/// <inheritdoc/>
protected override Matrix44F ComputeProjection()
{
var projection = Matrix44F.CreatePerspectiveOffCenter(Left, Right, Bottom, Top, Near, Far);
if (_nearClipPlane.HasValue)
{
Vector4F clipPlane = new Vector4F(_nearClipPlane.Value.Normal, -_nearClipPlane.Value.DistanceFromOrigin);
// Calculate the clip-space corner point opposite the clipping plane as
// (-sign(clipPlane.x), -sign(clipPlane.y), 1, 1) and transform it into
// camera space by multiplying it by the inverse of the projection matrix.
Vector4F q;
q.X = (-Math.Sign(clipPlane.X) + projection.M02) / projection.M00;
q.Y = (-Math.Sign(clipPlane.Y) + projection.M12) / projection.M11;
q.Z = -1.0f;
q.W = (1.0f + projection.M22) / projection.M23;
// Calculate the scaled plane vector
Vector4F c = clipPlane * (1.0f / Vector4F.Dot(clipPlane, q));
// Replace the third row of the projection matrix
projection.M20 = c.X;
projection.M21 = c.Y;
projection.M22 = c.Z;
projection.M23 = c.W;
}
return(projection);
}
public void DotProduct()
{
// 0°
Assert.AreEqual(1.0f, Vector4F.Dot(Vector4F.UnitX, Vector4F.UnitX));
Assert.AreEqual(1.0f, Vector4F.Dot(Vector4F.UnitY, Vector4F.UnitY));
Assert.AreEqual(1.0f, Vector4F.Dot(Vector4F.UnitZ, Vector4F.UnitZ));
Assert.AreEqual(1.0f, Vector4F.Dot(Vector4F.UnitW, Vector4F.UnitW));
// 180°
Assert.AreEqual(-1.0f, Vector4F.Dot(Vector4F.UnitX, -Vector4F.UnitX));
Assert.AreEqual(-1.0f, Vector4F.Dot(Vector4F.UnitY, -Vector4F.UnitY));
Assert.AreEqual(-1.0f, Vector4F.Dot(Vector4F.UnitZ, -Vector4F.UnitZ));
Assert.AreEqual(-1.0f, Vector4F.Dot(Vector4F.UnitW, -Vector4F.UnitW));
// 90°
Assert.AreEqual(0.0f, Vector4F.Dot(Vector4F.UnitX, Vector4F.UnitY));
Assert.AreEqual(0.0f, Vector4F.Dot(Vector4F.UnitY, Vector4F.UnitZ));
Assert.AreEqual(0.0f, Vector4F.Dot(Vector4F.UnitZ, Vector4F.UnitW));
Assert.AreEqual(0.0f, Vector4F.Dot(Vector4F.UnitW, Vector4F.UnitX));
// 45°
float angle = (float)Math.Acos(Vector4F.Dot(new Vector4F(1, 1, 0, 0).Normalized, Vector4F.UnitX));
Assert.IsTrue(Numeric.AreEqual(MathHelper.ToRadians(45), angle));
angle = (float)Math.Acos(Vector4F.Dot(new Vector4F(0, 1, 1, 0).Normalized, Vector4F.UnitY));
Assert.IsTrue(Numeric.AreEqual(MathHelper.ToRadians(45), angle));
angle = (float)Math.Acos(Vector4F.Dot(new Vector4F(1, 0, 1, 0).Normalized, Vector4F.UnitZ));
Assert.IsTrue(Numeric.AreEqual(MathHelper.ToRadians(45), angle));
angle = (float)Math.Acos(Vector4F.Dot(new Vector4F(1, 0, 0, 1).Normalized, Vector4F.UnitW));
Assert.IsTrue(Numeric.AreEqual(MathHelper.ToRadians(45), angle));
}
/// <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(Matrix44F matrix)
{
Vector4F v1 = matrix * Vector4F.UnitX;
Vector4F v2 = matrix * Vector4F.UnitY;
Vector4F v3 = matrix * Vector4F.UnitZ;
return(Numeric.AreEqual(v1.LengthSquared, 1) &&
Numeric.AreEqual(v2.LengthSquared, 1) &&
Numeric.AreEqual(v3.LengthSquared, 1) &&
Numeric.IsZero(Vector4F.Dot(v1, v2)) &&
Numeric.IsZero(Vector4F.Dot(v2, v3)) &&
Numeric.IsZero(Vector4F.Dot(v1, v3)) &&
Numeric.AreEqual(1.0f, matrix.Determinant) &&
Numeric.IsZero(matrix.M30) &&
Numeric.IsZero(matrix.M31) &&
Numeric.IsZero(matrix.M32) &&
Numeric.AreEqual(matrix.M33, 1));
}
public void Dot()
{
Vector4F a = new Vector4F(1.0f, 2.0f, 3.0f, 4.0f);
Vector4F b = new Vector4F(4.0f, 5.0f, 6.0f, 7.0f);
double dot = a.Dot(b);
Assert.AreEqual(1.0f * 4.0f + 2.0f * 5.0f + 3.0f * 6.0f + 4.0f * 7.0f, dot, 1e-14);
}