2 // Copyright 2004 Adam Megacz, see the COPYING file for licensing [GPL]
3 package org.ibex.graphics;
6 /** an abstract path; may contain splines and arcs */
9 public static final float PX_PER_INCH = 72;
10 public static final float INCHES_PER_CM = (float)0.3937;
11 public static final float INCHES_PER_MM = INCHES_PER_CM / 10;
12 private static final int DEFAULT_PATHLEN = 1000;
13 private static final float PI = (float)Math.PI;
15 // the number of vertices on this path
18 // the vertices of the path
19 float[] x = new float[DEFAULT_PATHLEN];
20 float[] y = new float[DEFAULT_PATHLEN];
22 // the type of each edge; type[i] is the type of the edge from x[i],y[i] to x[i+1],y[i+1]
23 byte[] type = new byte[DEFAULT_PATHLEN];
25 // bezier control points
26 float[] c1x = new float[DEFAULT_PATHLEN]; // or rx (arcto)
27 float[] c1y = new float[DEFAULT_PATHLEN]; // or ry (arcto)
28 float[] c2x = new float[DEFAULT_PATHLEN]; // or x-axis-rotation (arcto)
29 float[] c2y = new float[DEFAULT_PATHLEN]; // or large-arc << 1 | sweep (arcto)
31 boolean closed = false;
33 static final byte TYPE_MOVETO = 0;
34 static final byte TYPE_LINETO = 1;
35 static final byte TYPE_ARCTO = 2;
36 static final byte TYPE_CUBIC = 3;
37 static final byte TYPE_QUADRADIC = 4;
39 public static Path parse(String s) { return Tokenizer.parse(s); }
42 private String toString;
43 private Path(String s) { this.toString = s; }
44 public String toString() { return toString; }
46 public static class Tokenizer {
47 // FIXME: check array bounds exception for improperly terminated string
50 char lastCommand = 'M';
51 public Tokenizer(String s) { this.s = s; }
53 public static Path parse(String s) {
54 if (s == null) return null;
55 Tokenizer t = new Tokenizer(s);
56 Path ret = new Path(s);
57 char last_command = 'M';
59 while(t.hasMoreTokens()) {
60 char command = t.parseCommand();
61 if (first && command != 'M') throw new RuntimeException("the first command of a path must be 'M'");
63 boolean relative = Character.toLowerCase(command) == command;
64 command = Character.toLowerCase(command);
65 ret.parseSingleCommandAndArguments(t, command, relative);
66 last_command = command;
71 private void consumeWhitespace() {
72 while(i < s.length() && (Character.isWhitespace(s.charAt(i)))) i++;
73 if (i < s.length() && s.charAt(i) == ',') i++;
74 while(i < s.length() && (Character.isWhitespace(s.charAt(i)))) i++;
76 public boolean hasMoreTokens() { consumeWhitespace(); return i < s.length(); }
77 public char parseCommand() {
80 if (!Character.isLetter(c)) return lastCommand;
82 return lastCommand = c;
84 public float parseFloat() {
88 for(; i < s.length(); i++) {
90 if (Character.isWhitespace(c) || c == ',' || (c == '-' && i != start)) break;
91 if (!((c >= '0' && c <= '9') || c == '.' || c == 'e' || c == 'E' || c == '-')) {
92 if (c == '%') { // FIXME
93 } else if (s.regionMatches(i, "pt", 0, i+2)) { // FIXME
94 } else if (s.regionMatches(i, "em", 0, i+2)) { // FIXME
95 } else if (s.regionMatches(i, "pc", 0, i+2)) { // FIXME
96 } else if (s.regionMatches(i, "ex", 0, i+2)) { // FIXME
97 } else if (s.regionMatches(i, "mm", 0, i+2)) { i += 2; multiplier = INCHES_PER_MM * PX_PER_INCH; break;
