public Vector4D Cross_Product(Vector4D v) => new Vector4D(this.Y * v.Z - this.Z * v.Y, this.Z * v.X - this.X * v.Z, this.X * v.Y - this.Y * v.X, this.W);
public Vector3D(Vector4D v)
{
X = v.X;
Y = v.Y;
Z = v.Z;
}
public double Angle(Vector4D v) => Math.Acos((this * v) / (this.Magnitude() * v.Magnitude()));
public Vector4D Divide_By_W(Vector4D vertex) => vertex / vertex.W;
public Camera(Vector3D position, Vector3D direction, Vector3D direction_up)
{
Translation = position;
World_Origin = new Vector4D(position);
Set_Camera_Direction_1(direction, direction_up);
}
public Vector4D Apply_Camera_Matrices(Vector4D vertex) => World_to_screen * vertex;
// Only do at drawing stage? v public Vector4D Change_Y_Axis(Vector4D vertex) => Transform.Translate(new Vector3D(0, Height - 1, 0)) * Transform.Scale_Y(-1) * vertex;
public Vector4D Scale_to_screen(Vector4D vertex) => Transform.Scale(0.5 * (Width - 1), 0.5 * (Height - 1), 1) * Transform.Translate(new Vector3D(1, 1, 0)) * vertex;
public void Render(PictureBox canvas_box, Perspective_Camera camera)
{
// Only render if a change in scene has taken place.
// if (!Change_scene) return;
lock (locker)
{
// Create temporary canvas
Bitmap temp_canvas = new Bitmap(Width, Height);
// Reset buffers
for (int i = 0; i < Width; i++)
{
for (int j = 0; j < Height; j++)
{
z_buffer[i][j] = 2; // 2 is always greater than anything to be rendered.
}
}
for (int i = 0; i < Width; i++)
{
for (int j = 0; j < Height; j++)
{
colour_buffer[i][j] = Background_colour;
}
}
// Calculate camera matrices
camera.Calculate_Model_to_World_Matrix();
camera.Apply_World_Matrix();
camera.Calculate_World_to_Screen_Matrix();
// Clipping planes
Clipping_Plane[] world_clipping_planes = camera.Calculate_Clipping_Planes();
Vector3D near_bottom_left_point = new Vector3D(-1, -1, -1), far_top_right_point = new Vector3D(1, 1, 1);
Clipping_Plane[] projection_clipping_planes = new Clipping_Plane[]
{
new Clipping_Plane(near_bottom_left_point, Vector3D.Unit_X), // Left
new Clipping_Plane(near_bottom_left_point, Vector3D.Unit_Y), // Bottom
new Clipping_Plane(near_bottom_left_point, Vector3D.Unit_Z), // Near
new Clipping_Plane(far_top_right_point, Vector3D.Unit_Negative_X), // Right
new Clipping_Plane(far_top_right_point, Vector3D.Unit_Negative_Y), // Top
new Clipping_Plane(far_top_right_point, Vector3D.Unit_Negative_Z) // Far
};
// Draw graphics
using (Graphics g = Graphics.FromImage(temp_canvas))
{
foreach (Shape shape in Shape_List)
{
// Move shapes from model space to world space
shape.Render_Mesh.Calculate_Model_to_World_Matrix();
shape.Render_Mesh.Apply_World_Matrices();
// Draw faces
if (shape.Render_Mesh.Faces != null && shape.Render_Mesh.Draw_Faces)
{
foreach (Face face in shape.Render_Mesh.Faces)
{
if (face.Visible)
{
// Variable simplification
double point_1_x = shape.Render_Mesh.World_Vertices[face.P1].X;
double point_1_y = shape.Render_Mesh.World_Vertices[face.P1].Y;
double point_1_z = shape.Render_Mesh.World_Vertices[face.P1].Z;
double point_2_x = shape.Render_Mesh.World_Vertices[face.P2].X;
