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| 1 <!-- bezier clip visualizer --> |  | 
| 2 <html> |  | 
| 3 <head> |  | 
| 4 <div style="height:0"> |  | 
| 5 |  | 
| 6 <div id="clip1"> |  | 
| 7 (gdb) p smaller |  | 
| 8 $2 = {{ |  | 
| 9     x = 0.91292418204644155, |  | 
| 10     y = 0.41931201426549197 |  | 
| 11   }, { |  | 
| 12     x = 0.70491388044579517, |  | 
| 13     y = 0.64754305977710236 |  | 
| 14   }, { |  | 
| 15     x = 0, |  | 
| 16     y = 1 |  | 
| 17   }} |  | 
| 18 (gdb) p larger |  | 
| 19 $3 = {{ |  | 
| 20     x = 0.21875, |  | 
| 21     y = 0.765625 |  | 
| 22   }, { |  | 
| 23     x = 0.125, |  | 
| 24     y = 0.875 |  | 
| 25   }, { |  | 
| 26     x = 0, |  | 
| 27     y = 1 |  | 
| 28   }} |  | 
| 29 (gdb) p distance2y |  | 
| 30 $1 = {{ |  | 
| 31     x = 0, |  | 
| 32     y = 0.080355482722450078 |  | 
| 33   }, { |  | 
| 34     x = 0.5, |  | 
| 35     y = 0.038383741101172597 |  | 
| 36   }, { |  | 
| 37     x = 1, |  | 
| 38     y = 0 |  | 
| 39   }} |  | 
| 40 </div> |  | 
| 41 |  | 
| 42 <div id="quad21a"> |  | 
| 43 bezier_clip q1=(0,0 1,0 0,2) q2=(0.5,0.25 0.5,0.5 0,1) minT=0 maxT=1 |  | 
| 44 </div> |  | 
| 45 <div id="quad21b"> |  | 
| 46 bezier_clip q1=(0.5,0.25 0.5,0.375 0.375,0.5625) q2=(0,0 1,0 0,2) minT=0.3 maxT=
     0.78125 |  | 
| 47 </div> |  | 
| 48 <div id="quad21c"> |  | 
| 49 bezier_clip q1=(0.42,0.18 0.6125,0.46875 0.341796875,1.22070312) q2=(0.5,0.25 0.
     5,0.375 0.375,0.5625) minT=0 maxT=0.926710098 |  | 
| 50 </div> |  | 
| 51 <div id="quad21d"> |  | 
| 52 bezier_clip q1=(0.5,0.25 0.5,0.307919381 0.473162762,0.379257381) q2=(0.42,0.18 
     0.6125,0.46875 0.341796875,1.22070312) minT=0.187231244 maxT=0.729263299 |  | 
| 53 </div> |  | 
| 54 <div id="quad21e"> |  | 
| 55 bezier_clip q1=(0.475846194,0.304363878 0.53317904,0.507883959 0.454423387,0.847
     492538) q2=(0.5,0.25 0.5,0.307919381 0.473162762,0.379257381) minT=0 maxT=1 |  | 
| 56 </div> |  | 
| 57 <div id="quad21f"> |  | 
| 58 bezier_clip q1=(0.493290691,0.311274036 0.486581381,0.343588381 0.473162762,0.37
     9257381) q2=(0.475846194,0.304363878 0.53317904,0.507883959 0.454423387,0.847492
     538) minT=0.0828748517 maxT=0.150086861 |  | 
| 59 </div> |  | 
| 60 |  | 
| 61 <div id="quad21g"> |  | 
| 62 (gdb) p smaller |  | 
| 63 $1 = {{ |  | 
| 64     x = 0.48441440743366754, |  | 
| 65     y = 0.33903196011243797 |  | 
| 66   }, { |  | 
| 67     x = 0.48750982503868118, |  | 
| 68     y = 0.35346899178071778 |  | 
| 69   }, { |  | 
| 70     x = 0.48999046908865357, |  | 
| 71     y = 0.368520797004039 |  | 
| 72   }} |  | 
| 73 (gdb) p larger |  | 
| 74 $2 = {{ |  | 
| 75     x = 0.49329069058425024, |  | 
| 76     y = 0.31127403581536672 |  | 
| 77   }, { |  | 
| 78     x = 0.48658138116850047, |  | 
| 79     y = 0.34358838107698753 |  | 
| 80   }, { |  | 
| 81     x = 0.47316276233700094, |  | 
| 82     y = 0.37925738104648321 |  | 
| 83   }} |  | 
| 84 </div> |  | 
| 85 |  | 
| 86 <div id="quad36"> |  | 
| 87 (gdb) p fQ |  | 
| 88 $2 = {{ |  | 
