public void PuttingItTogether()
{
var a = new RTF.Matrix(4, 4);
a.SetRow(0, new double[] { 3, -9, 7, 3 });
a.SetRow(1, new double[] { 3, -8, 2, -9 });
a.SetRow(2, new double[] { -4, 4, 4, 1 });
a.SetRow(3, new double[] { -6, 5, -1, 1 });
var identity = RTF.Matrix.GetIdentity(4, 4);
Assert.Equal(identity, identity.Inverse());
var idInverted = a * a.Inverse();
CustomAssert.Equal(identity, idInverted, 0);
var transposeInvert = a.Transpose().Inverse();
var invertTranspose = a.Inverse().Transpose();
CustomAssert.Equal(transposeInvert, invertTranspose, 5);
var modifiedIdentity = RTF.Matrix.GetIdentity(4, 4);
modifiedIdentity[2, 2] = 6;
var tuple = new double[] { 1, 2, 3, 4 };
var tupleIdentity = identity * tuple;
var newTuple = modifiedIdentity * tuple;
Assert.Equal(tuple, tupleIdentity);
Assert.NotEqual(tuple, newTuple);
}
public void Determinant2x2()
{
var b = new RTF.Matrix(2, 2);
b.SetRow(0, new double[] { 1, 5 });
b.SetRow(1, new double[] { -3, 2 });
Assert.Equal(17, b.Determinant());
}
public void ViewTransformationMatrixPosZDir()
{
var from = RTF.PointType.Point(0, 0, 0);
var to = RTF.PointType.Point(0, 0, 1);
var up = RTF.PointType.Vector(0, 1, 0);
RTF.Matrix t = RTH.Transformations.ViewTransform(from, to, up);
var e = RTH.Transformations.Scaling(-1, 1, -1);
Assert.Equal(e, t);
}
public void InvertibleMatrix()
{
var e = new RTF.Matrix(4, 4);
e.SetRow(0, new double[] { 6, 4, 4, 4 });
e.SetRow(1, new double[] { 5, 5, 7, 6 });
e.SetRow(2, new double[] { 4, -9, 3, -7 });
e.SetRow(3, new double[] { 9, 1, 7, -6 });
Assert.True(e.IsInvertible());
}
public void NonInvertibleMatrix()
{
var e = new RTF.Matrix(4, 4);
e.SetRow(0, new double[] { -4, 2, -2, -3 });
e.SetRow(1, new double[] { 9, 6, 2, 6 });
e.SetRow(2, new double[] { 0, -5, 1, -5 });
e.SetRow(3, new double[] { 0, 0, 0, 0 });
Assert.False(e.IsInvertible());
}
public void ViewTransformationMatrixMovesWorld()
{
var from = RTF.PointType.Point(0, 0, 8);
var to = RTF.PointType.Point(0, 0, 0);
var up = RTF.PointType.Vector(0, 1, 0);
RTF.Matrix t = RTH.Transformations.ViewTransform(from, to, up);
var e = RTH.Transformations.Translation(0, 0, -8);
Assert.Equal(e, t);
}
public void TransformationMatrixForDefaultOrientation()
{
var from = RTF.PointType.Point(0, 0, 0);
var to = RTF.PointType.Point(0, 0, -1);
var up = RTF.PointType.Vector(0, 1, 0);
RTF.Matrix t = RTH.Transformations.ViewTransform(from, to, up);
var e = RTF.Matrix.GetIdentity();
Assert.Equal(e, t);
}
public void OughtTo2x2()
{
var M = new RTF.Matrix(2, 2);
M.SetColumn(0, new double[] { -3, 1 });
M.SetColumn(1, new double[] { 5, -2 });
Assert.Equal(-3, M[0, 0]);
Assert.Equal(5, M[0, 1]);
Assert.Equal(1, M[1, 0]);
Assert.Equal(-2, M[1, 1]);
}
public void OughtTo3x3()
{
var M = new RTF.Matrix(3, 3);
M.SetRow(0, new double[] { -3, 5, 0 });
M.SetRow(1, new double[] { 1, -2, 7 });
M.SetRow(2, new double[] { 0, 1, 1 });
