public void IsRotation()
{
Assert.IsTrue(!Matrix33D.Zero.IsRotation);
Assert.IsTrue(Matrix33D.Identity.IsRotation);
Assert.IsTrue(Matrix33D.CreateRotation(new Vector3D(1, 2, 3).Normalized, 0.5).IsRotation);
Assert.IsTrue(!new Matrix33D(1, 0, 0, 0, 1, 0, 0, 0, -1).IsRotation);
}
public void CreateRotationZ()
{
double angle = (double)MathHelper.ToRadians(30);
Matrix33D m = Matrix33D.CreateRotationZ(angle);
Assert.IsTrue(Vector3D.AreNumericallyEqual(new Vector3D((double)Math.Cos(angle), (double)Math.Sin(angle), 0), m * Vector3D.UnitX));
QuaternionD q = QuaternionD.CreateRotation(Vector3D.UnitZ, angle);
Assert.IsTrue(Vector3D.AreNumericallyEqual(q.Rotate(Vector3D.One), m * Vector3D.One));
Assert.IsTrue(Matrix33D.AreNumericallyEqual(Matrix33D.CreateRotation(Vector3D.UnitZ, angle), m));
}
public void RotationMatrix33()
{
double angle = -1.6;
Vector3D axis = new Vector3D(1.0, 2.0, -3.0);
QuaternionD q = QuaternionD.CreateRotation(axis, angle);
Matrix33D m33 = Matrix33D.CreateRotation(axis, angle);
Vector3D v = new Vector3D(0.3, -2.4, 5.6);
Vector3D result1 = q.ToRotationMatrix33() * v;
Vector3D result2 = m33 * v;
Assert.IsTrue(Vector3D.AreNumericallyEqual(result1, result2));
}
public void CreateRotation()
{
Matrix33D m = Matrix33D.CreateRotation(Vector3D.UnitX, 0.0);
Assert.AreEqual(Matrix33D.Identity, m);
m = Matrix33D.CreateRotation(Vector3D.UnitX, (double)Math.PI / 2);
Assert.IsTrue(Vector3D.AreNumericallyEqual(Vector3D.UnitZ, m * Vector3D.UnitY));
m = Matrix33D.CreateRotation(Vector3D.UnitY, (double)Math.PI / 2);
Assert.IsTrue(Vector3D.AreNumericallyEqual(Vector3D.UnitX, m * Vector3D.UnitZ));
m = Matrix33D.CreateRotation(Vector3D.UnitZ, (double)Math.PI / 2);
Assert.IsTrue(Vector3D.AreNumericallyEqual(Vector3D.UnitY, m * Vector3D.UnitX));
}
public void QuaternionDFromMatrix33()
{
Vector3D v = Vector3D.One;
Matrix33D m = Matrix33D.Identity;
QuaternionD q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = Matrix33D.CreateRotation(Vector3D.UnitX, 0.3);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = Matrix33D.CreateRotation(Vector3D.UnitY, 1.0);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = Matrix33D.CreateRotation(Vector3D.UnitZ, 4.0);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = Matrix33D.Identity;
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = Matrix33D.CreateRotation(-Vector3D.UnitX, 1.3);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = Matrix33D.CreateRotation(-Vector3D.UnitY, -1.4);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = Matrix33D.CreateRotation(-Vector3D.UnitZ, -0.1);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = new Matrix33D(0, 0, 1,
0, -1, 0,
1, 0, 0);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
m = new Matrix33D(-1, 0, 0,
0, 1, 0,
0, 0, -1);
q = QuaternionD.CreateRotation(m);
Assert.IsTrue(Vector3D.AreNumericallyEqual(m * v, q.Rotate(v)));
}
public void Division()
{
double angle1 = 0.4;
Vector3D axis1 = new Vector3D(1.0, 2.0, 3.0);
