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 = {
Line: function(/* array */start, /* array */end) {
// summary
// Creates a straight line object
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(/* float */n){
// summary
// Returns the point at point N (in terms of percentage) on this line.
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; // array
}
return this; // dojo.math.curves.Line
},
Bezier: function(/* array */pnts) {
// summary
// Creates a bezier curve
// 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.
this.getValue = function(/* float */step) {
// summary
// Returns the point at point N (in terms of percentage) on this curve.
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; // array
}
this.p = pnts;
return this; // dojo.math.curves.Bezier
},
CatmullRom : function(/* array */pnts, /* float */c) {
// summary
// Creates a catmull-rom spline curve with c tension.
this.getValue = function(/* float */step) {
// summary
// Returns the point at point N (in terms of percentage) on this curve.
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; // array
}
if(!c) this.c = 0.7;
else this.c = c;
this.p = pnts;
return this; // dojo.math.curves.CatmullRom
},
// 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(/* array */start, /* array */end, /* boolean? */ccw) {
// summary
// Creates an arc with a counter clockwise switch
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));
},
CenteredArc : function(/* array */center, /* float */radius, /* array */start, /* array */end) {
// summary
// 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
this.center = center;
this.radius = radius;
this.start = start || 0;
this.end = end;
this.getValue = function(/* float */n) {
// summary
// Returns the point at point N (in terms of percentage) on this curve.
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; // array
}
return this; // dojo.math.curves.CenteredArc
},
Circle : function(/* array */center, /* float */radius) {
// summary
// Special case of Arc (start = 0, end = 360)
dojo.math.curves.CenteredArc.call(this, center, radius, 0, 360);
return this; // dojo.math.curves.Circle
},
Path : function() {
// summary
// Generic path shape, created from curve segments
var curves = [];
var weights = [];
var ranges = [];
var totalWeight = 0;
this.add = function(/* dojo.math.curves.* */curve, /* float */weight) {
// summary
// Add a curve segment to this path
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(/* dojo.math.curves.* */curve) {
// summary
// Remove a curve segment from this path
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() {
// summary
// Remove all curve segments
curves = [];
weights = [];
totalWeight = 0;
}
this.getValue = function(/* float */n) {
// summary
// Returns the point at point N (in terms of percentage) on this curve.
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; // array
}
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; // dojo.math.curves.Path
}
};