integration, auc, interpolation fns

auc.js

	// get n linear steps between point{x, y} a and b
	function interPoints(a, b, n) {
		let int = (t) => ({
				x: a.x * (1 - t) + b.x * t,
				y: a.y * (1 - t) + b.y * t
			}),
			step = 1/(n+1),
			ret = [];
		
		for (let i=0; i<n; i++) {
			ret[i] = int(step*(i+1))
		}
		return ret;
	}
	
	function interpolate(points, interPoints) {
		interPoints = interPoints || 1;
		let pts = [];
		for (var i = 0; i < points.length-1; i++) {
			pts = pts.concat(points[i], this.interPoints(points[i], points[i+1], interPoints))
		}
		return pts.concat(points[points.length-1]);
	}
	
	function areaIntegration(points) {
		let rectArea = 0;
		for (var i = 0; i < points.length-1; i++) {
			let a = points[i],
				b = points[i+1],
				mid = this.interPoints(a, b, 1);
			
			rectArea += (b.x - a.x) * mid[0].y;
		}
		return rectArea;
	}