| 89     x = 1.8883839294261275, |  | 
| 90     y = 2.1108590606904345 |  | 
| 91   }, { |  | 
| 92     x = 1.888463903363252, |  | 
| 93     y = 2.1111576060205435 |  | 
| 94   }, { |  | 
| 95     x = 1.8885438199983176, |  | 
| 96     y = 2.1114561800016824 |  | 
| 97   }} |  | 
| 98 (gdb) p rh.fQ |  | 
| 99 $3 = {{ |  | 
| 100     x = 1.8883839294260976, |  | 
| 101     y = 2.1108590606903377 |  | 
| 102   }, { |  | 
| 103     x = 1.8886366953645748, |  | 
| 104     y = 2.1109850143489544 |  | 
| 105   }, { |  | 
| 106     x = 1.8888888888888888, |  | 
| 107     y = 2.1111111111111112 |  | 
| 108   }} |  | 
| 109 (gdb) |  | 
| 110 </div> |  | 
| 111 |  | 
| 112 <div id="quad37"> |  | 
| 113  {{x = 360.048828125, y = 229.2578125}, {x = 360.048828125, y = 224.4140625}, {x
      = 362.607421875, y = 221.3671875}} |  | 
| 114  {{x = 362.607421875, y = 221.3671875}, {x = 365.166015625, y = 218.3203125}, {x
      = 369.228515625, y = 218.3203125}} |  | 
| 115 </div> |  | 
| 116 |  | 
| 117 <div id="quad38"> |  | 
| 118 $2 = {{fX = 369.969421, fY = 137.94809}, {fX = 383.982849, fY = 121.260353}, {fX
      = 406.233154, fY = 121.260353}} |  | 
| 119 $4 = {{fX = 406.232788, fY = 121.260353}, {fX = 409.441956, fY = 121.260353}, {f
     X = 412.972046, fY = 121.795212}} |  | 
| 120 </div> |  | 
| 121 |  | 
| 122 <div id="quad39"> |  | 
| 123 {{x = 406.233154296875, y = 121.26035308837891}, {x = 406.23153587045397, y = 12
     1.26035308837891}, {x = 406.22991748761177, y = 121.26035317666889}}, |  | 
| 124 {{x = 406.23295158013377, y = 121.26035308872596}, {x = 406.2328698329315, y = 1
     21.26035308837889}, {x = 406.2327880859375, y = 121.26035308837891}}, |  | 
| 125 </div> |  | 
| 126 |  | 
| 127 </div> |  | 
| 128 |  | 
| 129 <script type="text/javascript"> |  | 
| 130 |  | 
| 131 var testDivs = [ |  | 
| 132     quad56, |  | 
| 133     quad39, |  | 
| 134     quad38, |  | 
| 135     quad37, |  | 
| 136     quad36, |  | 
| 137     quad21g, |  | 
| 138     quad21a, |  | 
| 139     quad21b, |  | 
| 140     quad21c, |  | 
| 141     quad21d, |  | 
| 142     quad21e, |  | 
| 143     quad21f, |  | 
| 144     clip1, |  | 
| 145 ]; |  | 
| 146 |  | 
| 147 var scale, columns, rows, xStart, yStart; |  | 
| 148 |  | 
| 149 var ticks = 10; |  | 
| 150 var at_x = 13 + 0.5; |  | 
| 151 var at_y = 13 + 0.5; |  | 
| 152 var init_decimal_places = 1; // make this 3 to show more precision |  | 
| 153 var decimal_places; |  | 
| 154 var tests = []; |  | 
| 155 var testTitles = []; |  | 
| 156 var testIndex = 0; |  | 
| 157 var ctx; |  | 
| 158 var fat1 = true; |  | 
| 159 var fat2 = false; |  | 
| 160 var ctl1 = true; |  | 
| 161 var ctl2 = false; |  | 
| 162 var ctlPts1 = true; |  | 
| 163 var ctlPts2 = false; |  | 
| 164 var minScale = 1; |  | 
| 165 var subscale = 1; |  | 
| 166 |  | 
| 167 function parse(test, title) { |  | 
| 168     var curveStrs = test.split("{{"); |  | 
| 169     if (curveStrs.length == 1) |  | 
| 170         curveStrs = test.split("=("); |  | 
| 171     var pattern = /[a-z$=]?-?\d+\.*\d*/g; |  | 
