about summary refs log tree commit diff stats
path: root/html/509bezier.mu.html
blob: eb630d94fd35d02e2b4310f09881389575e97eef (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8">
<title>Mu - 509bezier.mu</title>
<meta name="Generator" content="Vim/8.2">
<meta name="plugin-version" content="vim8.1_v2">
<meta name="syntax" content="none">
<meta name="settings" content="number_lines,use_css,pre_wrap,no_foldcolumn,expand_tabs,line_ids,prevent_copy=,use_input_for_pc=fallback">
<meta name="colorscheme" content="minimal-light">
<style>
<!--
pre { white-space: pre-wrap; font-family: monospace; color: #000000; background-color: #ffffd7; }
body { font-size:12pt; font-family: monospace; color: #000000; background-color: #ffffd7; }
a { color:inherit; }
* { font-size:12pt; font-size: 1em; }
.PreProc { color: #c000c0; }
.muRegEbx { color: #5f00ff; }
.muRegEcx { color: #870000; }
.muRegEdx { color: #af5f00; }
.LineNr { }
.Constant { color: #008787; }
.muFunction { color: #af5f00; text-decoration: underline; }
.Delimiter { color: #c000c0; }
.muComment { color: #005faf; }
.Special { color: #ff6060; }
-->
</style>

<script>
<!--

/* function to open any folds containing a jumped-to line before jumping to it */
function JumpToLine()
{
  var lineNum;
  lineNum = window.location.hash;
  lineNum = lineNum.substr(1); /* strip off '#' */

  if (lineNum.indexOf('L') == -1) {
    lineNum = 'L'+lineNum;
  }
  var lineElem = document.getElementById(lineNum);
  /* Always jump to new location even if the line was hidden inside a fold, or
   * we corrected the raw number to a line ID.
   */
  if (lineElem) {
    lineElem.scrollIntoView(true);
  }
  return true;
}
if ('onhashchange' in window) {
  window.onhashchange = JumpToLine;
}

-->
</script>
</head>
<body onload='JumpToLine();'>
<a href='https://github.com/akkartik/mu/blob/main/509bezier.mu'>https://github.com/akkartik/mu/blob/main/509bezier.mu</a>
<pre id='vimCodeElement'>
<span id="L1" class="LineNr">  1 </span><span class="muComment"># Draw a second-degree bezier curve using 3 control points.</span>
<span id="L2" class="LineNr">  2 </span><span class="muComment">#</span>
<span id="L3" class="LineNr">  3 </span><span class="muComment"># <a href="http://members.chello.at/easyfilter/bresenham.html">http://members.chello.at/easyfilter/bresenham.html</a> says that this algorithm</span>
<span id="L4" class="LineNr">  4 </span><span class="muComment"># works only if &quot;the gradient does not change sign&quot;. Either:</span>
<span id="L5" class="LineNr">  5 </span><span class="muComment">#   x0 &gt;= x1 &gt;= x2</span>
<span id="L6" class="LineNr">  6 </span><span class="muComment"># or:</span>
<span id="L7" class="LineNr">  7 </span><span class="muComment">#   x0 &lt;= x1 &lt;= x2</span>
<span id="L8" class="LineNr">  8 </span><span class="muComment"># Similarly for y0, y1 and y2.</span>
<span id="L9" class="LineNr">  9 </span><span class="muComment">#</span>
<span id="L10" class="LineNr"> 10 </span><span class="muComment"># This seems superficially similar to the notions of convex and concave, but I</span>
<span id="L11" class="LineNr"> 11 </span><span class="muComment"># think it isn't. I think it's purely a property of the frame of reference.</span>
<span id="L12" class="LineNr"> 12 </span><span class="muComment"># Rotating the axes can make the gradient change sign or stop changing sign</span>
<span id="L13" class="LineNr"> 13 </span><span class="muComment"># even as 3 points preserve fixed relative bearings to each other.</span>
<span id="L14" class="LineNr"> 14 </span><span class="PreProc">fn</span> <span class="muFunction"><a href='509bezier.mu.html#L14'>draw-monotonic-bezier</a></span> <a href='500fake-screen.mu.html#L14'>screen</a>: (addr <a href='500fake-screen.mu.html#L14'>screen</a>), x0: int, y0: int, x1: int, y1: int, x2: int, y2: int, color: int <span class="Delimiter">{</span>
<span id="L15" class="LineNr"> 15 </span>  <span class="PreProc">var</span> xx: int
<span id="L16" class="LineNr"> 16 </span>  <span class="PreProc">var</span> yy: int
<span id="L17" class="LineNr"> 17 </span>  <span class="PreProc">var</span> xy: int
<span id="L18" class="LineNr"> 18 </span>  <span class="PreProc">var</span> sx: int
<span id="L19" class="LineNr"> 19 </span>  <span class="PreProc">var</span> sy: int
<span id="L20" class="LineNr"> 20 </span>  <span class="muComment"># sx = x2-x1</span>
