/// <summary>
/// Converts the bases for the specified vector from the basis definition vectors.
/// </summary>
/// <param name="b1">The first basis definition vector.</param>
/// <param name="b2">The second basis definition vector.</param>
/// <param name="w">The vector to convert bases on.</param>
/// <returns>The new basis of the vector.</returns>
public static Vector2 ConvertBasis( Vector2 b1, Vector2 b2, Vector2 w )
{
//
// [w] = B^(-1) * w = [ B.M11 * w.X + B.M12 * w.Y ]
// [ B.M21 * w.X + B.M22 * w.Y ]
//
Vector2 basis = Vector2.Empty;
Matrix B = new Matrix();
// Build inverse basis matrix
B.M11 = b1.X;
B.M21 = b1.Y;
B.M12 = b2.X;
B.M22 = b2.Y;
B.M33 = 1;
B.M44 = 1;
B.Invert();
// Determine basis
basis.X = B.M11 * w.X + B.M12 * w.Y;
basis.Y = B.M21 * w.X + B.M22 * w.Y;
return basis;
}
public void TestInverse4()
{
// test identity inverse
var m = Matrix.GetIdentity(4);
Assert.IsTrue(Matrix.AreEqual(m.Invert(), new Matrix(new float[,] {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}})));
// test a known inverse
m = new Matrix(new[,]
{
{0.100f, 0.200f, 0.300f, 1.300f},
{-0.400f, 0.500f, 0.600f, 1.400f},
{0.700f, 0.800f, 0.900f, 1.500f},
{1.000f, 1.100f, 1.200f, -1.600f}
});
var r = new Matrix(new[,]
{
{0.62500f, -1.25000f, 0.62500f, 0.00000f},
{-18.12500f, 2.50000f, 9.37500f, -3.75000f},
{15.8854167f, -1.25000f, -8.4895833f, 3.854167f},
{-0.15625f, 0.00000f, 0.46875f, -0.31250f}
});
Assert.IsTrue(Matrix.AreEqual(m.Invert(), r, _tolerance));
// test inverse multiplied against original is the identity
m.SetRow(0, -1.1F, 2.6F, -7.1F, 2.2F);
m.SetRow(1, 4.6F, -3.7F, 9.1F, 6.9F);
m.SetRow(2, 4.1F, -3.1F, 7.7F, 7.1F);
m.SetRow(3, -9.9F, 0.2F, 4.3F, 5.5F);
Assert.IsTrue(Matrix.AreEqual(m*m.Invert(), Matrix.GetIdentity(4), _tolerance));
Assert.IsTrue(Matrix.AreEqual(m.Invert()*m, Matrix.GetIdentity(4), _tolerance));
// test non-invertible
m.SetRow(0, 1, 0, 0, 0);
m.SetRow(1, 0, 1, 0, 0);
m.SetRow(2, 0, 0, 1, 0);
m.SetRow(3, 0, 0, 5, 0);
try
{
m.Invert();
Assert.Fail("Expected an exception");
}
catch (ArgumentException) {}
}
public void TestInverse3()
{
// test identity inverse
var m = Matrix.GetIdentity(3);
Assert.IsTrue(Matrix.AreEqual(m.Invert(), new Matrix(new float[,] {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}})));
// test a known inverse
m = new Matrix(new[,]
{
{0.100f, 0.200f, 0.300f},
{-0.400f, 0.500f, 0.600f},
{0.700f, 0.800f, 0.900f}
});
var r = new Matrix(new[,]
{
{0.62500f, -1.25000f, 0.62500f},
{-16.25000f, 2.50000f, 3.75000f},
{13.95833f, -1.25000f, -2.70833f}
});
Assert.IsTrue(Matrix.AreEqual(m.Invert(), r, _tolerance));
// test inverse multiplied against original is the identity
m.SetRow(0, -1.1F, 2.6F, -7.1F);
m.SetRow(1, 4.6F, -3.7F, 9.1F);
m.SetRow(2, 4.1F, -3.1F, 7.7F);
Assert.IsTrue(Matrix.AreEqual(m*m.Invert(), Matrix.GetIdentity(3), _tolerance));
Assert.IsTrue(Matrix.AreEqual(m.Invert()*m, Matrix.GetIdentity(3), _tolerance));
// test non-invertible
m.SetRow(0, 1, 0, 0);
m.SetRow(1, 0, 1, 0);
m.SetRow(2, 0, 5, 0);
try
{
m.Invert();
