dwilliamson · February 8, 2022 16:20 · Feb 8, 2022
diff --git a/ModifiedMarchingCubes.js b/ModifiedMarchingCubes.js
@@ -0,0 +1,353 @@
+//
+// Lookup Tables for Transvoxel's Modified Marching Cubes
+//
+// Unlike the original paper (Marching Cubes: A High Resolution 3D Surface Construction Algorithm), these tables guarantee
+// a closed mesh "whose connected components are continuous and free of holes."
+//
+// Rotations are prioritised over inversions so that 3 of the 6 cases containing ambiguous faces are never added. 3 extra
+// cases are added as a post-process, overriding inverses through custom-build rotations to eliminate the rest.
+//
+// Uses the exact same co-ordinate system as https://gist.github.com/dwilliamson/c041e3454a713e58baf6e4f8e5fffecd
+//
+// The co-ordinate system has the more convenient properties:
+//
+//    i = cube index [0, 7]
+//    x = (i & 1) >> 0
+//    y = (i & 2) >> 1
+//    z = (i & 4) >> 2
+//
+// Axes are:
+//
+//      y
+//      |     z
+//      |   /
+//      | /
+//      +----- x
+//
+// Vertex and edge layout:
+//
+//            6             7
+//            +-------------+               +-----6-------+   
+//          / |           / |             / |            /|   
+//        /   |         /   |          11   7         10   5
+//    2 +-----+-------+  3  |         +-----+2------+     |   
+//      |   4 +-------+-----+ 5       |     +-----4-+-----+   
+//      |   /         |   /           3   8         1   9
+//      | /           | /             | /           | /       
+//    0 +-------------+ 1             +------0------+         
+//
+// Triangulation cases are generated prioritising rotations over inversions, which can introduce non-manifold geometry.
+//
+
+
+// Pair of vertex indices for each edge on the cube
+const EdgeVertexIndices = [
+	[0, 1],
+	[1, 3],
+	[3, 2],
+	[2, 0],
+	[4, 5],
+	[5, 7],
+	[7, 6],
