1 #include <u.h>
2 #include <libc.h>
3 #include <draw.h>
4 #include <memdraw.h>
5 #include <memlayer.h>
6
7 /*
8 * ellipse(dst, c, a, b, t, src, sp)
9 * draws an ellipse centered at c with semiaxes a,b>=0
10 * and semithickness t>=0, or filled if t<0. point sp
11 * in src maps to c in dst
12 *
13 * very thick skinny ellipses are brushed with circles (slow)
14 * others are approximated by filling between 2 ellipses
15 * criterion for very thick when b<a: t/b > 0.5*x/(1-x)
16 * where x = b/a
17 */
18
19 typedef struct Param Param;
20 typedef struct State State;
21
22 static void bellipse(int, State*, Param*);
23 static void erect(int, int, int, int, Param*);
24 static void eline(int, int, int, int, Param*);
25
26 struct Param {
27 Memimage *dst;
28 Memimage *src;
29 Point c;
30 int t;
31 Point sp;
32 Memimage *disc;
33 int op;
34 };
35
36 /*
37 * denote residual error by e(x,y) = b^2*x^2 + a^2*y^2 - a^2*b^2
38 * e(x,y) = 0 on ellipse, e(x,y) < 0 inside, e(x,y) > 0 outside
39 */
40
41 struct State {
42 int a;
43 int x;
44 vlong a2; /* a^2 */
45 vlong b2; /* b^2 */
46 vlong b2x; /* b^2 * x */
47 vlong a2y; /* a^2 * y */
48 vlong c1;
49 vlong c2; /* test criteria */
50 vlong ee; /* ee = e(x+1/2,y-1/2) - (a^2+b^2)/4 */
51 vlong dxe;
52 vlong dye;
53 vlong d2xe;
54 vlong d2ye;
55 };
56
57 static
58 State*
newstate(State * s,int a,int b)59 newstate(State *s, int a, int b)
60 {
61 s->x = 0;
62 s->a = a;
63 s->a2 = (vlong)(a*a);
64 s->b2 = (vlong)(b*b);
65 s->b2x = (vlong)0;
66 s->a2y = s->a2*(vlong)b;
67 s->c1 = -((s->a2>>2) + (vlong)(a&1) + s->b2);
68 s->c2 = -((s->b2>>2) + (vlong)(b&1));
69 s->ee = -s->a2y;
70 s->dxe = (vlong)0;
71 s->dye = s->ee<<1;
72 s->d2xe = s->b2<<1;
73 s->d2ye = s->a2<<1;
74 return s;
75 }
76
77 /*
78 * return x coord of rightmost pixel on next scan line
79 */
80 static
81 int
step(State * s)82 step(State *s)
83 {
84 while(s->x < s->a) {
85 if(s->ee+s->b2x <= s->c1 || /* e(x+1,y-1/2) <= 0 */
86 s->ee+s->a2y <= s->c2) { /* e(x+1/2,y) <= 0 (rare) */
87 s->dxe += s->d2xe;
88 s->ee += s->dxe;
89 s->b2x += s->b2;
90 s->x++;
91 continue;
92 }
93 s->dye += s->d2ye;
94 s->ee += s->dye;
95 s->a2y -= s->a2;
96 if(s->ee-s->a2y <= s->c2) { /* e(x+1/2,y-1) <= 0 */
97 s->dxe += s->d2xe;
98 s->ee += s->dxe;
99 s->b2x += s->b2;
100 return s->x++;
101 }
102 break;
103 }
104 return s->x;
105 }
106
107 void
memellipse(Memimage * dst,Point c,int a,int b,int t,Memimage * src,Point sp,int op)108 memellipse(Memimage *dst, Point c, int a, int b, int t, Memimage *src, Point sp, int op)
109 {
110 State in, out;
111 int y, inb, inx, outx, u;
112 Param p;
113
114 if(a < 0)
115 a = -a;
116 if(b < 0)
117 b = -b;
118 p.dst = dst;
119 p.src = src;
120 p.c = c;
121 p.t = t;
122 p.sp = subpt(sp, c);
123 p.disc = nil;
124 p.op = op;
125
126 u = (t<<1)*(a-b);
127 if((b<a && u>b*b) || (a<b && -u>a*a)) {
