QBezier.as

リビジョン 2161, 12.6 kB (コミッタ: nutsu, コミット時期: 3 年前)
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1	//
2	// Licensed under the MIT License
3	//
4	// Copyright (C) 2008-2009 TAKANAWA Tomoaki (http://nutsu.com) and
5	// Spark project (www.libspark.org)
6	//
7	// Permission is hereby granted, free of charge, to any person obtaining a copy
8	// of this software and associated documentation files (the "Software"), to deal
9	// in the Software without restriction, including without limitation the rights
10	// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
11	// copies of the Software, and to permit persons to whom the Software is
12	// furnished to do so, subject to the following conditions:
13	//
14	// The above copyright notice and this permission notice shall be included in
15	// all copies or substantial portions of the Software.
16	//
17	// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
18	// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
19	// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
20	// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
21	// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
22	// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
23	// THE SOFTWARE.
24	//
25
26	package snapfit.shape
27	{
28	import flash.geom.Point;
29	import flash.geom.Rectangle;
30
31	public class QBezier implements IPath{
32
33	//start point
34	private var _x0:Number;
35	private var _y0:Number;
36
37	//end point
38	private var _x1:Number;
39	private var _y1:Number;
40
41	//control point
42	private var _cx:Number;
43	private var _cy:Number;
44
45	//length of bezier line
46	private var _length:Number;
47
48	//fixed numbers for integration
49	private var XY:Number;
50	private var B:Number;
51	private var C:Number;
52	private var CS:Number;
53	private var CS2:Number;
54	private var INTG_0:Number;
55
56	//
57	private var __err_d:Number = 0.1;
58
59	/**
60	* Quadratic Bezier Constructor
61	* @param start x
62	* @param start y
63	* @param end x
64	* @param end y
65	* @param control x
66	* @param control y
67	*/
68	public function QBezier( x0:Number, y0:Number, cx:Number, cy:Number, x1:Number, y1:Number )
69	{
70	_x0 = x0;
71	_y0 = y0;
72	_cx = cx;
73	_cy = cy;
74	_x1 = x1;
75	_y1 = y1;
76	_length = -1;
77	}
78
79	/**
80	* Clone
81	*/
82	public function clone():QBezier
83	{
84	var c:QBezier = new QBezier( _x0, _y0, _cx, _cy, _x1, _y1 );
85	if ( isNaN(_length) == false )
86	{
87	c._length = _length;
88	c.XY = XY; c.B = B; c.C = C; c.CS = CS; c.CS2 = CS2; c.INTG_0 = INTG_0;
89	}
90	return c;
91	}
92
93	//--------------------------------------------------------------------------------------------------- F
94
95	/**
96	* Quadratic Bezier Function
97	*/
98	public static function point( a:Number, b:Number, c:Number, t:Number ):Number
99	{
100	var tp:Number = 1.0 - t;
101	return a * tp * tp + 2 * b * t * tp + c * t * t;
102	}
103
104	/**
105	* Quadratic Bezier Tangent
106	*/
107	public static function tangent( a:Number, b:Number, c:Number, t:Number ):Number
108	{
