a

libmemdraw/ellipse.c

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+#include <u.h>
+#include <libc.h>
+#include <draw.h>
+#include <memdraw.h>
+#include <memlayer.h>
+
+/*
+ * ellipse(dst, c, a, b, t, src, sp)
+ *   draws an ellipse centered at c with semiaxes a,b>=0
+ *   and semithickness t>=0, or filled if t<0.  point sp
+ *   in src maps to c in dst
+ *
+ *   very thick skinny ellipses are brushed with circles (slow)
+ *   others are approximated by filling between 2 ellipses
+ *   criterion for very thick when b<a: t/b > 0.5*x/(1-x)
+ *   where x = b/a
+ */
+
+typedef struct Param	Param;
+typedef struct State	State;
+
+static	void	bellipse(int, State*, Param*);
+static	void	erect(int, int, int, int, Param*);
+static	void	eline(int, int, int, int, Param*);
+
+struct Param {
+	Memimage	*dst;
+	Memimage	*src;
+	Point			c;
+	int			t;
+	Point			sp;
+	Memimage	*disc;
+	int			op;
+};
+
+/*
+ * denote residual error by e(x,y) = b^2*x^2 + a^2*y^2 - a^2*b^2
+ * e(x,y) = 0 on ellipse, e(x,y) < 0 inside, e(x,y) > 0 outside
+ */
+
+struct State {
+	int	a;
+	int	x;
+	vlong	a2;	/* a^2 */
+	vlong	b2;	/* b^2 */
+	vlong	b2x;	/* b^2 * x */
+	vlong	a2y;	/* a^2 * y */
+	vlong	c1;
+	vlong	c2;	/* test criteria */
+	vlong	ee;	/* ee = e(x+1/2,y-1/2) - (a^2+b^2)/4 */
+	vlong	dxe;
+	vlong	dye;
+	vlong	d2xe;
+	vlong	d2ye;
+};
+
+static
+State*
+newstate(State *s, int a, int b)
+{
+	s->x = 0;
+	s->a = a;
+	s->a2 = (vlong)(a*a);
+	s->b2 = (vlong)(b*b);
+	s->b2x = (vlong)0;
+	s->a2y = s->a2*(vlong)b;
+	s->c1 = -((s->a2>>2) + (vlong)(a&1) + s->b2);
+	s->c2 = -((s->b2>>2) + (vlong)(b&1));
+	s->ee = -s->a2y;
+	s->dxe = (vlong)0;
+	s->dye = s->ee<<1;
+	s->d2xe = s->b2<<1;
+	s->d2ye = s->a2<<1;
+	return s;
+}
+
+/*
+ * return x coord of rightmost pixel on next scan line
+ */
+static
+int
+step(State *s)
+{
+	while(s->x < s->a) {
+		if(s->ee+s->b2x <= s->c1 ||	/* e(x+1,y-1/2) <= 0 */
+		   s->ee+s->a2y <= s->c2) {	/* e(x+1/2,y) <= 0 (rare) */
+			s->dxe += s->d2xe;	  
+			s->ee += s->dxe;	  
+			s->b2x += s->b2;
+			s->x++;	  
+			continue;
+		}
+		s->dye += s->d2ye;	  
+		s->ee += s->dye;	  
+		s->a2y -= s->a2;
+		if(s->ee-s->a2y <= s->c2) {	/* e(x+1/2,y-1) <= 0 */
+			s->dxe += s->d2xe;	  
+			s->ee += s->dxe;	  
+			s->b2x += s->b2;
+			return s->x++;
+		}
+		break;
+	}
+	return s->x;	  
+}
+
+void
+memellipse(Memimage *dst, Point c, int a, int b, int t, Memimage *src, Point sp, int op)
+{
+	State in, out;
+	int y, inb, inx, outx, u;
+	Param p;
+
+	if(a < 0)
+		a = -a;
+	if(b < 0)
+		b = -b;
+	p.dst = dst;
+	p.src = src;
+	p.c = c;
+	p.t = t;
+	p.sp = subpt(sp, c);