double point_2_y = shape.Render_Mesh.World_Vertices[face.P2].Y;
double point_2_z = shape.Render_Mesh.World_Vertices[face.P2].Z;
double point_3_x = shape.Render_Mesh.World_Vertices[face.P3].X;
double point_3_y = shape.Render_Mesh.World_Vertices[face.P3].Y;
double point_3_z = shape.Render_Mesh.World_Vertices[face.P3].Z;
double texture_point_1_x = 0, texture_point_1_y = 0, texture_point_2_x = 0, texture_point_2_y = 0, texture_point_3_x = 0, texture_point_3_y = 0;
Vector3D texture_point_1 = null, texture_point_2 = null, texture_point_3 = null;
if (face.Texture != null)
{
texture_point_1_x = shape.Render_Mesh.Texture_Vertices[face.T1].X;
texture_point_1_y = shape.Render_Mesh.Texture_Vertices[face.T1].Y;
texture_point_2_x = shape.Render_Mesh.Texture_Vertices[face.T2].X;
texture_point_2_y = shape.Render_Mesh.Texture_Vertices[face.T2].Y;
texture_point_3_x = shape.Render_Mesh.Texture_Vertices[face.T3].X;
texture_point_3_y = shape.Render_Mesh.Texture_Vertices[face.T3].Y;
texture_point_1 = new Vector3D(texture_point_1_x, texture_point_1_y, 1);
texture_point_2 = new Vector3D(texture_point_2_x, texture_point_2_y, 1);
texture_point_3 = new Vector3D(texture_point_3_x, texture_point_3_y, 1);
}
// Triangle point vectors
Vector4D point_1 = new Vector4D(point_1_x, point_1_y, point_1_z);
Vector4D point_2 = new Vector4D(point_2_x, point_2_y, point_2_z);
Vector4D point_3 = new Vector4D(point_3_x, point_3_y, point_3_z);
Vector3D normal = Vector3D.Normal_From_Plane(new Vector3D(point_1), new Vector3D(point_2), new Vector3D(point_3));
Vector3D camera_to_face = new Vector3D(point_1 - camera.World_Origin);
// Adjust colour based on lighting
Color face_colour = face.Colour;
if (Light_List.Count > 0)
{
double max_intensity = 0, true_intensity = 0;
foreach (Light light in Light_List)
{
max_intensity += light.Intensity;
}
foreach (Light light in Light_List)
{
switch (light.GetType().Name)
{
case "Distant_Light":
true_intensity = Math.Max(0, -light.World_Direction * normal) * light.Intensity;
break;
case "Point_Light":
true_intensity = Math.Max(0, -new Vector3D(point_1 - light.World_Origin).Normalise() * normal) * light.Intensity;
break;
case "Spot_Light":
Vector3D light_to_shape = new Vector3D(point_1 - light.World_Origin);
if (light_to_shape.Angle(light.World_Direction) > ((Spotlight)light).Angle || light_to_shape * light.World_Direction > ((Spotlight)light).Distance)
{
continue;
}
true_intensity = Math.Max(0, -light.World_Direction * normal) * light.Intensity;
break;
case "Ambient_Light":
break;
}
double scaled_intensity = true_intensity / max_intensity;
if (face.Texture == null)
{
}
byte new_red = (byte)Round_To_Int((face.Colour.R + light.Colour.R) * 255 / 510 * scaled_intensity);
byte new_green = (byte)Round_To_Int((face.Colour.G + light.Colour.G) * 255 / 510 * scaled_intensity);
byte new_blue = (byte)Round_To_Int((face.Colour.B + light.Colour.B) * 255 / 510 * scaled_intensity);
face_colour = Color.FromArgb(face.Colour.A, new_red, new_green, new_blue);
}
}
// Include exemptions to back-face culling?