109	return 2( t( a + c - 2*b ) - a + b );
110	}
111
112	/**
113	* Quadratic Bezier Function
114	* @param t( 0～1.0 )
115	* @return 座標
116	*/
117	public function f(t:Number):PathPoint
118	{
119	var tp:Number = 1.0 - t;
120	return new PathPoint( _x0tptp + 2_cxttp + _x1tt, _y0tptp + 2_cyttp + _y1tt );
121	}
122
123	/**
124	* Diff of Bezier Function
125	* @param t( 0～1.0 )
126	* @return ベクトル
127	*/
128	public function diff(t:Number):PathPoint
129	{
130	return new PathPoint( 2( t( _x0 + _x1 - 2_cx ) - _x0 + _cx ) , 2( t( _y0 + _y1 - 2_cy ) - _y0 + _cy ) );
131	}
132
133	public function vector( t:Number ):PathVector
134	{
135	var tp:Number = 1.0 - t;
136	return new PathVector( _x0tptp + 2_cxttp + _x1tt, _y0tptp + 2_cyttp + _y1tt,
137	2( t( _x0 + _x1 - 2_cx ) - _x0 + _cx ) , 2( t( _y0 + _y1 - 2_cy ) - _y0 + _cy ) );
138	}
139
140	//--------------------------------------------------------------------------------------------------- LENGTH_T
141
142	/**
143	* Length of bezier curve
144	* @return 長さ
145	*/
146	public function get length():Number
147	{
148	if( _length<0 )
149	__integrateInit();
150	return _length;
151	}
152
153	/**
154	* get coordinates by length
155	* @param len
156	*/
157	public function lengthToPoint( len:Number ):PathPoint
158	{
159	return f( lengthToValue( len ) );
160	}
161
162	/**
163	* integrate of bezier curve
164	* @param t( 0～1.0 )
165	* @return 積分値
166	*/
167	public function integrate(t:Number):Number
168	{
169	return (integrateF(t) - INTG_0);
170	}
171
172	/**
173	* get value from length
174	* @param len target lenth (0,length)
175	* @return t value
176	*/
177	public function lengthToValue( len:Number ):Number
178	{
179	if( len<0 \|\| len>length )
180	return Number.NaN;
181	else
182	return __seek( len, __err_d );
183	}
184
185	/**
186	* seek value
187	* @param len target length
188	* @param d 許容誤差
189	* @param t0 check t value
190	* @param td next check t value
191	* @return t value
192	*/
193	private function __seek( len:Number, d:Number = 0.1, t0:Number = 0.5, td:Number = 0.25 ):Number
194	{
195	var lent0:Number = integrate(t0);
196	if( Math.abs( len-lent0 )<d )
197	return t0;
198	else
199	return __seek( len, d, (lent0<len) ? t0+td : t0-td, td/2 );
200	}
201
202	//------------------------------------------------------------------------------CUT
203
204	/**
205	* Split Bezier at t.
206	* @param t ( 0 to 1 )
207	* @return QBezier[]
208	*/
209	public function split( t:Number ):Array
210	{
211	if( t<0 \|\| t>1 )
212	throw new ArgumentError("parameter t:0<t<1");
213
214	if ( t == 0 )
215	{
216	return [ null, clone() ];
217	}
218	else if ( t == 1 )
219	{
220	return [ clone(), null ];
221	}
222	else
223	{
224	var tp:Number = 1-t;
225	var ax:Number = _x0tp + _cxt;
226	var ay:Number = _y0tp + _cyt;
227	var bx:Number = _cxtp + _x1t;
228	var by:Number = _cytp + _y1t;
229	var px:Number = axtp + bxt;
230	var py:Number = aytp + byt;
231	return [ new QBezier( _x0, _y0, ax, ay, px, py ), new QBezier( px, py, bx, by, _x1, _y1 )];
232	}
233	}
234
235	/**
236	* Clip Bezier between t0 to t1.
