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new pointAt() method for AdvancedQuadratic Bezier and first backup of quad. Bezier refinement in bezier utils

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This commit is contained in:
thealgorithmist 2010-11-15 23:30:40 +00:00
parent 974640d497
commit d1efa43a56
2 changed files with 101 additions and 9 deletions
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26
Degrafa/com/degrafa/geometry/AdvancedQuadraticBezier.as
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@ -58,13 +58,13 @@ package com.degrafa.geometry
**/
public class AdvancedQuadraticBezier extends QuadraticBezier
{
// bezier polynomial coefficients
private var _c0X:Number;
private var _c0Y:Number;
private var _c1X:Number;
private var _c1Y:Number;
private var _c2X:Number;
private var _c2Y:Number;
// bezier polynomial coefficients
private var _c0X:Number;
private var _c0Y:Number;
private var _c1X:Number;
private var _c1Y:Number;
private var _c2X:Number;
private var _c2Y:Number;
/**
* Constructor.
@ -507,12 +507,20 @@ package com.degrafa.geometry
return new AdvancedQuadraticBezier(x1,y1,pX,pY,_x,_y);
}
override public function pointAt(_t:Number):Point
{
var t:Number = _t < 0 ? 0 : _t;
t = t > 1 ? 1 : t;
return new Point( _c0X + t*(_c1X + t*(_c2X)), _c0Y + t*(_c1Y + t*(_c2Y)) );
}
// recompute polynomial coefficients
private function getBezierCoef():void
{
_c0X = x0;
_c0Y = y0;
_c0X = x0;
_c0Y = y0;
_c1X = 2.0*(cx-x0);
_c1Y = 2.0*(cy-y0);

84
Degrafa/com/degrafa/geometry/utilities/BezierUtils.as
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@ -28,6 +28,8 @@
//
// copyright (c) 2006-2007, Jim Armstrong. All Rights Reserved.
//
// version 1.2 added quad. bezier refinement as experimental method
//
// This software program is supplied 'as is' without any warranty, express, implied,
// or otherwise, including without limitation all warranties of merchantability or fitness
// for a particular purpose. Jim Armstrong shall not be liable for any special incidental, or
@ -572,5 +574,87 @@ package com.degrafa.geometry.utilities
_right[j] = p[index];
}
}
/**
* quadRefine refines a quadratic Bezier curve in the interval [t1,t2], where t1 and t2 are in (0,1), t2 > t1
*
* @param _q:AdvancedQuadraticBezier reference to quadratic Bezier curve to be refined
* @param _t1:Number left point in refinement interval
* @param _t2:Number right point in refinement interval
*
* @return Object x0, y0, cx, cy, x1, and y1 properties are control points of quadratic bezier curve representing the segment of the original curve in [t1,t2]
* returns a copy of the input quadratic bezier if input interval is invalid
*
* @since 1.2
*
*/
public static function quadRefine(_q:AdvancedQuadraticBezier, _t1:Number, _t2:Number):Object
{
if( _t1 < 0 || _t2 > 1 || _t2 <= _t1 )
return { x0:_q.x0, y0:_q.y0, cx:_q.cx, cy:_q.cy, x1:_q.x1, y1:_q.y1 };
// four points defining two lines
var p:Point = _q.pointAt(_t1);
var x1:Number = p.x;
var y1:Number = p.y;
var x2:Number = (1-_t1)*_q.cx + _t1*_q.x1;
var y2:Number = (1-_t1)*_q.cy + _t1*_q.y1;
var x3:Number = (1-_t2)*_q.x0 + _t2*_q.cx;
var y3:Number = (1-_t2)*_q.y0 + _t2*_q.cy;
var x4:Number = (1-_t2)*_q.cx + _t2*_q.x1;
var y4:Number = (1-_t2)*_q.cy + _t2*_q.y1;
var o:Object = intersect(x1, y1, x2, y2, x3, y3, x4, y4);
p = _q.pointAt(_t2);
return { x0:x1, y0:y1, cx:o.cx, cy:o.cy, x1:p.x, y1:p.y };
}
private static function intersect(x1:Number, y1:Number, x2:Number, y2:Number, x3:Number, y3:Number, x4:Number, y4:Number):Object
{
// tbd - haven't tested every path through this code yet - please feel free to do it for me so I can get back to the mundane
// task of making a living while you score some bucks off my free code :)
var deltaX1:Number = x2-x1;
var deltaX2:Number = x4-x3;
var d1Abs:Number = Math.abs(deltaX1);
var d2Abs:Number = Math.abs(deltaX2);
var m1:Number = 0;
var m2:Number = 0;
var pX:Number = 0;
var pY:Number = 0;
if( d1Abs <= 0.000001 )
{
pX = x1;
m2 = (y3 - y4)/deltaX2;
pY = (d2Abs <= 0.000001) ? (x1 + 3*(y1-x1)) : (m2*(x1-x4)+y4);
}
else if( d2Abs <= 0.000001 )
{
pX = x4;
m1 = (y2 - y1)/deltaX1;
pY = (d1Abs <= 0.000001) ? (x3 + 3*(x3-x4)) : (m1*(x4-x1)+y1);
}
else
{
m1 = (y2 - y1)/deltaX1;
m2 = (y4 - y3)/deltaX2;
if( Math.abs(m1) <= 0.000001 && Math.abs(m2) <= 0.000001 )
{
pX = 0.5*(x1 + x4);
pY = 0.5*(y1 + y4);
}
else
{
var b1:Number = y1 - m1*x1;
var b2:Number = y4 - m2*x4;
pX = (b2-b1)/(m1-m2);
pY = m1*pX + b1;
}
}
return {cx:pX, cy:pY};
}
}
}