Assert.Equal(-3, M[0, 0]);
Assert.Equal(-2, M[1, 1]);
Assert.Equal(1, M[2, 2]);
}
public void MultiplyingIdentityByMatrice()
{
var e = new RTF.Matrix(4, 4);
e.SetRow(0, new double[] { 0, 1, 2, 4 });
e.SetRow(1, new double[] { 1, 2, 4, 8 });
e.SetRow(2, new double[] { 2, 4, 8, 16 });
e.SetRow(3, new double[] { 4, 8, 16, 32 });
var M = RTF.Matrix.GetIdentity(4, 4) * e;
Assert.Equal(e, M);
}
public void Determinant3x3()
{
var e = new RTF.Matrix(3, 3);
e.SetRow(0, new double[] { 1, 2, 6 });
e.SetRow(1, new double[] { -5, 8, -4 });
e.SetRow(2, new double[] { 2, 6, 4 });
Assert.Equal(56, RTF.Matrix.Cofactor(e, 0, 0));
Assert.Equal(12, RTF.Matrix.Cofactor(e, 0, 1));
Assert.Equal(-46, RTF.Matrix.Cofactor(e, 0, 2));
Assert.Equal(-196, RTF.Matrix.Determinant(e));
}
public void GetIdentity()
{
var a = new RTF.Matrix(4, 4);
a.SetRow(0, new double[] { 1, 0, 0, 0 });
a.SetRow(1, new double[] { 0, 1, 0, 0 });
a.SetRow(2, new double[] { 0, 0, 1, 0 });
a.SetRow(3, new double[] { 0, 0, 0, 1 });
var M = RTF.Matrix.GetIdentity(4, 4);
Assert.Equal(a, M);
}
public void Cofactor3x3()
{
var e = new RTF.Matrix(3, 3);
e.SetRow(0, new double[] { 3, 5, 0 });
e.SetRow(1, new double[] { 2, -1, -7 });
e.SetRow(2, new double[] { 6, -1, 5 });
Assert.Equal(-12, RTF.Matrix.Minor(e, 0, 0));
Assert.Equal(-12, RTF.Matrix.Cofactor(e, 0, 0));
Assert.Equal(25, RTF.Matrix.Minor(e, 1, 0));
Assert.Equal(-25, RTF.Matrix.Cofactor(e, 1, 0));
}
public void Minor3x3()
{
var e = new RTF.Matrix(3, 3);
e.SetRow(0, new double[] { 3, 5, 0 });
e.SetRow(1, new double[] { 2, -1, -7 });
e.SetRow(2, new double[] { 6, -1, 5 });
var b = RTF.Matrix.Submatrix(e, 1, 0);
Assert.Equal(25, b.Determinant());
Assert.Equal(25, RTF.Matrix.Minor(e, 1, 0));
}
public void EqualityTrueSmall()
{
var M1 = new RTF.Matrix(2, 2);
M1.SetRow(0, new double[] { 0, 0 });
M1.SetRow(1, new double[] { 1, 1 });
var M2 = new RTF.Matrix(2, 2);
M2.SetRow(0, new double[] { 0, 0 });
M2.SetRow(1, new double[] { 1, 1 });
Assert.True(M1 == M2);
}
public void Determinant4x4()
{
var e = new RTF.Matrix(4, 4);
e.SetRow(0, new double[] { -2, -8, 3, 5 });
e.SetRow(1, new double[] { -3, 1, 7, 3 });
e.SetRow(2, new double[] { 1, 2, -9, 6 });
e.SetRow(3, new double[] { -6, 7, 7, -9 });
Assert.Equal(690, RTF.Matrix.Cofactor(e, 0, 0));
Assert.Equal(447, RTF.Matrix.Cofactor(e, 0, 1));
Assert.Equal(210, RTF.Matrix.Cofactor(e, 0, 2));
Assert.Equal(51, RTF.Matrix.Cofactor(e, 0, 3));
Assert.Equal(-4071, e.Determinant());
}
public void Submatrix3x3in2x2()
{
var b = new RTF.Matrix(3, 3);
b.SetRow(0, new double[] { 1, 5, 0 });
b.SetRow(1, new double[] { -3, 2, 7 });
b.SetRow(2, new double[] { 0, 6, -3 });
var e = new RTF.Matrix(2, 2);
e.SetRow(0, new double[] { -3, 2 });
e.SetRow(1, new double[] { 0, 6 });
Assert.Equal(e, RTF.Matrix.Submatrix(b, 0, 2));
}
public void ArbitraryTransformation()
{
var from = RTF.PointType.Point(1, 3, 2);
