public void DotProduct()
{
// 0°
Assert.AreEqual(1.0, Vector4D.Dot(Vector4D.UnitX, Vector4D.UnitX));
Assert.AreEqual(1.0, Vector4D.Dot(Vector4D.UnitY, Vector4D.UnitY));
Assert.AreEqual(1.0, Vector4D.Dot(Vector4D.UnitZ, Vector4D.UnitZ));
Assert.AreEqual(1.0, Vector4D.Dot(Vector4D.UnitW, Vector4D.UnitW));
// 180°
Assert.AreEqual(-1.0, Vector4D.Dot(Vector4D.UnitX, -Vector4D.UnitX));
Assert.AreEqual(-1.0, Vector4D.Dot(Vector4D.UnitY, -Vector4D.UnitY));
Assert.AreEqual(-1.0, Vector4D.Dot(Vector4D.UnitZ, -Vector4D.UnitZ));
Assert.AreEqual(-1.0, Vector4D.Dot(Vector4D.UnitW, -Vector4D.UnitW));
// 90°
Assert.AreEqual(0.0, Vector4D.Dot(Vector4D.UnitX, Vector4D.UnitY));
Assert.AreEqual(0.0, Vector4D.Dot(Vector4D.UnitY, Vector4D.UnitZ));
Assert.AreEqual(0.0, Vector4D.Dot(Vector4D.UnitZ, Vector4D.UnitW));
Assert.AreEqual(0.0, Vector4D.Dot(Vector4D.UnitW, Vector4D.UnitX));
// 45°
double angle = Math.Acos(Vector4D.Dot(new Vector4D(1, 1, 0, 0).Normalized, Vector4D.UnitX));
Assert.IsTrue(Numeric.AreEqual(MathHelper.ToRadians(45.0), angle));
angle = Math.Acos(Vector4D.Dot(new Vector4D(0, 1, 1, 0).Normalized, Vector4D.UnitY));
Assert.IsTrue(Numeric.AreEqual(MathHelper.ToRadians(45.0), angle));
angle = Math.Acos(Vector4D.Dot(new Vector4D(1, 0, 1, 0).Normalized, Vector4D.UnitZ));
Assert.IsTrue(Numeric.AreEqual(MathHelper.ToRadians(45.0), angle));
angle = Math.Acos(Vector4D.Dot(new Vector4D(1, 0, 0, 1).Normalized, Vector4D.UnitW));
Assert.IsTrue(Numeric.AreEqual(MathHelper.ToRadians(45.0), angle));
}
public void Dot()
{
Scalar expected = -(Value * Value * 4);
UnitHelper.RefOperationTester <Vector4D, Vector4D, Scalar>(op1, op2, expected, Vector4D.Dot, "Dot");
Assert.AreEqual(expected, op1 * op2, "Operator");
Assert.AreEqual(expected, Vector4D.Dot(op1, op2), "Method");
}
/// <summary>
/// Determines whether the specified matrix is a valid pose matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns>
/// <see langword="true"/> if the specified matrix is a valid pose matrix; otherwise,
/// <see langword="false"/>.
/// </returns>
/// <remarks>
/// This method makes a simple, low-performance test.
/// </remarks>
public static bool IsValid(Matrix44D matrix)
{
Vector4D v1 = matrix * Vector4D.UnitX;
Vector4D v2 = matrix * Vector4D.UnitY;
Vector4D v3 = matrix * Vector4D.UnitZ;
return(Numeric.AreEqual(v1.LengthSquared, 1) &&
Numeric.AreEqual(v2.LengthSquared, 1) &&
Numeric.AreEqual(v3.LengthSquared, 1) &&
Numeric.IsZero(Vector4D.Dot(v1, v2)) &&
Numeric.IsZero(Vector4D.Dot(v2, v3)) &&
Numeric.IsZero(Vector4D.Dot(v1, v3)) &&
Numeric.AreEqual(1.0, matrix.Determinant) &&
Numeric.IsZero(matrix.M30) &&
Numeric.IsZero(matrix.M31) &&
Numeric.IsZero(matrix.M32) &&
Numeric.AreEqual(matrix.M33, 1));
}
private Matrix3D QuatToMatrix3d(Vector4D q)
{
double n = q.Dot(q);
double s = (n > 0.0) ? (2.0 / n) : 0.0f;
double xs, ys, zs;
double wx, wy, wz;
double xx, xy, xz;
double yy, yz, zz;
xs = q.x * s; ys = q.y * s; zs = q.z * s;
wx = q.w * xs; wy = q.w * ys; wz = q.w * zs;
xx = q.x * xs; xy = q.x * ys; xz = q.x * zs;
yy = q.y * ys; yz = q.y * zs; zz = q.z * zs;
Matrix3D m = new Matrix3D();
m[0, 0] = 1.0 - (yy + zz); m[1, 0] = xy - wz; m[2, 0] = xz + wy;
m[0, 1] = xy + wz; m[1, 1] = 1.0 - (xx + zz); m[2, 1] = yz - wx;
m[0, 2] = xz - wy; m[1, 2] = yz + wx; m[2, 2] = 1.0 - (xx + yy);
return(m);
}
private Matrix4D QuatToMatrix4d(Vector4D q)
{
double n = q.Dot(q);
double s = (n > 0.0) ? (2.0 / n) : 0.0f;
double xs, ys, zs;
double wx, wy, wz;
double xx, xy, xz;
double yy, yz, zz;
xs = q.x * s; ys = q.y * s; zs = q.z * s;
wx = q.w * xs; wy = q.w * ys; wz = q.w * zs;
xx = q.x * xs; xy = q.x * ys; xz = q.x * zs;
yy = q.y * ys; yz = q.y * zs; zz = q.z * zs;
Matrix4D m = new Matrix4D();
m[0, 0] = 1.0 - (yy + zz); m[1, 0] = xy - wz; m[2, 0] = xz + wy;
m[0, 1] = xy + wz; m[1, 1] = 1.0 - (xx + zz); m[2, 1] = yz - wx;
m[0, 2] = xz - wy; m[1, 2] = yz + wx; m[2, 2] = 1.0 - (xx + yy);
m[3, 3] = 1.0;
return m;
}
public void Dot()
{
Vector4D a = new Vector4D(1.0, 2.0, 3.0, 4.0);
Vector4D b = new Vector4D(4.0, 5.0, 6.0, 7.0);
double dot = a.Dot(b);
Assert.AreEqual(1.0 * 4.0 + 2.0 * 5.0 + 3.0 * 6.0 + 4.0 * 7.0, dot, 1e-14);
}