98 } else if (s.regionMatches(i, "cm", 0, i+2)) { i += 2; multiplier = INCHES_PER_CM * PX_PER_INCH; break;
99 } else if (s.regionMatches(i, "in", 0, i+2)) { i += 2; multiplier = PX_PER_INCH; break;
100 } else if (s.regionMatches(i, "px", 0, i+2)) { i += 2; break;
101 } else if (Character.isLetter(c)) break;
102 throw new RuntimeException("didn't expect character \"" + c + "\" in a numeric constant");
105 if (start == i) throw new RuntimeException("FIXME");
106 return Float.parseFloat(s.substring(start, i)) * multiplier;
110 /** Creates a concrete vector path transformed through the given matrix. */
111 public Raster realize(Affine a) {
113 Raster ret = new Raster();
114 int NUMSTEPS = 5; // FIXME
116 ret.x[0] = (int)Math.round(a.multiply_px(x[0], y[0]));
117 ret.y[0] = (int)Math.round(a.multiply_py(x[0], y[0]));
119 for(int i=1; i<numvertices; i++) {
120 if (type[i] == TYPE_LINETO) {
123 ret.x[ret.numvertices] = (int)Math.round(a.multiply_px(rx, ry));
124 ret.y[ret.numvertices] = (int)Math.round(a.multiply_py(rx, ry));
125 ret.edges[ret.numedges++] = ret.numvertices - 1; ret.numvertices++;
127 } else if (type[i] == TYPE_MOVETO) {
130 ret.x[ret.numvertices] = (int)Math.round(a.multiply_px(rx, ry));
131 ret.y[ret.numvertices] = (int)Math.round(a.multiply_py(rx, ry));
134 } else if (type[i] == TYPE_ARCTO) {
138 float fa = ((int)c2y[i]) >> 1;
139 float fs = ((int)c2y[i]) & 1;
145 // F.6.5: given x1,y1,x2,y2,fa,fs, compute cx,cy,theta1,dtheta
146 float x1_ = (float)Math.cos(phi) * (x1 - x2) / 2 + (float)Math.sin(phi) * (y1 - y2) / 2;
147 float y1_ = -1 * (float)Math.sin(phi) * (x1 - x2) / 2 + (float)Math.cos(phi) * (y1 - y2) / 2;
148 float tmp = (float)Math.sqrt((rx * rx * ry * ry - rx * rx * y1_ * y1_ - ry * ry * x1_ * x1_) /
149 (rx * rx * y1_ * y1_ + ry * ry * x1_ * x1_));
150 float cx_ = (fa == fs ? -1 : 1) * tmp * (rx * y1_ / ry);
151 float cy_ = (fa == fs ? -1 : 1) * -1 * tmp * (ry * x1_ / rx);
152 float cx = (float)Math.cos(phi) * cx_ - (float)Math.sin(phi) * cy_ + (x1 + x2) / 2;
153 float cy = (float)Math.sin(phi) * cx_ + (float)Math.cos(phi) * cy_ + (y1 + y2) / 2;
155 // F.6.4 Conversion from center to endpoint parameterization
156 float ux = 1, uy = 0, vx = (x1_ - cx_) / rx, vy = (y1_ - cy_) / ry;
157 float det = ux * vy - uy * vx;
158 float theta1 = (det < 0 ? -1 : 1) *
159 (float)Math.acos((ux * vx + uy * vy) /
160 ((float)Math.sqrt(ux * ux + uy * uy) * (float)Math.sqrt(vx * vx + vy * vy)));
161 ux = (x1_ - cx_) / rx; uy = (y1_ - cy_) / ry;
162 vx = (-1 * x1_ - cx_) / rx; vy = (-1 * y1_ - cy_) / ry;
163 det = ux * vy - uy * vx;
164 float dtheta = (det < 0 ? -1 : 1) *
165 (float)Math.acos((ux * vx + uy * vy) /
166 ((float)Math.sqrt(ux * ux + uy * uy) * (float)Math.sqrt(vx * vx + vy * vy)));
167 dtheta = dtheta % (float)(2 * Math.PI);
169 if (fs == 0 && dtheta > 0) theta1 -= 2 * PI;
170 if (fs == 1 && dtheta < 0) theta1 += 2 * PI;
172 if (fa == 1 && dtheta < 0) dtheta = 2 * PI + dtheta;
173 else if (fa == 1 && dtheta > 0) dtheta = -1 * (2 * PI - dtheta);
175 // FIXME: integrate F.6.6
176 // FIXME: isn't quite ending where it should...