+	[6, 4],
+	[0, 4],
+	[1, 5],
+	[3, 7],
+	[2, 6],
+];
+
+// For each MC case, a mask of edge indices that need to be split
+const EdgeMasks = [
+	0x0, 0x109, 0x203, 0x30a, 0x80c, 0x905, 0xa0f, 0xb06, 
+	0x406, 0x50f, 0x605, 0x70c, 0xc0a, 0xd03, 0xe09, 0xf00, 
+	0x190, 0x99, 0x393, 0x29a, 0x99c, 0x895, 0xb9f, 0xa96, 
+	0x596, 0x49f, 0x795, 0x69c, 0xd9a, 0xc93, 0xf99, 0xe90, 
+	0x230, 0x339, 0x33, 0x13a, 0xa3c, 0xb35, 0x83f, 0x936, 
+	0x636, 0x73f, 0x435, 0x53c, 0xe3a, 0xf33, 0xc39, 0xd30, 
+	0x3a0, 0x2a9, 0x1a3, 0xaa, 0xbac, 0xaa5, 0x9af, 0x8a6, 
+	0x7a6, 0x6af, 0x5a5, 0x4ac, 0xfaa, 0xea3, 0xda9, 0xca0, 
+	0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc, 0x1c5, 0x2cf, 0x3c6, 
+	0xcc6, 0xdcf, 0xec5, 0xfcc, 0x4ca, 0x5c3, 0x6c9, 0x7c0, 
+	0x950, 0x859, 0xb53, 0xa5a, 0x15c, 0x55, 0x35f, 0x256, 
+	0xd56, 0xc5f, 0xf55, 0xe5c, 0x55a, 0x453, 0x759, 0x650, 
+	0xaf0, 0xbf9, 0x8f3, 0x9fa, 0x2fc, 0x3f5, 0xff, 0x1f6, 
+	0xef6, 0xfff, 0xcf5, 0xdfc, 0x6fa, 0x7f3, 0x4f9, 0x5f0, 
+	0xb60, 0xa69, 0x963, 0x86a, 0x36c, 0x265, 0x16f, 0x66, 
+	0xf66, 0xe6f, 0xd65, 0xc6c, 0x76a, 0x663, 0x569, 0x460, 
+	0x460, 0x569, 0x663, 0x76a, 0xc6c, 0xd65, 0xe6f, 0xf66, 
+	0x66, 0x16f, 0x265, 0x36c, 0x86a, 0x963, 0xa69, 0xb60, 
+	0x5f0, 0x4f9, 0x7f3, 0x6fa, 0xdfc, 0xcf5, 0xfff, 0xef6, 
+	0x1f6, 0xff, 0x3f5, 0x2fc, 0x9fa, 0x8f3, 0xbf9, 0xaf0, 
+	0x650, 0x759, 0x453, 0x55a, 0xe5c, 0xf55, 0xc5f, 0xd56, 
+	0x256, 0x35f, 0x55, 0x15c, 0xa5a, 0xb53, 0x859, 0x950, 
+	0x7c0, 0x6c9, 0x5c3, 0x4ca, 0xfcc, 0xec5, 0xdcf, 0xcc6, 
+	0x3c6, 0x2cf, 0x1c5, 0xcc, 0xbca, 0xac3, 0x9c9, 0x8c0, 
+	0xca0, 0xda9, 0xea3, 0xfaa, 0x4ac, 0x5a5, 0x6af, 0x7a6, 
+	0x8a6, 0x9af, 0xaa5, 0xbac, 0xaa, 0x1a3, 0x2a9, 0x3a0, 
+	0xd30, 0xc39, 0xf33, 0xe3a, 0x53c, 0x435, 0x73f, 0x636, 
+	0x936, 0x83f, 0xb35, 0xa3c, 0x13a, 0x33, 0x339, 0x230, 
+	0xe90, 0xf99, 0xc93, 0xd9a, 0x69c, 0x795, 0x49f, 0x596, 