QuaternionD q1 = QuaternionD.CreateRotation(axis1, angle1);
Matrix33D m1 = Matrix33D.CreateRotation(axis1, angle1);
double angle2 = -1.6;
Vector3D axis2 = new Vector3D(1.0, -2.0, -3.5);
QuaternionD q2 = QuaternionD.CreateRotation(axis2, angle2);
Matrix33D m2 = Matrix33D.CreateRotation(axis2, angle2);
Vector3D v = new Vector3D(0.3, -2.4, 5.6);
Vector3D result1 = QuaternionD.Divide(q2, q1).Rotate(v);
Vector3D result2 = m2 * m1.Inverse * v;
Assert.IsTrue(Vector3D.AreNumericallyEqual(result1, result2));
}
public void Test1()
{
PoseD p = PoseD.Identity;
Assert.AreEqual(Matrix44D.Identity, p.ToMatrix44D());
Assert.AreEqual(Matrix33D.Identity, p.Orientation);
Assert.AreEqual(Vector3D.Zero, p.Position);
p.Position = new Vector3D(1, 2, 3);
p.Orientation = Matrix33D.CreateRotation(new Vector3D(3, -4, 9), 0.49);
Assert.IsTrue(Vector4D.AreNumericallyEqual(new Vector4D(p.ToWorldDirection(Vector3D.UnitX), 0), p * new Vector4D(1, 0, 0, 0)));
Assert.IsTrue(Vector4D.AreNumericallyEqual(new Vector4D(p.ToWorldDirection(Vector3D.UnitY), 0), p * new Vector4D(0, 1, 0, 0)));
Assert.IsTrue(Vector4D.AreNumericallyEqual(new Vector4D(p.ToWorldDirection(Vector3D.UnitZ), 0), p * new Vector4D(0, 0, 1, 0)));
Assert.IsTrue(Vector4D.AreNumericallyEqual(new Vector4D(p.ToWorldPosition(Vector3D.UnitX), 1), p * new Vector4D(1, 0, 0, 1)));
Assert.IsTrue(Vector4D.AreNumericallyEqual(new Vector4D(p.ToWorldPosition(Vector3D.UnitY), 1), p * new Vector4D(0, 1, 0, 1)));
Assert.IsTrue(Vector4D.AreNumericallyEqual(new Vector4D(p.ToWorldPosition(Vector3D.UnitZ), 1), p * new Vector4D(0, 0, 1, 1)));
Assert.IsTrue(Vector4D.AreNumericallyEqual(new Vector4D(p.ToLocalDirection(Vector3D.UnitX), 0), p.Inverse * new Vector4D(1, 0, 0, 0)));
Assert.IsTrue(Vector4D.AreNumericallyEqual(new Vector4D(p.ToLocalDirection(Vector3D.UnitY), 0), p.Inverse * new Vector4D(0, 1, 0, 0)));
Assert.IsTrue(Vector4D.AreNumericallyEqual(new Vector4D(p.ToLocalDirection(Vector3D.UnitZ), 0), p.Inverse * new Vector4D(0, 0, 1, 0)));
Assert.IsTrue(Vector4D.AreNumericallyEqual(new Vector4D(p.ToLocalPosition(Vector3D.UnitX), 1), p.Inverse * new Vector4D(1, 0, 0, 1)));
Assert.IsTrue(Vector4D.AreNumericallyEqual(new Vector4D(p.ToLocalPosition(Vector3D.UnitY), 1), p.Inverse * new Vector4D(0, 1, 0, 1)));
Assert.IsTrue(Vector4D.AreNumericallyEqual(new Vector4D(p.ToLocalPosition(Vector3D.UnitZ), 1), p.Inverse * new Vector4D(0, 0, 1, 1)));
PoseD p2 = PoseD.FromMatrix(new Matrix44D(p.Orientation, Vector3D.Zero));
Assert.IsTrue(Matrix33D.AreNumericallyEqual(p.Orientation, p2.Orientation));
Assert.IsTrue(Vector3D.AreNumericallyEqual(p2.Position, Vector3D.Zero));
Matrix44D m = p2;
m.SetColumn(3, new Vector4D(p.Position, 1));
p2 = PoseD.FromMatrix(m);
Assert.IsTrue(Matrix33D.AreNumericallyEqual(p.Orientation, p2.Orientation));
Assert.AreEqual(p.Position, p2.Position);
//Assert.IsTrue(Vector3D.AreNumericallyEqual(p.Position, p2.Position));
// Test other constructors.