178 // F.6.3: Parameterization alternatives
179 float theta = theta1;
180 for(int j=0; j<NUMSTEPS; j++) {
181 float rasterx = rx * (float)Math.cos(theta) * (float)Math.cos(phi) -
182 ry * (float)Math.sin(theta) * (float)Math.sin(phi) + cx;
183 float rastery = rx * (float)Math.cos(theta) * (float)Math.sin(phi) +
184 ry * (float)Math.cos(phi) * (float)Math.sin(theta) + cy;
185 ret.x[ret.numvertices] = (int)Math.round(a.multiply_px(rasterx, rastery));
186 ret.y[ret.numvertices] = (int)Math.round(a.multiply_py(rasterx, rastery));
187 ret.edges[ret.numedges++] = ret.numvertices - 1; ret.numvertices++;
188 theta += dtheta / NUMSTEPS;
191 } else if (type[i] == TYPE_CUBIC) {
193 float ax = x[i+1] - 3 * c2x[i] + 3 * c1x[i] - x[i];
194 float bx = 3 * c2x[i] - 6 * c1x[i] + 3 * x[i];
195 float cx = 3 * c1x[i] - 3 * x[i];
197 float ay = y[i+1] - 3 * c2y[i] + 3 * c1y[i] - y[i];
198 float by = 3 * c2y[i] - 6 * c1y[i] + 3 * y[i];
199 float cy = 3 * c1y[i] - 3 * y[i];
202 for(float t=0; t<1; t += 1 / (float)NUMSTEPS) {
203 float rx = ax * t * t * t + bx * t * t + cx * t + dx;
204 float ry = ay * t * t * t + by * t * t + cy * t + dy;
205 ret.x[ret.numvertices] = (int)Math.round(a.multiply_px(rx, ry));
206 ret.y[ret.numvertices] = (int)Math.round(a.multiply_py(rx, ry));
207 ret.edges[ret.numedges++] = ret.numvertices - 1; ret.numvertices++;
211 } else if (type[i] == TYPE_QUADRADIC) {
213 float bx = x[i+1] - 2 * c1x[i] + x[i];
214 float cx = 2 * c1x[i] - 2 * x[i];
216 float by = y[i+1] - 2 * c1y[i] + y[i];
217 float cy = 2 * c1y[i] - 2 * y[i];
220 for(float t=0; t<1; t += 1 / (float)NUMSTEPS) {
221 float rx = bx * t * t + cx * t + dx;
222 float ry = by * t * t + cy * t + dy;
223 ret.x[ret.numvertices] = (int)Math.round(a.multiply_px(rx, ry));
224 ret.y[ret.numvertices] = (int)Math.round(a.multiply_py(rx, ry));
225 ret.edges[ret.numedges++] = ret.numvertices - 1; ret.numvertices++;
232 if (ret.numedges > 0) ret.sort(0, ret.numedges - 1, false);
236 protected void parseSingleCommandAndArguments(Tokenizer t, char command, boolean relative) {
237 if (numvertices == 0 && command != 'm') throw new RuntimeException("first command MUST be an 'm'");
238 if (numvertices > x.length - 2) {
239 float[] new_x = new float[x.length * 2]; System.arraycopy(x, 0, new_x, 0, x.length); x = new_x;
240 float[] new_y = new float[y.length * 2]; System.arraycopy(y, 0, new_y, 0, y.length); y = new_y;
245 type[numvertices-1] = TYPE_LINETO;
246 for(where = numvertices - 1; where > 0; where--)
247 if (type[where - 1] == TYPE_MOVETO) break;
248 x[numvertices] = x[where];
249 y[numvertices] = y[where];
256 if (numvertices > 0) type[numvertices-1] = TYPE_MOVETO;
257 x[numvertices] = t.parseFloat() + (relative ? x[numvertices - 1] : 0);
258 y[numvertices] = t.parseFloat() + (relative ? y[numvertices - 1] : 0);
263 case 'l': case 'h': case 'v': {
264 type[numvertices-1] = TYPE_LINETO;
265 float first = t.parseFloat(), second;
266 if (command == 'h') {
267 second = relative ? 0 : y[numvertices - 1];
268 } else if (command == 'v') {
269 second = first; first = relative ? 0 : x[numvertices - 1];