+	0xa96, 0xb9f, 0x895, 0x99c, 0x29a, 0x393, 0x99, 0x190, 
+	0xf00, 0xe09, 0xd03, 0xc0a, 0x70c, 0x605, 0x50f, 0x406, 
+	0xb06, 0xa0f, 0x905, 0x80c, 0x30a, 0x203, 0x109, 0x0, 
+];
+
+// For each MC case, a list of triangles, specified as triples of edge indices, terminated by -1
+const TriangleTable = [
+	[ -1 ],
+	[ 3, 8, 0, -1 ],
+	[ 1, 0, 9, -1 ],
+	[ 9, 1, 8, 8, 1, 3, -1 ],
+	[ 3, 2, 11, -1 ],
+	[ 2, 11, 0, 0, 11, 8, -1 ],
+	[ 1, 0, 9, 3, 2, 11, -1 ],
+	[ 11, 1, 2, 11, 9, 1, 11, 8, 9, -1 ],
+	[ 10, 2, 1, -1 ],
+	[ 2, 1, 10, 0, 3, 8, -1 ],
+	[ 0, 9, 2, 2, 9, 10, -1 ],
+	[ 8, 2, 3, 8, 10, 2, 8, 9, 10, -1 ],
+	[ 1, 10, 3, 3, 10, 11, -1 ],
+	[ 10, 0, 1, 10, 8, 0, 10, 11, 8, -1 ],
+	[ 9, 3, 0, 9, 11, 3, 9, 10, 11, -1 ],
+	[ 9, 10, 8, 8, 10, 11, -1 ],
+	[ 7, 4, 8, -1 ],
+	[ 0, 3, 4, 4, 3, 7, -1 ],
+	[ 0, 9, 1, 4, 8, 7, -1 ],
+	[ 1, 4, 9, 1, 7, 4, 1, 3, 7, -1 ],
+	[ 11, 3, 2, 8, 7, 4, -1 ],
+	[ 4, 11, 7, 4, 2, 11, 4, 0, 2, -1 ],
+	[ 3, 2, 11, 0, 9, 1, 4, 8, 7, -1 ],
+	[ 9, 1, 4, 4, 1, 7, 7, 1, 2, 7, 2, 11, -1 ],
+	[ 7, 4, 8, 1, 10, 2, -1 ],
+	[ 7, 4, 3, 3, 4, 0, 10, 2, 1, -1 ],
+	[ 10, 2, 9, 9, 2, 0, 7, 4, 8, -1 ],
+	[ 7, 4, 9, 7, 9, 2, 9, 10, 2, 3, 7, 2, -1 ],
+	[ 1, 10, 3, 3, 10, 11, 4, 8, 7, -1 ],
+	[ 4, 0, 7, 0, 1, 10, 7, 0, 10, 7, 10, 11, -1 ],
+	[ 7, 4, 8, 9, 3, 0, 9, 11, 3, 9, 10, 11, -1 ],
+	[ 7, 4, 11, 4, 9, 11, 9, 10, 11, -1 ],
+	[ 5, 9, 4, -1 ],
+	[ 8, 0, 3, 9, 4, 5, -1 ],
+	[ 1, 0, 5, 5, 0, 4, -1 ],
+	[ 5, 8, 4, 5, 3, 8, 5, 1, 3, -1 ],
+	[ 3, 2, 11, 5, 9, 4, -1 ],
+	[ 2, 11, 0, 0, 11, 8, 5, 9, 4, -1 ],
+	[ 4, 5, 0, 0, 5, 1, 11, 3, 2, -1 ],
+	[ 11, 8, 2, 8, 4, 5, 2, 8, 5, 2, 5, 1, -1 ],
+	[ 5, 9, 4, 1, 10, 2, -1 ],
+	[ 0, 3, 8, 1, 10, 2, 5, 9, 4, -1 ],
+	[ 2, 5, 10, 2, 4, 5, 2, 0, 4, -1 ],
+	[ 4, 5, 8, 8, 5, 3, 3, 5, 10, 3, 10, 2, -1 ],
+	[ 11, 3, 10, 10, 3, 1, 4, 5, 9, -1 ],
+	[ 4, 5, 9, 10, 0, 1, 10, 8, 0, 10, 11, 8, -1 ],
+	[ 4, 5, 10, 4, 10, 3, 10, 11, 3, 0, 4, 3, -1 ],
