spline.js

"use strict";

class Spline{
	constructor(points){
		if(points.length % 2 !== 0 || points.length < 6){
			return undefined;
		}
		this.x = [];
		this.y = [];
		for(var i=0; i < points.length; i+=2){
			this.x.push(points[i]);
			this.y.push(points[i+1]);
			
		}
		this.s = this.x.length-1;
		this.tl = 1/this.s;
		this.cpx = this.computeControlPoints(this.x);
		this.cpy = this.computeControlPoints(this.y);
	}
	computeControlPoints(K){
		var cp1= [], cp2= [], n = K.length-1;

		/*rhs vector*/
		var a= [], b= [], c= [], r= [];

		/*left most segment*/
		a[0]=0;
		b[0]=2;
		c[0]=1;
		r[0] = K[0]+2*K[1];

		/*internal segments*/
		for (var i = 1; i < n - 1; i++){
			a[i]=1;
			b[i]=4;
			c[i]=1;
			r[i] = 4 * K[i] + 2 * K[i+1];
		}
				
		/*right segment*/
		a[n-1]=2;
		b[n-1]=7;
		c[n-1]=0;
		r[n-1] = 8*K[n-1]+K[n];

		/*solves Ax=b with the Thomas algorithm (from Wikipedia)*/
		for (i = 1; i < n; i++) {
			var m = a[i]/b[i-1];
			b[i] = b[i] - m * c[i - 1];
			r[i] = r[i] - m*r[i-1];
		}

		cp1[n-1] = r[n-1]/b[n-1];
		for (i = n - 2; i >= 0; --i)
			cp1[i] = (r[i] - c[i] * cp1[i+1]) / b[i];
			
		/*we have p1, now compute p2*/
		for (i=0;i<n-1;i++)
			cp2[i]=2*K[i+1]-cp1[i+1];

		cp2[n-1]=0.5*(K[n]+cp1[n-1]);

		return [cp1, cp2];
	}
	curve(n){
		if(n < this.s){
			return [this.x[n], this.y[n], this.cpx[0][n], this.cpy[0][n], this.cpx[1][n], this.cpy[1][n], this.x[n+1], this.y[n+1]];
		}
		return false;
	}
	point(t){
		t = t / this.tl;
		var r = t % 1;
		var s = t - r;
		var c = this.curve(s);

		return {
			x: Math.pow(1-r,3)*c[0]+3*Math.pow(1-r,2)*r*c[2]+3*(1-r)*Math.pow(r,2)*c[4]+Math.pow(r,3)*c[6],
			y: Math.pow(1-r,3)*c[1]+3*Math.pow(1-r,2)*r*c[3]+3*(1-r)*Math.pow(r,2)*c[5]+Math.pow(r,3)*c[7]
		};
	}
	tangent(t){
		t = t / this.tl;
		var r = t % 1;
		var s = t - r;
		var c = this.curve(s);
		
		return Math.atan2(
			3*Math.pow(1-r,2)*(c[3]-c[1])+6*(1-r)*r*(c[5]-c[3])+3*Math.pow(r,2)*(c[7]-c[5]),
			3*Math.pow(1-r,2)*(c[2]-c[0])+6*(1-r)*r*(c[4]-c[2])+3*Math.pow(r,2)*(c[6]-c[4])
		);
	}
	normal(t){
		t = t / this.tl;
		var r = t % 1;
		var s = t - r;
		var c = this.curve(s);

		return [
			6*(1-r)*(c[4]-2*c[2]+c[0])+6*r*(c[6]-2*c[4]+c[2]),
			6*(1-r)*(c[5]-2*c[3]+c[1])+6*r*(c[7]-2*c[5]+c[3])
		];
	}
}