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Determine optimal tiling

  • July 4, 2018
  • 3 replies
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jdh
Contributor
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  • jdhContributor
  • Contributor
  • 2002 replies

I have an arbitrary rectangle I need to subdivide into equal tiles. I would like to optimise the number of tiles according to the following constraints in order of priority:

 

  • The original rectangle will always be an integer number of units
  • The maximum area of the tile is 12 units squared
  • All tiles should be equal in dimensions
  • Preference for compact tiles (closer to square)
  • Preference for tiles to be 8-9 units squared
  • Preference for tiles to be integer units
  • Preference for fewer tiles

Thoughts on how to calculate the number of horizontal and vertical tiles given the size of the original rectangle?

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    3 replies

    takashi
    Celebrity
    • takashiCelebrity
    • 7843 replies
    • July 5, 2018

    Hi @jdh, if I understood the requirements correctly, this Python script could determine the optimal tiling parameters according to the constraints.

    # PythonCaller Script Example
    def determineOptimalTiling(feature):
        # Width/Height of the original rectangle.
        width = float(feature.getAttribute('_width'))
        height = float(feature.getAttribute('_height'))
        
        # List of all possible numbers of columns/rows for tiling.
        columns = [c for c in range(1, int(width) + 1)]
        rows = [r for r in range(1, int(height) + 1)]
        
        # Collect every set of tiling parameters that satisfies these constraints.
        # - The maximum area of the tile is 12 units squared
        # - All tiles should be equal in dimensions
        tilingParams = []
        for c in columns:
            w = width / c
            for r in rows:
                h = height / r
                a = w * h
                if a <= 12:
                    tilingParams.append({
                        'width' : w,
                        'height' : h,
                        'area' : a,
                        'columns' : c,
                        'rows' : r,
                    })
                    
        # Sort the list of tiling parameters in the order of other constraints.
        tilingParams.sort(key=lambda p: (
            abs(p['width'] / p['height'] - 1.0), # compact tiles (closer to square)
            0 if (8 <= p['area'] and p['area'] <= 9) else 1, # tiles to be 8-9 units squared
            0 if (p['area'] == round(p['area'])) else 1, # tiles to be integer units
            p['columns'] * p['rows'], # fewer tiles
        ))    
        
        # Determine the first element in the sorted list as the optimal tiling parameters.
        feature.setAttribute('_num_columns', tilingParams[0]['columns'])
        feature.setAttribute('_num_rows', tilingParams[0]['rows'])
    Why not inspect features with Visual/Data Preview and Feature/Record Information before writing them into a destination dataset?
    jdh
    Contributor
    Forum|alt.badge.img+37
    • jdhContributor
    • Author
    • Contributor
    • 2002 replies
    • July 5, 2018

    Hi @jdh, if I understood the requirements correctly, this Python script could determine the optimal tiling parameters according to the constraints.

    # PythonCaller Script Example
    def determineOptimalTiling(feature):
        # Width/Height of the original rectangle.
        width = float(feature.getAttribute('_width'))
        height = float(feature.getAttribute('_height'))
        
        # List of all possible numbers of columns/rows for tiling.
        columns = [c for c in range(1, int(width) + 1)]
        rows = [r for r in range(1, int(height) + 1)]
        
        # Collect every set of tiling parameters that satisfies these constraints.
        # - The maximum area of the tile is 12 units squared
        # - All tiles should be equal in dimensions
        tilingParams = []
        for c in columns:
            w = width / c
            for r in rows:
                h = height / r
                a = w * h
                if a <= 12:
                    tilingParams.append({
                        'width' : w,
                        'height' : h,
                        'area' : a,
                        'columns' : c,
                        'rows' : r,
                    })
                    
        # Sort the list of tiling parameters in the order of other constraints.
        tilingParams.sort(key=lambda p: (
            abs(p['width'] / p['height'] - 1.0), # compact tiles (closer to square)
            0 if (8 <= p['area'] and p['area'] <= 9) else 1, # tiles to be 8-9 units squared
            0 if (p['area'] == round(p['area'])) else 1, # tiles to be integer units
            p['columns'] * p['rows'], # fewer tiles
        ))    
        
        # Determine the first element in the sorted list as the optimal tiling parameters.
        feature.setAttribute('_num_columns', tilingParams[0]['columns'])
        feature.setAttribute('_num_rows', tilingParams[0]['rows'])
    Hi Takashi,

     

     

    This gives me a very good starting point, though I think the constraints will have to be weighted, and then sorted to avoid cases like 5x5  being divided into 25 tiles.

     

     

    I also assume that line 32 should be 0 if (8 >= p['area'] and p['area'] <= 9) else 1,

     

     

     

    takashi
    Celebrity
    • takashiCelebrity
    • 7843 replies
    • July 5, 2018

    Hi @jdh, if I understood the requirements correctly, this Python script could determine the optimal tiling parameters according to the constraints.

    # PythonCaller Script Example
    def determineOptimalTiling(feature):
        # Width/Height of the original rectangle.
        width = float(feature.getAttribute('_width'))
        height = float(feature.getAttribute('_height'))
        
        # List of all possible numbers of columns/rows for tiling.
        columns = [c for c in range(1, int(width) + 1)]
        rows = [r for r in range(1, int(height) + 1)]
        
        # Collect every set of tiling parameters that satisfies these constraints.
        # - The maximum area of the tile is 12 units squared
        # - All tiles should be equal in dimensions
        tilingParams = []
        for c in columns:
            w = width / c
            for r in rows:
                h = height / r
                a = w * h
                if a <= 12:
                    tilingParams.append({
                        'width' : w,
                        'height' : h,
                        'area' : a,
                        'columns' : c,
                        'rows' : r,
                    })
                    
        # Sort the list of tiling parameters in the order of other constraints.
        tilingParams.sort(key=lambda p: (
            abs(p['width'] / p['height'] - 1.0), # compact tiles (closer to square)
            0 if (8 <= p['area'] and p['area'] <= 9) else 1, # tiles to be 8-9 units squared
            0 if (p['area'] == round(p['area'])) else 1, # tiles to be integer units
            p['columns'] * p['rows'], # fewer tiles
        ))    
        
        # Determine the first element in the sorted list as the optimal tiling parameters.
        feature.setAttribute('_num_columns', tilingParams[0]['columns'])
        feature.setAttribute('_num_rows', tilingParams[0]['rows'])
    Since the constraint "Preference for tiles to be integer units" has higher priority than the constraint "Preference for fewer tiles", cases like 5x5 being divided into 25 tiles cannot be avoided. However, if you replaced the line 32 with this expression, you might get a better result.

     

    "Preference for tiles to be 8-9 units squared or closer to the range"
    0 if (8 <= p['area'] and p['area'] <= 9) else max(8 - p['area'], p['area'] - 9)

     

    Why not inspect features with Visual/Data Preview and Feature/Record Information before writing them into a destination dataset?

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