+	[ 4, 5, 8, 5, 10, 8, 10, 11, 8, -1 ],
+	[ 5, 9, 7, 7, 9, 8, -1 ],
+	[ 3, 9, 0, 3, 5, 9, 3, 7, 5, -1 ],
+	[ 7, 0, 8, 7, 1, 0, 7, 5, 1, -1 ],
+	[ 3, 7, 1, 1, 7, 5, -1 ],
+	[ 5, 9, 7, 7, 9, 8, 2, 11, 3, -1 ],
+	[ 5, 9, 0, 5, 0, 11, 0, 2, 11, 7, 5, 11, -1 ],
+	[ 2, 11, 3, 7, 0, 8, 7, 1, 0, 7, 5, 1, -1 ],
+	[ 2, 11, 1, 11, 7, 1, 7, 5, 1, -1 ],
+	[ 8, 7, 9, 9, 7, 5, 2, 1, 10, -1 ],
+	[ 10, 2, 1, 3, 9, 0, 3, 5, 9, 3, 7, 5, -1 ],
+	[ 2, 0, 10, 0, 8, 7, 10, 0, 7, 10, 7, 5, -1 ],
+	[ 10, 2, 5, 2, 3, 5, 3, 7, 5, -1 ],
+	[ 5, 9, 8, 5, 8, 7, 1, 10, 3, 10, 11, 3, -1 ],
+	[ 1, 10, 0, 0, 10, 11, 0, 11, 7, 0, 7, 5, 0, 5, 9, -1 ],
+	[ 8, 7, 0, 0, 7, 5, 0, 5, 10, 0, 10, 11, 0, 11, 3, -1 ],
+	[ 5, 11, 7, 10, 11, 5, -1 ],
+	[ 11, 6, 7, -1 ],
+	[ 3, 8, 0, 7, 11, 6, -1 ],
+	[ 1, 0, 9, 7, 11, 6, -1 ],
+	[ 9, 1, 8, 8, 1, 3, 6, 7, 11, -1 ],
+	[ 6, 7, 2, 2, 7, 3, -1 ],
+	[ 0, 7, 8, 0, 6, 7, 0, 2, 6, -1 ],
+	[ 6, 7, 2, 2, 7, 3, 9, 1, 0, -1 ],
+	[ 9, 1, 2, 9, 2, 7, 2, 6, 7, 8, 9, 7, -1 ],
+	[ 10, 2, 1, 11, 6, 7, -1 ],
+	[ 2, 1, 10, 3, 8, 0, 7, 11, 6, -1 ],
+	[ 0, 9, 2, 2, 9, 10, 7, 11, 6, -1 ],
+	[ 6, 7, 11, 8, 2, 3, 8, 10, 2, 8, 9, 10, -1 ],
+	[ 7, 10, 6, 7, 1, 10, 7, 3, 1, -1 ],
+	[ 1, 10, 0, 0, 10, 8, 8, 10, 6, 8, 6, 7, -1 ],
+	[ 9, 10, 0, 10, 6, 7, 0, 10, 7, 0, 7, 3, -1 ],
+	[ 6, 7, 10, 7, 8, 10, 8, 9, 10, -1 ],
+	[ 4, 8, 6, 6, 8, 11, -1 ],
+	[ 6, 3, 11, 6, 0, 3, 6, 4, 0, -1 ],
+	[ 11, 6, 8, 8, 6, 4, 1, 0, 9, -1 ],
+	[ 6, 4, 11, 4, 9, 1, 11, 4, 1, 11, 1, 3, -1 ],
+	[ 2, 8, 3, 2, 4, 8, 2, 6, 4, -1 ],
+	[ 0, 2, 4, 4, 2, 6, -1 ],
+	[ 9, 1, 0, 2, 8, 3, 2, 4, 8, 2, 6, 4, -1 ],
+	[ 9, 1, 4, 1, 2, 4, 2, 6, 4, -1 ],
+	[ 4, 8, 6, 6, 8, 11, 1, 10, 2, -1 ],
+	[ 1, 10, 2, 6, 3, 11, 6, 0, 3, 6, 4, 0, -1 ],
+	[ 0, 9, 10, 0, 10, 2, 4, 8, 6, 8, 11, 6, -1 ],
+	[ 11, 6, 3, 3, 6, 4, 3, 4, 9, 3, 9, 10, 3, 10, 2, -1 ],
+	[ 1, 10, 6, 1, 6, 8, 6, 4, 8, 3, 1, 8, -1 ],
+	[ 1, 10, 0, 10, 6, 0, 6, 4, 0, -1 ],
