public void SlerpNegatedDoublePrecision()
{
QuaternionD q1 = new QuaternionD(-1.0, 0.0, 0.0, 0.0);
QuaternionD q2 = QuaternionD.CreateRotation(-Vector3.UnitZ, -Math.PI / 2);
QuaternionD slerp = InterpolationHelper.Slerp(q1, q2, 0.5);
Assert.IsTrue(slerp.IsNumericallyNormalized);
Vector3D v = slerp.Rotate(Vector3D.UnitX);
Vector3D result = new Vector3D(1.0, 1.0, 0.0).Normalized;
Assert.IsTrue(Vector3D.AreNumericallyEqual(result, v));
}
public void SlerpNegatedSinglePrecision()
{
Quaternion q1 = new Quaternion(-1.0f, 0.0f, 0.0f, 0.0f);
Quaternion q2 = Quaternion.CreateFromRotationMatrix(-Vector3.UnitZ, (float)-Math.PI / 2);
Quaternion slerp = InterpolationHelper.Slerp(q1, q2, 0.5f);
Assert.IsTrue(slerp.IsNumericallyNormalized);
Vector3 v = slerp.Rotate(Vector3.UnitX);
Vector3 result = new Vector3(1.0f, 1.0f, 0.0f).Normalized;
Assert.IsTrue(Vector3.AreNumericallyEqual(result, v));
}
public void SlerpXDoublePrecision()
{
QuaternionD q1 = QuaternionD.Identity;
QuaternionD q2 = QuaternionD.CreateRotation(Vector3.UnitX, Math.PI / 2);
QuaternionD slerp = InterpolationHelper.Slerp(q1, q2, 0.5);
Assert.IsTrue(slerp.IsNumericallyNormalized);
Vector3D v = slerp.Rotate(Vector3.UnitY);
Vector3D result = new Vector3D(0.0, 1.0, 1.0).Normalized;
Assert.IsTrue(Vector3D.AreNumericallyEqual(result, v));
}
public void SlerpXSinglePrecision()
{
QuaternionF q1 = QuaternionF.Identity;
QuaternionF q2 = QuaternionF.CreateRotation(Vector3F.UnitX, (float)Math.PI / 2);
QuaternionF slerp = InterpolationHelper.Slerp(q1, q2, 0.5f);
Assert.IsTrue(slerp.IsNumericallyNormalized);
Vector3F v = slerp.Rotate(Vector3F.UnitY);
Vector3F result = new Vector3F(0.0f, 1.0f, 1.0f).Normalized;
Assert.IsTrue(Vector3F.AreNumericallyEqual(result, v));
}
public void SlerpDoublePrecision()
{
// Warning: The not all results are not verified
QuaternionD q1 = new QuaternionD(1.0, 2.0, 3.0, 4.0).Normalized;
QuaternionD q2 = new QuaternionD(2.0, 4.0, 6.0, 8.0).Normalized;
QuaternionD slerp = InterpolationHelper.Slerp(q1, q2, 0.75);
Assert.IsTrue(slerp.IsNumericallyNormalized);
slerp = InterpolationHelper.Slerp(q1, q2, 0);
Assert.IsTrue(slerp.IsNumericallyNormalized);
Assert.IsTrue(QuaternionD.AreNumericallyEqual(q1, slerp));
slerp = InterpolationHelper.Slerp(q1, q2, 1);
Assert.IsTrue(slerp.IsNumericallyNormalized);
Assert.IsTrue(QuaternionD.AreNumericallyEqual(q2, slerp));
}
public void SlerpSinglePrecision()