<span id="L21" class="LineNr"> 21 </span>  <span class="PreProc">var</span> tmp/eax: int <span class="Special">&lt;-</span> copy x2
<span id="L22" class="LineNr"> 22 </span>  tmp <span class="Special">&lt;-</span> subtract x1
<span id="L23" class="LineNr"> 23 </span>  copy-to sx, tmp
<span id="L24" class="LineNr"> 24 </span>  <span class="muComment"># sy = y2-y1</span>
<span id="L25" class="LineNr"> 25 </span>  tmp <span class="Special">&lt;-</span> copy y2
<span id="L26" class="LineNr"> 26 </span>  tmp <span class="Special">&lt;-</span> subtract y1
<span id="L27" class="LineNr"> 27 </span>  copy-to sy, tmp
<span id="L28" class="LineNr"> 28 </span>  <span class="muComment"># xx = x0-x1</span>
<span id="L29" class="LineNr"> 29 </span>  tmp <span class="Special">&lt;-</span> copy x0
<span id="L30" class="LineNr"> 30 </span>  tmp <span class="Special">&lt;-</span> subtract x1
<span id="L31" class="LineNr"> 31 </span>  copy-to xx, tmp
<span id="L32" class="LineNr"> 32 </span>  <span class="muComment"># yy = y0-y1</span>
<span id="L33" class="LineNr"> 33 </span>  tmp <span class="Special">&lt;-</span> copy y0
<span id="L34" class="LineNr"> 34 </span>  tmp <span class="Special">&lt;-</span> subtract y1
<span id="L35" class="LineNr"> 35 </span>  copy-to yy, tmp
<span id="L36" class="LineNr"> 36 </span>  <span class="muComment"># cur = xx*sy - yy*sx</span>
<span id="L37" class="LineNr"> 37 </span>  <span class="PreProc">var</span> cur-f/<span class="Constant">xmm4</span>: float <span class="Special">&lt;-</span> convert xx
<span id="L38" class="LineNr"> 38 </span>  <span class="Delimiter">{</span>
<span id="L39" class="LineNr"> 39 </span>    <span class="PreProc">var</span> sy-f/<span class="Constant">xmm1</span>: float <span class="Special">&lt;-</span> convert sy
<span id="L40" class="LineNr"> 40 </span>    cur-f <span class="Special">&lt;-</span> multiply sy-f
<span id="L41" class="LineNr"> 41 </span>    <span class="PreProc">var</span> tmp2-f/<span class="Constant">xmm1</span>: float <span class="Special">&lt;-</span> convert yy
<span id="L42" class="LineNr"> 42 </span>    <span class="PreProc">var</span> sx-f/<span class="Constant">xmm2</span>: float <span class="Special">&lt;-</span> convert sx
<span id="L43" class="LineNr"> 43 </span>    tmp2-f <span class="Special">&lt;-</span> multiply sx-f
<span id="L44" class="LineNr"> 44 </span>    cur-f <span class="Special">&lt;-</span> subtract tmp2-f
<span id="L45" class="LineNr"> 45 </span>  <span class="Delimiter">}</span>
<span id="L46" class="LineNr"> 46 </span>  <span class="muComment"># if (xx*sx &gt; 0) abort</span>
<span id="L47" class="LineNr"> 47 </span>  <span class="Delimiter">{</span>
<span id="L48" class="LineNr"> 48 </span>    tmp <span class="Special">&lt;-</span> copy xx
<span id="L49" class="LineNr"> 49 </span>    tmp <span class="Special">&lt;-</span> multiply sx
<span id="L50" class="LineNr"> 50 </span>    compare tmp, <span class="Constant">0</span>
<span id="L51" class="LineNr"> 51 </span>    <span class="PreProc">break-if-&lt;=</span>
<span id="L52" class="LineNr"> 52 </span>    <a href='317abort.subx.html#L5'>abort</a> <span class="Constant">&quot;bezier: gradient of x changes sign&quot;</span>
<span id="L53" class="LineNr"> 53 </span>  <span class="Delimiter">}</span>
<span id="L54" class="LineNr"> 54 </span>  <span class="muComment"># if (yy*sy &gt; 0) abort</span>
<span id="L55" class="LineNr"> 55 </span>  <span class="Delimiter">{</span>
<span id="L56" class="LineNr"> 56 </span>    tmp <span class="Special">&lt;-</span> copy yy
<span id="L57" class="LineNr"> 57 </span>    tmp <span class="Special">&lt;-</span> multiply sy
<span id="L58" class="LineNr"> 58 </span>    compare tmp, <span class="Constant">0</span>
<span id="L59" class="LineNr"> 59 </span>    <span class="PreProc">break-if-&lt;=</span>
<span id="L60" class="LineNr"> 60 </span>    <a href='317abort.subx.html#L5'>abort</a> <span class="Constant">&quot;bezier: gradient of y changes sign&quot;</span>
<span id="L61" class="LineNr"> 61 </span>  <span class="Delimiter">}</span>
<span id="L62" class="LineNr"> 62 </span>  <span class="muComment"># swap P0 and P2 if necessary</span>
<span id="L63" class="LineNr"> 63 </span>  <span class="Delimiter">{</span>
<span id="L64" class="LineNr"> 64 </span>    <span class="muComment"># dist1 = sx*sx + sy*sy</span>
