private static Mesh CreateDodecahedron(double r)
{
var vertices = new MyMatrix <double>(new double[, ] {
{ 0.469, 0.469, 0.469, 1 },
{ 0.290, 0.000, 0.759, 1 },
{ -0.759, -0.290, 0.000, 1 },
{ 0.759, 0.290, 0.000, 1 },
{ -0.469, 0.469, -0.469, 1 },
{ 0.000, -0.759, -0.290, 1 },
{ -0.759, 0.290, 0.000, 1 },
{ 0.469, -0.469, 0.469, 1 },
{ -0.469, 0.469, 0.469, 1 },
{ -0.469, -0.469, 0.469, 1 },
{ 0.469, -0.469, -0.469, 1 },
{ 0.290, 0.000, -0.759, 1 },
{ -0.469, -0.469, -0.469, 1 },
{ 0.000, -0.759, 0.290, 1 },
{ 0.000, 0.759, -0.290, 1 },
{ -0.290, 0.000, 0.759, 1 },
{ 0.759, -0.290, 0.000, 1 },
{ -0.290, 0.000, -0.759, 1 },
{ 0.469, 0.469, -0.469, 1 },
{ 0.000, 0.759, 0.290, 1 }
});
var incident = MyMatrix <double> .Incident(4, r);
vertices = vertices * incident;
for (var i = 0; i < vertices.Height; ++i)
{
vertices[i, 3] = 1;
}
var faces = new MyMatrix <int>(new int[, ]
{
{ 9, 13, 7, 1, 15 },
{ 6, 4, 14, 19, 8 },
{ 12, 5, 13, 9, 2 },
{ 6, 2, 12, 17, 4 },
{ 16, 10, 11, 18, 3 },
{ 19, 8, 15, 1, 0 },
{ 16, 7, 1, 0, 3 },
{ 5, 12, 17, 11, 10 },
{ 18, 14, 4, 17, 11 },
{ 16, 10, 5, 13, 7 },
{ 2, 6, 8, 15, 9 },
{ 19, 0, 3, 18, 14 }
});
return(new Mesh(faces, vertices));
}
private MyMatrix <int> CalculateScreenCoordinates(MyMatrix <double> projectedVertices)
{
var result = new MyMatrix <int>(projectedVertices.Height, 2);
int halfWidth = m_screenWidth / 2;
int halfHeight = m_screenHeight / 2;
for (var i = 0; i < result.Height; ++i)
{
result[i, 0] = (int)(halfWidth * projectedVertices[i, 0] + halfWidth);
result[i, 1] = (int)(-halfHeight * projectedVertices[i, 1] + halfHeight);
}
return(result);
}
private static Mesh CreateGrarlic(double r)
{
var horizontalSegments = 20;
var verticalSegments = 16;
var vertices = new MyMatrix <double>(horizontalSegments * (verticalSegments + 1), 4);
for (var i = 0; i <= verticalSegments; ++i)
{
var theta = -Math.PI / 2 + Math.PI / verticalSegments * i;
var y = r * Math.Sin(theta);
if (theta > 0)
{
var t = theta / (Math.PI / 2.0);
t = Math.Pow(t, 5);
t = r * t;
}
var projection = r * Math.Cos(theta);
for (var j = 0; j < horizontalSegments; ++j)
{
var fi = 2 * Math.PI / horizontalSegments * j;
var multiplier = 1.0 + 0.5 * Math.Abs(Math.Sin(2 * fi));
var x = projection * Math.Cos(fi) * multiplier;
var z = projection * Math.Sin(fi) * multiplier;
vertices[i * horizontalSegments + j, 0] = x;
vertices[i * horizontalSegments + j, 1] = y + (theta > 0 ? r * Math.Pow(theta / (Math.PI / 2.0), 5) : 0.0);
vertices[i * horizontalSegments + j, 2] = z;
vertices[i * horizontalSegments + j, 3] = 1;
}
}
var faces = new MyMatrix <int>(2 * horizontalSegments * verticalSegments, 3);
for (var i = 0; i < verticalSegments; ++i)
{
for (var j = 0; j < horizontalSegments; ++j)
{
var index = i * horizontalSegments + j;
faces[2 * index, 0] = index;
faces[2 * index, 1] = (index + 1) % horizontalSegments == 0 ? index - horizontalSegments + 1 : index + 1;
faces[2 * index, 2] = (index + 1) % horizontalSegments == 0 ? index + 1 : index + horizontalSegments + 1;
faces[2 * index + 1, 0] = index;
faces[2 * index + 1, 1] = (index + 1) % horizontalSegments == 0 ? index + 1 : index + horizontalSegments + 1;
faces[2 * index + 1, 2] = index + horizontalSegments;
}
}
return(new Mesh(faces, vertices));
}
