Generate vertices/edges for a n-dimensional cube

ncubegen.cpp

// Generate n-dimensional cube vertex/edges (opengl)

void genVerts (int dimensions, float scale = 1.0f) {
	assert(dimensions > 1 && dimensions <= 4);

	auto posVal = scale * 0.5f;
	auto negVal = -posVal;
	
	auto n = 1 << dimensions;
	
	for (auto i = 0; i < n; ++i) {
		for (auto bit_scan = 1; bit_scan & (n - 1); bit_scan <<= 1) {
			emitVertexComponent( i & bit_scan ? posVal : negVal );
		}
	}
}


void genEdges (int dimensions) {
	
	// Algorithm based (sort of) on graycode:
	// If vertex (0, 0, 0) is at index 000, vertex (0, 1, 0) at index 010, etc., then generating
	// edges between the vertices becomes a matter of connecting the vertices whose components differ
	// by at most 1 (x-axis, y-axis, or z-axis). To prevent duplicates, we only connect verts *upwards*
	// (eg 010 -> 110, 011, but not 110 -> 010 or 100, and do this via connecting an index i to each 
	// other i w/ one extra set bit (if it exists)). In three dimensions, this works as follows:
	//   000 -> 100, 010, 001
	//   100 -> 110, 101
	//   010 -> 110, 011
	//   110 -> 111
	//   ...
	//   111 -> (nothing)
	//

	assert(dimensions > 1 && dimensions <= 4);
	
	auto n = 1 << dimensions;
	auto mask = n - 1;
	
	for (auto i = 0; i < n; ++i) {
		for (auto b = 1; b & mask; b <<= 1) {
			if ((i & b) == 0) {
				emitEdgeIndexPair(i, i | b);
			}
		}
	}
}

Shared credit w/ Michael Snowden (the genEdges algorithm and the bitwise optimizations are mine).
For a full graphical impl, see https://gist.github.com/MichaelSnowden/0d03155e3cbd20fcd04c.