<span id="L65" class="LineNr"> 65 </span>    <span class="PreProc">var</span> dist1/<span class="muRegEcx">ecx</span>: int <span class="Special">&lt;-</span> copy sx
<span id="L66" class="LineNr"> 66 </span>    <span class="Delimiter">{</span>
<span id="L67" class="LineNr"> 67 </span>      dist1 <span class="Special">&lt;-</span> multiply sx
<span id="L68" class="LineNr"> 68 </span>      <span class="Delimiter">{</span>
<span id="L69" class="LineNr"> 69 </span>        <span class="PreProc">break-if-not-overflow</span>
<span id="L70" class="LineNr"> 70 </span>        <a href='317abort.subx.html#L5'>abort</a> <span class="Constant">&quot;bezier: overflow 1&quot;</span>
<span id="L71" class="LineNr"> 71 </span>      <span class="Delimiter">}</span>
<span id="L72" class="LineNr"> 72 </span>      tmp <span class="Special">&lt;-</span> copy sy
<span id="L73" class="LineNr"> 73 </span>      tmp <span class="Special">&lt;-</span> multiply sy
<span id="L74" class="LineNr"> 74 </span>      <span class="Delimiter">{</span>
<span id="L75" class="LineNr"> 75 </span>        <span class="PreProc">break-if-not-overflow</span>
<span id="L76" class="LineNr"> 76 </span>        <a href='317abort.subx.html#L5'>abort</a> <span class="Constant">&quot;bezier: overflow 2&quot;</span>
<span id="L77" class="LineNr"> 77 </span>      <span class="Delimiter">}</span>
<span id="L78" class="LineNr"> 78 </span>      dist1 <span class="Special">&lt;-</span> add tmp
<span id="L79" class="LineNr"> 79 </span>    <span class="Delimiter">}</span>
<span id="L80" class="LineNr"> 80 </span>    <span class="muComment"># dist2 = xx*xx + yy*yy</span>
<span id="L81" class="LineNr"> 81 </span>    <span class="PreProc">var</span> dist2/<span class="muRegEdx">edx</span>: int <span class="Special">&lt;-</span> copy xx
<span id="L82" class="LineNr"> 82 </span>    <span class="Delimiter">{</span>
<span id="L83" class="LineNr"> 83 </span>      dist2 <span class="Special">&lt;-</span> multiply xx
<span id="L84" class="LineNr"> 84 </span>      <span class="Delimiter">{</span>
<span id="L85" class="LineNr"> 85 </span>        <span class="PreProc">break-if-not-overflow</span>
<span id="L86" class="LineNr"> 86 </span>        <a href='317abort.subx.html#L5'>abort</a> <span class="Constant">&quot;bezier: overflow 3&quot;</span>
<span id="L87" class="LineNr"> 87 </span>      <span class="Delimiter">}</span>
<span id="L88" class="LineNr"> 88 </span>      tmp <span class="Special">&lt;-</span> copy yy
<span id="L89" class="LineNr"> 89 </span>      tmp <span class="Special">&lt;-</span> multiply yy
<span id="L90" class="LineNr"> 90 </span>      <span class="Delimiter">{</span>
<span id="L91" class="LineNr"> 91 </span>        <span class="PreProc">break-if-not-overflow</span>
<span id="L92" class="LineNr"> 92 </span>        <a href='317abort.subx.html#L5'>abort</a> <span class="Constant">&quot;bezier: overflow 4&quot;</span>
<span id="L93" class="LineNr"> 93 </span>      <span class="Delimiter">}</span>
<span id="L94" class="LineNr"> 94 </span>      dist2 <span class="Special">&lt;-</span> add tmp
<span id="L95" class="LineNr"> 95 </span>    <span class="Delimiter">}</span>
<span id="L96" class="LineNr"> 96 </span>    <span class="muComment"># if (dist1 &lt;= dist2) break</span>
<span id="L97" class="LineNr"> 97 </span>    compare dist1, dist2
<span id="L98" class="LineNr"> 98 </span>    <span class="PreProc">break-if-&lt;=</span>
<span id="L99" class="LineNr"> 99 </span>    <span class="muComment"># swap x0 and x2</span>
<span id="L100" class="LineNr">100 </span>    tmp <span class="Special">&lt;-</span> copy x0
<span id="L101" class="LineNr">101 </span>    copy-to x2, tmp
<span id="L102" class="LineNr">102 </span>    tmp <span class="Special">&lt;-</span> copy sx
<span id="L103" class="LineNr">103 </span>    tmp <span class="Special">&lt;-</span> add x1
<span id="L104" class="LineNr">104 </span>    copy-to x0, tmp
<span id="L105" class="LineNr">105 </span>    <span class="muComment"># swap y0 and y2</span>
<span id="L106" class="LineNr">106 </span>    tmp <span class="Special">&lt;-</span> copy y0
<span id="L107" class="LineNr">107 </span>    copy-to y2, tmp
<span id="L108" class="LineNr">108 </span>    tmp <span class="Special">&lt;-</span> copy sy
<span id="L109" class="LineNr">109 </span>    tmp <span class="Special">&lt;-</span> add y1
<span id="L110" class="LineNr">110 </span>    copy-to y0, tmp
