14. Bezier Curve

Adapted from the bresenham bezier found at this page, as well as this stackoverflow post

void btprnt_draw_bezier(btprnt_region *reg,
                        int x0, int y0,
                        int x1, int y1,
                        int x2, int y2,
                        int c);

<<draw_bezier_seg>>
void btprnt_draw_bezier(btprnt_region *reg,
                        int x0, int y0,
                        int x1, int y1,
                        int x2, int y2,
                        int c)
{
    int x, y;
    double t, r;

    x = x0-x1;
    y = y0-y1;
    t = x0-2*x1+x2;

    if ((long)x*(x2-x1) > 0) {
        if ((long)y*(y2-y1) > 0)
            if (fabs((y0-2*y1+y2)/t*x) > abs(y)) {
                x0 = x2; x2 = x+x1; y0 = y2; y2 = y+y1;
            }
        t = (x0-x1)/t;
        r = (1-t)*((1-t)*y0+2.0*t*y1)+t*t*y2;
        t = (x0*x2-x1*x1)*t/(x0-x1);
        x = floor(t+0.5); y = floor(r+0.5);
        r = (y1-y0)*(t-x0)/(x1-x0)+y0;
        bezierseg(reg, x0, y0, x, floor(r+0.5), x, y, c);
        r = (y1-y2)*(t-x2)/(x1-x2)+y2;
        x0 = x1 = x; y0 = y; y1 = floor(r+0.5);
    }

    if ((long)(y0-y1)*(y2-y1) > 0) {
        t = y0-2*y1+y2; t = (y0-y1)/t;
        r = (1-t)*((1-t)*x0+2.0*t*x1)+t*t*x2;
        t = (y0*y2-y1*y1)*t/(y0-y1);
        x = floor(r+0.5); y = floor(t+0.5);
        r = (x1-x0)*(t-y0)/(y1-y0)+x0;
        bezierseg(reg, x0, y0, floor(r+0.5), y, x, y, c);
        r = (x1-x2)*(t-y2)/(y1-y2)+x2;
        x0 = x; x1 = floor(r+0.5); y0 = y1 = y;
    }

    bezierseg(reg, x0, y0, x1, y1, x2, y2, c);
}

static void bezierseg(btprnt_region *r,
                      int x0, int y0,
                      int x1, int y1,
                      int x2, int y2,
                      int c)
{
    int sx, sy;
    long xx, yy, xy;
    double dx, dy, err, cur;
    int rc;

    sx = x2-x1;
    sy = y2-y1;
    xx = x0-x1;
    yy = y0-y1;

    cur = xx*sy-yy*sx;

    rc = xx*sx <= 0 && yy*sy <= 0;

    if (!rc) return;

    if (sx*(long)sx+sy*(long)sy > xx*xx+yy*yy) {
        x2 = x0;
        x0 = sx+x1;
        y2 = y0;
        y0 = sy+y1;
        cur = -cur;
    }

    if (cur != 0) {
        xx += sx;
        xx *= sx = x0 < x2 ? 1 : -1;

        yy += sy;
        yy *= sy = y0 < y2 ? 1 : -1;

        xy = 2*xx*yy;
        xx *= xx;
        yy *= yy;

        if (cur*sx*sy < 0) {
            xx = -xx;
            yy = -yy;
            xy = -xy;
            cur = -cur;
        }

        dx = 4.0*sy*cur*(x1-x0)+xx-xy;
        dy = 4.0*sx*cur*(y0-y1)+yy-xy;

        xx += xx;
        yy += yy;
        err = dx+dy+xy;

        do {
            btprnt_region_draw(r, x0, y0, c);

            if (x0 == x2 && y0 == y2) return;

            y1 = 2*err < dx;

            if (2*err > dy) {
                x0 += sx;
                dx -= xy;
                err += dy += yy;
            }

            if (y1) {
                y0 += sy;
                dy -= xy;
                err += dx += xx;
            }
        } while (dy < dx );
    }

    btprnt_draw_line(r, x0, y0, x2, y2, c);
}

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