Coefficients Generation for Optimized Gaussian Blurs using Linear Sampling

gistfile1.js

/*
 * @author zz85 / https://github.com/zz85
 *
 * Related Readings
 *
 * http://rastergrid.com/blog/2010/09/efficient-gaussian-blur-with-linear-sampling/
 * http://www.sunsetlakesoftware.com/2013/10/21/optimizing-gaussian-blurs-mobile-gpu
 * http://xissburg.com/faster-gaussian-blur-in-glsl/
 * https://github.com/manuelbua/blur-ninja
 *
 *
 * I'm writing this in the process of exploring optimized gaussian blurs,
 * but how well it really works in the real world I've yet to figure out.
 * For example, using varying to prevent dependent texture reads in the fragment 
 * shader might be a thing of the past.
 * http://stackoverflow.com/questions/1054096/what-is-a-dependent-texture-read 
 * 
 */

calc(13);

function calc( level ) {

	if ( level % 2 != 1 ) {
		console.log( 'odd number taps only ');
		return;
	}

	var edgesToRemove = 2;

	var binom = binomial( level );

	console.log('Initial gaussian distribution', binom);

	var total = 0;
	for (var i = 0; i < binom.length; i++) {
		total += binom[ i ];
	}

	var weights = [];
	var offsets = [];
	var off = binom.length / 2 + 0.5

	for (var i = off - 1; i >= 0; i--) {
		weights.push( binom[i] / total );
		offsets.push( Math.abs(i + 1 - off));
	}

	console.log('discrete weights', weights);
	console.log('discrete offsets', offsets);

	// Remove edges with too little weight.
	var weight = 1;

	while (edgesToRemove--) {
		weight -= weights.pop() * 2;
		offsets.pop();
	}

	for (i = 0; i < weights.length; i++) {
		weight[ i ] /= weight;
	}

	// Calculate linear sampling weights
	var linear_weights = [ weights[0] ];
	var linear_offsets = [ offsets[0] ];

	for (var t1 = 1; t1 < weights.length; t1+=2) {
		var t2 = t1 + 1;
		linear_weights.push(weights[t1] + weights[t2]);
		linear_offsets.push( (offsets[t1] * weights[t1] + offsets[t2] * weights[t2]) / linear_weights[linear_weights.length-1]);

	}

	console.log('linear weights', linear_weights);
	console.log('linear offsets', linear_offsets);

	
}

// Returns binomial sequence at level n.
// 1 - 1
// 2 - 1, 1
// 3 - 1, 2, 1
// 4 - 1, 3, 3, 1
function binomial( level ) {

	var previous = [1];

	for (var i = 1; i < level; i++) {
		var current = [ 1 ];

		for (var j = 0; j < previous.length-1; j++) {
			current.push( previous[j] + previous[j + 1] );
		}

		current.push( 1 );

		previous = current;

	}

	return previous;
	
}