C++ triangle rasterization

问题:

I'm trying to fix this triangle rasterizer, but cannot make it work correctly. For some reason it only draws half of the triangles.

void DrawTriangle(Point2D p0, Point2D p1, Point2D p2)
{
    Point2D Top, Middle, Bottom;
    bool MiddleIsLeft;

    if (p0.y < p1.y)                    // case: 1, 2, 5
    {
        if (p0.y < p2.y)                // case: 1, 2
        {
            if (p1.y < p2.y)            // case: 1
            {
                Top = p0;
                Middle = p1;
                Bottom = p2;
                MiddleIsLeft = true;
            }
            else                        // case: 2
            {
                Top = p0;
                Middle = p2;
                Bottom = p1;
                MiddleIsLeft = false;
            }
        }
        else                            // case: 5
        {
            Top = p2;
            Middle = p0;
            Bottom = p1;
            MiddleIsLeft = true;                
        }
    }
    else                        // case: 3, 4, 6
    {
        if (p0.y < p2.y)        // case: 4
        {
            Top = p1;
            Middle = p0;
            Bottom = p2;
            MiddleIsLeft = false;
        }
        else                    // case: 3, 6
        {
            if (p1.y < p2.y)    // case: 3
            {
                Top = p1;
                Middle = p2;
                Bottom = p0;
                MiddleIsLeft = true;
            }
            else                // case 6
            {
                Top = p2;
                Middle = p1;
                Bottom = p0;
                MiddleIsLeft = false;
            }
        }
    }

    float xLeft, xRight;
    xLeft = xRight = Top.x;
    float mLeft, mRight;
    // Region 1
    if(MiddleIsLeft)
    {
        mLeft = (Top.x - Middle.x) / (Top.y - Middle.y);
        mRight = (Top.x - Bottom.x) / (Top.y - Bottom.y);
    }
    else
    {
        mLeft = (Top.x - Bottom.x) / (Top.y - Bottom.y);
        mRight = (Middle.x - Top.x) / (Middle.y - Top.y);
    }
    int finalY;
    float Tleft, Tright;
    for (int y = ceil(Top.y); y < (int)Middle.y; y++)
    {        
        Tleft=float(Top.y-y)/(Top.y-Middle.y);
        Tright=float(Top.y-y)/(Top.y-Bottom.y);
        for (int x = ceil(xLeft); x <= ceil(xRight) - 1 ; x++)
        {
            FrameBuffer::SetPixel(x, y, p0.r,p0.g,p0.b);

        }  
        xLeft += mLeft;
        xRight += mRight;
        finalY = y;
    }

    // Region 2 
    if (MiddleIsLeft)
    {
        mLeft = (Bottom.x - Middle.x) / (Bottom.y - Middle.y);
    }
    else
    {
        mRight = (Middle.x - Bottom.x) / (Middle.y - Bottom.y);
    }

    for (int y = Middle.y; y <= ceil(Bottom.y) - 1; y++)
    {
        Tleft=float(Bottom.y-y)/(Bottom.y-Middle.y);
        Tright=float(Top.y-y)/(Top.y-Bottom.y);
        for (int x = ceil(xLeft); x <= ceil(xRight) - 1; x++)
        {
            FrameBuffer::SetPixel(x, y, p0.r,p0.g,p0.b);
        }
        xLeft += mLeft;
        xRight += mRight; 

    }
}

Here is what happens when I use it to draw shapes.

When I disable the second region, all those weird triangles disappear.

The wireframe mode works perfect, so this eliminates all the other possibilities other than the triangle rasterizer.

回答1:

I kind of got lost in your implementation, but here's what I do (I have a slightly more complex version for arbitrary convex polygons, not just triangles) and I think apart from the Bresenham's algorithm it's very simple (actually the algorithm is simple too):

#include <stddef.h>
#include <limits.h>
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <time.h>

#define SCREEN_HEIGHT 22
#define SCREEN_WIDTH  78

// Simulated frame buffer
char Screen[SCREEN_HEIGHT][SCREEN_WIDTH];

void SetPixel(long x, long y, char color)
{
  if ((x < 0) || (x >= SCREEN_WIDTH) ||
      (y < 0) || (y >= SCREEN_HEIGHT))
  {
    return;
  }

