static void Main(string[] args)
{
//
ScalarFunction x = "x";
ScalarFunction y = "y";
ScalarFunction a = "a";
ScalarFunction b = "b";
ScalarFunction c = "c";
ScalarFunction d = "d";
ScalarFunction i = "i";
ScalarFunction j = "j";
MatrixFunction m = NewMatrix(new Matrix <ScalarFunction>(
new[] {
new ScalarFunction[] { a, b },
new ScalarFunction[] { c, d }
}));
VectorFunction v = NewColumnVector(new ScalarFunction[] { x, y });
VectorFunction r = NewColumnVector(new ScalarFunction[] { i, j });
BinaryFunction k = MatrixMethods.RotationMethod(m, v, r);
k = k.Calculate();
//Console.WriteLine(((a * i + c * j) / (a * a + c * c)).Calculate());
//var sqrt = op_Exponentiation(op_Exponentiation(a, 2) + op_Exponentiation(c, 2), 0.5);
//var d_y = ((a * j - c * i) / (a * d - c * b)) * (a * b + c * d);
//var gg = ((x * (a * a + c * c)) + y) / sqrt == (a * i + c * j) / sqrt;
//var gg2 = NewScalarFind(x, gg).Calculate();
//var gg3 = gg2.Calculate(NewScalarFind(y, y == d_y));
Console.ReadKey();
}
#pragma warning disable CA1822 // Mark members as static
#pragma warning disable IDE0051 // Remove unused private members
private void RunGauElim(Matrix mat1, Matrix mat2)
#pragma warning restore IDE0051 // Remove unused private members
#pragma warning restore CA1822 // Mark members as static
{
for (int i = 0; i < interval; i++)
{
_ = MatrixMethods.GaussianElimination(mat1, mat2);
}
}
public void RotateMethod()
{
MatrixFunction m = NewMatrix(new Matrix <ScalarFunction>(
new[] {
new ScalarFunction[] { "a", "b" },
new ScalarFunction[] { "c", "d" }
}));
VectorFunction v = NewColumnVector(new ScalarFunction[] { "x", "y" });
VectorFunction r = NewColumnVector(new ScalarFunction[] { "i", "j" });
BinaryFunction b = MatrixMethods.RotationMethod(m, v, r);
}
void ButtonMethodsOnClick(object obj, EventArgs ea)
{
MatrixMethods dlg = new MatrixMethods();
dlg.Matrix = Matrix;
if (dlg.ShowDialog() == DialogResult.OK)
{
Matrix = dlg.Matrix;
btnUpdate.PerformClick();
}
}
public void GaussianEliminationTest()
{
var mat1 = new Matrix(new[, ] {
{ 1936.0 / 45, 692.0 / 15 },
{ 692.0 / 15, 324.0 / 5 }
});
var polyu = KtPolynomial.Create(1);
var poly1 = KtPolynomial.Create(0, 572.0 / 45, 0, -11.0 / 90);
var poly2 = KtPolynomial.Create(-32.0 / 3, 932.0 / 45, -2, 2.0 / 45);
var expression1 = new Expression(
((poly1, polyu), Limit.Create(0, 4)),
((poly2, polyu), Limit.Create(4, 9)),
((poly2, polyu), Limit.Create(9, 15)));
var poly3 = KtPolynomial.Create(0, 63.0 / 5, 0, -1 / 15.0);
var poly4 = KtPolynomial.Create(-243 / 2.0, 531.0 / 10, -9.0 / 2, 1.0 / 10);
var expression2 = new Expression(
((poly3, polyu), Limit.Create(0, 4)),
((poly3, polyu), Limit.Create(4, 9)),
((poly4, polyu), Limit.Create(9, 15)));
var mat2 = new Matrix(new[, ] {
{ expression1 }, { expression2 }
});
var actual = MatrixMethods.GaussianElimination(mat1, mat2);
//GetEllapsedTime(mat1, mat2);
var expPoly1a = KtPolynomial.Create(0, 2727.0 / 7420, 0, -109.0 / 14840);
var expPoly1b = KtPolynomial.Create(-1944.0 / 1855, 8559.0 / 7420, -729.0 / 3710, 67.0 / 7420);
var expPoly1c = KtPolynomial.Create(3159.0 / 424, -24921.0 / 14840, 351.0 / 2968, -39.0 / 14840);
var expPoly2a = KtPolynomial.Create(0, -374.0 / 5565, 0, 187.0 / 44520);
var expPoly2b = KtPolynomial.Create(1384.0 / 1855, -3488.0 / 5565, 519.0 / 3710, -83.0 / 11130);
var expPoly2c = KtPolynomial.Create(-761.0 / 106, 22427.0 / 11130, -57.0 / 371, 19.0 / 5565);
var expected1 = new Expression(
((expPoly1a, polyu), Limit.Create(0, 4)),
((expPoly1b, polyu), Limit.Create(4, 9)),
((expPoly1c, polyu), Limit.Create(9, 15)));
var expected2 = new Expression(
((expPoly2a, polyu), Limit.Create(0, 4)),
((expPoly2b, polyu), Limit.Create(4, 9)),
((expPoly2c, polyu), Limit.Create(9, 15)));