if (camera_to_face * normal < 0 || shape.Render_Mesh.GetType().Name == "Plane")
{
// Create a queue
Queue <Clipped_Face> world_face_clip = new Queue <Clipped_Face>();
// Add initial triangle to clipping queue
if (face.Texture == null)
{
world_face_clip.Enqueue(new Clipped_Face(point_1, point_2, point_3, face.Colour, face.Draw_Outline, face.Visible));
}
else
{
world_face_clip.Enqueue(new Clipped_Face(point_1, point_2, point_3, texture_point_1, texture_point_2, texture_point_3, face.Texture, face.Draw_Outline, face.Visible));
}
int no_triangles = 1;
// Clip face against each world clipping plane
foreach (Clipping_Plane world_clipping_plane in world_clipping_planes)
{
while (no_triangles > 0)
{
Clipped_Face triangle = world_face_clip.Dequeue();
Clipped_Face[] triangles = new Clipped_Face[2];
int num_intersection_points = Clip_Face(world_clipping_plane.Point, world_clipping_plane.Normal, triangle, out triangles[0], out triangles[1]);
for (int i = 0; i < num_intersection_points; i++)
{
world_face_clip.Enqueue(triangles[i]);
}
no_triangles--;
}
no_triangles = world_face_clip.Count;
}
if (no_triangles > 0)
{
Queue <Clipped_Face> projection_face_clip = world_face_clip;
// Move remaining faces into projection space
foreach (Clipped_Face projection_clipped_face in projection_face_clip)
{
projection_clipped_face.P1 = camera.Apply_Camera_Matrices(projection_clipped_face.P1);
projection_clipped_face.P2 = camera.Apply_Camera_Matrices(projection_clipped_face.P2);
projection_clipped_face.P3 = camera.Apply_Camera_Matrices(projection_clipped_face.P3);
projection_clipped_face.P1 = camera.Divide_By_W(projection_clipped_face.P1);
projection_clipped_face.P2 = camera.Divide_By_W(projection_clipped_face.P2);
projection_clipped_face.P3 = camera.Divide_By_W(projection_clipped_face.P3);
if (face.Texture != null)
{
projection_clipped_face.T1 /= projection_clipped_face.P1.W;
projection_clipped_face.T2 /= projection_clipped_face.P1.W;
projection_clipped_face.T3 /= projection_clipped_face.P1.W;
}
}
// Clip face against each projection clipping plane
foreach (Clipping_Plane projection_clipping_plane in projection_clipping_planes)
{
while (no_triangles > 0)
{
Clipped_Face triangle = projection_face_clip.Dequeue();
Clipped_Face[] triangles = new Clipped_Face[2];
int num_intersection_points = Clip_Face(projection_clipping_plane.Point, projection_clipping_plane.Normal, triangle, out triangles[0], out triangles[1]);
for (int i = 0; i < num_intersection_points; i++)
{
projection_face_clip.Enqueue(triangles[i]);
}
no_triangles--;
}
no_triangles = projection_face_clip.Count;
}
foreach (Clipped_Face projection_clipped_face in projection_face_clip)
{
Vector4D result_point_1 = Scale_to_screen(projection_clipped_face.P1);
Vector4D result_point_2 = Scale_to_screen(projection_clipped_face.P2);
Vector4D result_point_3 = Scale_to_screen(projection_clipped_face.P3);
// Why? (and check rounding)
result_point_1 = Change_Y_Axis(result_point_1);
result_point_2 = Change_Y_Axis(result_point_2);
result_point_3 = Change_Y_Axis(result_point_3);
// More variable simplification
int result_point_1_x = (int)Math.Round(result_point_1.X, MidpointRounding.AwayFromZero);
int result_point_1_y = (int)Math.Round(result_point_1.Y, MidpointRounding.AwayFromZero);
double result_point_1_z = result_point_1.Z;
int result_point_2_x = (int)Math.Round(result_point_2.X, MidpointRounding.AwayFromZero);
int result_point_2_y = (int)Math.Round(result_point_2.Y, MidpointRounding.AwayFromZero);
double result_point_2_z = result_point_2.Z;
int result_point_3_x = (int)Math.Round(result_point_3.X, MidpointRounding.AwayFromZero);
int result_point_3_y = (int)Math.Round(result_point_3.Y, MidpointRounding.AwayFromZero);
double result_point_3_z = result_point_3.Z;
// Finally draw the triangle
if (face.Draw_Outline)
{
// Method for drawing edges?