| 172     var curves = []; |  | 
| 173     for (var c in curveStrs) { |  | 
| 174         var curveStr = curveStrs[c]; |  | 
| 175         var points = curveStr.match(pattern); |  | 
| 176         var pts = []; |  | 
| 177         for (var wd in points) { |  | 
| 178             var num = parseFloat(points[wd]); |  | 
| 179             if (isNaN(num)) continue; |  | 
| 180             pts.push(num); |  | 
| 181         } |  | 
| 182         if (pts.length > 0) |  | 
| 183             curves.push(pts); |  | 
| 184     } |  | 
| 185     if (curves.length >= 2) { |  | 
| 186         tests.push(curves); |  | 
| 187         testTitles.push(title); |  | 
| 188     } |  | 
| 189 } |  | 
| 190 |  | 
| 191 function init(test) { |  | 
| 192     var canvas = document.getElementById('canvas'); |  | 
| 193     if (!canvas.getContext) return; |  | 
| 194     canvas.width = window.innerWidth - at_x; |  | 
| 195     canvas.height = window.innerHeight - at_y; |  | 
| 196     ctx = canvas.getContext('2d'); |  | 
| 197     var xmin = Infinity; |  | 
| 198     var xmax = -Infinity; |  | 
| 199     var ymin = Infinity; |  | 
| 200     var ymax = -Infinity; |  | 
| 201     for (var curves in test) { |  | 
| 202         var curve = test[curves]; |  | 
| 203         var last = curve.length; |  | 
| 204         for (var idx = 0; idx < last; idx += 2) { |  | 
| 205             xmin = Math.min(xmin, curve[idx]); |  | 
| 206             xmax = Math.max(xmax, curve[idx]); |  | 
| 207             ymin = Math.min(ymin, curve[idx + 1]); |  | 
| 208             ymax = Math.max(ymax, curve[idx + 1]); |  | 
| 209         } |  | 
| 210     } |  | 
| 211     subscale = 1; |  | 
| 212     decimal_places = init_decimal_places; |  | 
| 213     if (xmax != xmin && ymax != ymin) { |  | 
| 214         while ((xmax - xmin) * subscale < 0.1 && (ymax - ymin) * subscale < 0.1)
      { |  | 
| 215             subscale *= 10; |  | 
| 216             decimal_places += 1; |  | 
| 217      //       if (subscale > 100000) { |  | 
| 218      //           break; |  | 
| 219      //       } |  | 
| 220         } |  | 
| 221     } |  | 
| 222     columns = Math.ceil(xmax * subscale) - Math.floor(xmin * subscale) + 1; |  | 
| 223     rows = Math.ceil(ymax * subscale) - Math.floor(ymin * subscale) + 1; |  | 
| 224 |  | 
| 225     xStart = Math.floor(xmin * subscale) / subscale; |  | 
| 226     yStart = Math.floor(ymin * subscale) / subscale; |  | 
| 227     var hscale = ctx.canvas.width / columns / ticks; |  | 
| 228     var vscale = ctx.canvas.height / rows / ticks; |  | 
| 229     minScale = Math.floor(Math.min(hscale, vscale)); |  | 
| 230     scale = minScale * subscale; |  | 
| 231  //   while (columns < 1000 && rows < 1000) { |  | 
| 232   //      columns *= 2; |  | 
| 233  //       rows *= 2; |  | 
| 234  //   } |  | 
| 235 } |  | 
| 236 |  | 
| 237 function drawPoint(px, py, xoffset, yoffset, unit) { |  | 
| 238     var label = px.toFixed(decimal_places) + ", " + py.toFixed(decimal_places); |  | 
| 239     var _px = px * unit + xoffset; |  | 