{
// Warning: The not all results are not verified
Quaternion q1 = new Quaternion(1.0f, 2.0f, 3.0f, 4.0f).Normalized;
Quaternion q2 = new Quaternion(2.0f, 4.0f, 6.0f, 8.0f).Normalized;
Quaternion slerp = InterpolationHelper.Slerp(q1, q2, 0.75f);
Assert.IsTrue(slerp.IsNumericallyNormalized);
slerp = InterpolationHelper.Slerp(q1, q2, 0);
Assert.IsTrue(slerp.IsNumericallyNormalized);
Assert.IsTrue(Quaternion.AreNumericallyEqual(q1, slerp));
slerp = InterpolationHelper.Slerp(q1, q2, 1);
Assert.IsTrue(slerp.IsNumericallyNormalized);
Assert.IsTrue(Quaternion.AreNumericallyEqual(q2, slerp));
}
public void SlerpGeneralDoublePrecision()
{
QuaternionD q1 = QuaternionD.CreateRotation(-Vector3D.UnitY, Math.PI / 2);
QuaternionD q2 = QuaternionD.CreateRotation(Vector3D.UnitZ, Math.PI / 2);
QuaternionD slerp = InterpolationHelper.Slerp(q1, q2, 0.5);
Assert.IsTrue(slerp.IsNumericallyNormalized);
Vector3D v = slerp.Rotate(Vector3D.UnitX);
Vector3D result = new Vector3D(1.0 / 3.0, 2.0 / 3.0, 2.0 / 3.0); // I hope this is correct.
Assert.IsTrue(Vector3D.AreNumericallyEqual(result, v));
q1 = QuaternionD.CreateRotation(-Vector3D.UnitY, Math.PI / 2);
q2 = QuaternionD.CreateRotation(-Vector3D.UnitZ, -Math.PI / 2);
slerp = InterpolationHelper.Slerp(q1, q2, 0.5);
Assert.IsTrue(slerp.IsNumericallyNormalized);
v = slerp.Rotate(Vector3D.UnitX);
result = new Vector3D(1.0 / 3.0, 2.0 / 3.0, 2.0 / 3.0); // I hope this is correct.
Assert.IsTrue(Vector3D.AreNumericallyEqual(result, v));
}
public void SlerpGeneralSinglePrecision()
{
Quaternion q1 = Quaternion.CreateFromRotationMatrix(-Vector3.UnitY, (float)Math.PI / 2);
Quaternion q2 = Quaternion.CreateFromRotationMatrix(Vector3.UnitZ, (float)Math.PI / 2);
Quaternion slerp = InterpolationHelper.Slerp(q1, q2, 0.5f);
Assert.IsTrue(slerp.IsNumericallyNormalized);
Vector3 v = slerp.Rotate(Vector3.UnitX);
Vector3 result = new Vector3(1.0f / 3.0f, 2.0f / 3.0f, 2.0f / 3.0f); // I hope this is correct.
Assert.IsTrue(Vector3.AreNumericallyEqual(result, v));
q1 = Quaternion.CreateFromRotationMatrix(-Vector3.UnitY, (float)Math.PI / 2);
q2 = Quaternion.CreateFromRotationMatrix(-Vector3.UnitZ, (float)-Math.PI / 2);
slerp = InterpolationHelper.Slerp(q1, q2, 0.5f);
Assert.IsTrue(slerp.IsNumericallyNormalized);
v = slerp.Rotate(Vector3.UnitX);
result = new Vector3(1.0f / 3.0f, 2.0f / 3.0f, 2.0f / 3.0f); // I hope this is correct.