Assert.AreEqual(Vector3D.Zero, new PoseD(QuaternionD.CreateRotationX(0.3)).Position);
Assert.AreEqual(Matrix33D.CreateRotationX(0.3), new PoseD(Matrix33D.CreateRotationX(0.3)).Orientation);
Assert.AreEqual(new Vector3D(1, 2, 3), new PoseD(new Vector3D(1, 2, 3)).Position);
Assert.AreEqual(Matrix33D.Identity, new PoseD(new Vector3D(1, 2, 3)).Orientation);
}
public void Axis()
{
Vector3D axis = new Vector3D(1.0, 2.0, 3.0);
double angle = 0.2;
QuaternionD q = QuaternionD.CreateRotation(axis, angle);
Assert.IsTrue(Numeric.AreEqual(angle, q.Angle));
Assert.IsTrue(Vector3D.AreNumericallyEqual(axis.Normalized, q.Axis));
axis = new Vector3D(1.0, 1.0, 1.0);
q.Axis = axis;
Assert.IsTrue(Numeric.AreEqual(angle, q.Angle));
Assert.IsTrue(Vector3D.AreNumericallyEqual(axis.Normalized, q.Axis));
Assert.IsTrue(Vector3D.AreNumericallyEqual(Matrix33D.CreateRotation(axis, angle) * Vector3D.One, q.Rotate(Vector3D.One)));
Assert.AreEqual(Vector3D.Zero, QuaternionD.Identity.Axis);
q.Axis = Vector3D.Zero;
Assert.AreEqual(QuaternionD.Identity, q);
}
public void CreateRotation()
{
QuaternionD q;
// From matrix vs. from angle/axis
Matrix33D m = Matrix33D.CreateRotation(Vector3D.UnitX, (double)Math.PI / 4);
q = QuaternionD.CreateRotation(m);
QuaternionD q2 = QuaternionD.CreateRotation(Vector3D.UnitX, (double)Math.PI / 4);
Assert.IsTrue(QuaternionD.AreNumericallyEqual(q2, q));
m = Matrix33D.CreateRotation(Vector3D.UnitY, (double)Math.PI / 4);
q = QuaternionD.CreateRotation(m);
q2 = QuaternionD.CreateRotation(Vector3D.UnitY, (double)Math.PI / 4);
Assert.IsTrue(QuaternionD.AreNumericallyEqual(q2, q));
m = Matrix33D.CreateRotation(Vector3D.UnitZ, (double)Math.PI / 4);
q = QuaternionD.CreateRotation(m);
q2 = QuaternionD.CreateRotation(Vector3D.UnitZ, (double)Math.PI / 4);
Assert.IsTrue(QuaternionD.AreNumericallyEqual(q2, q));
// From vector-vector
Vector3D start, end;
start = Vector3D.UnitX;
end = Vector3D.UnitY;
q = QuaternionD.CreateRotation(start, end);
Assert.IsTrue(Vector3D.AreNumericallyEqual(end, q.ToRotationMatrix33() * start));
start = Vector3D.UnitY;
end = Vector3D.UnitZ;
q = QuaternionD.CreateRotation(start, end);
Assert.IsTrue(Vector3D.AreNumericallyEqual(end, q.ToRotationMatrix33() * start));
start = Vector3D.UnitZ;
end = Vector3D.UnitX;
q = QuaternionD.CreateRotation(start, end);
Assert.IsTrue(Vector3D.AreNumericallyEqual(end, q.ToRotationMatrix33() * start));
start = new Vector3D(1, 1, 1);
end = new Vector3D(1, 1, 1);
q = QuaternionD.CreateRotation(start, end);
Assert.IsTrue(Vector3D.AreNumericallyEqual(end, q.ToRotationMatrix33() * start));
start = new Vector3D(1.0, 1.0, 1.0);
end = new Vector3D(-1.0, -1.0, -1.0);
q = QuaternionD.CreateRotation(start, end);
Assert.IsTrue(Vector3D.AreNumericallyEqual(end, q.ToRotationMatrix33() * start));
start = new Vector3D(-1.0, 2.0, 1.0);
end = new Vector3D(-2.0, -1.0, -1.0);
q = QuaternionD.CreateRotation(start, end);
Assert.IsTrue(Vector3D.AreNumericallyEqual(end, q.ToRotationMatrix33() * start));
double degree45 = MathHelper.ToRadians(45);
q = QuaternionD.CreateRotation(degree45, Vector3D.UnitZ, degree45, Vector3D.UnitY, degree45, Vector3D.UnitX, false);
QuaternionD expected = QuaternionD.CreateRotation(Vector3D.UnitZ, degree45) * QuaternionD.CreateRotation(Vector3D.UnitY, degree45)
* QuaternionD.CreateRotation(Vector3D.UnitX, degree45);
Assert.IsTrue(QuaternionD.AreNumericallyEqual(expected, q));
q = QuaternionD.CreateRotation(degree45, Vector3D.UnitZ, degree45, Vector3D.UnitY, degree45, Vector3D.UnitX, true);
expected = QuaternionD.CreateRotation(Vector3D.UnitX, degree45) * QuaternionD.CreateRotation(Vector3D.UnitY, degree45)
* QuaternionD.CreateRotation(Vector3D.UnitZ, degree45);
Assert.IsTrue(QuaternionD.AreNumericallyEqual(expected, q));
}
public void CreateRotationException()
{
Matrix33D.CreateRotation(Vector3D.Zero, 1);
}