Triangle(result_point_1_x, result_point_1_y, result_point_1_z, result_point_2_x, result_point_2_y, result_point_2_z, result_point_3_x, result_point_3_y, result_point_3_z, face_colour);
}
else
{
if (face.Texture == null)
{
Triangle(result_point_1_x, result_point_1_y, result_point_1_z, result_point_2_x, result_point_2_y, result_point_2_z, result_point_3_x, result_point_3_y, result_point_3_z, face_colour);
}
else
{
// Scale the texture co-ordinates
int width = face.Texture.Width - 1;
int height = face.Texture.Height - 1;
// AFTERWARDS?
int result_texture_point_1_x = Round_To_Int(texture_point_1_x * width);
int result_texture_point_1_y = Round_To_Int(texture_point_1_y * height);
int result_texture_point_2_x = Round_To_Int(texture_point_2_x * width);
int result_texture_point_2_y = Round_To_Int(texture_point_2_y * height);
int result_texture_point_3_x = Round_To_Int(texture_point_3_x * width);
int result_texture_point_3_y = Round_To_Int(texture_point_3_y * height);
Textured_Triangle(result_point_1_x, result_point_1_y, result_point_1_z, result_point_2_x, result_point_2_y, result_point_2_z, result_point_3_x, result_point_3_y, result_point_3_z, result_texture_point_1_x, result_texture_point_1_y, result_texture_point_2_x, result_texture_point_2_y, result_texture_point_3_x, result_texture_point_3_y, face.Texture);
}
}
}
}
}
/*
* // between [-1,1]
* // between [0,2] (+1)
* // => between [0,1] (/2)
* // => between [0,width-1] (*(width-1))
*
* // RANGE TO DRAW X: [0,WIDTH-1] Y: [0,HEIGHT-1]
*
*
* // ROUDNING?
*/
}
}
}
// Draw edges
if (shape.Render_Mesh.Edges != null && shape.Render_Mesh.Draw_Edges)
{
foreach (Edge edge in shape.Render_Mesh.Edges)
{
if (edge.Visible)
{
// Variable simplification
double point_1_x = shape.Render_Mesh.World_Vertices[edge.P1].X;
double point_1_y = shape.Render_Mesh.World_Vertices[edge.P1].Y;
double point_1_z = shape.Render_Mesh.World_Vertices[edge.P1].Z;
double point_2_x = shape.Render_Mesh.World_Vertices[edge.P2].X;
double point_2_y = shape.Render_Mesh.World_Vertices[edge.P2].Y;
double point_2_z = shape.Render_Mesh.World_Vertices[edge.P2].Z;
// Line points
Vector4D point_1 = new Vector4D(point_1_x, point_1_y, point_1_z);
Vector4D point_2 = new Vector4D(point_2_x, point_2_y, point_2_z);
Clipped_Edge world_new_edge = new Clipped_Edge(point_1, point_2, shape.Render_Mesh.Edge_Colour, shape.Render_Mesh.Visible);
bool world_draw_edge = true;
foreach (Clipping_Plane world_clipping_plane in world_clipping_planes)
{
world_new_edge = Clip_Line(world_clipping_plane.Point, world_clipping_plane.Normal, world_new_edge);
if (world_new_edge == null)
{
// != null
world_draw_edge = false;
break;
}
}
if (world_draw_edge)
{
Clipped_Edge projection_new_edge = world_new_edge;
projection_new_edge.P1 = camera.Apply_Camera_Matrices(projection_new_edge.P1);
projection_new_edge.P2 = camera.Apply_Camera_Matrices(projection_new_edge.P2);
projection_new_edge.P1 = camera.Divide_By_W(projection_new_edge.P1);
projection_new_edge.P2 = camera.Divide_By_W(projection_new_edge.P2);
bool projection_draw_edge = true;
foreach (Clipping_Plane projection_clipping_plane in projection_clipping_planes)
{
projection_new_edge = Clip_Line(projection_clipping_plane.Point, projection_clipping_plane.Normal, projection_new_edge);
if (projection_new_edge == null)
{
projection_draw_edge = false;
break;
}
}
if (projection_draw_edge)
{
// Scale to screen space?