<span id="L111" class="LineNr">111 </span>    <span class="muComment"># cur = -cur</span>
<span id="L112" class="LineNr">112 </span>    <span class="PreProc">var</span> negative-1/eax: int <span class="Special">&lt;-</span> copy <span class="Constant">-1</span>
<span id="L113" class="LineNr">113 </span>    <span class="PreProc">var</span> negative-1-f/<span class="Constant">xmm1</span>: float <span class="Special">&lt;-</span> convert negative-1
<span id="L114" class="LineNr">114 </span>    cur-f <span class="Special">&lt;-</span> multiply negative-1-f
<span id="L115" class="LineNr">115 </span>  <span class="Delimiter">}</span>
<span id="L116" class="LineNr">116 </span>  <span class="PreProc">var</span> x/<span class="muRegEcx">ecx</span>: int <span class="Special">&lt;-</span> copy x0
<span id="L117" class="LineNr">117 </span>  <span class="PreProc">var</span> y/<span class="muRegEdx">edx</span>: int <span class="Special">&lt;-</span> copy y0
<span id="L118" class="LineNr">118 </span>  <span class="PreProc">var</span> zero-f: float
<span id="L119" class="LineNr">119 </span>  <span class="muComment"># plot a curved part if necessary</span>
<span id="L120" class="LineNr">120 </span>  $draw-monotonic-bezier:curve: <span class="Delimiter">{</span>
<span id="L121" class="LineNr">121 </span>    compare cur-f, zero-f
<span id="L122" class="LineNr">122 </span>    <span class="PreProc">break-if-=</span>
<span id="L123" class="LineNr">123 </span>    <span class="muComment"># xx += sx</span>
<span id="L124" class="LineNr">124 </span>    tmp <span class="Special">&lt;-</span> copy sx
<span id="L125" class="LineNr">125 </span>    add-to xx, tmp
<span id="L126" class="LineNr">126 </span>    <span class="muComment"># sx = sgn(x2-x)</span>
<span id="L127" class="LineNr">127 </span>    tmp <span class="Special">&lt;-</span> copy x2
<span id="L128" class="LineNr">128 </span>    tmp <span class="Special">&lt;-</span> subtract x
<span id="L129" class="LineNr">129 </span>    tmp <span class="Special">&lt;-</span> <a href='506math.mu.html#L10'>sgn</a> tmp
<span id="L130" class="LineNr">130 </span>    copy-to sx, tmp
<span id="L131" class="LineNr">131 </span>    <span class="muComment"># xx *= sx</span>
<span id="L132" class="LineNr">132 </span>    tmp <span class="Special">&lt;-</span> copy sx
<span id="L133" class="LineNr">133 </span>    tmp <span class="Special">&lt;-</span> multiply xx
<span id="L134" class="LineNr">134 </span>    copy-to xx, tmp
<span id="L135" class="LineNr">135 </span>    <span class="muComment"># yy += sy</span>
<span id="L136" class="LineNr">136 </span>    tmp <span class="Special">&lt;-</span> copy sy
<span id="L137" class="LineNr">137 </span>    add-to yy, tmp
<span id="L138" class="LineNr">138 </span>    <span class="muComment"># sy = sgn(y2-y)</span>
<span id="L139" class="LineNr">139 </span>    tmp <span class="Special">&lt;-</span> copy y2
<span id="L140" class="LineNr">140 </span>    tmp <span class="Special">&lt;-</span> subtract y
<span id="L141" class="LineNr">141 </span>    tmp <span class="Special">&lt;-</span> <a href='506math.mu.html#L10'>sgn</a> tmp
<span id="L142" class="LineNr">142 </span>    copy-to sy, tmp
<span id="L143" class="LineNr">143 </span>    <span class="muComment"># yy *= sy</span>
<span id="L144" class="LineNr">144 </span>    tmp <span class="Special">&lt;-</span> copy sy
<span id="L145" class="LineNr">145 </span>    tmp <span class="Special">&lt;-</span> multiply yy
<span id="L146" class="LineNr">146 </span>    copy-to yy, tmp
<span id="L147" class="LineNr">147 </span>    <span class="muComment"># xy = 2*xx*xy</span>
<span id="L148" class="LineNr">148 </span>    tmp <span class="Special">&lt;-</span> copy xx
<span id="L149" class="LineNr">149 </span>    tmp <span class="Special">&lt;-</span> multiply yy
<span id="L150" class="LineNr">150 </span>    <span class="Delimiter">{</span>
<span id="L151" class="LineNr">151 </span>      <span class="PreProc">break-if-not-overflow</span>
<span id="L152" class="LineNr">152 </span>      <a href='317abort.subx.html#L5'>abort</a> <span class="Constant">&quot;bezier: overflow 5&quot;</span>
<span id="L153" class="LineNr">153 </span>    <span class="Delimiter">}</span>
<span id="L154" class="LineNr">154 </span>    tmp <span class="Special">&lt;-</span> shift-left <span class="Constant">1</span>
<span id="L155" class="LineNr">155 </span>    <span class="Delimiter">{</span>
