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8.9

Polygon Outlines : Small features at concave vertexes

Asked by FalconZero in 3D Game Programming, Algorithms, C++ Programming Language

Tags: Polygon Outline, Concave Vertex, Geometry

I have a function  to calculate a polygon which is outset a fixed distance from an input polygon (Fig 1). My function operates on a vector representing the input polygon by taking three consecutive vertexes and calculating new vertexes based on them.

For colinear vertexes it does not output any vertex.

For convex vertexes it calculates an arc of vertexes around the input vertex (Shown below)

For concave vertexes it calculates the intersection point of two lines offset from the segments described by the two vertexes. In Fig 2, The line AB becomes DE, the line BC becomes FG, the intersect of DE with FG (marked H) is the new vertex.

My problem is that the convex vertex C produces the new vertexes around K (circled green). which are too close to AB. The correct output would eliminate the vertexes around K, eliminate vertex H and add a new vertex at M.

The Figures below give a clearer explanation of the problem.

My program already has OpenGL tessalator functions available for CSG, which might be useful, but a pure solution would be much better.
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bool polygon_c::outline_vertex(polygon_c* newpoly, doublePair prev, doublePair cur, doublePair next, double distance){	
	//Get vectors representing the lines
	doublePair A = cur-prev;
	doublePair B = next-cur;
 
	//Calculate the offset vectors for the lines (rotate by 90degrees, divide by length to get unit perp vector, multiply by 'distance')
	doublePair offsetA=doublePair(-A.y,A.x).unit()*distance;
	doublePair offsetB=doublePair(-B.y,B.x).unit()*distance;
 
	//Determine if the angle made by A-B is convex, concave, straight or reverse
	double ang=A.angle(B);
 
	//Clamp really small angles to zero
	(abs(ang)<10e-5) && (ang=0);
 
	//Straight, convex or concave?
	if ((ang<0) || (prev==next)){			//Concave - return arc at 'distance' around cur starting from cur+offsetA, ending at cur+offsetB
		//TODO : Draw arc		
		double incAng=PI2/18;
		double angle;
		double endAng;
		
		//Add arc startpoints
		newpoly->verts.push_back(cur+offsetA);
 
		//For straight lines (IE prev==next), 'fix' the angle to account for lack of 'clockwiseness' in doubleback nodes
		if (prev==next){ang=-PI;}
 
		//Determine start and end angles
		angle=atan2(offsetA.y, offsetA.x)-incAng;
		endAng=(angle+ang)+incAng;
 
		double points=ceil((endAng-angle)/incAng);
		incAng=(endAng-angle)/points;
 
		//Add arc
		while (angle>endAng){
			newpoly->verts.push_back(cur+doublePair(cos(angle)*distance,sin(angle)*distance));
			angle-=incAng;
		}
 
		//Add the arc endpoint
		newpoly->verts.push_back(cur+offsetB);
 
	}else if (ang>0){	//Convex - return intersect(prev+offsetA->cur+offsetA, cur+offsetB->next+offsetB)
		doublePair intersect=doublePair::line_intersect(prev+offsetA,cur+offsetA,  cur+offsetB,next+offsetB);
		newpoly->verts.push_back(intersect);
	}else{				//Straigh line - return cur+offsetA		
		//Comment out to simplify the polygon
		//newpoly->verts.push_back(cur+offsetA);
	}
 
	return true;
}
Attachments:
 
Fig 1 : Graphical depiction of problem
Fig 1 : Graphical depiction of problem
 
 
Fig 2 : Extended graphical depiction of problem
Fig 2 : Extended graphical depiction of problem
 
 
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Keywords: Polygon Outlines : Small features at c…
 
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[+][-]10/03/09 01:24 PM, ID: 25486890Accepted Solution

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Zones: 3D Game Programming, Algorithms, C++ Programming Language
Tags: Polygon Outline, Concave Vertex, Geometry
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Solution Provided By: JoseParrot
Participating Experts: 4
Solution Grade: A
 
[+][-]09/30/09 12:22 AM, ID: 25456226Expert Comment

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