Vector4D result_point_1 = Scale_to_screen(projection_new_edge.P1);
Vector4D result_point_2 = Scale_to_screen(projection_new_edge.P2);
// WHHY?
result_point_1 = Change_Y_Axis(result_point_1);
result_point_2 = Change_Y_Axis(result_point_2);
int result_point_1_x = (int)Math.Round(result_point_1.X, MidpointRounding.AwayFromZero);
int result_point_1_y = (int)Math.Round(result_point_1.Y, MidpointRounding.AwayFromZero);
double result_point_1_z = result_point_1.Z;
int result_point_2_x = (int)Math.Round(result_point_2.X, MidpointRounding.AwayFromZero);
int result_point_2_y = (int)Math.Round(result_point_2.Y, MidpointRounding.AwayFromZero);
double result_point_2_z = result_point_2.Z;
// Finally draw the line
Line(result_point_1_x, result_point_1_y, result_point_1_z, result_point_2_x, result_point_2_y, result_point_2_z, shape.Render_Mesh.Edge_Colour);
}
}
}
}
}
/*
* // Draw vertices
* if (shape.Render_Mesh.Camera_Vertices != null && shape.Render_Mesh.Draw_Vertices)
* {
* foreach (Vertex vertex in shape.Render_Mesh.Camera_Vertices)
* {
* if (vertex.Visible)
* {
* // Variable simplification
* int point_x = (int)vertex.X;
* int point_y = (int)vertex.Y;
* double point_z = vertex.Z;
*
* for (int x = point_x - vertex.Diameter / 2; x <= point_x + vertex.Diameter / 2; x++)
* {
* for (int y = point_y - vertex.Diameter / 2; y <= point_y + vertex.Diameter / 2; y++)
* {
* // Check against z buffer
* if (z_buffer[x][y] > point_z)
* {
* z_buffer[x][y] = point_z;
* colour_buffer[x][y] = shape.Render_Mesh.Vertex_Colour;
* }
* }
* }
* }
* }
* }
*/
}
// Draw each pixel from colour buffer
for (int x = 0; x < Width; x++)
{
for (int y = 0; y < Height; y++)
{
using (SolidBrush face_brush = new SolidBrush(colour_buffer[x][y])) g.FillRectangle(face_brush, x, y, 1, 1);
}
}
}
Canvas = temp_canvas;
canvas_box.Invalidate();
Change_scene = false;
}
}
private static int Clip_Face(Vector3D plane_point, Vector3D plane_normal, Clipped_Face f, out Clipped_Face f1, out Clipped_Face f2)
{
f1 = null; f2 = null;
Vector3D point_1 = new Vector3D(f.P1), point_2 = new Vector3D(f.P2), point_3 = new Vector3D(f.P3);
int inside_point_count = 0;
List <Vector3D> inside_points = new List <Vector3D>(3);
List <Vector3D> outside_points = new List <Vector3D>(3);
List <Vector3D> inside_texture_points = new List <Vector3D>(3);
List <Vector3D> outside_texture_points = new List <Vector3D>(3);
if (Vector3D.Point_Distance_From_Plane(point_1, plane_point, plane_normal) >= 0)
{
inside_point_count++;
inside_points.Add(point_1);
inside_texture_points.Add(f.T1);
}
else
{
outside_points.Add(point_1);
outside_texture_points.Add(f.T1);
}
if (Vector3D.Point_Distance_From_Plane(point_2, plane_point, plane_normal) >= 0)
{
inside_point_count++;
inside_points.Add(point_2);
inside_texture_points.Add(f.T2);
}
else
{
outside_points.Add(point_2);
outside_texture_points.Add(f.T2);
}
if (Vector3D.Point_Distance_From_Plane(point_3, plane_point, plane_normal) >= 0)
{
