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POAlgorithm to fit fewest rectangles to irregular shape
 

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  1. POAlgorithm to fit fewest rectangles to irregular shape
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    <p>I have a rendering application that renders lots and lots of cubes in a 3-dimensional grid. This is inherently inefficient as each cube represents 4 vertices, and often the cubes are adjacent, creating one surface that could be represented by a single rectangle.</p> <p>To populate the area I use a 3-dimensional array, where a value of 0 denotes empty space and a non-0 value denotes a block.</p> <p>e.g. (where X denotes where a cube would be placed)</p> <pre><code>OOOXXXOOOO OOXXXXXXXO OOXXXXXXXO OOXXXXOOOO </code></pre> <p>would currently be represented as 21 cubes, or 252 triangles, whereas it could easily be represented as (where each letter denotes a part of a rectangle)</p> <pre><code>OOOAAAOOOO OOBAAACCCO OOBAAACCCO OOBAAAOOOO </code></pre> <p>which is a mere 3 rectangles, or 26 triangles.</p> <p>The typical size of these grids is 128x128x128, so it's clear I would benefit from a massive performance boost if I could efficiently reduce the shapes to the fewest rectangles possible in a reasonable amount of time, but I'm stuck for ideas for an algorithm.</p> <p>Using <a href="https://stackoverflow.com/questions/1726632/dynamic-programming-largest-square-block">Dynamic programming - Largest square block</a> would be one option, but it wouldn't result in an optimal answer, although if the solution is too complex to perform efficiently then this would have to be the way to go.</p> <p>Eventually I will have multiple types of cubes (e.g. green, brown, blue, referenced using different non-0 numbers in the array) so if possible a version that would work with multiple categories would be very helpful.</p>
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    1. USNick Udell
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    1. COIs there a single "shape" in your grid?
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      1. USNicolas Repiquet
    2. COIt is possible that isolated "islands" of Xs can be generated (I'm generating these maps using Ken Perlin's simplex noise)
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      1. USNick Udell
    3. COIf you're rendering, shouldn't you go for the smallest number of vertices instead of fewest rectangles? You can probably throw out all the vertices inside your volume... (unless you have transparency)
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