/*	Copyright (c) 2004-2006, The Dojo Foundation	All Rights Reserved.	Licensed under the Academic Free License version 2.1 or above OR the	modified BSD license. For more information on Dojo licensing, see:		http://dojotoolkit.org/community/licensing.shtml*/dojo.provide("dojo.math.curves");dojo.require("dojo.math");/* Curves from Dan's 13th lib stuff. * See: http://pupius.co.uk/js/Toolkit.Drawing.js *      http://pupius.co.uk/dump/dojo/Dojo.Math.js */dojo.math.curves = {	//Creates a straight line object	Line: function(start, end) {		this.start = start;		this.end = end;		this.dimensions = start.length;		for(var i = 0; i < start.length; i++) {			start[i] = Number(start[i]);		}		for(var i = 0; i < end.length; i++) {			end[i] = Number(end[i]);		}		//simple function to find point on an n-dimensional, straight line		this.getValue = function(n) {			var retVal = new Array(this.dimensions);			for(var i=0;i<this.dimensions;i++)				retVal[i] = ((this.end[i] - this.start[i]) * n) + this.start[i];			return retVal;		}		return this;	},	//Takes an array of points, the first is the start point, the last is end point and the ones in	//between are the Bezier control points.	Bezier: function(pnts) {		this.getValue = function(step) {			if(step >= 1) return this.p[this.p.length-1];	// if step>=1 we must be at the end of the curve			if(step <= 0) return this.p[0];					// if step<=0 we must be at the start of the curve			var retVal = new Array(this.p[0].length);			for(var k=0;j<this.p[0].length;k++) { retVal[k]=0; }			for(var j=0;j<this.p[0].length;j++) {				var C=0; var D=0;				for(var i=0;i<this.p.length;i++) {					C += this.p[i][j] * this.p[this.p.length-1][0]						* dojo.math.bernstein(step,this.p.length,i);				}				for(var l=0;l<this.p.length;l++) {					D += this.p[this.p.length-1][0] * dojo.math.bernstein(step,this.p.length,l);				}				retVal[j] = C/D;			}			return retVal;		}		this.p = pnts;		return this;	},	//Catmull-Rom Spline - allows you to interpolate a smooth curve through a set of points in n-dimensional space	CatmullRom : function(pnts,c) {		this.getValue = function(step) {			var percent = step * (this.p.length-1);			var node = Math.floor(percent);			var progress = percent - node;			var i0 = node-1; if(i0 < 0) i0 = 0;			var i = node;			var i1 = node+1; if(i1 >= this.p.length) i1 = this.p.length-1;			var i2 = node+2; if(i2 >= this.p.length) i2 = this.p.length-1;			var u = progress;			var u2 = progress*progress;			var u3 = progress*progress*progress;			var retVal = new Array(this.p[0].length);			for(var k=0;k<this.p[0].length;k++) {				var x1 = ( -this.c * this.p[i0][k] ) + ( (2 - this.c) * this.p[i][k] ) + ( (this.c-2) * this.p[i1][k] ) + ( this.c * this.p[i2][k] );				var x2 = ( 2 * this.c * this.p[i0][k] ) + ( (this.c-3) * this.p[i][k] ) + ( (3 - 2 * this.c) * this.p[i1][k] ) + ( -this.c * this.p[i2][k] );				var x3 = ( -this.c * this.p[i0][k] ) + ( this.c * this.p[i1][k] );				var x4 = this.p[i][k];				retVal[k] = x1*u3 + x2*u2 + x3*u + x4;			}			return retVal;		}		if(!c) this.c = 0.7;		else this.c = c;		this.p = pnts;		return this;	},	// FIXME: This is the bad way to do a partial-arc with 2 points. We need to have the user	// supply the radius, otherwise we always get a half-circle between the two points.	Arc : function(start, end, ccw) {		var center = dojo.math.points.midpoint(start, end);		var sides = dojo.math.points.translate(dojo.math.points.invert(center), start);		var rad = Math.sqrt(Math.pow(sides[0], 2) + Math.pow(sides[1], 2));		var theta = dojo.math.radToDeg(Math.atan(sides[1]/sides[0]));		if( sides[0] < 0 ) {			theta -= 90;		} else {			theta += 90;		}		dojo.math.curves.CenteredArc.call(this, center, rad, theta, theta+(ccw?-180:180));	},	// Creates an arc object, with center and radius (Top of arc = 0 degrees, increments clockwise)	//  center => 2D point for center of arc	//  radius => scalar quantity for radius of arc	//  start  => to define an arc specify start angle (default: 0)	//  end    => to define an arc specify start angle	CenteredArc : function(center, radius, start, end) {		this.center = center;		this.radius = radius;		this.start = start || 0;		this.end = end;		this.getValue = function(n) {			var retVal = new Array(2);			var theta = dojo.math.degToRad(this.start+((this.end-this.start)*n));			retVal[0] = this.center[0] + this.radius*Math.sin(theta);			retVal[1] = this.center[1] - this.radius*Math.cos(theta);			return retVal;		}		return this;	},	// Special case of Arc (start = 0, end = 360)	Circle : function(center, radius) {		dojo.math.curves.CenteredArc.call(this, center, radius, 0, 360);		return this;	},	Path : function() {		var curves = [];		var weights = [];		var ranges = [];		var totalWeight = 0;		this.add = function(curve, weight) {			if( weight < 0 ) { dojo.raise("dojo.math.curves.Path.add: weight cannot be less than 0"); }			curves.push(curve);			weights.push(weight);			totalWeight += weight;			computeRanges();		}		this.remove = function(curve) {			for(var i = 0; i < curves.length; i++) {				if( curves[i] == curve ) {					curves.splice(i, 1);					totalWeight -= weights.splice(i, 1)[0];					break;				}			}			computeRanges();		}		this.removeAll = function() {			curves = [];			weights = [];			totalWeight = 0;		}		this.getValue = function(n) {			var found = false, value = 0;			for(var i = 0; i < ranges.length; i++) {				var r = ranges[i];				//w(r.join(" ... "));				if( n >= r[0] && n < r[1] ) {					var subN = (n - r[0]) / r[2];					value = curves[i].getValue(subN);					found = true;					break;				}			}			// FIXME: Do we want to assume we're at the end?			if( !found ) {				value = curves[curves.length-1].getValue(1);			}			for(var j = 0; j < i; j++) {				value = dojo.math.points.translate(value, curves[j].getValue(1));			}			return value;		}		function computeRanges() {			var start = 0;			for(var i = 0; i < weights.length; i++) {				var end = start + weights[i] / totalWeight;				var len = end - start;				ranges[i] = [start, end, len];				start = end;			}		}		return this;	}};