Assert.Fail("Expected an exception");
}
catch (ArgumentException) {}
}
public void TestInverse2()
{
// test identity inverse
var m = Matrix.GetIdentity(2);
Assert.IsTrue(Matrix.AreEqual(m.Invert(), new Matrix(new float[,] {{1, 0}, {0, 1}})));
// test a known inverse
m = new Matrix(new[,]
{
{0.100f, 0.200f},
{-0.400f, 0.500f}
});
var r = new Matrix(new[,]
{
{3.84615f, -1.53846f},
{3.07692f, 0.76923f}
});
Assert.IsTrue(Matrix.AreEqual(m.Invert(), r, _tolerance));
// test inverse multiplied against original is the identity
m.SetRow(0, -1.1F, 2.6F);
m.SetRow(1, 4.6F, -3.7F);
Assert.IsTrue(Matrix.AreEqual(m*m.Invert(), Matrix.GetIdentity(2), _tolerance));
Assert.IsTrue(Matrix.AreEqual(m.Invert()*m, Matrix.GetIdentity(2), _tolerance));
// test non-invertible
m.SetRow(0, 1, 0);
m.SetRow(1, 5, 0);
try
{
m.Invert();
Assert.Fail("Expected an exception");
}
catch (ArgumentException) {}
}
public void TestInverse1()
{
// test identity inverse
var m = Matrix.GetIdentity(1);
Assert.IsTrue(Matrix.AreEqual(m.Invert(), new Matrix(new float[,] {{1}})));
// test a known inverse
m = new Matrix(new[,]
{
{0.100f}
});
var r = new Matrix(new[,]
{
{10.00f}
});
Assert.IsTrue(Matrix.AreEqual(m.Invert(), r, _tolerance));
// test inverse multiplied against original is the identity
m.SetRow(0, -1.1F);
Assert.IsTrue(Matrix.AreEqual(m*m.Invert(), Matrix.GetIdentity(1), _tolerance));
Assert.IsTrue(Matrix.AreEqual(m.Invert()*m, Matrix.GetIdentity(1), _tolerance));
// test non-invertible
m.SetRow(0, 0);
try
{
m.Invert();
Assert.Fail("Expected an exception");
}
catch (ArgumentException) {}
}
public void TestInverse()
{
try
{
var m = new Matrix(3, 2);
m.Invert();
Assert.Fail("Expected an exception");
}
catch (ArgumentException) {}
try
{
var m = Matrix.GetIdentity(5);
m.Invert();
Assert.Fail("Expected an exception");
}
catch (NotImplementedException) {}
}
public Vector2 IntersectPlane(Plane plane, Vector2 relativeMousePos)
{
// Relative screen position.
float xRayView = relativeMousePos.X / Projection.M11;
float yRayView = relativeMousePos.Y / Projection.M22;
viewDirection.Normalize();
Vector3 ray = viewDirection
+ rightVec * xRayView
- upVec * yRayView;
Vector4 pointVec = new Vector4(position - plane.Origin, 0);
Matrix dirMat = new Matrix();
Matrix test = Matrix.Translation(1, 1, 1);
//var x = test.get_Rows(3);
dirMat.set_Rows(0, new Vector4(plane.XAxis, 0));
dirMat.set_Rows(1, new Vector4(plane.YAxis, 0));
dirMat.set_Rows(2, new Vector4(-ray, 0));
dirMat.set_Rows(3, Vector4.UnitW);
dirMat.Invert();
Vector4 res = Vector4.Transform(pointVec, dirMat);
Vector2 xy = new Vector2(Vector4.Dot(dirMat.get_Rows(0), pointVec), Vector4.Dot(dirMat.get_Rows(1), pointVec));
return new Vector2(res.X, res.Y);
}
/// <summary>
/// Pushes a matrix transformation.
/// </summary>
/// <param name="matrix">The matrix</param>
/// <returns>A disposable used to undo the transformation.</returns>
public IDisposable PushTransform(Matrix matrix)
{
_context.Transform(matrix.ToCairo());
return Disposable.Create(() =>
{
_context.Transform(matrix.Invert().ToCairo());
});
}