271 second = t.parseFloat();
273 x[numvertices] = first + (relative ? x[numvertices - 1] : 0);
274 y[numvertices] = second + (relative ? y[numvertices - 1] : 0);
280 type[numvertices-1] = TYPE_ARCTO;
281 c1x[numvertices-1] = t.parseFloat() + (relative ? x[numvertices - 1] : 0);
282 c1y[numvertices-1] = t.parseFloat() + (relative ? y[numvertices - 1] : 0);
283 c2x[numvertices-1] = (t.parseFloat() / 360) * 2 * PI;
284 c2y[numvertices-1] = (((int)t.parseFloat()) << 1) | (int)t.parseFloat();
285 x[numvertices] = t.parseFloat() + (relative ? x[numvertices - 1] : 0);
286 y[numvertices] = t.parseFloat() + (relative ? y[numvertices - 1] : 0);
291 case 's': case 'c': {
292 type[numvertices-1] = TYPE_CUBIC;
293 if (command == 'c') {
294 c1x[numvertices-1] = t.parseFloat() + (relative ? x[numvertices - 1] : 0);
295 c1y[numvertices-1] = t.parseFloat() + (relative ? y[numvertices - 1] : 0);
296 } else if (numvertices > 1 && type[numvertices-2] == TYPE_CUBIC) {
297 c1x[numvertices-1] = 2 * x[numvertices - 1] - c2x[numvertices-2];
298 c1y[numvertices-1] = 2 * y[numvertices - 1] - c2y[numvertices-2];
300 c1x[numvertices-1] = x[numvertices-1];
301 c1y[numvertices-1] = y[numvertices-1];
303 c2x[numvertices-1] = t.parseFloat() + (relative ? x[numvertices - 1] : 0);
304 c2y[numvertices-1] = t.parseFloat() + (relative ? y[numvertices - 1] : 0);
305 x[numvertices] = t.parseFloat() + (relative ? x[numvertices - 1] : 0);
306 y[numvertices] = t.parseFloat() + (relative ? y[numvertices - 1] : 0);
311 case 't': case 'q': {
312 type[numvertices-1] = TYPE_QUADRADIC;
313 if (command == 'q') {
314 c1x[numvertices-1] = t.parseFloat() + (relative ? x[numvertices - 1] : 0);
315 c1y[numvertices-1] = t.parseFloat() + (relative ? y[numvertices - 1] : 0);
316 } else if (numvertices > 1 && type[numvertices-2] == TYPE_QUADRADIC) {
317 c1x[numvertices-1] = 2 * x[numvertices - 1] - c1x[numvertices-2];
318 c1y[numvertices-1] = 2 * y[numvertices - 1] - c1y[numvertices-2];
320 c1x[numvertices-1] = x[numvertices-1];
321 c1y[numvertices-1] = y[numvertices-1];
323 x[numvertices] = t.parseFloat() + (relative ? x[numvertices - 1] : 0);
324 y[numvertices] = t.parseFloat() + (relative ? y[numvertices - 1] : 0);
334 // invariant: after this loop, no two lines intersect other than at a vertex
336 int index = numvertices - 2;
337 for(int i=0; i<Math.min(numvertices - 3, index); i++) {
338 for(int j = index; j < numvertices - 1; j++) {
340 // I'm not sure how to deal with vertical lines...
341 if (x[i+1] == x[i] || x[j+1] == x[j]) continue;
343 float islope = (y[i+1] - y[i]) / (x[i+1] - x[i]);
344 float jslope = (y[j+1] - y[j]) / (x[j+1] - x[j]);
345 if (islope == jslope) continue; // parallel lines can't intersect
347 float _x = (islope * x[i] - jslope * x[j] + y[j] - y[i]) / (islope - jslope);
348 float _y = islope * (_x - x[i]) + y[i];
350 if (_x > Math.min(x[i+1], x[i]) && _x < Math.max(x[i+1], x[i]) &&
351 _x > Math.min(x[j+1], x[j]) && _x < Math.max(x[j+1], x[j])) {
352 // FIXME: something's not right in here. See if we can do without fracturing line 'i'.
