[HN Gopher] Interpolating Polygons (2017)
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       Interpolating Polygons (2017)
        
       Author : mcovalt
       Score  : 16 points
       Date   : 2023-07-15 10:26 UTC (12 hours ago)
        
 (HTM) web link (lambdafunk.com)
 (TXT) w3m dump (lambdafunk.com)
        
       | Someone wrote:
       | FTA: _"As shown, interpolating polygons with the same number of
       | points is straightforward"_
       | 
       | I disagree. The code uses a mapping between the corners of the
       | two polygons, but doesn't discuss how to pick the best one (out
       | of a possible _2n_ for n-sided polygons).
       | 
       | For example, if you want to interpolate a square to the same
       | square, rotated by 181 degrees, the mapping that maps each corner
       | to its opposite corner produces a nicer animation than the
       | identity mapping.
       | 
       | I don't think picking the best looking mapping is entirely
       | straightforward. For example, which of these produces nicer
       | results:
       | 
       | - minimize the sum of the distances that the corners move
       | 
       | - minimize the sum of the squares of the distances that the
       | corners move
       | 
       | - minimize the area removed/added during the interpolation
       | 
       | - minimize the amount by which the area of the polygon varies
       | during the interpolation
       | 
       | ?
       | 
       | Of course, opinions will differ on what is nicer, but I think
       | everybody will agree the identity mapping isn't always the
       | nicest.
       | 
       | = I would also use a smarter algorithm for equal-sided polygons
        
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       (page generated 2023-07-15 23:01 UTC)