public static MyMatrix <double> Inverse(MyMatrix <double> matrix)
{
var array1d = matrix.GetInternalStorage().Cast <double>().ToArray();
var mathnetMatrix = new DenseMatrix(matrix.Height, matrix.Width, array1d);
var inversedMathnetMatrix = mathnetMatrix.Inverse();
var result = new MyMatrix <double>(inversedMathnetMatrix.RowCount, inversedMathnetMatrix.ColumnCount);
for (int i = 0; i < inversedMathnetMatrix.RowCount; ++i)
{
for (int j = 0; j < inversedMathnetMatrix.ColumnCount; ++j)
{
result[i, j] = inversedMathnetMatrix[i, j];
}
}
return(result);
}
private static void CreateVerticesForFace(
double xStart
, double yStart
, double zStart
, double newLineXStep
, double newLineYStep
, double newLineZStep
, double xStep
, double yStep
, double zStep
, double radius
, int subdivisions
, int startIndex
, MyMatrix <double> vertices)
{
vertices[startIndex, 0] = xStart;
vertices[startIndex, 1] = yStart;
vertices[startIndex, 2] = zStart;
var numberOfLines = (int)Math.Pow(2, subdivisions) + 1;
for (int lineNumber = 1, index = startIndex + 1; lineNumber < numberOfLines; ++lineNumber)
{
var firstVertexX = xStart + newLineXStep * lineNumber;
var firstVertexY = yStart + newLineYStep * lineNumber;
var firstVertexZ = zStart + newLineZStep * lineNumber;
var numberOfVerticesInLine = lineNumber + 1;
for (int vertexNumberInLine = 0; vertexNumberInLine < numberOfVerticesInLine; ++vertexNumberInLine)
{
var x = firstVertexX + xStep * vertexNumberInLine;
var y = firstVertexY + yStep * vertexNumberInLine;
var z = firstVertexZ + zStep * vertexNumberInLine;
var length = Utilities.Length(x, y, z, 0, 0, 0);
x *= radius / length;
y *= radius / length;
z *= radius / length;
vertices[index, 0] = x;
vertices[index, 1] = y;
vertices[index, 2] = z;
++index;
}
}
}
public MainWindow()
{
InitializeComponent();
m_bitmap = new WriteableBitmap((int)image.Width, (int)image.Height, 96, 96, PixelFormats.Bgr32, null);
image.Source = m_bitmap;
image.Stretch = Stretch.None;
image.HorizontalAlignment = HorizontalAlignment.Left;
image.VerticalAlignment = VerticalAlignment.Top;
var vertices = new double[, ]
{
{ 0, 0, 0, 1 },
{ 1, 0, 0, 1 },
{ 0.5, -0.2, 1, 1 },
{ 0.5, 1, 0.5, 1 }
};
var faces = new int[, ]
{
{ 1, 0, 3 },
{ 2, 1, 3 },
{ 0, 2, 3 },
{ 2, 0, 1 }
};
var defaultObject = new MyObject("default", new Vector3D(0, 0, 0), new Vector3D(0, 0, 0), Default.SCALE, Shape.Tetrahedron);
AddObject(defaultObject);
objectsListBox.SelectedIndex = 0;
var r = -1.0 / 15.0;
var perspective = new double[, ]
{
{ 1, 0, 0, 0 },
{ 0, 1, 0, 0 },
{ 0, 0, 0, r },
{ 0, 0, 0, 1 }
};
var projection = new MyMatrix <double>(perspective);
m_currentObject = GetCurrentObject();
m_drawer = new Drawer(projection, (int)m_bitmap.Width, (int)m_bitmap.Height);
projectionComboBox.SelectedIndex = 0;
Redraw();
}
private static Mesh CreateSphere(double r)
{
var horizontalSegments = 14;
var verticalSegments = 14;
var vertices = new MyMatrix <double>(horizontalSegments * (verticalSegments + 1), 4);
for (var i = 0; i <= verticalSegments; ++i)
{
var theta = -Math.PI / 2 + Math.PI / verticalSegments * i;
var y = r * Math.Sin(theta);
var projection = r * Math.Cos(theta);
for (var j = 0; j < horizontalSegments; ++j)
{
var fi = 2 * Math.PI / horizontalSegments * j;
var x = projection * Math.Cos(fi);