+	[ 0, 9, 3, 3, 9, 10, 3, 10, 6, 3, 6, 4, 3, 4, 8, -1 ],
+	[ 4, 10, 6, 9, 10, 4, -1 ],
+	[ 4, 5, 9, 6, 7, 11, -1 ],
+	[ 7, 11, 6, 8, 0, 3, 9, 4, 5, -1 ],
+	[ 1, 0, 5, 5, 0, 4, 11, 6, 7, -1 ],
+	[ 11, 6, 7, 5, 8, 4, 5, 3, 8, 5, 1, 3, -1 ],
+	[ 3, 2, 7, 7, 2, 6, 9, 4, 5, -1 ],
+	[ 5, 9, 4, 0, 7, 8, 0, 6, 7, 0, 2, 6, -1 ],
+	[ 1, 0, 4, 1, 4, 5, 3, 2, 7, 2, 6, 7, -1 ],
+	[ 4, 5, 8, 8, 5, 1, 8, 1, 2, 8, 2, 6, 8, 6, 7, -1 ],
+	[ 6, 7, 11, 5, 9, 4, 1, 10, 2, -1 ],
+	[ 5, 9, 4, 7, 11, 6, 0, 3, 8, 2, 1, 10, -1 ],
+	[ 7, 11, 6, 2, 5, 10, 2, 4, 5, 2, 0, 4, -1 ],
+	[ 6, 7, 11, 3, 8, 4, 3, 4, 5, 3, 5, 2, 2, 5, 10, -1 ],
+	[ 9, 4, 5, 7, 10, 6, 7, 1, 10, 7, 3, 1, -1 ],
+	[ 5, 9, 4, 8, 0, 1, 8, 1, 10, 8, 10, 7, 7, 10, 6, -1 ],
+	[ 6, 7, 10, 10, 7, 3, 10, 3, 0, 10, 0, 4, 10, 4, 5, -1 ],
+	[ 4, 5, 8, 8, 5, 10, 8, 10, 6, 8, 6, 7, -1 ],
+	[ 9, 6, 5, 9, 11, 6, 9, 8, 11, -1 ],
+	[ 0, 3, 9, 9, 3, 5, 5, 3, 11, 5, 11, 6, -1 ],
+	[ 1, 0, 8, 1, 8, 6, 8, 11, 6, 5, 1, 6, -1 ],
+	[ 11, 6, 3, 6, 5, 3, 5, 1, 3, -1 ],
+	[ 2, 6, 3, 6, 5, 9, 3, 6, 9, 3, 9, 8, -1 ],
+	[ 5, 9, 6, 9, 0, 6, 0, 2, 6, -1 ],
+	[ 3, 2, 8, 8, 2, 6, 8, 6, 5, 8, 5, 1, 8, 1, 0, -1 ],
+	[ 1, 6, 5, 2, 6, 1, -1 ],
+	[ 2, 1, 10, 9, 6, 5, 9, 11, 6, 9, 8, 11, -1 ],
+	[ 2, 1, 10, 5, 9, 0, 5, 0, 3, 5, 3, 6, 6, 3, 11, -1 ],
+	[ 10, 2, 5, 5, 2, 0, 5, 0, 8, 5, 8, 11, 5, 11, 6, -1 ],
+	[ 10, 2, 5, 5, 2, 3, 5, 3, 11, 5, 11, 6, -1 ],
+	[ 5, 9, 6, 6, 9, 8, 6, 8, 3, 6, 3, 1, 6, 1, 10, -1 ],
+	[ 5, 9, 6, 6, 9, 0, 6, 0, 1, 6, 1, 10, -1 ],
+	[ 8, 3, 0, 5, 10, 6, -1 ],
+	[ 6, 5, 10, -1 ],
+	[ 6, 10, 5, -1 ],
+	[ 3, 8, 0, 5, 6, 10, -1 ],
+	[ 9, 1, 0, 10, 5, 6, -1 ],
+	[ 3, 8, 1, 1, 8, 9, 6, 10, 5, -1 ],
+	[ 6, 10, 5, 2, 11, 3, -1 ],
+	[ 8, 0, 11, 11, 0, 2, 5, 6, 10, -1 ],
+	[ 10, 5, 6, 1, 0, 9, 3, 2, 11, -1 ],
+	[ 5, 6, 10, 11, 1, 2, 11, 9, 1, 11, 8, 9, -1 ],
+	[ 2, 1, 6, 6, 1, 5, -1 ],
+	[ 5, 6, 1, 1, 6, 2, 8, 0, 3, -1 ],