+	p.disc = nil;
+	p.op = op;
+
+	u = (t<<1)*(a-b);
+	if(b<a && u>b*b || a<b && -u>a*a) {
+/*	if(b<a&&(t<<1)>b*b/a || a<b&&(t<<1)>a*a/b)	# very thick */
+		bellipse(b, newstate(&in, a, b), &p);
+		return;
+	}
+
+	if(t < 0) {
+		inb = -1;
+		newstate(&out, a, y = b);
+	} else {	
+		inb = b - t;
+		newstate(&out, a+t, y = b+t);
+	}
+	if(t > 0)
+		newstate(&in, a-t, inb);
+	inx = 0;
+	for( ; y>=0; y--) {
+		outx = step(&out);
+		if(y > inb) {
+			erect(-outx, y, outx, y, &p);
+			if(y != 0)
+				erect(-outx, -y, outx, -y, &p);
+			continue;
+		}
+		if(t > 0) {
+			inx = step(&in);
+			if(y == inb)
+				inx = 0;
+		} else if(inx > outx)
+			inx = outx;
+		erect(inx, y, outx, y, &p);
+		if(y != 0)
+			erect(inx, -y, outx, -y, &p);
+		erect(-outx, y, -inx, y, &p);
+		if(y != 0)
+			erect(-outx, -y, -inx, -y, &p);
+		inx = outx + 1;
+	}
+}
+
+static Point p00 = {0, 0};
+
+/*
+ * a brushed ellipse
+ */
+static
+void
+bellipse(int y, State *s, Param *p)
+{
+	int t, ox, oy, x, nx;
+
+	t = p->t;
+	p->disc = allocmemimage(Rect(-t,-t,t+1,t+1), GREY1);
+	if(p->disc == nil)
+		return;
+	memfillcolor(p->disc, DTransparent);
+	memellipse(p->disc, p00, t, t, -1, memopaque, p00, p->op);
+	oy = y;
+	ox = 0;
+	nx = x = step(s);
+	do {
+		while(nx==x && y-->0)
+			nx = step(s);
+		y++;
+		eline(-x,-oy,-ox, -y, p);
+		eline(ox,-oy,  x, -y, p);
+		eline(-x,  y,-ox, oy, p);
+		eline(ox,  y,  x, oy, p);
+		ox = x+1;
+		x = nx;
+		y--;
+		oy = y;
+	} while(oy > 0);
+}
+
+/*
+ * a rectangle with closed (not half-open) coordinates expressed
+ * relative to the center of the ellipse
+ */
+static
+void
+erect(int x0, int y0, int x1, int y1, Param *p)
+{
+	Rectangle r;
+
+/*	print("R %d,%d %d,%d\n", x0, y0, x1, y1); /**/
+	r = Rect(p->c.x+x0, p->c.y+y0, p->c.x+x1+1, p->c.y+y1+1);
+	memdraw(p->dst, r, p->src, addpt(p->sp, r.min), memopaque, p00, p->op);
+}
+
+/*
+ * a brushed point similarly specified
+ */
+static
+void
+epoint(int x, int y, Param *p)
+{
+	Point p0;
+	Rectangle r;
+
+/*	print("P%d %d,%d\n", p->t, x, y);	/**/
+	p0 = Pt(p->c.x+x, p->c.y+y);
+	r = Rpt(addpt(p0, p->disc->r.min), addpt(p0, p->disc->r.max));
+	memdraw(p->dst, r, p->src, addpt(p->sp, r.min), p->disc, p->disc->r.min, p->op);
+}
+
+/* 
+ * a brushed horizontal or vertical line similarly specified
+ */
+static
+void
+eline(int x0, int y0, int x1, int y1, Param *p)
+{
+/*	print("L%d %d,%d %d,%d\n", p->t, x0, y0, x1, y1); /**/
+	if(x1 > x0+1)
+		erect(x0+1, y0-p->t, x1-1, y1+p->t, p);
+	else if(y1 > y0+1)
+		erect(x0-p->t, y0+1, x1+p->t, y1-1, p);
+	epoint(x0, y0, p);
+	if(x1-x0 || y1-y0)
+		epoint(x1, y1, p);
+}