<span id="L156" class="LineNr">156 </span>      <span class="PreProc">break-if-not-overflow</span>
<span id="L157" class="LineNr">157 </span>      <a href='317abort.subx.html#L5'>abort</a> <span class="Constant">&quot;bezier: overflow 6&quot;</span>
<span id="L158" class="LineNr">158 </span>    <span class="Delimiter">}</span>
<span id="L159" class="LineNr">159 </span>    copy-to xy, tmp
<span id="L160" class="LineNr">160 </span>    <span class="muComment"># xx *= xx</span>
<span id="L161" class="LineNr">161 </span>    tmp <span class="Special">&lt;-</span> copy xx
<span id="L162" class="LineNr">162 </span>    tmp <span class="Special">&lt;-</span> multiply tmp
<span id="L163" class="LineNr">163 </span>    <span class="Delimiter">{</span>
<span id="L164" class="LineNr">164 </span>      <span class="PreProc">break-if-not-overflow</span>
<span id="L165" class="LineNr">165 </span>      <a href='317abort.subx.html#L5'>abort</a> <span class="Constant">&quot;bezier: overflow 7&quot;</span>
<span id="L166" class="LineNr">166 </span>    <span class="Delimiter">}</span>
<span id="L167" class="LineNr">167 </span>    copy-to xx, tmp
<span id="L168" class="LineNr">168 </span>    <span class="muComment"># yy *= yy</span>
<span id="L169" class="LineNr">169 </span>    tmp <span class="Special">&lt;-</span> copy yy
<span id="L170" class="LineNr">170 </span>    tmp <span class="Special">&lt;-</span> multiply tmp
<span id="L171" class="LineNr">171 </span>    <span class="Delimiter">{</span>
<span id="L172" class="LineNr">172 </span>      <span class="PreProc">break-if-not-overflow</span>
<span id="L173" class="LineNr">173 </span>      <a href='317abort.subx.html#L5'>abort</a> <span class="Constant">&quot;bezier: overflow 7&quot;</span>
<span id="L174" class="LineNr">174 </span>    <span class="Delimiter">}</span>
<span id="L175" class="LineNr">175 </span>    copy-to yy, tmp
<span id="L176" class="LineNr">176 </span>    <span class="muComment"># if (cur*sx*sy &lt; 0) negative curvature</span>
<span id="L177" class="LineNr">177 </span>    <span class="Delimiter">{</span>
<span id="L178" class="LineNr">178 </span>      <span class="PreProc">var</span> tmp-f/<span class="Constant">xmm0</span>: float <span class="Special">&lt;-</span> copy cur-f
<span id="L179" class="LineNr">179 </span>      <span class="PreProc">var</span> sx-f/<span class="Constant">xmm1</span>: float <span class="Special">&lt;-</span> convert sx
<span id="L180" class="LineNr">180 </span>      tmp-f <span class="Special">&lt;-</span> multiply sx-f
<span id="L181" class="LineNr">181 </span>      <span class="PreProc">var</span> sy-f/<span class="Constant">xmm1</span>: float <span class="Special">&lt;-</span> convert sy
<span id="L182" class="LineNr">182 </span>      tmp-f <span class="Special">&lt;-</span> multiply sy-f
<span id="L183" class="LineNr">183 </span>      compare tmp-f, zero-f
<span id="L184" class="LineNr">184 </span>      <span class="PreProc">break-if-float&gt;=</span>
<span id="L185" class="LineNr">185 </span>      <span class="muComment">#</span>
<span id="L186" class="LineNr">186 </span>      negate xx
<span id="L187" class="LineNr">187 </span>      negate yy
<span id="L188" class="LineNr">188 </span>      negate xy
<span id="L189" class="LineNr">189 </span>      <span class="muComment"># cur = -cur</span>
<span id="L190" class="LineNr">190 </span>      <span class="PreProc">var</span> negative-1/eax: int <span class="Special">&lt;-</span> copy <span class="Constant">-1</span>
<span id="L191" class="LineNr">191 </span>      <span class="PreProc">var</span> negative-1-f/<span class="Constant">xmm1</span>: float <span class="Special">&lt;-</span> convert negative-1
<span id="L192" class="LineNr">192 </span>      cur-f <span class="Special">&lt;-</span> multiply negative-1-f
<span id="L193" class="LineNr">193 </span>    <span class="Delimiter">}</span>
<span id="L194" class="LineNr">194 </span>    <span class="PreProc">var</span> four/<span class="muRegEbx">ebx</span>: int <span class="Special">&lt;-</span> copy <span class="Constant">4</span>
<span id="L195" class="LineNr">195 </span>    <span class="PreProc">var</span> dx-f/<span class="Constant">xmm5</span>: float <span class="Special">&lt;-</span> convert four
<span id="L196" class="LineNr">196 </span>    <span class="PreProc">var</span> dy-f/<span class="Constant">xmm6</span>: float <span class="Special">&lt;-</span> convert four
