## 14. Bezier Curve

<<funcdefs>>=
``````void btprnt_draw_bezier(btprnt_region *reg,
int x0, int y0,
int x1, int y1,
int x2, int y2,
int c);``````
<<funcs>>=
``````<<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);
}``````
<<draw_bezier_seg>>=
``````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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