Create non-convex, complex shapes with Box2D
If you are working with Box2D for a while, probably you have already met the problem you can’t create non-convex shapes. This is a problem Box2D faces for years, as you can see from this post, and due to Box2D’s structure itself, we will never be able to create concave shapes.
That’s why some 3rd party libraries like PhysicsEditor allow us to break a concave shape into a set of convex shapes and make possible the creation of complex bodies.
Antoan Angelov, the author of the optimized version of the Box2d slicing engine, strikes back with another great Box2D class called b2Separator.
« The class is called b2Separator, and yes – it is made to work specifically with Box2D! What does it do, you ask? Well, we all hate when we have to make a more complex, non-convex shape for our b2Body – because we have to manually make many b2Fixtures, and make those really confusing and time-wasting calculations to see how each fixture is supposed to fit in with the others. Well, our troubles are now over, because what b2Separator does is separate a non-convex shape into smaller, convex shapes in a very optimized way and add them as b2Fixtures to a b2Body. All you need to do is give it the vertices of the shape you want! »
This is the fully commented class:
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/* * Convex Separator for Box2D Flash * * This class has been written by Antoan Angelov. * It is designed to work with Erin Catto's Box2D physics library. * * Everybody can use this software for any purpose, under two restrictions: * 1. You cannot claim that you wrote this software. * 2. You can not remove or alter this notice. * */ package Box2DSeparator{ import Box2D.Collision.Shapes.b2PolygonShape; import Box2D.Common.Math.b2Vec2; import Box2D.Dynamics.b2Body; import Box2D.Dynamics.b2FixtureDef; public class b2Separator; { public function b2Separator() { } /** * Separates a non-convex polygon into convex polygons and adds them as fixtures to the <code>body</code> parameter.<br/> * There are some rules you should follow (otherwise you might get unexpected results) : * <ul> * <li>This class is specifically for non-convex polygons. If you want to create a convex polygon, you don't need to use this class - Box2D's <code>b2PolygonShape</code> class allows you to create convex shapes with the <code>setAsArray()</code>/<code>setAsVector()</code> method.</li> * <li>The vertices must be in clockwise order.</li> * <li>No three neighbouring points should lie on the same line segment.</li> * <li>There must be no overlapping segments and no "holes".</li> * </ul> <p/> * @param body The b2Body, in which the new fixtures will be stored. * @param fixtureDef A b2FixtureDef, containing all the properties (friction, density, etc.) which the new fixtures will inherit. * @param verticesVec The vertices of the non-convex polygon, in clockwise order. * @param scale <code>[optional]</code> The scale which you use to draw shapes in Box2D. The bigger the scale, the better the precision. The default value is 30. * @see b2PolygonShape * @see b2PolygonShape.SetAsArray() * @see b2PolygonShape.SetAsVector() * @see b2Fixture * */ public function Separate(body:b2Body,fixtureDef:b2FixtureDef,verticesVec:Vector.<b2Vec2>,scale:Number=30):void { var i:int,n:int=verticesVec.length,j:int,m:int; var vec:Vector.<b2Vec2>=new Vector.<b2Vec2> ,figsVec:Array; var polyShape:b2PolygonShape; for (i=0; i<n; i++) { vec.push(new b2Vec2(verticesVec[i].x*scale,verticesVec[i].y*scale)); } figsVec=calcShapes(vec); n=figsVec.length; for (i=0; i<n; i++) { verticesVec=new Vector.<b2Vec2> ; vec=figsVec[i]; m=vec.length; for (j=0; j<m; j++) { verticesVec.push(new b2Vec2(vec[j].x/scale,vec[j].y/scale)); } polyShape=new b2PolygonShape ; polyShape.SetAsVector(verticesVec); fixtureDef.shape=polyShape; body.CreateFixture(fixtureDef); } } /** * Checks whether the vertices in <code>verticesVec</code> can be properly distributed into the new fixtures (more specifically, it makes sure there are no overlapping segments and the vertices are in clockwise order). * It is recommended that you use this method for debugging only, because it may cost more CPU usage. * <p/> * @param verticesVec The vertices to be validated. * @return An integer which can have the following values: * <ul> * <li>0 if the vertices can be properly processed.