  Screen[y][x] = color;
}

void Visualize(void)
{
  long x, y;

  for (y = 0; y < SCREEN_HEIGHT; y++)
  {
    for (x = 0; x < SCREEN_WIDTH; x++)
    {
      printf("%c", Screen[y][x]);
    }

    printf("\n");
  }
}

typedef struct
{
  long x, y;
  unsigned char color;
} Point2D;


// min X and max X for every horizontal line within the triangle
long ContourX[SCREEN_HEIGHT][2];

#define ABS(x) ((x >= 0) ? x : -x)

// Scans a side of a triangle setting min X and max X in ContourX[][]
// (using the Bresenham's line drawing algorithm).
void ScanLine(long x1, long y1, long x2, long y2)
{
  long sx, sy, dx1, dy1, dx2, dy2, x, y, m, n, k, cnt;

  sx = x2 - x1;
  sy = y2 - y1;

  if (sx > 0) dx1 = 1;
  else if (sx < 0) dx1 = -1;
  else dx1 = 0;

  if (sy > 0) dy1 = 1;
  else if (sy < 0) dy1 = -1;
  else dy1 = 0;

  m = ABS(sx);
  n = ABS(sy);
  dx2 = dx1;
  dy2 = 0;

  if (m < n)
  {
    m = ABS(sy);
    n = ABS(sx);
    dx2 = 0;
    dy2 = dy1;
  }

  x = x1; y = y1;
  cnt = m + 1;
  k = n / 2;

  while (cnt--)
  {
    if ((y >= 0) && (y < SCREEN_HEIGHT))
    {
      if (x < ContourX[y][0]) ContourX[y][0] = x;
      if (x > ContourX[y][1]) ContourX[y][1] = x;
    }

    k += n;
    if (k < m)
    {
      x += dx2;
      y += dy2;
    }
    else
    {
      k -= m;
      x += dx1;
      y += dy1;
    }
  }
}

void DrawTriangle(Point2D p0, Point2D p1, Point2D p2)
{
  int y;

  for (y = 0; y < SCREEN_HEIGHT; y++)
  {
    ContourX[y][0] = LONG_MAX; // min X
    ContourX[y][1] = LONG_MIN; // max X
  }

  ScanLine(p0.x, p0.y, p1.x, p1.y);
  ScanLine(p1.x, p1.y, p2.x, p2.y);
  ScanLine(p2.x, p2.y, p0.x, p0.y);

  for (y = 0; y < SCREEN_HEIGHT; y++)
  {
    if (ContourX[y][1] >= ContourX[y][0])
    {
      long x = ContourX[y][0];
      long len = 1 + ContourX[y][1] - ContourX[y][0];

      // Can draw a horizontal line instead of individual pixels here
      while (len--)
      {
        SetPixel(x++, y, p0.color);
      }
    }
  }
}

int main(void)
{
  Point2D p0, p1, p2;

  // clear the screen
  memset(Screen, ' ', sizeof(Screen));

  // generate random triangle coordinates
  srand((unsigned)time(NULL));

  p0.x = rand() % SCREEN_WIDTH;
  p0.y = rand() % SCREEN_HEIGHT;

  p1.x = rand() % SCREEN_WIDTH;
  p1.y = rand() % SCREEN_HEIGHT;

  p2.x = rand() % SCREEN_WIDTH;
  p2.y = rand() % SCREEN_HEIGHT;

  // draw the triangle
  p0.color = '1';
  DrawTriangle(p0, p1, p2);

  // also draw the triangle's vertices
  SetPixel(p0.x, p0.y, '*');
  SetPixel(p1.x, p1.y, '*');
  SetPixel(p2.x, p2.y, '*');

  Visualize();

  return 0;
}

Output:

   *111111
    1111111111111
      111111111111111111
         1111111111111111111111
           111111111111111111111111111
             11111111111111111111111111111111
                111111111111111111111111111111111111
                  11111111111111111111111111111111111111111
                    111111111111111111111111111111111111111*
                       11111111111111111111111111111111111
                         1111111111111111111111111111111
                            111111111111111111111111111
                              11111111111111111111111
                                1111111111111111111
                                   11111111111111
                                     11111111111
                                       1111111
                                          1*

回答2:

The original code will only work properly with triangles that have counter-clockwise winding because of the if-else statements on top that determines whether middle is left or right. It could be that the triangles which aren't drawing have the wrong winding.

This stack overflow shows how to Determine winding of a 2D triangles after triangulation

The original code is fast because it doesn't save the points of the line in a temporary memory buffer. Seems a bit over-complicated even given that, but that's another problem.