Optimize ColorMap

[fosskers]

TODO

Let: k be the number of pixels to colour, and n the number of colour breaks, where usually k > n by several orders of magnitude

• Use a TrieMap to memoize IntColorMap.map results
  • Worst case (all unique pixel values): O(kn)
  • Best case (all pixels same value): O(k + n)
• Write BTree[T]
• Use a custom BTree for DoubleColorMap
  • Via B-tree: O(nlogn + klogn) == O((n + k)logn) ~= O(klogn)
• Fix tests
• BTree.pretty should return String
• Use BTree for IntColorMap

Motivation

This addresses #1489 . Currently every call to IntColorMap.map or DoubleColorMap.map performs a O(n) search for the correct colour ramp value, given some raster's pixel value. The total cost to colour a raster is then O(kn).

Next Steps

Use Spire to generalize over Int and Double?

[fosskers]

Bonus, BTrees have a nice string representation:

└── 4
    ├── 6
    │   ├── 7
    │   │   ├── ∅
    │   │   └── ∅
    │   └── 5
    │       ├── ∅
    │       └── ∅
    └── 2
        ├── 3
        │   ├── ∅
        │   └── ∅
        └── 1
            ├── ∅
            └── ∅

[fosskers]

Don't merge yet: I still need to run benchmarks.

[fosskers]

1280x1280 pixel Tile, 50 Breaks, 5 trials each, same JVM

 ORIGINAL LINEAR
 ---------------
 Rendering => 176.53 ms
 Rendering => 180.56 ms
 Rendering => 170.98 ms
 Rendering => 170.94 ms
 Rendering => 170.47 ms

 Mean: 173.89 ms

 WITH BTREE
 ----------
 Rendering => 120.25 ms
 Rendering => 117.32 ms
 Rendering => 121.19 ms
 Rendering => 117.35 ms
 Rendering => 116.86 ms

 Mean: 118.6 ms

 Speedup: ~47%