var z = projection * Math.Sin(fi);
vertices[i * horizontalSegments + j, 0] = x;
vertices[i * horizontalSegments + j, 1] = y;
vertices[i * horizontalSegments + j, 2] = z;
vertices[i * horizontalSegments + j, 3] = 1;
}
}
var faces = new MyMatrix <int>(2 * horizontalSegments * verticalSegments, 3);
for (var i = 0; i < verticalSegments; ++i)
{
for (var j = 0; j < horizontalSegments; ++j)
{
var index = i * horizontalSegments + j;
faces[2 * index, 0] = index;
faces[2 * index, 1] = (index + 1) % horizontalSegments == 0 ? index - horizontalSegments + 1 : index + 1;
faces[2 * index, 2] = (index + 1) % horizontalSegments == 0 ? index + 1 : index + horizontalSegments + 1;
faces[2 * index + 1, 0] = index;
faces[2 * index + 1, 1] = (index + 1) % horizontalSegments == 0 ? index + 1 : index + horizontalSegments + 1;
faces[2 * index + 1, 2] = index + horizontalSegments;
}
}
return(new Mesh(faces, vertices));
}
private static void CreateSpherePart(
MyMatrix <double> tethraederVertices
, int fristVertexIndex
, int secondVertexIndex
, int thirdVertexIndex
, int subdivisions
, int startIndex
, double radius
, MyMatrix <double> vertices
, List <Face> faces)
{
var numberOfSegments = (int)Math.Pow(2, subdivisions);
var newLineXStep = (tethraederVertices[secondVertexIndex, 0] - tethraederVertices[fristVertexIndex, 0]) / numberOfSegments;
var newLineYStep = (tethraederVertices[secondVertexIndex, 1] - tethraederVertices[fristVertexIndex, 1]) / numberOfSegments;
var newLineZStep = (tethraederVertices[secondVertexIndex, 2] - tethraederVertices[fristVertexIndex, 2]) / numberOfSegments;
var xStep = (tethraederVertices[thirdVertexIndex, 0] - tethraederVertices[secondVertexIndex, 0]) / numberOfSegments;
var yStep = (tethraederVertices[thirdVertexIndex, 1] - tethraederVertices[secondVertexIndex, 1]) / numberOfSegments;
var zStep = (tethraederVertices[thirdVertexIndex, 2] - tethraederVertices[secondVertexIndex, 2]) / numberOfSegments;
CreateVerticesForFace(
tethraederVertices[fristVertexIndex, 0]
, tethraederVertices[fristVertexIndex, 1]
, tethraederVertices[fristVertexIndex, 2]
, newLineXStep
, newLineYStep
, newLineZStep
, xStep
, yStep
, zStep
, radius
, subdivisions
, startIndex
, vertices);
CreateFacesForFace(
startIndex
, subdivisions
, vertices
, faces);
}
private static Mesh CreateModifiedTorus(double r, double torusRadius)
{
var verticalSegments = 8;
var horizontalSegments = 36;
var vertices = new MyMatrix <double>(2 * verticalSegments * (horizontalSegments + 1), 4);
for (var i = 0; i <= horizontalSegments; ++i)
{
var fi = 4 * Math.PI / horizontalSegments * i;
for (var j = 0; j < verticalSegments; ++j)
{
var theta = 2 * Math.PI / verticalSegments * j;
var x = (r + torusRadius * Math.Cos(theta)) * Math.Cos(fi);
var y = (r + torusRadius * Math.Cos(theta)) * Math.Sin(fi);
var z = torusRadius * Math.Sin(theta) + torusRadius * fi;
vertices[i * verticalSegments + j, 0] = x;
vertices[i * verticalSegments + j, 1] = y;
vertices[i * verticalSegments + j, 2] = z;
vertices[i * verticalSegments + j, 3] = 1;
}
}
var faces = new MyMatrix <int>(4 * verticalSegments * (horizontalSegments + 1), 3);
for (var i = 0; i < horizontalSegments; ++i)
{
for (var j = 0; j < verticalSegments; ++j)
{
var index = i * verticalSegments + j;