inside_point_count++;
inside_points.Add(point_3);
inside_texture_points.Add(f.T3);
}
else
{
outside_points.Add(point_3);
outside_texture_points.Add(f.T3);
}
Vector4D first_intersection, second_intersection;
double d;
switch (inside_point_count)
{
case 0:
// All points are on the outside, so no valid triangles to return
return(0);
case 1:
// One point is on the inside, so only a smaller triangle is needed
first_intersection = new Vector4D(Vector3D.Line_Intersect_Plane(inside_points[0], outside_points[0], plane_point, plane_normal, out d));
second_intersection = new Vector4D(Vector3D.Line_Intersect_Plane(inside_points[0], outside_points[1], plane_point, plane_normal, out d));
if (f.Texture == null)
{
f1 = new Clipped_Face(new Vector4D(inside_points[0]), first_intersection, second_intersection, f.Colour, f.Draw_Outline, f.Visible);
}
else
{
Vector3D t_intersection_1 = (outside_texture_points[0] - inside_texture_points[0]) * d + inside_texture_points[0];
Vector3D t_intersection_2 = (outside_texture_points[1] - inside_texture_points[0]) * d + inside_texture_points[0];
f1 = new Clipped_Face(new Vector4D(inside_points[0]), first_intersection, second_intersection, inside_texture_points[0], t_intersection_1, t_intersection_2, f.Texture, f.Draw_Outline, f.Visible);
}
return(1);
case 2:
// Two points are on the inside, so a quadrilateral is formed and split into two triangles
first_intersection = new Vector4D(Vector3D.Line_Intersect_Plane(inside_points[0], outside_points[0], plane_point, plane_normal, out d));
second_intersection = new Vector4D(Vector3D.Line_Intersect_Plane(inside_points[1], outside_points[0], plane_point, plane_normal, out d));
if (f.Texture == null)
{
f1 = new Clipped_Face(new Vector4D(inside_points[0]), new Vector4D(inside_points[1]), first_intersection, f.Colour, f.Draw_Outline, f.Visible);
f2 = new Clipped_Face(new Vector4D(inside_points[1]), second_intersection, first_intersection, f.Colour, f.Draw_Outline, f.Visible);
}
else
{
Vector3D t_intersection_1 = (outside_texture_points[0] - inside_texture_points[0]) * d + inside_texture_points[0];
Vector3D t_intersection_2 = (outside_texture_points[0] - inside_texture_points[1]) * d + inside_texture_points[1];
f1 = new Clipped_Face(new Vector4D(inside_points[0]), new Vector4D(inside_points[1]), first_intersection, inside_texture_points[0], inside_texture_points[1], t_intersection_1, f.Texture, f.Draw_Outline, f.Visible);
f2 = new Clipped_Face(new Vector4D(inside_points[1]), second_intersection, first_intersection, inside_texture_points[1], t_intersection_2, t_intersection_1, f.Texture, f.Draw_Outline, f.Visible);
}
return(2);
case 3:
// All points are on the inside, so return the triangle unchanged
if (f.Texture == null)
{
f1 = new Clipped_Face(f.P1, f.P2, f.P3, f.Colour, f.Draw_Outline, f.Visible);
}
else
{
f1 = new Clipped_Face(f.P1, f.P2, f.P3, f.T1, f.T2, f.T3, f.Texture, f.Draw_Outline, f.Visible);
}
return(1);
}
return(0);
}