three
Version:
JavaScript 3D library
285 lines (173 loc) • 5.87 kB
JavaScript
/**
* @author zz85 / http://www.lab4games.net/zz85/blog
* Extensible curve object
*
* Some common of Curve methods
* .getPoint(t), getTangent(t)
* .getPointAt(u), getTagentAt(u)
* .getPoints(), .getSpacedPoints()
* .getLength()
* .updateArcLengths()
*
* This following classes subclasses THREE.Curve:
*
* -- 2d classes --
* THREE.LineCurve
* THREE.QuadraticBezierCurve
* THREE.CubicBezierCurve
* THREE.SplineCurve
* THREE.ArcCurve
* THREE.EllipseCurve
*
* -- 3d classes --
* THREE.LineCurve3
* THREE.QuadraticBezierCurve3
* THREE.CubicBezierCurve3
* THREE.SplineCurve3
*
* A series of curves can be represented as a THREE.CurvePath
*
**/
/**************************************************************
* Abstract Curve base class
**************************************************************/
THREE.Curve = function () {
};
THREE.Curve.prototype = {
constructor: THREE.Curve,
// Virtual base class method to overwrite and implement in subclasses
// - t [0 .. 1]
getPoint: function ( t ) {
console.warn( "THREE.Curve: Warning, getPoint() not implemented!" );
return null;
},
// Get point at relative position in curve according to arc length
// - u [0 .. 1]
getPointAt: function ( u ) {
var t = this.getUtoTmapping( u );
return this.getPoint( t );
},
// Get sequence of points using getPoint( t )
getPoints: function ( divisions ) {
if ( ! divisions ) divisions = 5;
var d, pts = [];
for ( d = 0; d <= divisions; d ++ ) {
pts.push( this.getPoint( d / divisions ) );
}
return pts;
},
// Get sequence of points using getPointAt( u )
getSpacedPoints: function ( divisions ) {
if ( ! divisions ) divisions = 5;
var d, pts = [];
for ( d = 0; d <= divisions; d ++ ) {
pts.push( this.getPointAt( d / divisions ) );
}
return pts;
},
// Get total curve arc length
getLength: function () {
var lengths = this.getLengths();
return lengths[ lengths.length - 1 ];
},
// Get list of cumulative segment lengths
getLengths: function ( divisions ) {
if ( ! divisions ) divisions = ( this.__arcLengthDivisions ) ? ( this.__arcLengthDivisions ) : 200;
if ( this.cacheArcLengths
&& ( this.cacheArcLengths.length === divisions + 1 )
&& ! this.needsUpdate ) {
//console.log( "cached", this.cacheArcLengths );
return this.cacheArcLengths;
}
this.needsUpdate = false;
var cache = [];
var current, last = this.getPoint( 0 );
var p, sum = 0;
cache.push( 0 );
for ( p = 1; p <= divisions; p ++ ) {
current = this.getPoint ( p / divisions );
sum += current.distanceTo( last );
cache.push( sum );
last = current;
}
this.cacheArcLengths = cache;
return cache; // { sums: cache, sum:sum }; Sum is in the last element.
},
updateArcLengths: function() {
this.needsUpdate = true;
this.getLengths();
},
// Given u ( 0 .. 1 ), get a t to find p. This gives you points which are equidistant
getUtoTmapping: function ( u, distance ) {
var arcLengths = this.getLengths();
var i = 0, il = arcLengths.length;
var targetArcLength; // The targeted u distance value to get
if ( distance ) {
targetArcLength = distance;
} else {
targetArcLength = u * arcLengths[ il - 1 ];
}
//var time = Date.now();
// binary search for the index with largest value smaller than target u distance
var low = 0, high = il - 1, comparison;
while ( low <= high ) {
i = Math.floor( low + ( high - low ) / 2 ); // less likely to overflow, though probably not issue here, JS doesn't really have integers, all numbers are floats
comparison = arcLengths[ i ] - targetArcLength;
if ( comparison < 0 ) {
low = i + 1;
} else if ( comparison > 0 ) {
high = i - 1;
} else {
high = i;
break;
// DONE
}
}
i = high;
//console.log('b' , i, low, high, Date.now()- time);
if ( arcLengths[ i ] === targetArcLength ) {
var t = i / ( il - 1 );
return t;
}
// we could get finer grain at lengths, or use simple interpolation between two points
var lengthBefore = arcLengths[ i ];
var lengthAfter = arcLengths[ i + 1 ];
var segmentLength = lengthAfter - lengthBefore;
// determine where we are between the 'before' and 'after' points
var segmentFraction = ( targetArcLength - lengthBefore ) / segmentLength;
// add that fractional amount to t
var t = ( i + segmentFraction ) / ( il - 1 );
return t;
},
// Returns a unit vector tangent at t
// In case any sub curve does not implement its tangent derivation,
// 2 points a small delta apart will be used to find its gradient
// which seems to give a reasonable approximation
getTangent: function( t ) {
var delta = 0.0001;
var t1 = t - delta;
var t2 = t + delta;
// Capping in case of danger
if ( t1 < 0 ) t1 = 0;
if ( t2 > 1 ) t2 = 1;
var pt1 = this.getPoint( t1 );
var pt2 = this.getPoint( t2 );
var vec = pt2.clone().sub( pt1 );
return vec.normalize();
},
getTangentAt: function ( u ) {
var t = this.getUtoTmapping( u );
return this.getTangent( t );
}
};
// TODO: Transformation for Curves?
/**************************************************************
* 3D Curves
**************************************************************/
// A Factory method for creating new curve subclasses
THREE.Curve.create = function ( constructor, getPointFunc ) {
constructor.prototype = Object.create( THREE.Curve.prototype );
constructor.prototype.constructor = constructor;
constructor.prototype.getPoint = getPointFunc;
return constructor;
};