353 for(int k = ++numvertices; k>i; k--) { x[k] = x[k - 1]; y[k] = y[k - 1]; }
356 x[numvertices] = x[numvertices - 1]; x[numvertices - 1] = _x;
357 y[numvertices] = y[numvertices - 1]; y[numvertices - 1] = _y;
358 edges[numedges++] = numvertices - 1; numvertices++;
360 break; // actually 'continue' the outermost loop
369 // Rasterized Vector Path //////////////////////////////////////////////////////////////////////////////
372 public static class Raster {
374 // the vertices of this path
375 int[] x = new int[DEFAULT_PATHLEN];
376 int[] y = new int[DEFAULT_PATHLEN];
380 * A list of the vertices on this path which *start* an *edge* (rather than a moveto), sorted by increasing y.
381 * example: x[edges[1]],y[edges[1]] - x[edges[i]+1],y[edges[i]+1] is the second-topmost edge
382 * note that if x[i],y[i] - x[i+1],y[i+1] is a MOVETO, then no element in edges will be equal to i
384 int[] edges = new int[DEFAULT_PATHLEN];
387 /** translate a rasterized path */
388 public void translate(int dx, int dy) { for(int i=0; i<numvertices; i++) { x[i] += dx; y[i] += dy; } }
390 /** simple quicksort, from http://sourceforge.net/snippet/detail.php?type=snippet&id=100240 */
391 int sort(int left, int right, boolean partition) {
394 middle = (left + right) / 2;
395 int s = edges[right]; edges[right] = edges[middle]; edges[middle] = s;
396 for (i = left - 1, j = right; ; ) {
397 while (y[edges[++i]] < y[edges[right]]);
398 while (j > left && y[edges[--j]] > y[edges[right]]);
400 s = edges[i]; edges[i] = edges[j]; edges[j] = s;
402 s = edges[right]; edges[right] = edges[i]; edges[i] = s;
405 if (left >= right) return 0;
406 int p = sort(left, right, true);
407 sort(left, p - 1, false);
408 sort(p + 1, right, false);
413 /** finds the x value at which the line intercepts the line y=_y */
414 private int intercept(int i, float _y, boolean includeTop, boolean includeBottom) {
415 if (includeTop ? (_y < Math.min(y[i], y[i+1])) : (_y <= Math.min(y[i], y[i+1])))
416 return Integer.MIN_VALUE;
417 if (includeBottom ? (_y > Math.max(y[i], y[i+1])) : (_y >= Math.max(y[i], y[i+1])))
418 return Integer.MIN_VALUE;
419 return (int)Math.round((((float)(x[i + 1] - x[i])) /
420 ((float)(y[i + 1] - y[i])) ) * ((float)(_y - y[i])) + x[i]);
423 /** fill the interior of the path */
424 public void fill(PixelBuffer buf, Paint paint) {
425 if (numedges == 0) return;
426 int y0 = y[edges[0]], y1 = y0;
427 boolean useEvenOdd = false;
429 // we iterate over all endpoints in increasing y-coordinate order
430 for(int index = 1; index<numedges; index++) {
433 // we now examine the horizontal band between y=y0 and y=y1
435 y1 = y[edges[index]];
436 if (y0 == y1) continue;
438 // within this band, we iterate over all edges
439 int x0 = Integer.MIN_VALUE;
440 int leftSegment = -1;
442 int x1 = Integer.MAX_VALUE;
443 int rightSegment = Integer.MAX_VALUE;
444 for(int i=0; i<numedges; i++) {
445 if (y[edges[i]] == y[edges[i]+1]) continue; // ignore horizontal lines; they are irrelevant.