<span id="L197" class="LineNr">197 </span>    <span class="muComment"># dx = 4*sy*cur*(x1-x0) + xx - xy</span>
<span id="L198" class="LineNr">198 </span>    <span class="Delimiter">{</span>
<span id="L199" class="LineNr">199 </span>      <span class="PreProc">var</span> tmp/<span class="Constant">xmm0</span>: float <span class="Special">&lt;-</span> convert sy
<span id="L200" class="LineNr">200 </span>      dx-f <span class="Special">&lt;-</span> multiply tmp
<span id="L201" class="LineNr">201 </span>      dx-f <span class="Special">&lt;-</span> multiply cur-f
<span id="L202" class="LineNr">202 </span>      tmp <span class="Special">&lt;-</span> convert x1
<span id="L203" class="LineNr">203 </span>      <span class="PreProc">var</span> tmp2/<span class="Constant">xmm3</span>: float <span class="Special">&lt;-</span> convert x
<span id="L204" class="LineNr">204 </span>      tmp <span class="Special">&lt;-</span> subtract tmp2
<span id="L205" class="LineNr">205 </span>      dx-f <span class="Special">&lt;-</span> multiply tmp
<span id="L206" class="LineNr">206 </span>      tmp <span class="Special">&lt;-</span> convert xx
<span id="L207" class="LineNr">207 </span>      dx-f <span class="Special">&lt;-</span> add tmp
<span id="L208" class="LineNr">208 </span>      tmp <span class="Special">&lt;-</span> convert xy
<span id="L209" class="LineNr">209 </span>      dx-f <span class="Special">&lt;-</span> subtract tmp
<span id="L210" class="LineNr">210 </span>    <span class="Delimiter">}</span>
<span id="L211" class="LineNr">211 </span>    <span class="muComment"># dy-f = 4*sx*cur*(y0-y1) + yy - xy</span>
<span id="L212" class="LineNr">212 </span>    <span class="Delimiter">{</span>
<span id="L213" class="LineNr">213 </span>      <span class="PreProc">var</span> tmp/<span class="Constant">xmm0</span>: float <span class="Special">&lt;-</span> convert sx
<span id="L214" class="LineNr">214 </span>      dy-f <span class="Special">&lt;-</span> multiply tmp
<span id="L215" class="LineNr">215 </span>      dy-f <span class="Special">&lt;-</span> multiply cur-f
<span id="L216" class="LineNr">216 </span>      tmp <span class="Special">&lt;-</span> convert y
<span id="L217" class="LineNr">217 </span>      <span class="PreProc">var</span> tmp2/<span class="Constant">xmm3</span>: float <span class="Special">&lt;-</span> convert y1
<span id="L218" class="LineNr">218 </span>      tmp <span class="Special">&lt;-</span> subtract tmp2
<span id="L219" class="LineNr">219 </span>      dy-f <span class="Special">&lt;-</span> multiply tmp
<span id="L220" class="LineNr">220 </span>      tmp <span class="Special">&lt;-</span> convert yy
<span id="L221" class="LineNr">221 </span>      dy-f <span class="Special">&lt;-</span> add tmp
<span id="L222" class="LineNr">222 </span>      tmp <span class="Special">&lt;-</span> convert xy
<span id="L223" class="LineNr">223 </span>      dy-f <span class="Special">&lt;-</span> subtract tmp
<span id="L224" class="LineNr">224 </span>    <span class="Delimiter">}</span>
<span id="L225" class="LineNr">225 </span>    <span class="muComment"># xx += xx</span>
<span id="L226" class="LineNr">226 </span>    tmp <span class="Special">&lt;-</span> copy xx
<span id="L227" class="LineNr">227 </span>    add-to xx, tmp
<span id="L228" class="LineNr">228 </span>    <span class="muComment"># yy += yy</span>
<span id="L229" class="LineNr">229 </span>    tmp <span class="Special">&lt;-</span> copy yy
<span id="L230" class="LineNr">230 </span>    add-to yy, tmp
<span id="L231" class="LineNr">231 </span>    <span class="muComment"># err = dx+dy+xy</span>
<span id="L232" class="LineNr">232 </span>    <span class="PreProc">var</span> err-f/<span class="Constant">xmm7</span>: float <span class="Special">&lt;-</span> copy dx-f
<span id="L233" class="LineNr">233 </span>    err-f <span class="Special">&lt;-</span> add dy-f
<span id="L234" class="LineNr">234 </span>    <span class="PreProc">var</span> xy-f/<span class="Constant">xmm0</span>: float <span class="Special">&lt;-</span> convert xy
<span id="L235" class="LineNr">235 </span>    err-f <span class="Special">&lt;-</span> add xy-f
<span id="L236" class="LineNr">236 </span>    <span class="muComment">#</span>
<span id="L237" class="LineNr">237 </span>    $draw-monotonic-bezier:<span class="PreProc">loop</span>: <span class="Delimiter">{</span>
