.go

@@ -702,6 +702,7 @@ func TestQuatSlerp(t *testing.T) {
 		{Quat{0.5, Vec3{-0.5, -0.5, 0.5}}, Quat{0.996, Vec3{-0.080, -0.080, 0}}, 0.2, Quat{0.6553097459373098, Vec3{-0.44231939784548874, -0.44231939784548874, 0.4237176207195655}}},
 		{Quat{0.996, Vec3{-0.080, -0.080, 0}}, Quat{0.5, Vec3{-0.5, -0.5, 0.5}}, 0.8, Quat{0.6553097459373098, Vec3{-0.44231939784548874, -0.44231939784548874, 0.4237176207195655}}},
 		{Quat{1, Vec3{0, 0, 0}}, Quat{-0.9999999, Vec3{0, 0, 0}}, 0, Quat{1, Vec3{0, 0, 0}}},
+		{Quat{-0.707, Vec3{0, 0, 0.707}}, Quat{1, Vec3{0, 0, 0}}, 0.12, Quat{-0.7705132, Vec3{0, 0, 0.637424}}},
 	}
 
 	for _, c := range tests {

mgl64/quat.go

@@ -212,14 +212,20 @@ func (q1 Quat) OrientationEqualThreshold(q2 Quat, epsilon float64) bool {
 }
 
 // QuatSlerp is *S*pherical *L*inear Int*erp*olation, a method of interpolating
-// between two quaternions. This always takes the straightest path on the sphere between
+// between two quaternions. This always takes the straightest and shortest path on the sphere between
 // the two quaternions, and maintains constant velocity.
 //
 // However, it's expensive and QuatSlerp(q1,q2) is not the same as QuatSlerp(q2,q1)
 func QuatSlerp(q1, q2 Quat, amount float64) Quat {
 	q1, q2 = q1.Normalize(), q2.Normalize()
 	dot := q1.Dot(q2)
 
+	// Make sure we take the shortest path in case dot product is negative.
+	if dot < 0.0 {
+		q2 = q2.Scale(-1)
+		dot = -dot
+	}
+
 	// If the inputs are too close for comfort, linearly interpolate and normalize the result.
 	if dot > 0.9995 {
 		return QuatNlerp(q1, q2, amount)

mgl64/quat_test.go

@@ -704,6 +704,7 @@ func TestQuatSlerp(t *testing.T) {
 		{Quat{0.5, Vec3{-0.5, -0.5, 0.5}}, Quat{0.996, Vec3{-0.080, -0.080, 0}}, 0.2, Quat{0.6553097459373098, Vec3{-0.44231939784548874, -0.44231939784548874, 0.4237176207195655}}},
 		{Quat{0.996, Vec3{-0.080, -0.080, 0}}, Quat{0.5, Vec3{-0.5, -0.5, 0.5}}, 0.8, Quat{0.6553097459373098, Vec3{-0.44231939784548874, -0.44231939784548874, 0.4237176207195655}}},
 		{Quat{1, Vec3{0, 0, 0}}, Quat{-0.9999999, Vec3{0, 0, 0}}, 0, Quat{1, Vec3{0, 0, 0}}},
+		{Quat{-0.707, Vec3{0, 0, 0.707}}, Quat{1, Vec3{0, 0, 0}}, 0.12, Quat{-0.7705132, Vec3{0, 0, 0.637424}}},
 	}
 
 	for _, c := range tests {