Assert.IsTrue(Vector3.AreNumericallyEqual(result, v));
}
public void SquadDoublePrecision()
{
QuaternionD q0 = QuaternionD.CreateRotation(new Vector3D(1, 1, 1), 0.3);
QuaternionD q1 = QuaternionD.CreateRotation(new Vector3D(1, 0, 1), 0.4);
QuaternionD q2 = QuaternionD.CreateRotation(new Vector3D(1, 0, -1), -0.6);
QuaternionD q3 = QuaternionD.CreateRotation(new Vector3D(0, 1, 1), 0.2);
QuaternionD q, a, b, p;
QuaternionD expected;
InterpolationHelper.SquadSetup(q0, q1, q2, q3, out q, out a, out b, out p);
// t = 0
QuaternionD result = InterpolationHelper.Squad(q, a, b, p, 0.0);
Assert.IsTrue(QuaternionD.AreNumericallyEqual(q1, result));
// t = 1.0f
result = InterpolationHelper.Squad(q, a, b, p, 1.0);
Assert.IsTrue(QuaternionD.AreNumericallyEqual(q2, result));
// Check series (just for debugging)
QuaternionD r1, r2, r3, r4, r5, r6, r7, r8, r9;
r1 = InterpolationHelper.Squad(q, a, b, p, 0.1);
r2 = InterpolationHelper.Squad(q, a, b, p, 0.2);
r3 = InterpolationHelper.Squad(q, a, b, p, 0.3);
r4 = InterpolationHelper.Squad(q, a, b, p, 0.4);
r5 = InterpolationHelper.Squad(q, a, b, p, 0.5);
r6 = InterpolationHelper.Squad(q, a, b, p, 0.6);
r7 = InterpolationHelper.Squad(q, a, b, p, 0.7);
r8 = InterpolationHelper.Squad(q, a, b, p, 0.8);
r9 = InterpolationHelper.Squad(q, a, b, p, 0.9);
// q0 = q1, q2 = q3
InterpolationHelper.SquadSetup(q1, q1, q2, q2, out q, out a, out b, out p);
result = InterpolationHelper.Squad(q, a, b, p, 0.5);
expected = InterpolationHelper.Slerp(q1, q2, 0.5);
Assert.IsTrue(QuaternionD.AreNumericallyEqual(expected, result));
}
public void SquadSinglePrecision()
{
Quaternion q0 = Quaternion.CreateFromRotationMatrix(new Vector3(1, 1, 1), 0.3f);
Quaternion q1 = Quaternion.CreateFromRotationMatrix(new Vector3(1, 0, 1), 0.4f);
Quaternion q2 = Quaternion.CreateFromRotationMatrix(new Vector3(1, 0, -1), -0.6f);
Quaternion q3 = Quaternion.CreateFromRotationMatrix(new Vector3(0, 1, 1), 0.2f);
Quaternion q, a, b, p;
Quaternion expected;
InterpolationHelper.SquadSetup(q0, q1, q2, q3, out q, out a, out b, out p);
// t = 0
Quaternion result = InterpolationHelper.Squad(q, a, b, p, 0.0f);
Assert.IsTrue(Quaternion.AreNumericallyEqual(q1, result));
// t = 1.0f
result = InterpolationHelper.Squad(q, a, b, p, 1.0f);
Assert.IsTrue(Quaternion.AreNumericallyEqual(q2, result));
// Check series (just for debugging)
Quaternion r1, r2, r3, r4, r5, r6, r7, r8, r9;
r1 = InterpolationHelper.Squad(q, a, b, p, 0.1f);
r2 = InterpolationHelper.Squad(q, a, b, p, 0.2f);
r3 = InterpolationHelper.Squad(q, a, b, p, 0.3f);
r4 = InterpolationHelper.Squad(q, a, b, p, 0.4f);
r5 = InterpolationHelper.Squad(q, a, b, p, 0.5f);
r6 = InterpolationHelper.Squad(q, a, b, p, 0.6f);
r7 = InterpolationHelper.Squad(q, a, b, p, 0.7f);
r8 = InterpolationHelper.Squad(q, a, b, p, 0.8f);
r9 = InterpolationHelper.Squad(q, a, b, p, 0.9f);
// q0 = q1, q2 = q3
InterpolationHelper.SquadSetup(q1, q1, q2, q2, out q, out a, out b, out p);
result = InterpolationHelper.Squad(q, a, b, p, 0.5f);
expected = InterpolationHelper.Slerp(q1, q2, 0.5f);
Assert.IsTrue(Quaternion.AreNumericallyEqual(expected, result));
}