| 240     var _py = py * unit + yoffset; |  | 
| 241     ctx.beginPath(); |  | 
| 242     ctx.arc(_px, _py, 3, 0, Math.PI*2, true); |  | 
| 243     ctx.closePath(); |  | 
| 244     ctx.fill(); |  | 
| 245     ctx.fillText(label, _px + 5, _py); |  | 
| 246 } |  | 
| 247 |  | 
| 248 function draw(test, title, _at_x, _at_y, scale) { |  | 
| 249     ctx.fillStyle = "rgba(0,0,0, 0.1)"; |  | 
| 250     ctx.font = "normal 50px Arial"; |  | 
| 251     ctx.fillText(title, 50, 50); |  | 
| 252     ctx.font = "normal 10px Arial"; |  | 
| 253 |  | 
| 254     var unit = scale * ticks; |  | 
| 255     ctx.lineWidth = 1; |  | 
| 256     var i; |  | 
| 257     for (i = 0; i <= rows * ticks; ++i) { |  | 
| 258         ctx.strokeStyle = (i % ticks) != 0 ? "rgb(160,160,160)" : "black"; |  | 
| 259         ctx.beginPath(); |  | 
| 260         ctx.moveTo(_at_x + 0, _at_y + i * minScale); |  | 
| 261         ctx.lineTo(_at_x + unit * columns, _at_y + i * minScale); |  | 
| 262         ctx.stroke(); |  | 
| 263     } |  | 
| 264     for (i = 0; i <= columns * ticks; ++i) { |  | 
| 265         ctx.strokeStyle = (i % ticks) != 0 ? "rgb(160,160,160)" : "black"; |  | 
| 266         ctx.beginPath(); |  | 
| 267         ctx.moveTo(_at_x + i * minScale, _at_y + 0); |  | 
| 268         ctx.lineTo(_at_x + i * minScale, _at_y + unit * rows); |  | 
| 269         ctx.stroke(); |  | 
| 270     } |  | 
| 271 |  | 
| 272     var xoffset = xStart * -unit + _at_x; |  | 
| 273     var yoffset = yStart * -unit + _at_y; |  | 
| 274 |  | 
| 275     ctx.fillStyle = "rgb(40,80,60)" |  | 
| 276     for (i = 0; i <= columns; i += (1 / ticks)) |  | 
| 277     { |  | 
| 278         num = xStart + i / subscale; |  | 
| 279         ctx.fillText(num.toFixed(decimal_places), xoffset + num * unit - 5, 10); |  | 
| 280     } |  | 
| 281     for (i = 0; i <= rows; i += (1 / ticks)) |  | 
| 282     { |  | 
| 283         num = yStart + i / subscale; |  | 
| 284         ctx.fillText(num.toFixed(decimal_places), 0, yoffset + num * unit + 0); |  | 
| 285     } |  | 
| 286 |  | 
| 287     // draw curve 1 and 2 |  | 
| 288     var curves, pts; |  | 
| 289     for (curves in test) { |  | 
| 290         var curve = test[curves]; |  | 
| 291         ctx.beginPath(); |  | 
| 292         ctx.moveTo(xoffset + curve[0] * unit, yoffset + curve[1] * unit); |  | 
| 293         switch (curve.length) { |  | 
| 294             case 6: |  | 
| 295                 ctx.quadraticCurveTo( |  | 
| 296                     xoffset + curve[2] * unit, yoffset + curve[3] * unit, |  | 
| 297                     xoffset + curve[4] * unit, yoffset + curve[5] * unit); |  | 
| 298                 break; |  | 
| 299             case 8: |  | 
| 300                 ctx.bezierCurveTo( |  | 
| 301                     xoffset + curve[2] * unit, yoffset + curve[3] * unit, |  | 
| 302                     xoffset + curve[4] * unit, yoffset + curve[5] * unit, |  | 
| 303                     xoffset + curve[6] * unit, yoffset + curve[7] * unit); |  | 
| 304                 break; |  | 