var to = RTF.PointType.Point(4, -2, 8);
var up = RTF.PointType.Vector(1, 1, 0);
RTF.Matrix t = RTH.Transformations.ViewTransform(from, to, up);
var e = new RTF.Matrix(4, 4);
e.SetRow(0, new double[] { -0.50709, 0.50709, 0.67612, -2.36643 });
e.SetRow(1, new double[] { 0.76772, 0.60609, 0.12122, -2.82843 });
e.SetRow(2, new double[] { -0.35857, 0.59761, -0.71714, 0 });
e.SetRow(3, new double[] { 0, 0, 0, 1 });
CustomAssert.Equal(e, t, 5);
}
public void MultiplyTuple()
{
var a = new RTF.Matrix(4, 4);
a.SetRow(0, new double[] { 1, 2, 3, 4 });
a.SetRow(1, new double[] { 2, 4, 4, 2 });
a.SetRow(2, new double[] { 8, 6, 4, 1 });
a.SetRow(3, new double[] { 0, 0, 0, 1 });
double[] b = { 1, 2, 3, 1 };
double[] e = { 18, 24, 33, 1 };
var M = a * b;
Assert.Equal(e, M);
}
public void ConstructAndInspectMatrice4x4()
{
var M = new RTF.Matrix(4, 4);
M.SetRow(0, new double[] { 1, 2, 3, 4 });
M.SetRow(1, new double[] { 5.5, 6.5, 7.5, 8.5 });
M.SetRow(2, new double[] { 9, 10, 11, 12 });
M.SetRow(3, new double[] { 13.5, 14.5, 15.5, 16.5 });
Assert.Equal(1, M[0, 0]);
Assert.Equal(4, M[0, 3]);
Assert.Equal(5.5, M[1, 0]);
Assert.Equal(7.5, M[1, 2]);
Assert.Equal(11, M[2, 2]);
Assert.Equal(13.5, M[3, 0]);
Assert.Equal(15.5, M[3, 2]);
}
public void Submatrix4x4in3x3()
{
var b = new RTF.Matrix(4, 4);
b.SetRow(0, new double[] { -6, 1, 1, 6 });
b.SetRow(1, new double[] { -8, 5, 8, 6, });
b.SetRow(2, new double[] { -1, 0, 8, 2 });
b.SetRow(3, new double[] { -7, 1, -1, 1 });
var e = new RTF.Matrix(3, 3);
e.SetRow(0, new double[] { -6, 1, 6 });
e.SetRow(1, new double[] { -8, 8, 6 });
e.SetRow(2, new double[] { -7, -1, 1 });
Assert.Equal(e, RTF.Matrix.Submatrix(b, 2, 1));
}
public void EqualityFalse()
{
var M1 = new RTF.Matrix(4, 4);
M1.SetRow(0, new double[] { 1, 2, 3, 4 });
M1.SetRow(1, new double[] { 5, 6, 7, 8 });
M1.SetRow(2, new double[] { 9, 8, 7, 6 });
M1.SetRow(3, new double[] { 5, 4, 3, 2 });
var M2 = new RTF.Matrix(4, 4);
M2.SetRow(0, new double[] { 2, 3, 4, 5 });
M2.SetRow(1, new double[] { 6, 7, 8, 9 });
M2.SetRow(2, new double[] { 8, 7, 6, 5 });
M2.SetRow(3, new double[] { 4, 3, 2, 1 });
Assert.False(M1 == M2);
}
public void TestTranspose()
{
var b = new RTF.Matrix(4, 4);
b.SetRow(0, new double[] { 0, 9, 3, 0 });
b.SetRow(1, new double[] { 9, 8, 0, 8 });
b.SetRow(2, new double[] { 1, 8, 5, 3 });
b.SetRow(3, new double[] { 0, 0, 5, 8 });
var e = new RTF.Matrix(4, 4);
e.SetColumn(0, new double[] { 0, 9, 3, 0 });
e.SetColumn(1, new double[] { 9, 8, 0, 8 });
e.SetColumn(2, new double[] { 1, 8, 5, 3 });
e.SetColumn(3, new double[] { 0, 0, 5, 8 });
Assert.Equal(e, b.Transpose());
}
public void EqualityTrue()
{
var M1 = new RTF.Matrix(4, 4);
M1.SetRow(0, new double[] { 1, 2, 3, 4 });
M1.SetRow(1, new double[] { 5, 6, 7, 8 });
M1.SetRow(2, new double[] { 9, 8, 7, 6 });
M1.SetRow(3, new double[] { 5, 4, 3, 2 });
var M2 = new RTF.Matrix(4, 4);