237	* @param t0
238	* @param t1
239	* @return QBezier
240	*/
241	public function clip( t0:Number, t1:Number ):QBezier
242	{
243	//両端の座標とベクトル
244	var tp0:Number = 1-t0;
245	var tp1:Number = 1-t1;
246	var tx0:Number = _x0tp0tp0 + 2_cxt0tp0 + _x1t0*t0;
247	var ty0:Number = _y0tp0tp0 + 2_cyt0tp0 + _y1t0*t0;
248	var tx1:Number = _x0tp1tp1 + 2_cxt1tp1 + _x1t1*t1;
249	var ty1:Number = _y0tp1tp1 + 2_cyt1tp1 + _y1t1*t1;
250	var vx0:Number = 2( t0( _x0 + _x1 - 2*_cx ) - _x0 + _cx );
251	var vy0:Number = 2( t0( _y0 + _y1 - 2*_cy ) - _y0 + _cy );
252	var vx1:Number = 2( t1( _x0 + _x1 - 2*_cx ) - _x0 + _cx );
253	var vy1:Number = 2( t1( _y0 + _y1 - 2*_cy ) - _y0 + _cy );
254	//両端の差分
255	var dx:Number = tx1 - tx0;
256	var dy:Number = ty1 - ty0;
257
258	// Point(dx,dy) = a*(pv0 + pv1) のaを求める
259	var a:Number = ( dx != 0 ) ? dx/(vx0+vx1) : dy/(vy0+vy1);
260
261	return new QBezier( tx0, ty0, tx0+avx0, ty0+avy0, tx1, ty1 );
262	}
263
264	/**
265	* Clip Bezier by rectangle
266	* @param Cut Rectangle
267	* @return QBezier[]
268	*/
269	/*
270	public function clipByRect( cutRect:Rectangle ):Array
271	{
272	var ts:Array = clipTValueByRect(cutRect);
273	//result
274	var res:Array = [];
275	for( var i:int=0; i<ts.length ;i+=2 )
276	res.push( clip(ts[i],ts[i+1]) );
277
278	return res;
279	}
280	*/
281	/**
282	* Clip tVlaue by rectangle
283	* @param Cut Rectangle
284	* @return t[]
285	* @private
286	*/
287	/*
288	internal function clipTValueByRect( cutRect:Rectangle ):Array
289	{
290	var rect:Rectangle = getRect();
291	if ( cutRect.intersects( rect ) )
292	{
293	//内包かどうか
294	if ( cutRect.containsRect( rect ) )
295	{
296	return [0,1];
297	}
298
299	var ts:Array = QBezierUtil.intersectionTByRect(this,cutRect);
300	if( cutRect.contains( _x0, _y0 ) && ts[0]>1e-10 ) ts.unshift(0);
301	if( cutRect.contains( _x1, _y1 ) && ts[ts.length-1]<(1-1e-10) ) ts.push(1);
302
303	//端点のrect.containsが微妙に外れる場合の誤差処理
304	if ( ts.length == 1 )
305	{
306	if( cutRect.containsPoint( f(ts[0]-1e-10) ) ){
307	ts.unshift( 0 );
308	}else{
309	ts.push( 1 );
310	}
311	}
312
313	//端点が交点の場合
314	if ( ts.length == 3 )
315	{
316	if( cutRect.containsPoint( f((ts[1]+ts[0])/2) ) ){
317	ts.pop();
318	}else{
319	ts.shift();
320	}
321	}
322
323	//result
324	return ts;
325	}
326	else
327	{
328	return [];
329	}
330	}
331	*/
332	//------------------------------------------------------------------------------INTERSECTION
333
334	/**
335	* Rectangle of bezier curve
336	*/
337	public function getRect():Rectangle
338	{
339	var xlim:Number = _x0;
340	var ylim:Number = _y0;
341	var xt:Number = (_x0 - _cx)/( _x0 + _x1 - 2*_cx );
342	var yt:Number = (_y0 - _cy)/( _y0 + _y1 - 2*_cy );
343
344	//xt,ytがInfinity,NaNのときも切り捨て
345	if( xt>0 && xt<1 )
346	xlim = _x0(1-xt)(1-xt) + 2_cxxt(1-xt) + _x1xt*xt;
347
348	if( yt>0 && yt<1 )
349	ylim = _y0(1-yt)(1-yt) + 2_cyyt(1-yt) + _y1yt*yt;
350
351	var rx0:Number = Math.min( _x0, Math.min( _x1, xlim ) );
352	var ry0:Number = Math.min( _y0, Math.min( _y1, ylim ) );
353	var rx1:Number = Math.max( _x0, Math.max( _x1, xlim ) );
354	var ry1:Number = Math.max( _y0, Math.max( _y1, ylim ) );
355	return new Rectangle( rx0, ry0, rx1-rx0, ry1-ry0 );
356	}
357
358	/**
359	* fat line for intersection
360	*/
361	public function getFatLine():Array
362	{