<span id="L238" class="LineNr">238 </span>      <a href='500fake-screen.mu.html#L483'>pixel</a> <a href='500fake-screen.mu.html#L14'>screen</a>, x, y, color
<span id="L239" class="LineNr">239 </span>      <span class="muComment"># if (x == x2 &amp;&amp; y == y2) return</span>
<span id="L240" class="LineNr">240 </span>      <span class="Delimiter">{</span>
<span id="L241" class="LineNr">241 </span>        compare x, x2
<span id="L242" class="LineNr">242 </span>        <span class="PreProc">break-if-!=</span>
<span id="L243" class="LineNr">243 </span>        compare y, y2
<span id="L244" class="LineNr">244 </span>        <span class="PreProc">break-if-!=</span>
<span id="L245" class="LineNr">245 </span>        <span class="PreProc">return</span>
<span id="L246" class="LineNr">246 </span>      <span class="Delimiter">}</span>
<span id="L247" class="LineNr">247 </span>      <span class="muComment"># perform-y-step? = (2*err &lt; dx)</span>
<span id="L248" class="LineNr">248 </span>      <span class="PreProc">var</span> perform-y-step?/eax: boolean <span class="Special">&lt;-</span> copy <span class="Constant">0</span>/false
<span id="L249" class="LineNr">249 </span>      <span class="PreProc">var</span> two-err-f/<span class="Constant">xmm0</span>: float <span class="Special">&lt;-</span> copy err-f
<span id="L250" class="LineNr">250 </span>      <span class="Delimiter">{</span>
<span id="L251" class="LineNr">251 </span>        <span class="PreProc">var</span> two/<span class="muRegEbx">ebx</span>: int <span class="Special">&lt;-</span> copy <span class="Constant">2</span>
<span id="L252" class="LineNr">252 </span>        <span class="PreProc">var</span> two-f/<span class="Constant">xmm1</span>: float <span class="Special">&lt;-</span> convert two
<span id="L253" class="LineNr">253 </span>        two-err-f <span class="Special">&lt;-</span> multiply two-f
<span id="L254" class="LineNr">254 </span>        compare two-err-f, dx-f
<span id="L255" class="LineNr">255 </span>        <span class="PreProc">break-if-float&gt;=</span>
<span id="L256" class="LineNr">256 </span>        perform-y-step? <span class="Special">&lt;-</span> copy <span class="Constant">1</span>/true
<span id="L257" class="LineNr">257 </span>      <span class="Delimiter">}</span>
<span id="L258" class="LineNr">258 </span>      <span class="muComment"># if (2*err &gt; dy)</span>
<span id="L259" class="LineNr">259 </span>      <span class="Delimiter">{</span>
<span id="L260" class="LineNr">260 </span>        compare two-err-f, dy-f
<span id="L261" class="LineNr">261 </span>        <span class="PreProc">break-if-float&lt;=</span>
<span id="L262" class="LineNr">262 </span>        <span class="muComment"># x += sx</span>
<span id="L263" class="LineNr">263 </span>        x <span class="Special">&lt;-</span> add sx
<span id="L264" class="LineNr">264 </span>        <span class="muComment"># dx -= xy</span>
<span id="L265" class="LineNr">265 </span>        <span class="PreProc">var</span> xy-f/<span class="Constant">xmm0</span>: float <span class="Special">&lt;-</span> convert xy
<span id="L266" class="LineNr">266 </span>        dx-f <span class="Special">&lt;-</span> subtract xy-f
<span id="L267" class="LineNr">267 </span>        <span class="muComment"># dy += yy</span>
<span id="L268" class="LineNr">268 </span>        <span class="PreProc">var</span> yy-f/<span class="Constant">xmm0</span>: float <span class="Special">&lt;-</span> convert yy
<span id="L269" class="LineNr">269 </span>        dy-f <span class="Special">&lt;-</span> add yy-f
<span id="L270" class="LineNr">270 </span>        <span class="muComment"># err += dy</span>
<span id="L271" class="LineNr">271 </span>        err-f <span class="Special">&lt;-</span> add dy-f
<span id="L272" class="LineNr">272 </span>      <span class="Delimiter">}</span>
<span id="L273" class="LineNr">273 </span>      <span class="muComment"># if perform-y-step?</span>
<span id="L274" class="LineNr">274 </span>      <span class="Delimiter">{</span>
<span id="L275" class="LineNr">275 </span>        compare perform-y-step?, <span class="Constant">0</span>/false
<span id="L276" class="LineNr">276 </span>        <span class="PreProc">break-if-=</span>
<span id="L277" class="LineNr">277 </span>        <span class="muComment"># y += sy</span>
<span id="L278" class="LineNr">278 </span>        y <span class="Special">&lt;-</span> add sy