var expected = new Matrix(new[, ] {
{ expected1 }, { expected2 }
});
Assert.AreEqual(expected1, actual[0, 0]);
Assert.AreEqual(expected2, actual[1, 0]);
Assert.AreEqual(expected, actual);
}
public void MatrixNotSquareExceptionTest()
{
var d = new double[, ]
{
{ 0.0, 1.0, 1 },
{ 0, 1, 1 }
};
var e = new double[, ]
{
{ 0.0, 1.0, 1 },
{ 0, 1, 1 }
};
var ex = Assert.ThrowsException <MatrixNotSquareExeption>(() =>
{
var x = MatrixMethods.GaussianElimination(new Matrix(d), new Matrix(e));
}
);
Console.WriteLine(ex.Message);
}
private void Scene()
{
Graphics graphics = Graphics.FromImage(bitmap);
SolidBrush brush = new SolidBrush(Color.Black);
graphics.FillRectangle(brush, 0, 0, bitmap.Width, bitmap.Height);
//Tworzenie macierzy rzutowania na 2d
float nearDistance = 0.1f;
float farDistance = 1000.0f;
float angle = 90.0f; //kąt widzenia
float aspectRatio = (float)bitmap.Height / (float)bitmap.Width; // wspołczynnik proporcji wyświetlanego ekranu (bitmapy)
matProjection = MatrixMethods.Projection(angle, aspectRatio, nearDistance, farDistance);
//Tworzenie macierzy rotacji wkierunkach Z, X
matRotationZ = MatrixMethods.RotationZ(angleZ);
matRotationX = MatrixMethods.RotationX(angleX);
List <Triangle> trianglesToRaster = new List <Triangle>();
matTranslation = MatrixMethods.Translation(0.0f, 0.0f, zPosition);
//nowa pozycja po rotacji
matWorld = MatrixMethods.MatrixIdentity();
matWorld = MatrixMethods.MultiplyMatrix(matRotationZ, matRotationX);
matWorld = MatrixMethods.MultiplyMatrix(matWorld, matTranslation);
//Vector kierunku poruszania się kamery.
VectorMethods vLookDiraction = new VectorMethods();
VectorMethods vUp = new VectorMethods {
x = 0, y = 1, z = 0
};
VectorMethods vTarget = new VectorMethods {
x = 0, y = 0, z = 5
};
MatrixMethods matCameraRot = MatrixMethods.RotationY(0);
vLookDiraction = MatrixMethods.Multiply(matCameraRot, vTarget);
vTarget = VectorMethods.AddVectors(vCamera, vLookDiraction);
MatrixMethods matCamera = MatrixMethods.CalculatePoint(vCamera, vTarget, vUp);
//Tworzenie macierzy widoku kamery
MatrixMethods matView = MatrixMethods.InverseMatrix(matCamera);
foreach (var triangle in scene.triangles)
{
Triangle projectedTriangle, transformedTriangle, viewedTriangle;
projectedTriangle = new Triangle(3);
transformedTriangle = new Triangle(3);
viewedTriangle = new Triangle(3);
//Tworzenie vektorów transormacji
for (int i = 0; i < 3; i++)
{
transformedTriangle.points[i] = MatrixMethods.Multiply(matWorld, triangle.points[i]);
}
//Wygląd 'trojkatow' od frontu, z widoku kamery
VectorMethods normal, edge1, edge2;
edge1 = VectorMethods.SubVectors(transformedTriangle.points[1], transformedTriangle.points[0]);
edge2 = VectorMethods.SubVectors(transformedTriangle.points[2], transformedTriangle.points[0]);
normal = VectorMethods.CrossProduct(edge1, edge2);
normal = VectorMethods.VectorNormalise(normal);
// stworzenie wektora z promieniem kamery
VectorMethods cameraRay = VectorMethods.SubVectors(transformedTriangle.points[0], vCamera);
if (VectorMethods.ScalarProduct(normal, cameraRay) < 0.0f)
{
//Kierunek światła i cienowanie
VectorMethods lightDirection = new VectorMethods
{
x = 0.0f,
y = 1.0f,
z = -1.0f
};
lightDirection = VectorMethods.VectorNormalise(lightDirection);
//wspołczynnik cieniowania
float dp = (float)Math.Max(0.1f, VectorMethods.ScalarProduct(lightDirection, normal));
Color c = draw.ChangeColor(Color.Black, dp);
//zmiana wektora transormacji korzystając z widoku kamery
viewedTriangle.points[0] = MatrixMethods.Multiply(matView, transformedTriangle.points[0]);
viewedTriangle.points[1] = MatrixMethods.Multiply(matView, transformedTriangle.points[1]);
viewedTriangle.points[2] = MatrixMethods.Multiply(matView, transformedTriangle.points[2]);