faces[2 * index, 0] = index;
faces[2 * index, 1] = index + verticalSegments;
faces[2 * index, 2] = (index + 1) % verticalSegments == 0 ? (i + 1) * verticalSegments : index + verticalSegments + 1;
faces[2 * index + 1, 0] = index;
faces[2 * index + 1, 1] = (index + 1) % verticalSegments == 0 ? (i + 1) * verticalSegments : index + verticalSegments + 1;
faces[2 * index + 1, 2] = (index + 1) % verticalSegments == 0 ? i * verticalSegments : index + 1;
}
}
return(new Mesh(faces, vertices));
}
public static MyMatrix <T> operator *(MyMatrix <T> first, MyMatrix <T> second)
{
if (first.Width != second.Height)
{
throw new ArgumentException("Matrix multiplication: first matrix width must be equal to second matrix height");
}
var result = new MyMatrix <T>(first.m_matrix.GetLength(0), second.m_matrix.GetLength(1));
for (var i = 0; i < first.Height; ++i)
{
for (var j = 0; j < second.Width; ++j)
{
for (var k = 0; k < first.Width; ++k)
{
result[i, j] += (dynamic)first[i, k] * (dynamic)second[k, j]; // some cheats with dynamic
}
}
}
return(result);
}
public Mesh(MyMatrix <int> faces, MyMatrix <double> vertices)
{
CheckNullFacesOrVertices(faces, vertices);
if (faces.Height <= 0 || faces.Width < 3)
{
throw new ArgumentException(
"Wrong faces matrix size, height = " + faces.Height +
", width = " + faces.Width
);
}
CheckVerticesShape(vertices);
for (int i = 0; i < faces.Height; ++i)
{
var faceBuilder = new FaceBuilder();
for (var j = 0; j < faces.Width; ++j)
{
faceBuilder.Add(faces[i, j]);
}
m_faces.Add(faceBuilder.Build());
}
m_vertices = vertices;
}
private static Mesh CreateSphereWithoutPole(double r, int subdivisions)
{
var vertices = new MyMatrix <double>(4, 4);
var a = 4 * r / Math.Sqrt(6);
var c = (a / 2) / Math.Cos(Utilities.ToRadians(30));
for (var i = 0; i < 3; ++i)
{
vertices[i, 0] = c * (Math.Cos(Utilities.ToRadians(150 + i * 120)));
vertices[i, 1] = -Math.Sqrt(r * r - c * c);
vertices[i, 2] = c * (Math.Sin(Utilities.ToRadians(-30 + i * 120)));
}
vertices[3, 0] = 0;
vertices[3, 1] = r;
vertices[3, 2] = 0;
for (var i = 0; i < vertices.Height; ++i)
{
vertices[i, 3] = 1;
}
var sphereVertices = new MyMatrix <double>(4 * ((int)Math.Pow(2, subdivisions) + 1) * ((int)Math.Pow(2, subdivisions) + 2), 4);
var faces = new List <Face>();
var numberOfSegments = (int)Math.Pow(2, subdivisions);
var numberOfVerticesInFace = ((int)Math.Pow(2, subdivisions) + 1) * ((int)Math.Pow(2, subdivisions) + 2) / 2;
CreateSpherePart(vertices, 3, 0, 2, subdivisions, 0, r, sphereVertices, faces);
CreateSpherePart(vertices, 3, 1, 0, subdivisions, numberOfVerticesInFace, r, sphereVertices, faces);
CreateSpherePart(vertices, 3, 2, 1, subdivisions, 2 * numberOfVerticesInFace, r, sphereVertices, faces);
CreateSpherePart(vertices, 2, 1, 0, subdivisions, 3 * numberOfVerticesInFace, r, sphereVertices, faces);
for (int i = 0; i < sphereVertices.Height; ++i)
{
sphereVertices[i, 3] = 1;
}
return(new Mesh(faces, sphereVertices));
}
private static Mesh CreateOctahedron(double r)
{
var vertices = new MyMatrix <double>(6, 4);
var a = 6 * r / Math.Sqrt(6);
vertices[0, 0] = vertices[1, 0] = -a / 2;
vertices[2, 0] = vertices[3, 0] = a / 2;
vertices[4, 0] = vertices[5, 0] = 0;
vertices[0, 1] = vertices[1, 1] = vertices[2, 1] = vertices[3, 1] = 0;