M2.SetRow(0, new double[] { 1, 2, 3, 4 });
M2.SetRow(1, new double[] { 5, 6, 7, 8 });
M2.SetRow(2, new double[] { 9, 8, 7, 6 });
M2.SetRow(3, new double[] { 5, 4, 3, 2 });
Assert.True(M1 == M2);
}
public void Inverse()
{
var e = new RTF.Matrix(4, 4);
e.SetRow(0, new double[] { -5, 2, 6, -8 });
e.SetRow(1, new double[] { 1, -5, 1, 8 });
e.SetRow(2, new double[] { 7, 7, -6, -7 });
e.SetRow(3, new double[] { 1, -3, 7, 4 });
double r1 = -160d / 532;
double r2 = 105d / 532;
var b = e.Inverse();
Assert.Equal(532, e.Determinant());
Assert.Equal(-160, RTF.Matrix.Cofactor(e, 2, 3));
Assert.Equal(r1, b[3, 2]);
Assert.Equal(105, RTF.Matrix.Cofactor(e, 3, 2));
Assert.Equal(r2, b[2, 3]);
}
public void Multiply()
{
var M1 = new RTF.Matrix(4, 4);
M1.SetRow(0, new double[] { 1, 2, 3, 4 });
M1.SetRow(1, new double[] { 2, 3, 4, 5 });
M1.SetRow(2, new double[] { 3, 4, 5, 6 });
M1.SetRow(3, new double[] { 4, 5, 6, 7 });
var M2 = new RTF.Matrix(4, 4);
M2.SetRow(0, new double[] { 0, 1, 2, 4 });
M2.SetRow(1, new double[] { 1, 2, 4, 8 });
M2.SetRow(2, new double[] { 2, 4, 8, 16 });
M2.SetRow(3, new double[] { 4, 8, 16, 32 });
var M = M1 * M2;
Assert.Equal(31, M[1, 0]);
}
public void Inverse2()
{
var a = new RTF.Matrix(4, 4);
a.SetRow(0, new double[] { 8, -5, 9, 2 });
a.SetRow(1, new double[] { 7, 5, 6, 1 });
a.SetRow(2, new double[] { -6, 0, 9, 6 });
a.SetRow(3, new double[] { -3, 0, -9, -4 });
var e = new RTF.Matrix(4, 4);
e.SetRow(0, new double[] { -0.15385, -0.15385, -0.28205, -0.53846 });
e.SetRow(1, new double[] { -0.07692, 0.12308, 0.02564, 0.03077 });
e.SetRow(2, new double[] { 0.35897, 0.35897, 0.43590, 0.92308 });
e.SetRow(3, new double[] { -0.69231, -0.69231, -0.76923, -1.92308 });
var inverse = a.Inverse();
CustomAssert.Equal(e, inverse, 5);
}
public void Inverse3()
{
var a = new RTF.Matrix(4, 4);
a.SetRow(0, new double[] { 9, 3, 0, 9 });
a.SetRow(1, new double[] { -5, -2, -6, -3 });
a.SetRow(2, new double[] { -4, 9, 6, 4 });
a.SetRow(3, new double[] { -7, 6, 6, 2 });
var e = new RTF.Matrix(4, 4);
e.SetRow(0, new double[] { -0.04074, -0.07778, 0.14444, -0.22222 });
e.SetRow(1, new double[] { -0.07778, 0.03333, 0.36667, -0.33333 });
e.SetRow(2, new double[] { -0.02901, -0.14630, -0.10926, 0.12963 });
e.SetRow(3, new double[] { 0.17778, 0.06667, -0.26667, 0.33333 });
var inverse = a.Inverse();
CustomAssert.Equal(e, inverse, 5);
}
public void MultiplyingProductByInverse()
{
var a = new RTF.Matrix(4, 4);
a.SetRow(0, new double[] { 3, -9, 7, 3 });
a.SetRow(1, new double[] { 3, -8, 2, -9 });
a.SetRow(2, new double[] { -4, 4, 4, 1 });
a.SetRow(3, new double[] { -6, 5, -1, 1 });
var b = new RTF.Matrix(4, 4);
b.SetRow(0, new double[] { 8, 2, 2, 2 });
b.SetRow(1, new double[] { 3, -1, 7, 0 });
b.SetRow(2, new double[] { 7, 0, 5, 4 });
b.SetRow(3, new double[] { 6, -2, 0, 5 });
var c = a * b;
var e = c * b.Inverse();
CustomAssert.Equal(e, a, 0);
}