</li> * <li>1 If there are overlapping lines.</li> * <li>2 if the points are <b>not</b> in clockwise order.</li> * <li>3 if there are overlapping lines <b>and</b> the points are <b>not</b> in clockwise order.</li> * </ul> * */ public function Validate(verticesVec:Vector.<b2Vec2>):int { var i:int,n:int=verticesVec.length,j:int,j2:int,i2:int,i3:int,d:Number,ret:int=0; var fl:Boolean,fl2:Boolean=false; for (i=0; i<n; i++) { i2=(i<n-1)?i+1:0; i3=(i>0)?i-1:n-1; fl=false; for (j=0; j<n; j++) { if (((j!=i)&&j!=i2)) { if (! fl) { d=det(verticesVec[i].x,verticesVec[i].y,verticesVec[i2].x,verticesVec[i2].y,verticesVec[j].x,verticesVec[j].y); if ((d>0)) { fl=true; } } if ((j!=i3)) { j2=(j<n-1)?j+1:0; if (hitSegment(verticesVec[i].x,verticesVec[i].y,verticesVec[i2].x,verticesVec[i2].y,verticesVec[j].x,verticesVec[j].y,verticesVec[j2].x,verticesVec[j2].y)) { ret=1; } } } } if (! fl) { fl2=true; } } if (fl2) { if ((ret==1)) { ret=3; } else { ret=2; } } return ret; } private function calcShapes(verticesVec:Vector.<b2Vec2>):Array { var vec:Vector.<b2Vec2>; var i:int,n:int,j:int; var d:Number,t:Number,dx:Number,dy:Number,minLen:Number; var i1:int,i2:int,i3:int,p1:b2Vec2,p2:b2Vec2,p3:b2Vec2; var j1:int,j2:int,v1:b2Vec2,v2:b2Vec2,k:int,h:int; var vec1:Vector.<b2Vec2>,vec2:Vector.<b2Vec2>; var v:b2Vec2,hitV:b2Vec2; var isConvex:Boolean; var figsVec:Array=[],queue:Array=[]; queue.push(verticesVec); while (queue.length) { vec=queue[0]; n=vec.length; isConvex=true; for (i=0; i<n; i++) { i1=i; i2=(i<n-1)?i+1:i+1-n; i3=(i<n-2)?i+2:i+2-n; p1=vec[i1]; p2=vec[i2]; p3=vec[i3]; d=det(p1.x,p1.y,p2.x,p2.y,p3.x,p3.y); if ((d<0)) { isConvex=false; minLen=Number.MAX_VALUE; for (j=0; j<n; j++) { if (((j!=i1)&&j!=i2)) { j1=j; j2=(j<n-1)?j+1:0; v1=vec[j1]; v2=vec[j2]; v=hitRay(p1.x,p1.y,p2.x,p2.y,v1.x,v1.y,v2.x,v2.y); if (v) { dx=p2.x-v.x; dy=p2.y-v.y; t=dx*dx+dy*dy; if ((t<minLen)) { h=j1; k=j2; hitV=v; minLen=t; } } } } if ((minLen==Number.MAX_VALUE)) { err(); } vec1=new Vector.<b2Vec2> ; vec2=new Vector.<b2Vec2> ; j1=h; j2=k; v1=vec[j1]; v2=vec[j2]; if (! pointsMatch(hitV.x,hitV.y,v2.x,v2.y)) { vec1.push(hitV); } if (! pointsMatch(hitV.x,hitV.y,v1.x,v1.y)) { vec2.push(hitV); } h=-1; k=i1; while (true) { if ((k!=j2)) { vec1.push(vec[k]); } else { if (((h<0)||h>=n)) { err(); } if (! this.isOnSegment(v2.x,v2.y,vec[h].x,vec[h].y,p1.x,p1.y)) { vec1.push(vec[k]); } break; } h=k; if (((k-1)<0)) { k=n-1; } else { k--; } } vec1=vec1.reverse(); h=-1; k=i2; while (true) { if ((k!=j1)) { vec2.push(vec[k]); } else { if (((h<0)||h>=n)) { err(); } if (((k==j1)&&! this.isOnSegment(v1.x,v1.y,vec[h].x,vec[h].y,p2.x,p2.y))) { vec2.push(vec[k]); } break; } h=k; if (((k+1)>n-1)) { k=0; } else { k++; } } queue.push(vec1,vec2); queue.shift(); break; } } if (isConvex) { figsVec.push(queue.shift()); } } return figsVec; } private function hitRay(x1:Number,y1:Number,x2:Number,y2:Number,x3:Number,y3:Number,x4:Number,y4:Number):b2Vec2 { var t1:Number=x3-x1,t2:Number=y3-y1,t3:Number=x2-x1,t4:Number=y2-y1,t5:Number=x4-x3,t6:Number=y4-y3,t7:Number=t4*t5-t3*t6,a:Number; a=(((t5*t2)-t6*t1)/t7); var px:Number=x1+a*t3,py:Number=y1+a*t4; var b1:Boolean=isOnSegment(x2,y2,x1,y1,px,py); var b2:Boolean=isOnSegment(px,py,x3,y3,x4,y4); if ((b1&&b2)) { return new b2Vec2(px,py); } return null; } private function hitSegment(x1:Number,y1:Number,x2:Number,y2:Number,x3:Number,y3:Number,x4:Number,y4:Number):b2Vec2 { var t1:Number=x3-x1,t2:Number=y3-y1,t3:Number=x2-x1,t4:Number=y2-y1,t5:Number=x4-x3,t6:Number=y4-y3,t7:Number=t4*t5-t3*t6,a:Number; a=(((t5*t2)-t6*t1)/t7); var px:Number=x1+a*t3,py:Number=y1+a*t4; var b1:Boolean=isOnSegment(px,py,x1,y1,x2,y2); var