vertices[4, 1] = r;
vertices[5, 1] = -r;
vertices[1, 2] = vertices[2, 2] = -a / 2;
vertices[0, 2] = vertices[3, 2] = a / 2;
vertices[4, 2] = vertices[5, 2] = 0;
for (var i = 0; i < vertices.Height; ++i)
{
vertices[i, 3] = 1;
}
var faces = new MyMatrix <int>(new int[, ]
{
{ 1, 0, 4 },
{ 2, 1, 4 },
{ 3, 2, 4 },
{ 0, 3, 4 },
{ 0, 1, 5 },
{ 1, 2, 5 },
{ 2, 3, 5 },
{ 3, 0, 5 }
});
return(new Mesh(faces, vertices));
}
public IList <Face> GetVisibleFaces(double x, double y, double z)
{
//var inversedMatrix = Utilities.Inverse(m_rotation);
//var inversedMatrix = m_rotation;
//var vertices = m_vertices;
var vertices = GetWorldCoordinates();
double barycenterX = 0;
double barycenterY = 0;
double barycenterZ = 0;
for (var i = 0; i < vertices.Height; ++i)
{
barycenterX += vertices[i, 0];
barycenterY += vertices[i, 1];
barycenterZ += vertices[i, 2];
}
barycenterX /= vertices.Height;
barycenterY /= vertices.Height;
barycenterZ /= vertices.Height;
IList <Face> result = new List <Face>();
var planes = new MyMatrix <double>(4, Faces.Count);
for (var i = 0; i < Faces.Count; ++i)
{
var x1 = vertices[Faces[i].Indices[1], 0] - vertices[Faces[i].Indices[0], 0];
var y1 = vertices[Faces[i].Indices[1], 1] - vertices[Faces[i].Indices[0], 1];
var z1 = vertices[Faces[i].Indices[1], 2] - vertices[Faces[i].Indices[0], 2];
var x2 = vertices[Faces[i].Indices[2], 0] - vertices[Faces[i].Indices[1], 0];
var y2 = vertices[Faces[i].Indices[2], 1] - vertices[Faces[i].Indices[1], 1];
var z2 = vertices[Faces[i].Indices[2], 2] - vertices[Faces[i].Indices[1], 2];
var a = y1 * z2 - y2 * z1;
var b = z1 * x2 - z2 * x1;
var c = x1 * y2 - x2 * y1;
var d = -(a * vertices[Faces[i].Indices[0], 0] + b * vertices[Faces[i].Indices[0], 1] + c * vertices[Faces[i].Indices[0], 2]);
planes[0, i] = a;
planes[1, i] = b;
planes[2, i] = c;
planes[3, i] = d;
var sign = -Math.Sign(a * barycenterX + b * barycenterY + c * barycenterZ + d);
if (sign == -1)
{
planes[0, i] *= -1;
planes[1, i] *= -1;
planes[2, i] *= -1;
planes[3, i] *= -1;
}
}
//planes = inversedMatrix * planes;
for (var i = 0; i < planes.Width; ++i)
{
//if (planes[0, i] * (x - barycenterX) + planes[1, i] * (y - barycenterY) + planes[2, i] * (z - barycenterZ) + planes[3, i] > 0 )
if (planes[0, i] * x + planes[1, i] * y + planes[2, i] * z + planes[3, i] > 0)
{
result.Add(Faces[i]);
}
}
return(result);
}
public void ResetScale()
{
m_scale = MyMatrix <double> .Incident(4);
}
public void AddScale(MyMatrix <double> scale)
{
m_scale = m_scale * scale;
}
public void SetScale(MyMatrix <double> scale)
{
m_scale = scale;
}
public void ResetRotation()
{
m_rotation = MyMatrix <double> .Incident(4);
}
public void AddRotation(MyMatrix <double> rotation)
{
m_rotation = m_rotation * rotation;
}
public void SetRotation(MyMatrix <double> rotation)
{
m_rotation = rotation;
}
public void ResetTranslation()
{
m_translation = MyMatrix <double> .Incident(4);
}
public void AddTranslation(MyMatrix <double> translation)
{
m_translation = m_translation * translation;
}
public void SetTranslation(MyMatrix <double> translation)
{
m_translation = translation;
}
public Drawer(MyMatrix <double> projection, int width, int height)
{
m_projection = projection;
m_screenWidth = width;
m_screenHeight = height;
}