446 // we order the segments by the x-coordinate of their midpoint;
447 // since segments cannot intersect, this is a well-ordering
448 int i0 = intercept(edges[i], y0, true, false);
449 int i1 = intercept(edges[i], y1, false, true);
450 if (i0 == Integer.MIN_VALUE || i1 == Integer.MIN_VALUE) continue;
451 int midpoint = i0 + i1;
452 if (midpoint < x0) continue;
453 if (midpoint == x0 && i <= leftSegment) continue;
454 if (midpoint > x1) continue;
455 if (midpoint == x1 && i >= rightSegment) continue;
459 if (leftSegment == rightSegment || rightSegment == Integer.MAX_VALUE) break;
460 if (leftSegment != -1)
461 if ((useEvenOdd && count % 2 != 0) || (!useEvenOdd && count != 0))
462 paint.fillTrapezoid(intercept(edges[leftSegment], y0, true, true),
463 intercept(edges[rightSegment], y0, true, true), y0,
464 intercept(edges[leftSegment], y1, true, true),
465 intercept(edges[rightSegment], y1, true, true), y1,
467 if (useEvenOdd) count++;
468 else count += (y[edges[rightSegment]] < y[edges[rightSegment]+1]) ? -1 : 1;
469 leftSegment = rightSegment; x0 = x1;
474 /** stroke the outline of the path */
475 public void stroke(PixelBuffer buf, int width, int color) { stroke(buf, width, color, null, 0, 0); }
476 public void stroke(PixelBuffer buf, int width, int color, String dashArray, int dashOffset, float segLength) {
478 if (dashArray == null) {
479 for(int i=0; i<numedges; i++)
480 buf.drawLine((int)x[edges[i]],
481 (int)y[edges[i]], (int)x[edges[i]+1], (int)y[edges[i]+1], width, color, false);
487 float actualLength = 0;
488 for(int i=0; i<numvertices; i++) {
489 // skip over MOVETOs -- they do not contribute to path length
490 if (x[i] == x[i+1] && y[i] == y[i+1]) continue;
491 if (x[i+1] == x[i+2] && y[i+1] == y[i+2]) continue;
496 actualLength += java.lang.Math.sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
498 ratio = actualLength / segLength;
500 Tokenizer pt = new Tokenizer(dashArray);
501 Vector v = new Vector();
502 while (pt.hasMoreTokens()) v.addElement(new Float(pt.parseFloat()));
503 float[] dashes = new float[v.size() % 2 == 0 ? v.size() : 2 * v.size()];
504 for(int i=0; i<dashes.length; i++) dashes[i] = ((Float)v.elementAt(i % v.size())).floatValue();
505 int dashpos = dashOffset;
506 boolean on = dashpos % 2 == 0;
507 for(int i=0; i<numvertices; i++) {
508 // skip over MOVETOs -- they do not contribute to path length
509 if (x[i] == x[i+1] && y[i] == y[i+1]) continue;
510 if (x[i+1] == x[i+2] && y[i+1] == y[i+2]) continue;
512 int x2 = (int)x[i + 1];
514 int y2 = (int)y[i + 1];
515 float segmentLength = (float)java.lang.Math.sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
516 int _x1 = x1, _y1 = y1;
519 pos = Math.min(segmentLength, pos + dashes[dashpos] * ratio);
520 if (pos != segmentLength) dashpos = (dashpos + 1) % dashes.length;
521 int _x2 = (int)((x2 * pos + x1 * (segmentLength - pos)) / segmentLength);
522 int _y2 = (int)((y2 * pos + y1 * (segmentLength - pos)) / segmentLength);
523 if (on) buf.drawLine(_x1, _y1, _x2, _y2, width, color, false);
525 _x1 = _x2; _y1 = _y2;
526 } while(pos < segmentLength);
530 // FEATURE: make this faster and cache it; also deal with negative coordinates
531 public int boundingBoxWidth() {
533 for(int i=0; i<numvertices; i++) ret = Math.max(ret, x[i]);
537 // FEATURE: make this faster and cache it; also deal with negative coordinates
538 public int boundingBoxHeight() {
540 for(int i=0; i<numvertices; i++) ret = Math.max(ret, y[i]);