ol-ext/utils/cspline.js

/** Create a cardinal spline version of this geometry. 
*	Original https://github.com/epistemex/cardinal-spline-js
*	@see https://en.wikipedia.org/wiki/Cubic_Hermite_spline#Cardinal_spline
*
* @param {} options
*	- tension {Number} a [0,1] number / can be interpreted as the "length" of the tangent, default 0.5
*	- resolution {Number} size of segment to split
*	- pointsPerSeg {Interger} number of points per segment to add if no resolution is provided, default add 10 points per segment
*/

/** Cache cspline calculation
*/
ol.geom.Geometry.prototype.cspline = function(options)
{	// Calculate cspline
	if (this.calcCSpline_)
	{	if (this.csplineGeometryRevision != this.getRevision() 
			|| this.csplineOption != JSON.stringify(options))
		{	this.csplineGeometry_ = this.calcCSpline_(options)
			this.csplineGeometryRevision = this.getRevision();
			this.csplineOption = JSON.stringify(options);
		}
		return this.csplineGeometry_;
	}
	// Default do nothing
	else
	{	return this;
	}
}

ol.geom.GeometryCollection.prototype.calcCSpline_ = function(options)
{	var g=[], g0=this.getGeometries();
	for (var i=0; i<g0.length; i++)
	{	g.push(g0[i].cspline());
	}
	return new ol.geom.GeometryCollection(g);
}

ol.geom.MultiLineString.prototype.calcCSpline_ = function(options)
{	var g=[], g0=this.getLineStrings();
	for (var i=0; i<g0.length; i++)
	{	g.push(g0[i].cspline().getCoordinates());
	}
	return new ol.geom.MultiLineString(g);
}

ol.geom.Polygon.prototype.calcCSpline_ = function(options)
{	var g=[], g0=this.getCoordinates();
	for (var i=0; i<g0.length; i++)
	{	g.push((new ol.geom.LineString(g0[i])).cspline().getCoordinates());
	}
	return new ol.geom.Polygon(g);
}

ol.geom.MultiPolygon.prototype.calcCSpline_ = function(options)
{	var g=[], g0=this.getPolygons();
	for (var i=0; i<g0.length; i++)
	{	g.push(g0[i].cspline().getCoordinates());
	}
	return new ol.geom.MultiPolygon(g);
}

/**
*/
ol.geom.LineString.prototype.calcCSpline_ = function(options)
 {	if (!options) options={};
	var line = this.getCoordinates();
	var tension = typeof options.tension === "number" ? options.tension : 0.5;
	var resolution = options.resolution || (this.getLength() / line.length / (options.pointsPerSeg || 10));

	var pts, res = [],			// clone array
		x, y,					// our x,y coords
		t1x, t2x, t1y, t2y,		// tension vectors
		c1, c2, c3, c4,			// cardinal points
		st, t, i;				// steps based on num. of segments

	// clone array so we don't change the original
	//
	pts = line.slice(0);

	// The algorithm require a previous and next point to the actual point array.
	// Check if we will draw closed or open curve.
	// If closed, copy end points to beginning and first points to end
	// If open, duplicate first points to befinning, end points to end
	if (line.length>2 && line[0][0]==line[line.length-1][0] && line[0][1]==line[line.length-1][1]) 
	{	pts.unshift(line[line.length-2]);
		pts.push(line[1]);
	}
	else 
	{	pts.unshift(line[0]);
		pts.push(line[line.length-1]);
	}

	// ok, lets start..
	function dist2d(x1, y1, x2, y2)
	{	var dx = x2-x1;
		var dy = y2-y1;
		return Math.sqrt(dx*dx+dy*dy);
	}

	// 1. loop goes through point array
	// 2. loop goes through each segment between the 2 pts + 1e point before and after
	for (i=1; i < (pts.length - 2); i++) 
	{	var d1 = dist2d (pts[i][0], pts[i][1], pts[i+1][0], pts[i+1][1]);
		var numOfSegments = Math.round(d1/resolution);
		
		var d=1;
		if (options.normalize)
		{	var d1 = dist2d (pts[i+1][0], pts[i+1][1], pts[i-1][0], pts[i-1][1]);
			var d2 = dist2d (pts[i+2][0], pts[i+2][1], pts[i][0], pts[i][1]);
			if (d1<d2) d = d1/d2;
			else d = d2/d1;
		}

		// calc tension vectors
		t1x = (pts[i+1][0] - pts[i-1][0]) * tension *d;
		t2x = (pts[i+2][0] - pts[i][0]) * tension *d;

		t1y = (pts[i+1][1] - pts[i-1][1]) * tension *d;
		t2y = (pts[i+2][1] - pts[i][1]) * tension *d;

		for (t=0; t <= numOfSegments; t++) 
		{	// calc step
			st = t / numOfSegments;

			// calc cardinals
			c1 =   2 * Math.pow(st, 3) 	- 3 * Math.pow(st, 2) + 1; 
			c2 = -(2 * Math.pow(st, 3)) + 3 * Math.pow(st, 2); 
			c3 = 	   Math.pow(st, 3)	- 2 * Math.pow(st, 2) + st; 
			c4 = 	   Math.pow(st, 3)	- 	  Math.pow(st, 2);

			// calc x and y cords with common control vectors
			x = c1 * pts[i][0]	+ c2 * pts[i+1][0] + c3 * t1x + c4 * t2x;
			y = c1 * pts[i][1]	+ c2 * pts[i+1][1] + c3 * t1y + c4 * t2y;

			//store points in array
			res.push([x,y]);
		}
	}

	return new ol.geom.LineString(res);
}