<span id="L279" class="LineNr">279 </span>        <span class="muComment"># dy -= xy</span>
<span id="L280" class="LineNr">280 </span>        <span class="PreProc">var</span> xy-f/<span class="Constant">xmm0</span>: float <span class="Special">&lt;-</span> convert xy
<span id="L281" class="LineNr">281 </span>        dy-f <span class="Special">&lt;-</span> subtract xy-f
<span id="L282" class="LineNr">282 </span>        <span class="muComment"># dx += xx</span>
<span id="L283" class="LineNr">283 </span>        <span class="PreProc">var</span> xx-f/<span class="Constant">xmm0</span>: float <span class="Special">&lt;-</span> convert xx
<span id="L284" class="LineNr">284 </span>        dx-f <span class="Special">&lt;-</span> add xx-f
<span id="L285" class="LineNr">285 </span>        <span class="muComment"># err += dx</span>
<span id="L286" class="LineNr">286 </span>        err-f <span class="Special">&lt;-</span> add dx-f
<span id="L287" class="LineNr">287 </span>      <span class="Delimiter">}</span>
<span id="L288" class="LineNr">288 </span>      <span class="muComment"># if (dy &lt; dx) loop</span>
<span id="L289" class="LineNr">289 </span>      compare dy-f, dx-f
<span id="L290" class="LineNr">290 </span>      <span class="PreProc">loop-if-float&lt;</span>
<span id="L291" class="LineNr">291 </span>    <span class="Delimiter">}</span>
<span id="L292" class="LineNr">292 </span>  <span class="Delimiter">}</span>
<span id="L293" class="LineNr">293 </span>  <span class="muComment"># plot the remaining straight line</span>
<span id="L294" class="LineNr">294 </span>  <a href='507line.mu.html#L1'>draw-line</a> <a href='500fake-screen.mu.html#L14'>screen</a>, x y, x2 y2, color
<span id="L295" class="LineNr">295 </span><span class="Delimiter">}</span>
<span id="L296" class="LineNr">296 </span>
<span id="L297" class="LineNr">297 </span><span class="muComment"># 0 &lt;= u &lt;= 1</span>
<span id="L298" class="LineNr">298 </span><span class="PreProc">fn</span> <span class="muFunction"><a href='509bezier.mu.html#L298'>bezier-point</a></span> u: float, x0: int, x1: int, x2: int<span class="PreProc"> -&gt; </span>_/eax: int <span class="Delimiter">{</span>
<span id="L299" class="LineNr">299 </span>  <span class="PreProc">var</span> one/eax: int <span class="Special">&lt;-</span> copy <span class="Constant">1</span>
<span id="L300" class="LineNr">300 </span>  <span class="PreProc">var</span> u-prime/<span class="Constant">xmm0</span>: float <span class="Special">&lt;-</span> convert one
<span id="L301" class="LineNr">301 </span>  u-prime <span class="Special">&lt;-</span> subtract u
<span id="L302" class="LineNr">302 </span>  <span class="PreProc">var</span> result/<span class="Constant">xmm1</span>: float <span class="Special">&lt;-</span> convert x0
<span id="L303" class="LineNr">303 </span>  result <span class="Special">&lt;-</span> multiply u-prime
<span id="L304" class="LineNr">304 </span>  result <span class="Special">&lt;-</span> multiply u-prime
<span id="L305" class="LineNr">305 </span>  <span class="PreProc">var</span> term2/<span class="Constant">xmm2</span>: float <span class="Special">&lt;-</span> convert x1
<span id="L306" class="LineNr">306 </span>  term2 <span class="Special">&lt;-</span> multiply u
<span id="L307" class="LineNr">307 </span>  term2 <span class="Special">&lt;-</span> multiply u-prime
<span id="L308" class="LineNr">308 </span>  result <span class="Special">&lt;-</span> add term2
<span id="L309" class="LineNr">309 </span>  result <span class="Special">&lt;-</span> add term2
<span id="L310" class="LineNr">310 </span>  <span class="PreProc">var</span> term3/<span class="Constant">xmm2</span>: float <span class="Special">&lt;-</span> convert x2
<span id="L311" class="LineNr">311 </span>  term3 <span class="Special">&lt;-</span> multiply u
<span id="L312" class="LineNr">312 </span>  term3 <span class="Special">&lt;-</span> multiply u
<span id="L313" class="LineNr">313 </span>  result <span class="Special">&lt;-</span> add term3
<span id="L314" class="LineNr">314 </span>  <span class="PreProc">var</span> result/eax: int <span class="Special">&lt;-</span> convert result
<span id="L315" class="LineNr">315 </span>  <span class="PreProc">return</span> result
<span id="L316" class="LineNr">316 </span><span class="Delimiter">}</span>
</pre>
</body>
</html>
<!-- vim: set foldmethod=manual : -->