363	var vx:Number = _x1 - _x0;
364	var vy:Number = _y1 - _y0;
365	var vcx:Number = point( _x0, _cx, _x1, 0.5 ) - _x0;
366	var vcy:Number = point( _y0, _cy, _y1, 0.5 ) - _y0;
367	var vlen:Number = Math.sqrt( vx * vx + vy * vy );
368	var d:Number = (vx * vcy - vy * vcx) / vlen;
369	vx /= vlen;
370	vy /= vlen;
371	var vdx:Number = -vy * d;
372	var vdy:Number = vx * d;
373	return [ _x0, _y0, _x1, _y1, _x1 + vdx, _y1 + vdy, _x0 + vdx, _y0 + vdy ];
374	}
375
376	//--------------------------------------------------------------------------------------------------- INTEGRATE
377
378	/**
379	* 積分定数初期化
380	*/
381	private function __integrateInit():void
382	{
383	var kx:Number = _x0 + _x1 - 2 * _cx;
384	var ky:Number = _y0 + _y1 - 2 * _cy;
385	var ax:Number = - _x0 + _cx;
386	var ay:Number = - _y0 + _cy;
387
388	if( kx==0 && ky==0 )
389	{
390	XY = 0;
391	B = 0;
392	C = 0;
393	CS = CS2 = 1.0;
394	_length = 0;
395	}
396	else
397	{
398	//積分計算の為の定数
399	XY = kxkx + kyky;
400	B = ( axkx + ayky )/XY;
401	C = ( axax + ayay )/XY - B*B;
402	if( C>1e-10 ){
403	CS = Math.sqrt(C);
404	CS2 = 0.0;
405	}else{
406	C = 0;
407	CS = CS2 = 1.0;
408	}
409	INTG_0 = integrateF(0.0);
410
411	//長さ
412	_length = integrate(1.0);
413	}
414	}
415
416	/**
417	* 積分関数
418	* @param t( 0～1.0 )
419	* @return 積分結果
420	*/
421	private function integrateF( t:Number ):Number
422	{
423	var BT:Number = B+t;
424	var BTS:Number = Math.sqrt( BT*BT+C );
425	return Math.sqrt(XY) * ( BTSBT + C Math.log( (BT + BTS)/CS + CS2 ) );
426	}
427
428	//--------------------------------------------------------------------------------------------------- COORDINATES
429
430	/**
431	* offset coordinates
432	* @param x offset
433	* @param y offset
434	*/
435	public function offset( x:Number, y:Number ):void
436	{
437	_x0 += x;
438	_y0 += y;
439	_x1 += x;
440	_y1 += y;
441	_cx += x;
442	_cx += y;
443	}
444
445	public function get point0():Point{ return new Point(_x0,_y0); }
446	public function set point0(p:Point):void
447	{
448	_x0 = p.x; _y0 = p.y; _length = Number.NaN;
449	}
450
451	public function get point1():Point{ return new Point(_x1,_y1); }
452	public function set point1(p:Point):void
453	{
454	_x1 = p.x; _y1 = p.y; _length = Number.NaN;
455	}
456
457	public function get control():Point{ return new Point(_cx,_cy); }
458	public function set control(p:Point):void
459	{
460	_cx = p.x; _cx = p.y; _length = -1;
461	}
462
463	//------
464
465	public function get x0():Number{ return _x0; }
466	public function set x0(v:Number):void
467	{
468	_x0 = v; _length = -1;
469	}
470
471	public function get y0():Number{ return _y0; }
472	public function set y0(v:Number):void
473	{
474	_y0 = v; _length = -1;
475	}
476	public function get x1():Number{ return _x1; }
477	public function set x1(v:Number):void
478	{
479	_x1 = v; _length = -1;
480	}
481
482	public function get y1():Number{ return _y1; }
483	public function set y1(v:Number):void
484	{
485	_y1 = v; _length = -1;
486	}
487
488	public function get cx():Number{ return _cx; }
489	public function set cx(v:Number):void
490	{
491	_cx = v; _length = -1;
492	}
493
494	public function get cy():Number{ return _cy; }
495	public function set cy(v:Number):void
496	{
497	_cy = v; _length = -1;
498	}
499	}
500	}

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