//rzutowanie wektorow(trojkątów) na 2d
for (int i = 0; i < 3; i++)
{
projectedTriangle.points[i] = MatrixMethods.Multiply(matProjection, viewedTriangle.points[i]);
}
for (int i = 0; i < 3; i++)
{
projectedTriangle.points[i] = VectorMethods.DivideByNumber(projectedTriangle.points[i], projectedTriangle.points[i].w);
}
projectedTriangle.color = c;
//przeskalowanie figur na ekranie(współrzedne x,y)
VectorMethods vectorOffSetView = new VectorMethods {
x = 1, y = 1, z = 0
};
for (int i = 0; i < 3; i++)
{
projectedTriangle.points[i] = VectorMethods.AddVectors(projectedTriangle.points[i], vectorOffSetView);
}
//skalowanie do wielkości wyświetlanej bitmapy
projectedTriangle.points[0].x *= 0.5f * (float)bitmap.Width;
projectedTriangle.points[0].y *= 0.5f * (float)bitmap.Height;
projectedTriangle.points[1].x *= 0.5f * (float)bitmap.Width;
projectedTriangle.points[1].y *= 0.5f * (float)bitmap.Height;
projectedTriangle.points[2].x *= 0.5f * (float)bitmap.Width;
projectedTriangle.points[2].y *= 0.5f * (float)bitmap.Height;
//Tworzeni listy do sortowania trojkątów
projectedTriangle.zValue = (projectedTriangle.points[0].z + projectedTriangle.points[1].z + projectedTriangle.points[2].z) / 3.0f;
trianglesToRaster.Add(projectedTriangle);
}
}
//sortowanie trojkatów względem wspołrzednej z
trianglesToRaster.Sort((a, b) => b.zValue.CompareTo(a.zValue));
//rysowanie trojkatow
foreach (var triangle in trianglesToRaster)
{
draw.DrawTriangle(triangle, bitmap, triangle.color);
pictureBox1.Image = bitmap;
}
}
#pragma warning disable IDE0051 // Remove unused private members
private static void GetEllapsedTime(Matrix mat1, Matrix mat2)
#pragma warning restore IDE0051 // Remove unused private members
{
Console.WriteLine(DiagnosticsExtensions.ElapsedTime(() => { for (int i = 0; i < interval; i++)
{
var actual2 = MatrixMethods.GaussianElimination(mat1, mat2);
}
}));
Console.WriteLine(DiagnosticsExtensions.ElapsedTime(() => { for (int i = 0; i < interval; i++)
{
var actual2 = MatrixMethods.GaussianElimination2(mat1, mat2);
}
}));
Console.WriteLine(DiagnosticsExtensions.ElapsedTime(() => { for (int i = 0; i < interval; i++)
{
var actual2 = MatrixMethods.GaussianElimination2(mat1, mat2);
}
}));
Console.WriteLine(DiagnosticsExtensions.ElapsedTime(() => { for (int i = 0; i < interval; i++)
{
var actual1 = MatrixMethods.GaussianElimination(mat1, mat2);
}
}));
Console.WriteLine(DiagnosticsExtensions.ElapsedTime(() => { for (int i = 0; i < interval; i++)
{
var actual1 = MatrixMethods.GaussianElimination(mat1, mat2);
}
}));
Console.WriteLine(DiagnosticsExtensions.ElapsedTime(() => { for (int i = 0; i < interval; i++)
{
var actual2 = MatrixMethods.GaussianElimination2(mat1, mat2);
}
}));
Console.WriteLine(DiagnosticsExtensions.ElapsedTime(() => { for (int i = 0; i < interval; i++)
{
var actual2 = MatrixMethods.GaussianElimination2(mat1, mat2);
}
}));
Console.WriteLine(DiagnosticsExtensions.ElapsedTime(() => { for (int i = 0; i < interval; i++)
{
var actual1 = MatrixMethods.GaussianElimination(mat1, mat2);
}
}));
Console.WriteLine(DiagnosticsExtensions.ElapsedTime(() => { for (int i = 0; i < interval; i++)
{
var actual1 = MatrixMethods.GaussianElimination(mat1, mat2);
}
}));
Console.WriteLine(DiagnosticsExtensions.ElapsedTime(() => { for (int i = 0; i < interval; i++)
{
var actual2 = MatrixMethods.GaussianElimination2(mat1, mat2);
}
}));
Console.WriteLine(DiagnosticsExtensions.ElapsedTime(() => { for (int i = 0; i < interval; i++)
{
var actual2 = MatrixMethods.GaussianElimination2(mat1, mat2);
}
}));
Console.WriteLine(DiagnosticsExtensions.ElapsedTime(() => { for (int i = 0; i < interval; i++)
{
var actual1 = MatrixMethods.GaussianElimination(mat1, mat2);
}
}));
}