b2:Boolean=isOnSegment(px,py,x3,y3,x4,y4); if ((b1&&b2)) { return new b2Vec2(px,py); } return null; } private function isOnSegment(px:Number,py:Number,x1:Number,y1:Number,x2:Number,y2:Number):Boolean { var b1:Boolean=((((x1+0.1)>=px)&&px>=x2-0.1)||(((x1-0.1)<=px)&&px<=x2+0.1)); var b2:Boolean=((((y1+0.1)>=py)&&py>=y2-0.1)||(((y1-0.1)<=py)&&py<=y2+0.1)); return ((b1&&b2)&&isOnLine(px,py,x1,y1,x2,y2)); } private function pointsMatch(x1:Number,y1:Number,x2:Number,y2:Number):Boolean { var dx:Number=(x2>=x1)?x2-x1:x1-x2,dy:Number=(y2>=y1)?y2-y1:y1-y2; return ((dx<0.1)&&dy<0.1); } private function isOnLine(px:Number,py:Number,x1:Number,y1:Number,x2:Number,y2:Number):Boolean { if ((((x2-x1)>0.1)||x1-x2>0.1)) { var a:Number=(y2-y1)/(x2-x1),possibleY:Number=a*(px-x1)+y1,diff:Number=(possibleY>py)?possibleY-py:py-possibleY; return (diff<0.1); } return (((px-x1)<0.1)||x1-px<0.1); } private function det(x1:Number,y1:Number,x2:Number,y2:Number,x3:Number,y3:Number):Number { return x1*y2+x2*y3+x3*y1-y1*x2-y2*x3-y3*x1; } private function err():void { throw new Error("A problem has occurred. Use the Validate() method to see where the problem is."); } } } |
And this is what you can do with it:
Download the source code and all required libraries.
They can be easily customized to meet the unique requirements of your project.














This post has 16 comments
Danny Phantom
wow. Amazing. I don’t work with Box2D – But I think I’m gonna try it :). Thanks for helping
Scott Mitchell
Hey Emanuele, Thanks for this tut, was great. I contribute to your web traffic everyday ;0 By checking everyday for new tuts. I was wondering if you were to carry on with the plant vs zombies or tiny wings game? Would be great to know its coming :)
Many thanks Scott
mmankt
WIN, thx Anton!
Bruce Isabelle
nice tutorial, thanks, i did created many shapes using Box2D..
Andreas Burg
Nice, now I can stop pushing shapes through PhysicsEditor only for that very purpose. :)
Many thanks!
Ben Reynolds
As always, a great tutorial. I’m not the most comfortable with box2d, it’s always useful to see applications like this :)
MC
I remember that in the WCK (world construcion kit from box2D alchemy port) you can create shapes, even non-convex shapes :s
Ari
Like MC mentioned, the alchemy version of box2d actually has this built in.
This is in the b2PolygonShape class:
/// Decompose a concave polygon into a bunch of convex ones. Pass it vector of vertices
/// in [x1, y1, x2, y2...] format. Returns a vector list of b2PolygonShapes that represent
/// the decomposition.
public static function Decompose(v:Vector.):Vector. {…
Chris Moeller
Awesome! I had gotten hung up on this step for a game in the past. Soon as I get more time put aside, need to get back to it :/
Olli
Excellent tool! Now one question. Given a bitmap image what would you suggest I should do to dynamically create a body for it? Is it even feasible?
Cool Stuff with the Flash Platform - 9/19/2011 | Remote Synthesis
[...] Feronato introduces b2Separator, a Box2d class written by Antoan Angelov to assist in creating non-convex, complex shapes with Box2D by automatically separating a non-convex shape into smaller convex [...]
Eric
Why do you only support CW(Clockwise Winding), according to the Box2D manual you must create polygons using CCW(Counter Clockwise windind).
See the manual for explenation:
http://box2d.org/manual.pdf
ToneTone
This is a great class – I’ve converted it to C++ (for use with the standard box2d library) and also to C# (for use in Unity). If anyone wants a copy tweet me @physmotone
tian
Hello,sir, can you covert the code to c++? if you can, thank you very much!
Jarad
This is a fantastic class! I’ve also converted it to C++ for use with Cocos2D-X. If anyone would like to fork it, be my guest =) http://github.com/delorenj
Jacob
This is an old post but… You have an error in your code. There is a semicolon at the end of line 19 which declares the public class. If you delete that the rest seems to be fine.