+	[ 6, 9, 5, 6, 0, 9, 6, 2, 0, -1 ],
+	[ 8, 9, 3, 9, 5, 6, 3, 9, 6, 3, 6, 2, -1 ],
+	[ 3, 6, 11, 3, 5, 6, 3, 1, 5, -1 ],
+	[ 5, 6, 11, 5, 11, 0, 11, 8, 0, 1, 5, 0, -1 ],
+	[ 0, 9, 3, 3, 9, 11, 11, 9, 5, 11, 5, 6, -1 ],
+	[ 5, 6, 9, 6, 11, 9, 11, 8, 9, -1 ],
+	[ 7, 4, 8, 5, 6, 10, -1 ],
+	[ 0, 3, 4, 4, 3, 7, 10, 5, 6, -1 ],
+	[ 4, 8, 7, 9, 1, 0, 10, 5, 6, -1 ],
+	[ 6, 10, 5, 1, 4, 9, 1, 7, 4, 1, 3, 7, -1 ],
+	[ 11, 3, 2, 7, 4, 8, 5, 6, 10, -1 ],
+	[ 10, 5, 6, 4, 11, 7, 4, 2, 11, 4, 0, 2, -1 ],
+	[ 7, 4, 8, 3, 2, 11, 9, 1, 0, 10, 5, 6, -1 ],
+	[ 10, 5, 6, 7, 4, 9, 7, 9, 1, 7, 1, 11, 11, 1, 2, -1 ],
+	[ 2, 1, 6, 6, 1, 5, 8, 7, 4, -1 ],
+	[ 7, 4, 0, 7, 0, 3, 5, 6, 1, 6, 2, 1, -1 ],
+	[ 8, 7, 4, 6, 9, 5, 6, 0, 9, 6, 2, 0, -1 ],
+	[ 5, 6, 9, 9, 6, 2, 9, 2, 3, 9, 3, 7, 9, 7, 4, -1 ],
+	[ 4, 8, 7, 3, 6, 11, 3, 5, 6, 3, 1, 5, -1 ],
+	[ 7, 4, 11, 11, 4, 0, 11, 0, 1, 11, 1, 5, 11, 5, 6, -1 ],
+	[ 4, 8, 7, 11, 3, 0, 11, 0, 9, 11, 9, 6, 6, 9, 5, -1 ],
+	[ 5, 6, 9, 9, 6, 11, 9, 11, 7, 9, 7, 4, -1 ],
+	[ 9, 4, 10, 10, 4, 6, -1 ],
+	[ 6, 10, 4, 4, 10, 9, 3, 8, 0, -1 ],
+	[ 0, 10, 1, 0, 6, 10, 0, 4, 6, -1 ],
+	[ 3, 8, 4, 3, 4, 10, 4, 6, 10, 1, 3, 10, -1 ],
+	[ 9, 4, 10, 10, 4, 6, 3, 2, 11, -1 ],
+	[ 8, 0, 2, 8, 2, 11, 9, 4, 10, 4, 6, 10, -1 ],
+	[ 11, 3, 2, 0, 10, 1, 0, 6, 10, 0, 4, 6, -1 ],
+	[ 2, 11, 1, 1, 11, 8, 1, 8, 4, 1, 4, 6, 1, 6, 10, -1 ],
+	[ 4, 1, 9, 4, 2, 1, 4, 6, 2, -1 ],
+	[ 3, 8, 0, 4, 1, 9, 4, 2, 1, 4, 6, 2, -1 ],
+	[ 4, 6, 0, 0, 6, 2, -1 ],
+	[ 3, 8, 2, 8, 4, 2, 4, 6, 2, -1 ],
+	[ 3, 1, 11, 1, 9, 4, 11, 1, 4, 11, 4, 6, -1 ],
+	[ 9, 4, 1, 1, 4, 6, 1, 6, 11, 1, 11, 8, 1, 8, 0, -1 ],
+	[ 11, 3, 6, 3, 0, 6, 0, 4, 6, -1 ],
+	[ 8, 6, 11, 4, 6, 8, -1 ],
+	[ 10, 7, 6, 10, 8, 7, 10, 9, 8, -1 ],
+	[ 10, 9, 6, 9, 0, 3, 6, 9, 3, 6, 3, 7, -1 ],
+	[ 8, 7, 0, 0, 7, 1, 1, 7, 6, 1, 6, 10, -1 ],
+	[ 6, 10, 7, 10, 1, 7, 1, 3, 7, -1 ],
+	[ 3, 2, 11, 10, 7, 6, 10, 8, 7, 10, 9, 8, -1 ],
