surfaceNet.js

/**
 * SurfaceNets in JavaScript
 *
 * Written by Mikola Lysenko (C) 2012
 *
 * MIT License
 *
 * Based on: S.F. Gibson, 'Constrained Elastic Surface Nets'. (1998) MERL Tech Report.
 * from https://github.com/mikolalysenko/isosurface/tree/master
 * 
 */

let surfaceNet = ( dims, potential, bounds ) => {
		
	
	//Precompute edge table, like Paul Bourke does.
	// This saves a bit of time when computing the centroid of each boundary cell
	var cube_edges = new Int32Array(24) , edge_table = new Int32Array(256);
	(function() {

		//Initialize the cube_edges table
		// This is just the vertex number of each cube
		var k = 0;
		for(var i=0; i<8; ++i) {
			for(var j=1; j<=4; j<<=1) {
				var p = i^j;
				if(i <= p) {
					cube_edges[k++] = i;
					cube_edges[k++] = p;
				}
			}
		}

		//Initialize the intersection table.
		//  This is a 2^(cube configuration) ->  2^(edge configuration) map
		//  There is one entry for each possible cube configuration, and the output is a 12-bit vector enumerating all edges crossing the 0-level.
		for(var i=0; i<256; ++i) {
			var em = 0;
			for(var j=0; j<24; j+=2) {
				var a = !!(i & (1<<cube_edges[j]))
					, b = !!(i & (1<<cube_edges[j+1]));
				em |= a !== b ? (1 << (j >> 1)) : 0;
			}
			edge_table[i] = em;
		}
	})();

	//Internal buffer, this may get resized at run time
	var buffer = new Array(4096);
	(function() {
		for(var i=0; i<buffer.length; ++i) {
			buffer[i] = 0;
		}
	})();

	if(!bounds) {
		bounds = [[0,0,0],dims];
	}
	
	var scale     = [0,0,0];
	var shift     = [0,0,0];
	for(var i=0; i<3; ++i) {
		scale[i] = (bounds[1][i] - bounds[0][i]) / dims[i];
		shift[i] = bounds[0][i];
	}
	
	var vertices = []
		, faces = []
		, n = 0
		, x = [0, 0, 0]
		, R = [1, (dims[0]+1), (dims[0]+1)*(dims[1]+1)]
		, grid = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
		, buf_no = 1;
	
		
	//Resize buffer if necessary 
	if(R[2] * 2 > buffer.length) {
		var ol = buffer.length;
		buffer.length = R[2] * 2;
		while(ol < buffer.length) {
			buffer[ol++] = 0;
		}
	}
	
	//March over the voxel grid
	for(x[2]=0; x[2]<dims[2]-1; ++x[2], n+=dims[0], buf_no ^= 1, R[2]=-R[2]) {
	
		//m is the pointer into the buffer we are going to use.  
		//This is slightly obtuse because javascript does not have good support for packed data structures, so we must use typed arrays :(
		//The contents of the buffer will be the indices of the vertices on the previous x/y slice of the volume
		var m = 1 + (dims[0]+1) * (1 + buf_no * (dims[1]+1));
		
		for(x[1]=0; x[1]<dims[1]-1; ++x[1], ++n, m+=2)
		for(x[0]=0; x[0]<dims[0]-1; ++x[0], ++n, ++m) {
		
			//Read in 8 field values around this vertex and store them in an array
			//Also calculate 8-bit mask, like in marching cubes, so we can speed up sign checks later
			var mask = 0, g = 0;
			for(var k=0; k<2; ++k)
			for(var j=0; j<2; ++j)      
			for(var i=0; i<2; ++i, ++g) {
				var p = potential(
					scale[0]*(x[0]+i)+shift[0],
					scale[1]*(x[1]+j)+shift[1],
					scale[2]*(x[2]+k)+shift[2]);
				grid[g] = p;
				mask |= (p < 0) ? (1<<g) : 0;
			}
			
			//Check for early termination if cell does not intersect boundary
			if(mask === 0 || mask === 0xff) {
				continue;
			}
			
			//Sum up edge intersections
			var edge_mask = edge_table[mask]
				, v = [0.0,0.0,0.0]
				, e_count = 0;
				
			//For every edge of the cube...
			for(var i=0; i<12; ++i) {
			
				//Use edge mask to check if it is crossed
				if(!(edge_mask & (1<<i))) {
					continue;
				}
				
				//If it did, increment number of edge crossings
				++e_count;
				
				//Now find the point of intersection
				var e0 = cube_edges[ i<<1 ]       //Unpack vertices
					, e1 = cube_edges[(i<<1)+1]
					, g0 = grid[e0]                 //Unpack grid values
					, g1 = grid[e1]
					, t  = g0 - g1;                 //Compute point of intersection
				if(Math.abs(t) > 1e-6) {
					t = g0 / t;
				} else {
					continue;
				}
				
				//Interpolate vertices and add up intersections (this can be done without multiplying)
				for(var j=0, k=1; j<3; ++j, k<<=1) {
					var a = e0 & k
						, b = e1 & k;
					if(a !== b) {
						v[j] += a ? 1.0 - t : t;
					} else {
						v[j] += a ? 1.0 : 0;
					}
				}
			}
			
			//Now we just average the edge intersections and add them to coordinate
			var s = 1.0 / e_count;
			for(var i=0; i<3; ++i) {
				v[i] = scale[i] * (x[i] + s * v[i]) + shift[i];
			}
			
			//Add vertex to buffer, store pointer to vertex index in buffer
			buffer[m] = vertices.length;
			vertices.push(v);
			
			//Now we need to add faces together, to do this we just loop over 3 basis components
			for(var i=0; i<3; ++i) {
				//The first three entries of the edge_mask count the crossings along the edge
				if(!(edge_mask & (1<<i)) ) {
					continue;
				}
				
				// i = axes we are point along.  iu, iv = orthogonal axes
				var iu = (i+1)%3
					, iv = (i+2)%3;
					
				//If we are on a boundary, skip it
				if(x[iu] === 0 || x[iv] === 0) {
					continue;
				}
				
				//Otherwise, look up adjacent edges in buffer
				var du = R[iu]
					, dv = R[iv];
				
				//Remember to flip orientation depending on the sign of the corner.
				if(mask & 1) {
					faces.push([buffer[m],    buffer[m-du],    buffer[m-dv]]);
					faces.push([buffer[m-dv], buffer[m-du],    buffer[m-du-dv]]);
				} else {
					faces.push([buffer[m],    buffer[m-dv],    buffer[m-du]]);
					faces.push([buffer[m-du], buffer[m-dv],    buffer[m-du-dv]]);
				}
			}
		}
	}
	
	//All done!  Return the result
	return { positions: vertices, cells: faces };
}

export { surfaceNet }