public void TestHermiteAsSphericalInterpolation()
{
// given two quaternions, we must find a tangent quaternion so that the quaternion
// hermite interpolation gives roughly the same results as a plain spherical interpolation.
// reference implementation with matrices
var m1 = Matrix4x4.CreateFromAxisAngle(Vector3.UnitX, 1);
var m2 = Matrix4x4.CreateFromAxisAngle(Vector3.UnitY, 2);
var mt = Matrix4x4.Multiply(m2, Matrix4x4.Transpose(m1));
var m2bis = Matrix4x4.Multiply(mt, m1); // roundtrip; M2 == M2BIS
// implementation with quaternions
var q1 = Quaternion.CreateFromAxisAngle(Vector3.UnitX, 1);
var q2 = Quaternion.CreateFromAxisAngle(Vector3.UnitY, 2);
var qt = Quaternion.Concatenate(q2, Quaternion.Conjugate(q1));
var q2bis = Quaternion.Concatenate(qt, q1); // roundtrip; Q2 == Q2BIS
NumericsAssert.AreEqual(qt, Animations.SamplerFactory.CreateTangent(q1, q2), 0.000001f);
var angles = new List <Vector2>();
for (float amount = 0; amount <= 1; amount += 0.025f)
{
// slerp interpolation
var sq = Quaternion.Normalize(Quaternion.Slerp(q1, q2, amount));
// hermite interpolation with a unit tangent
var hermite = Animations.SamplerFactory.CreateHermitePointWeights(amount);
var hq = default(Quaternion);
hq += q1 * hermite.Item1;
hq += q2 * hermite.Item2;
hq += qt * hermite.Item3;
hq += qt * hermite.Item4;
hq = Quaternion.Normalize(hq);
// check
NumericsAssert.AreEqual(sq, hq, 0.1f);
NumericsAssert.AngleLessOrEqual(sq, hq, 0.22f);
// diff
var a = VectorsUtils.GetAngle(sq, hq) * 180.0f / 3.141592f;
angles.Add(new Vector2(amount, a));
}
angles.ToPointSeries()
.WithLineType(Plotting.LineType.Continuous)
.AttachToCurrentTest("plot.png");
}
public static void AngleLessOrEqual(Quaternion a, Quaternion b, double radians)
{
var angle = VectorsUtils.GetAngle(a, b);
Assert.LessOrEqual(angle, radians, "Angle");
}
public static void AngleLessOrEqual(Vector3 a, Vector3 b, double radians)
{
var angle = VectorsUtils.GetAngle(a, b);
Assert.LessOrEqual(angle, radians, "Angle");
}