| 305         } |  | 
| 306         if (curves == 2) ctx.strokeStyle = curves ? "red" : "blue"; |  | 
| 307         ctx.stroke(); |  | 
| 308         ctx.strokeStyle = "rgba(0,0,0, 0.3)"; |  | 
| 309         ctx.beginPath(); |  | 
| 310         ctx.moveTo(xoffset + curve[0] * unit, yoffset + curve[1] * unit); |  | 
| 311         ctx.lineTo(xoffset + curve[2] * unit, yoffset + curve[3] * unit); |  | 
| 312         ctx.lineTo(xoffset + curve[4] * unit, yoffset + curve[5] * unit); |  | 
| 313         if (curve.length == 8) |  | 
| 314             ctx.lineTo(xoffset + curve[6] * unit, yoffset + curve[7] * unit); |  | 
| 315         ctx.stroke(); |  | 
| 316     } |  | 
| 317     // optionally draw fat lines for curve |  | 
| 318     if (fat1) |  | 
| 319         drawFat(test[0], xoffset, yoffset, unit); |  | 
| 320     if (fat2) |  | 
| 321         drawFat(test[1], xoffset, yoffset, unit); |  | 
| 322     if (ctl1) |  | 
| 323         drawCtl(test[0], xoffset, yoffset, unit); |  | 
| 324     if (ctl2) |  | 
| 325         drawCtl(test[1], xoffset, yoffset, unit); |  | 
| 326     if (ctlPts1) |  | 
| 327         drawCtlPts(test[0], xoffset, yoffset, unit); |  | 
| 328     if (ctlPts2) |  | 
| 329         drawCtlPts(test[1], xoffset, yoffset, unit); |  | 
| 330 } |  | 
| 331 |  | 
| 332 function drawCtl(curve, xoffset, yoffset, unit) { |  | 
| 333     var last = curve.length - 2; |  | 
| 334     ctx.strokeStyle = "rgba(0,0,0, 0.5)"; |  | 
| 335     ctx.beginPath(); |  | 
| 336     ctx.moveTo(xoffset + curve[0] * unit, yoffset + curve[1] * unit); |  | 
| 337     ctx.lineTo(xoffset + curve[2] * unit, yoffset + curve[3] * unit); |  | 
| 338     ctx.lineTo(xoffset + curve[4] * unit, yoffset + curve[5] * unit); |  | 
| 339     ctx.stroke(); |  | 
| 340 } |  | 
| 341 |  | 
| 342 function drawCtlPts(curve, xoffset, yoffset, unit) { |  | 
| 343     drawPoint(curve[0], curve[1], xoffset, yoffset, unit); |  | 
| 344     drawPoint(curve[2], curve[3], xoffset, yoffset, unit); |  | 
| 345     drawPoint(curve[4], curve[5], xoffset, yoffset, unit); |  | 
| 346 } |  | 
| 347 |  | 
| 348 function drawFat(curve, xoffset, yoffset, unit) { |  | 
| 349     var last = curve.length - 2; |  | 
| 350     ctx.strokeStyle = "rgba(0,0,0, 0.5)"; |  | 
| 351     ctx.beginPath(); |  | 
| 352     ctx.moveTo(xoffset + curve[0] * unit, yoffset + curve[1] * unit); |  | 
| 353     ctx.lineTo(xoffset + curve[last] * unit, yoffset + curve[last + 1] * unit); |  | 
| 354     ctx.stroke(); |  | 
| 355     // draw line parallel to end points through control points |  | 
| 356     var dx = curve[last] - curve[0]; |  | 
| 357     var dy = curve[last + 1] - curve[1]; |  | 
| 358     drawParallelLine(curve[2], curve[3], dx, dy, xoffset, yoffset, unit); |  | 
| 359     if (curve.length == 8) |  | 
| 360         drawParallelLine(curve[4], curve[5], dx, dy, xoffset, yoffset, unit); |  | 
| 361 } |  | 
| 362 |  | 
| 363 function drawParallelLine(x, y, dx, dy, xoffset, yoffset, unit) { |  | 
| 364     var x1 = x - dx; |  | 
| 365     var y1 = y - dy; |  | 