+	[ 6, 10, 7, 7, 10, 9, 7, 9, 0, 7, 0, 2, 7, 2, 11, -1 ],
+	[ 11, 3, 2, 1, 0, 8, 1, 8, 7, 1, 7, 10, 10, 7, 6, -1 ],
+	[ 6, 10, 7, 7, 10, 1, 7, 1, 2, 7, 2, 11, -1 ],
+	[ 8, 7, 6, 8, 6, 1, 6, 2, 1, 9, 8, 1, -1 ],
+	[ 0, 3, 9, 9, 3, 7, 9, 7, 6, 9, 6, 2, 9, 2, 1, -1 ],
+	[ 8, 7, 0, 7, 6, 0, 6, 2, 0, -1 ],
+	[ 7, 2, 3, 6, 2, 7, -1 ],
+	[ 11, 3, 6, 6, 3, 1, 6, 1, 9, 6, 9, 8, 6, 8, 7, -1 ],
+	[ 11, 7, 6, 1, 9, 0, -1 ],
+	[ 11, 3, 6, 6, 3, 0, 6, 0, 8, 6, 8, 7, -1 ],
+	[ 11, 7, 6, -1 ],
+	[ 10, 5, 11, 11, 5, 7, -1 ],
+	[ 10, 5, 11, 11, 5, 7, 0, 3, 8, -1 ],
+	[ 7, 11, 5, 5, 11, 10, 0, 9, 1, -1 ],
+	[ 3, 8, 9, 3, 9, 1, 7, 11, 5, 11, 10, 5, -1 ],
+	[ 5, 2, 10, 5, 3, 2, 5, 7, 3, -1 ],
+	[ 0, 2, 8, 2, 10, 5, 8, 2, 5, 8, 5, 7, -1 ],
+	[ 0, 9, 1, 5, 2, 10, 5, 3, 2, 5, 7, 3, -1 ],
+	[ 10, 5, 2, 2, 5, 7, 2, 7, 8, 2, 8, 9, 2, 9, 1, -1 ],
+	[ 1, 11, 2, 1, 7, 11, 1, 5, 7, -1 ],
+	[ 8, 0, 3, 1, 11, 2, 1, 7, 11, 1, 5, 7, -1 ],
+	[ 0, 9, 5, 0, 5, 11, 5, 7, 11, 2, 0, 11, -1 ],
+	[ 3, 8, 2, 2, 8, 9, 2, 9, 5, 2, 5, 7, 2, 7, 11, -1 ],
+	[ 5, 7, 1, 1, 7, 3, -1 ],
+	[ 8, 0, 7, 0, 1, 7, 1, 5, 7, -1 ],
+	[ 0, 9, 3, 9, 5, 3, 5, 7, 3, -1 ],
+	[ 9, 7, 8, 5, 7, 9, -1 ],
+	[ 8, 5, 4, 8, 10, 5, 8, 11, 10, -1 ],
+	[ 10, 5, 4, 10, 4, 3, 4, 0, 3, 11, 10, 3, -1 ],
+	[ 1, 0, 9, 8, 5, 4, 8, 10, 5, 8, 11, 10, -1 ],
+	[ 9, 1, 4, 4, 1, 3, 4, 3, 11, 4, 11, 10, 4, 10, 5, -1 ],
+	[ 10, 5, 2, 2, 5, 3, 3, 5, 4, 3, 4, 8, -1 ],
+	[ 10, 5, 2, 5, 4, 2, 4, 0, 2, -1 ],
+	[ 9, 1, 0, 3, 2, 10, 3, 10, 5, 3, 5, 8, 8, 5, 4, -1 ],
+	[ 10, 5, 2, 2, 5, 4, 2, 4, 9, 2, 9, 1, -1 ],
+	[ 1, 5, 2, 5, 4, 8, 2, 5, 8, 2, 8, 11, -1 ],
+	[ 2, 1, 11, 11, 1, 5, 11, 5, 4, 11, 4, 0, 11, 0, 3, -1 ],
+	[ 4, 8, 5, 5, 8, 11, 5, 11, 2, 5, 2, 0, 5, 0, 9, -1 ],
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+	[ 1, 8, 3, 9, 8, 1, -1 ],
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+	[ 8, 3, 0, -1 ],
+	[ -1 ],
+];