Algorithm to fill triangle

问题

i'm thinking about rasterization triangle algorithm. ( triangle_rasterization_lesson )

I wtote the following code:

void triangle(int xa, int ya, int xb, int yb, int xc, int yc, TGAImage &image, TGAColor color)
{
    line(xa, ya, xb, yb, image, color);
    line(xa, ya, xc, yc, image, color);
    line(xb, yb, xc, yc, image, color);
    for (int x = xa; x<=xb; x++)
    {
        for (int y = ya; y<=yb; y++)
        {
            line(xc, yc, x, y, image, white);
        }
    }
}

With triangle(100, 100, 100, 400, 400, 100, image, red); it works properly. But if i swap X(xa, ya) and Z(xc, yc) coordinates to doesn't fill my square.

With triangle(70, 50, 200, 100, 20, 150, image, red); it draws triangle, but filling comes out of bounds.

Where is the problem?

回答1:

if it helps a bit here is my ancient C++ source for triangle in VCL/GDI:

//---------------------------------------------------------------------------
class gfx_main
    {
public:
    Graphics::TBitmap *bmp;
    int **pyx,xs,ys;
    gfx_main();
    ~gfx_main();
    void resize(int _xs=-1,int _ys=-1);

    void troj(int x0,int y0,int x1,int y1,int x2,int y2,int col); // this is filled triangle
    void _troj_line(int *pl,int *pr,int x0,int y0,int x1,int y1); // this is just subroutine
    };
//---------------------------------------------------------------------------
gfx_main::gfx_main()
    {
    bmp=new Graphics::TBitmap;
    pyx=NULL;
    resize(1,1);
    }
//---------------------------------------------------------------------------
gfx_main::~gfx_main()
    {
    delete bmp;
    if (pyx) delete[] pyx;
    }
//---------------------------------------------------------------------------
void gfx_main::resize(int _xs,int _ys)
    {
    if (pyx) delete[] pyx;
    if ((_xs>0)&&(_ys>0)) { bmp->Width=_xs; bmp->Height=_ys; }
    xs=bmp->Width;
    ys=bmp->Height;
    bmp->HandleType=bmDIB;
    bmp->PixelFormat=pf32bit;
    pyx=new int*[ys];
    for (int y=0;y<ys;y++) pyx[y]=(int*)bmp->ScanLine[y];
    }
//---------------------------------------------------------------------------
//--- rasterisations: -------------------------------------------------------
//---------------------------------------------------------------------------
void gfx_main::_troj_line(int *pl,int *pr,int x0,int y0,int x1,int y1)
    {
    int *pp;
    int x,y,kx,ky,dx,dy,k,m,p;
    // DDA variables (d)abs delta,(k)step direction
    kx=0; dx=x1-x0; if (dx>0) kx=+1;  if (dx<0) { kx=-1; dx=-dx; }
    ky=0; dy=y1-y0; if (dy>0) ky=+1;  if (dy<0) { ky=-1; dy=-dy; }
    // target buffer according to ky direction
    if (ky>0) pp=pl; else pp=pr;
    // integer DDA line start point
    x=x0; y=y0;
    // fix endpoints just to be sure (wrong division constants by +/-1 can cause that last point is missing)
    pp[y1]=x1; pp[y0]=x0;
    if (dx>=dy) // x axis is major
        {
        k=dy+dy;
        m=(dy-dx); m+=m;
        p=m;
        for (;;)
            {
            pp[y]=x;
            if (x==x1) break;
            x+=kx;
            if (p>0) { y+=ky; p+=m; } else p+=k;
            }
        }
    else{       // y axis is major
        k=dx+dx;
        m=(dx-dy); m+=m;
        p=m;
        for (;;)
            {
            pp[y]=x;
            if (y==y1) break;
            y+=ky;
            if (p>0) { x+=kx; p+=m; } else p+=k;
            }
        }
    }
//---------------------------------------------------------------------------
int rgb2bgr(int col)
    {
    union
        {
        BYTE db[4];
        int  dd;
        } c;
    BYTE q;
    c.dd=col;
    q=c.db[0]; c.db[0]=c.db[2]; c.db[2]=q;
    return c.dd;
    }
//---------------------------------------------------------------------------
void gfx_main::troj(int x0,int y0,int x1,int y1,int x2,int y2,int col)
    {
    col=rgb2bgr(col);
    int *pl,*pr;        // left/right buffers
    pl=new int[ys];
    pr=new int[ys];
    int x,y,yy0,yy1,xx0,xx1;
    // boundary line coordinates to buffers
    _troj_line(pl,pr,x0,y0,x1,y1);
    _troj_line(pl,pr,x1,y1,x2,y2);
    _troj_line(pl,pr,x2,y2,x0,y0);
    // y range
    yy0=y0; if (yy0>y1) yy0=y1; if (yy0>y2) yy0=y2;
    yy1=y0; if (yy1<y1) yy1=y1; if (yy1<y2) yy1=y2;
    // fill with horizontal lines
    for (y=yy0;y<=yy1;y++)
        {
        if (pl[y]<pr[y]) { xx0=pl[y]; xx1=pr[y]; }
        else             { xx1=pl[y]; xx0=pr[y]; }
        for (x=xx0;x<=xx1;x++)
         pyx[y][x]=col;
        }
    delete[] pl;
    delete[] pr;
    }
//---------------------------------------------------------------------------

example usage:

// init
gfx_main gfx;
gfx.resize(640,480);
// clear screen
TCanvas *scr=gfx.bmp->Canvas;
scr->Pen  ->Color=clAqua;
scr->Font ->Color=clYellow;
scr->Brush->Color=clBlack;
scr->FillRect(TRect(0,0,xs,ys));
// triangle    
troj(10,10,120,60,70,100,clAqua);
// here gfx.bmp holds the rendered image ...    

Source is based on this:

• how to rasterize rotated rectangle (in 2d by setpixel)
• Display an array of color in C

回答2:

Your are increasing x and y one every loop. But you can't do this for every triangle. Depend on triangle angle when x increasing , maybe y decreasing. For example if triangle has 90 degree, you will not increase x or y. I can't explain myself very well but there is code and imaged explanation:

http://www.sunshine2k.de/coding/java/TriangleRasterization/TriangleRasterization.html

来源：https://stackoverflow.com/questions/39038505/algorithm-to-fill-triangle