Feature: non-uniform beam intensity

[joedf]

Demo/test using a Gaussian point spread function like beam:
https://codepen.io/joedf/pen/jOeyKZg?editors=0111

[joedf]

// gaussian where the curve is defined by a=1,b=0,c=0.3
// to get a bell curve that is going from 1 to 0 in y, centered on 0 in x.
// https://www.desmos.com/calculator/pbnihoalbr
// sampled at 10 spots: 0 to 1 at 0.1 increments
// Approximation (by hand):
// (0,1), (.1,.95), (.2,.8), (.4,.4), (.5,.25),
// (.6,.135), (.7,.06), (.8,.03), (.9,.01), (1,0)
var gaussianStops = [0,gg(1), 0.1,gg(.95), .2,gg(.8), .4,gg(.4), .5,gg(.25),
                    .6,gg(.135), .7,gg(.06), .8,gg(.03), .9,gg(.01), 1,gg(0)];

// calculate it with a function instead!
// basic gaussian curve: g = a exp(- (x-b)^2 / (2c^2))
// https://en.wikipedia.org/wiki/Gaussian_function
// make a function that calculates gradient stops
// where r is the sampling rate (along the x-axis)
// returns r+1 stops (because with count the 0,1 point)
function gaussianGradient(a,b,c,r=10,useAlpha=false) {
  var stops = [];
  for(var i=0; i<=r; i++){
    const x = i / r;
    const g = a * Math.exp( (-Math.pow(x-b,2)) / (2*Math.pow(c,2)) );
    stops.push(x, scaledIntensityRGBA(g, useAlpha));
  }
  return stops;
}

// replace with a calculated/more accurate one
gaussianStops = gaussianGradient(1,0,0.3,1000,1);