/// <summary>
/// Получение промежуточных точек линии. Интерполирование, можно сказать.
/// </summary>
/// <param name="p1">start point</param>
/// <param name="p2">end point</param>
/// <returns></returns>
public static Point3D[] GetLine3DPoints(Point3D start, Point3D end)
{
var points = new List <Point3D>();
double diffx = end.X - start.X;
double diffy = end.Y - start.Y;
if (Math.Abs(diffx) > Math.Abs(diffy)) // abs - убирание знака
{
// упорядочиваем точки по X
if (diffx < 0)
{
MathHelpers.Swap(ref start, ref end);
}
// получаем массив координат
// их длина = |diffx|+1 (потому что рисуем отрезок, с начальной И конечной точкой.)
double[] yCoords = MathHelpers.GetYsByXsBetweenTwoPoints2D(start.X, start.Y, end.X, end.Y);
double[] zCoords = MathHelpers.GetYsByXsBetweenTwoPoints2D(start.X, start.Z, end.X, end.Z);
// идем по X, получаем Y и Z
for (double x = start.X; x <= end.X; ++x)
{
//(x - start.X) и так будет int.
int y = (int)yCoords[(int)(x - start.X)];
double z = zCoords[(int)(x - start.X)];
var point = new Point3D(x, y, z);
points.Add(point);
}
}
else
{
// упорядочиваем точки по y
if (diffy < 0)
{
MathHelpers.Swap(ref start, ref end);
}
double[] xCoords = MathHelpers.GetYsByXsBetweenTwoPoints2D(start.Y, start.X, end.Y, end.X);
double[] zCoords = MathHelpers.GetYsByXsBetweenTwoPoints2D(start.Y, start.Z, end.Y, end.Z);
// идем по Y, получаем X и Z
for (double y = start.Y; y <= end.Y; y++)
{
int x = (int)xCoords[(int)(y - start.Y)];
double z = zCoords[(int)(y - start.Y)];
var point = new Point3D(x, y, z);
points.Add(point);
}
}
return(points.ToArray());
}
/// <summary>
/// Draw line on the bitmap. Using z-buffer and color.
/// </summary>
private void DrawLine(FastBitmap bitmap, double[,] buffer, Point3D start, Point3D end, Color color)
{
// dx and dy are coord diffs between two points
double diffx = end.X - start.X;
double diffy = end.Y - start.Y;
if (Math.Abs(diffx) > Math.Abs(diffy))
{
// I want to work with point1 is 'greater' than point2
if (diffx < 0)
{
MathHelpers.Swap(ref start, ref end);
}
// here we are getting the segment coordinates as an array of Double values
double[] yCoords = MathHelpers.GetYsByXsBetweenTwoPoints2D(start.X, start.Y, end.X, end.Y);
double[] zCoords = MathHelpers.GetYsByXsBetweenTwoPoints2D(start.X, start.Z, end.X, end.Z);
// and here we draw the points
for (double x = start.X; x <= end.X; ++x)
{
int y = (int)yCoords[(int)(x - start.X)];
double z = zCoords[(int)(x - start.X)];
if (IsWithinImage((int)x, y) && buffer[(int)x, y] >= z)
{
// in fact, there is smth like ray-tracing
// using z-buffer: if current point is closer to us than old one, we remember this...
buffer[(int)x, y] = z;
// and draw the point on the image. At last, the nearest point is drawing, other don't.
bitmap.SetPixel((int)x, y, color);
}
}
}
else
{
// I want to work with point1 is 'greater' than point2
if (diffy < 0)
{
MathHelpers.Swap(ref start, ref end);
}
double[] xCoords = MathHelpers.GetYsByXsBetweenTwoPoints2D(start.Y, start.X, end.Y, end.X);
double[] zCoords = MathHelpers.GetYsByXsBetweenTwoPoints2D(start.Y, start.Z, end.Y, end.Z);
for (double y = start.Y; y <= end.Y; y++)
{
int x = (int)xCoords[(int)(y - start.Y)];
double z = zCoords[(int)(y - start.Y)];
if (IsWithinImage(x, (int)y) && buffer[x, (int)y] >= z)
{
buffer[x, (int)y] = z;
bitmap.SetPixel(x, (int)y, color);
}
}
}
}
/// <summary>
/// Draws triangle on bitmap using specified point vectors and color (and z-buffer)
/// </summary>
private void DrawTriangle(Vector3D p0, Vector3D p1, Vector3D p2, Color color, FastBitmap bitmap, double[,] buffer)
{
if (p0.Y != p1.Y || p0.Y != p2.Y)
{
// упорядочение
if (p0.Y > p1.Y)
{
MathHelpers.Swap(ref p0, ref p1);
}
if (p0.Y > p2.Y)
{
MathHelpers.Swap(ref p0, ref p2);
}
if (p1.Y > p2.Y)
{
MathHelpers.Swap(ref p1, ref p2);
}
// in the next section, I turn the triangle into points, then draw them (using z-buffer): split the triangle into 2 segments (vertically), and rasterize them separately. The algorithm is described here: https://compgraphics.info/2D/triangle_rasterization.php
int totalHeight = (int)Math.Round(p2.Y - p0.Y);
for (int i = 0; i < totalHeight; ++i)
{
bool secondHalf = i > p1.Y - p0.Y || p1.Y == p0.Y;
int segmentHeight = (int)Math.Round(secondHalf ? p2.Y - p1.Y : p1.Y - p0.Y);
double alpha = (double)i / totalHeight;
double beta = (i - (secondHalf ? p1.Y - p0.Y : 0.0)) / segmentHeight;
Vector3D a = p0 + (p2 - p0) * alpha;
Vector3D b = (secondHalf ? p1 + (p2 - p1) * beta : p0 + (p1 - p0) * beta);
if (a.X > b.X)
{ // I want first to be greater than second
MathHelpers.Swap(ref a, ref b);
}
for (int j = (int)Math.Round(a.X); j <= (int)Math.Round(b.X); ++j)
{
double scale = (a.X == b.X) ? 1 : (j - a.X) / (b.X - a.X);
Vector3D p = a + (b - a) * scale;
int x = (int)Math.Round(p.X);
int y = (int)Math.Round(p.Y);
if (IsWithinImage(x, y) && buffer[x, y] >= p.Z)
{
// z-buffer, we remember this new point
buffer[x, y] = p.Z;
bitmap.SetPixel(x, y, color);
}
}
}
}
}