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Scale polygon by vertex

Posted on 2008-10-14
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Last Modified: 2013-11-20
I am working with some code that calcs area of a polygon by summing the vertexes, etc.. with a mathematical formula. How can I rescale this polygon when I have vertex coordinates to work with?
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Question by:steenpat
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10 Comments
 
LVL 84

Expert Comment

by:ozo
ID: 22715229
new = vertex + scale*(old - vertex)
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Author Comment

by:steenpat
ID: 22716018
By old are you meaning the last vertex before this one? I tried this formula and its not working..
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Author Comment

by:steenpat
ID: 22716332
let me rephrase what i am doing..
i guess i am not scaling the entire thing by one factor, I am rounding each segment to the nearest round quantity. like if a side is 5'7" it rounds to 6'0"
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Author Comment

by:steenpat
ID: 22716702
i guess i should say this works for scaling by a single factor...
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LVL 84

Expert Comment

by:ozo
ID: 22717279
Could you give an example of what you mean?
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Author Comment

by:steenpat
ID: 22720552
say i have a box,
it has dimensions 11'6 x 10'1,
the new dimensions of the box are 12'x10' after rounding the segments
and now area is 120, as opposed to 115.95. I tried your formula with success if there is a constant scale factor, but if the scale changes after each pass through the vertexes, the area is different depending on which vertex it starts with if the polygon has more than four verts(for some reason it calcs right for equal or less than that). the way it calcs polygon area is by using a mathematical formula:
 1/2 * sum of [(x1y2-x2y1) + (x2y3-y2x3)...etc]
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Author Comment

by:steenpat
ID: 22721290
probably some logic issue.. ill do some debugigng and get back to you
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LVL 84

Expert Comment

by:ozo
ID: 22723290
1/2 * sum of [(x1y2-x2y1) + (x2y3-y2x3)...etc]
should work regardless of the scale factor and how many vertices and  where it starts (as long as it ends in the same place)
but I'm not sure what you mean that the scale changes after each pass through the vertexes
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LVL 18

Accepted Solution

by:
Jose Parrot earned 500 total points
ID: 22723465
This is not scaling.
The scaling tranformation is a resizing of a geometric entity by multiplying its coordiantes by a scaling factor. In multi dimensional words we can have a different factor for each dimension.
What you are looking for is just rounding, which can be solved by using trunc / round / floor / ceil functions. In your case, round(value): round(10.2) = 10;    round(10.6) = 11;
In C/C++ can be done by casting the variables.
Example: sum( (int)x1*(int)y2 - (int)x2*(int)y1) + (int)x2*(int)y3 - (int)y2*(int)x3 + ...)
Jose
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Author Comment

by:steenpat
ID: 22726721
this is my code.. it is not working.
it cals the mag between vertexes and rounds that number then readjusts each vertex in the struct, to start from 0,0 on forwards.
void RoundPolygonVertices( VERTEXES& vcVertexes, double dRound )
	{
		VERTEXES vt;
		CVertex v0,v1;
		long lCount = vcVertexes.size();
 
		for( int i = 0; i < lCount; ++i )
		{
			if(i)
			{
				double dLength = Magnitude(vcVertexes[i], vcVertexes[i-1]);
				double slope=(vcVertexes[i].dY-vcVertexes[i-1].dY)/(vcVertexes[i].dX-vcVertexes[i-1].dX);
				double slopeAngle;
				if(!_isnan(slope))
					slopeAngle=atan(slope);
				else
				{
					slope=0;
					slopeAngle=0;
				}
 
				if( dLength > 0.0 && dRound > 0.0 )
				{
 
					if(fmod( dLength, dRound) > 0)
					{
						double dUpper, dLower;
						dLower = floor(dLength / dRound) * dRound;
						dUpper = dLower+dRound;
 
						if((dLength-dLower) >= (dUpper-dLength))
							dLength=dUpper;
						else
							dLength=dLower;
					}
				
					v1=vcVertexes[i]-vcVertexes[i-1];
 
					if(v1.dX)
						v1.dX=v1.dX/fabs(v1.dX);
					if(v1.dY)
						v1.dY=v1.dY/fabs(v1.dY);
 
					v1.dY=v1.dY*fabs(sin(slopeAngle)*dLength);
					v1.dX=v1.dX*fabs(cos(slopeAngle)*dLength);
 
					v0=v1+v0;
				}
 
				vt.push_back(v0);
					
			}
			else
				vt.push_back( v0 );
				
		}
 
		vcVertexes.clear();
		vcVertexes.insert( vcVertexes.begin(), vt.begin(), vt.end() );

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