| 366     var x2 = x + dx; |  | 
| 367     var y2 = y + dy; |  | 
| 368     ctx.beginPath(); |  | 
| 369     ctx.moveTo(xoffset + x1 * unit, yoffset + y1 * unit); |  | 
| 370     ctx.lineTo(xoffset + x2 * unit, yoffset + y2 * unit); |  | 
| 371     ctx.stroke(); |  | 
| 372 } |  | 
| 373 |  | 
| 374 function drawTop() { |  | 
| 375     init(tests[testIndex]); |  | 
| 376     redraw(); |  | 
| 377 } |  | 
| 378 |  | 
| 379 function redraw() { |  | 
| 380     ctx.beginPath(); |  | 
| 381     ctx.rect(0, 0, ctx.canvas.width, ctx.canvas.height); |  | 
| 382     ctx.fillStyle="white"; |  | 
| 383     ctx.fill(); |  | 
| 384     draw(tests[testIndex], testTitles[testIndex], at_x, at_y, scale); |  | 
| 385 } |  | 
| 386 |  | 
| 387 function doKeyPress(evt) { |  | 
| 388     var char = String.fromCharCode(evt.charCode); |  | 
| 389     switch (char) { |  | 
| 390     case 'c': |  | 
| 391         ctl2 ^= true; |  | 
| 392         if (ctl2 == false) |  | 
| 393             ctl1 ^= true; |  | 
| 394         drawTop(); |  | 
| 395         break; |  | 
| 396     case 'd': |  | 
| 397         ctlPts2 ^= true; |  | 
| 398         if (ctlPts2 == false) |  | 
| 399             ctlPts1 ^= true; |  | 
| 400         drawTop(); |  | 
| 401         break; |  | 
| 402     case 'f': |  | 
| 403         fat2 ^= true; |  | 
| 404         if (fat2 == false) |  | 
| 405             fat1 ^= true; |  | 
| 406         drawTop(); |  | 
| 407         break; |  | 
| 408     case 'N': |  | 
| 409         testIndex += 9; |  | 
| 410     case 'n': |  | 
| 411         if (++testIndex >= tests.length) |  | 
| 412             testIndex = 0; |  | 
| 413         mouseX = Infinity; |  | 
| 414         drawTop(); |  | 
| 415         break; |  | 
| 416     case 'P': |  | 
| 417         testIndex -= 9; |  | 
| 418     case 'p': |  | 
| 419         if (--testIndex < 0) |  | 
| 420             testIndex = tests.length - 1; |  | 
| 421         mouseX = Infinity; |  | 
| 422         drawTop(); |  | 
| 423         break; |  | 
| 424     } |  | 
| 425 } |  | 
| 426 |  | 
| 427 function handleMouseClick() { |  | 
| 428 } |  | 
| 429 |  | 
| 430 function handleMouseOver() { |  | 
| 431 } |  | 
| 432 |  | 
| 433 function start() { |  | 
| 434     for (i = 0; i < testDivs.length; ++i) { |  | 
| 435         var title = testDivs[i].id.toString(); |  | 
| 436         var str = testDivs[i].firstChild.data; |  | 
| 437         parse(str, title); |  | 
| 438     } |  | 
| 439     drawTop(); |  | 
| 440     window.addEventListener('keypress', doKeyPress, true); |  | 
| 441     window.onresize = function() { |  | 
| 442         drawTop(); |  | 
| 443     } |  | 
| 444 } |  | 
| 445 |  | 
| 446 </script> |  | 
| 447 </head> |  | 
| 448 |  | 
| 449 <body onLoad="start();"> |  | 
| 450 <canvas id="canvas" width="750" height="500" |  | 
| 451     onmousemove="handleMouseOver()" |  | 
| 452     onclick="handleMouseClick()" |  | 
| 453     ></canvas > |  | 
| 454 </body> |  | 
| 455 </html> |  | 
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