128 /* if(b<a&&(t<<1)>b*b/a || a<b&&(t<<1)>a*a/b) # very thick */
129 bellipse(b, newstate(&in, a, b), &p);
130 return;
131 }
132
133 if(t < 0) {
134 inb = -1;
135 newstate(&out, a, y = b);
136 } else {
137 inb = b - t;
138 newstate(&out, a+t, y = b+t);
139 }
140 if(t > 0)
141 newstate(&in, a-t, inb);
142 inx = 0;
143 for( ; y>=0; y--) {
144 outx = step(&out);
145 if(y > inb) {
146 erect(-outx, y, outx, y, &p);
147 if(y != 0)
148 erect(-outx, -y, outx, -y, &p);
149 continue;
150 }
151 if(t > 0) {
152 inx = step(&in);
153 if(y == inb)
154 inx = 0;
155 } else if(inx > outx)
156 inx = outx;
157 erect(inx, y, outx, y, &p);
158 if(y != 0)
159 erect(inx, -y, outx, -y, &p);
160 erect(-outx, y, -inx, y, &p);
161 if(y != 0)
162 erect(-outx, -y, -inx, -y, &p);
163 inx = outx + 1;
164 }
165 }
166
167 static Point p00 = {0, 0};
168
169 /*
170 * a brushed ellipse
171 */
172 static
173 void
bellipse(int y,State * s,Param * p)174 bellipse(int y, State *s, Param *p)
175 {
176 int t, ox, oy, x, nx;
177
178 t = p->t;
179 p->disc = allocmemimage(Rect(-t,-t,t+1,t+1), GREY1);
180 if(p->disc == nil)
181 return;
182 memfillcolor(p->disc, DTransparent);
183 memellipse(p->disc, p00, t, t, -1, memopaque, p00, p->op);
184 oy = y;
185 ox = 0;
186 nx = x = step(s);
187 do {
188 while(nx==x && y-->0)
189 nx = step(s);
190 y++;
191 eline(-x,-oy,-ox, -y, p);
192 eline(ox,-oy, x, -y, p);
193 eline(-x, y,-ox, oy, p);
194 eline(ox, y, x, oy, p);
195 ox = x+1;
196 x = nx;
197 y--;
198 oy = y;
199 } while(oy > 0);
200 }
201
202 /*
203 * a rectangle with closed (not half-open) coordinates expressed
204 * relative to the center of the ellipse
205 */
206 static
207 void
erect(int x0,int y0,int x1,int y1,Param * p)208 erect(int x0, int y0, int x1, int y1, Param *p)
209 {
210 Rectangle r;
211
212 /* print("R %d,%d %d,%d\n", x0, y0, x1, y1); */
213 r = Rect(p->c.x+x0, p->c.y+y0, p->c.x+x1+1, p->c.y+y1+1);
214 memdraw(p->dst, r, p->src, addpt(p->sp, r.min), memopaque, p00, p->op);
215 }
216
217 /*
218 * a brushed point similarly specified
219 */
220 static
221 void
epoint(int x,int y,Param * p)222 epoint(int x, int y, Param *p)
223 {
224 Point p0;
225 Rectangle r;
226
227 /* print("P%d %d,%d\n", p->t, x, y); */
228 p0 = Pt(p->c.x+x, p->c.y+y);
229 r = Rpt(addpt(p0, p->disc->r.min), addpt(p0, p->disc->r.max));
230 memdraw(p->dst, r, p->src, addpt(p->sp, r.min), p->disc, p->disc->r.min, p->op);
231 }
232
233 /*
234 * a brushed horizontal or vertical line similarly specified
235 */
236 static
237 void
eline(int x0,int y0,int x1,int y1,Param * p)238 eline(int x0, int y0, int x1, int y1, Param *p)
239 {
240 /* print("L%d %d,%d %d,%d\n", p->t, x0, y0, x1, y1); */
241 if(x1 > x0+1)
242 erect(x0+1, y0-p->t, x1-1, y1+p->t, p);
243 else if(y1 > y0+1)
244 erect(x0-p->t, y0+1, x1+p->t, y1-1, p);
245 epoint(x0, y0, p);
246 if(x1-x0 || y1-y0)
247 epoint(x1, y1, p);
248 }
249