File: //var/www/aspa/three/extras/core/Curve.js
import * as MathUtils from '../../math/MathUtils.js';
import { Vector2 } from '../../math/Vector2.js';
import { Vector3 } from '../../math/Vector3.js';
import { Matrix4 } from '../../math/Matrix4.js';
/**
* Extensible curve object.
*
* Some common of curve methods:
* .getPoint( t, optionalTarget ), .getTangent( t, optionalTarget )
* .getPointAt( u, optionalTarget ), .getTangentAt( u, optionalTarget )
* .getPoints(), .getSpacedPoints()
* .getLength()
* .updateArcLengths()
*
* This following curves inherit from THREE.Curve:
*
* -- 2D curves --
* THREE.ArcCurve
* THREE.CubicBezierCurve
* THREE.EllipseCurve
* THREE.LineCurve
* THREE.QuadraticBezierCurve
* THREE.SplineCurve
*
* -- 3D curves --
* THREE.CatmullRomCurve3
* THREE.CubicBezierCurve3
* THREE.LineCurve3
* THREE.QuadraticBezierCurve3
*
* A series of curves can be represented as a THREE.CurvePath.
*
**/
class Curve {
constructor() {
this.type = 'Curve';
this.arcLengthDivisions = 200;
}
// Virtual base class method to overwrite and implement in subclasses
// - t [0 .. 1]
getPoint( /* t, optionalTarget */ ) {
console.warn( 'THREE.Curve: .getPoint() not implemented.' );
return null;
}
// Get point at relative position in curve according to arc length
// - u [0 .. 1]
getPointAt( u, optionalTarget ) {
const t = this.getUtoTmapping( u );
return this.getPoint( t, optionalTarget );
}
// Get sequence of points using getPoint( t )
getPoints( divisions = 5 ) {
const points = [];
for ( let d = 0; d <= divisions; d ++ ) {
points.push( this.getPoint( d / divisions ) );
}
return points;
}
// Get sequence of points using getPointAt( u )
getSpacedPoints( divisions = 5 ) {
const points = [];
for ( let d = 0; d <= divisions; d ++ ) {
points.push( this.getPointAt( d / divisions ) );
}
return points;
}
// Get total curve arc length
getLength() {
const lengths = this.getLengths();
return lengths[ lengths.length - 1 ];
}
// Get list of cumulative segment lengths
getLengths( divisions = this.arcLengthDivisions ) {
if ( this.cacheArcLengths &&
( this.cacheArcLengths.length === divisions + 1 ) &&
! this.needsUpdate ) {
return this.cacheArcLengths;
}
this.needsUpdate = false;
const cache = [];
let current, last = this.getPoint( 0 );
let sum = 0;
cache.push( 0 );
for ( let 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() {
this.needsUpdate = true;
this.getLengths();
}
// Given u ( 0 .. 1 ), get a t to find p. This gives you points which are equidistant
getUtoTmapping( u, distance ) {
const arcLengths = this.getLengths();
let i = 0;
const il = arcLengths.length;
let targetArcLength; // The targeted u distance value to get
if ( distance ) {
targetArcLength = distance;
} else {
targetArcLength = u * arcLengths[ il - 1 ];
}
// binary search for the index with largest value smaller than target u distance
let 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;
if ( arcLengths[ i ] === targetArcLength ) {
return i / ( il - 1 );
}
// we could get finer grain at lengths, or use simple interpolation between two points
const lengthBefore = arcLengths[ i ];
const lengthAfter = arcLengths[ i + 1 ];
const segmentLength = lengthAfter - lengthBefore;
// determine where we are between the 'before' and 'after' points
const segmentFraction = ( targetArcLength - lengthBefore ) / segmentLength;
// add that fractional amount to t
const 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( t, optionalTarget ) {
const delta = 0.0001;
let t1 = t - delta;
let t2 = t + delta;
// Capping in case of danger
if ( t1 < 0 ) t1 = 0;
if ( t2 > 1 ) t2 = 1;
const pt1 = this.getPoint( t1 );
const pt2 = this.getPoint( t2 );
const tangent = optionalTarget || ( ( pt1.isVector2 ) ? new Vector2() : new Vector3() );
tangent.copy( pt2 ).sub( pt1 ).normalize();
return tangent;
}
getTangentAt( u, optionalTarget ) {
const t = this.getUtoTmapping( u );
return this.getTangent( t, optionalTarget );
}
computeFrenetFrames( segments, closed ) {
// see http://www.cs.indiana.edu/pub/techreports/TR425.pdf
const normal = new Vector3();
const tangents = [];
const normals = [];
const binormals = [];
const vec = new Vector3();
const mat = new Matrix4();
// compute the tangent vectors for each segment on the curve
for ( let i = 0; i <= segments; i ++ ) {
const u = i / segments;
tangents[ i ] = this.getTangentAt( u, new Vector3() );
}
// select an initial normal vector perpendicular to the first tangent vector,
// and in the direction of the minimum tangent xyz component
normals[ 0 ] = new Vector3();
binormals[ 0 ] = new Vector3();
let min = Number.MAX_VALUE;
const tx = Math.abs( tangents[ 0 ].x );
const ty = Math.abs( tangents[ 0 ].y );
const tz = Math.abs( tangents[ 0 ].z );
if ( tx <= min ) {
min = tx;
normal.set( 1, 0, 0 );
}
if ( ty <= min ) {
min = ty;
normal.set( 0, 1, 0 );
}
if ( tz <= min ) {
normal.set( 0, 0, 1 );
}
vec.crossVectors( tangents[ 0 ], normal ).normalize();
normals[ 0 ].crossVectors( tangents[ 0 ], vec );
binormals[ 0 ].crossVectors( tangents[ 0 ], normals[ 0 ] );
// compute the slowly-varying normal and binormal vectors for each segment on the curve
for ( let i = 1; i <= segments; i ++ ) {
normals[ i ] = normals[ i - 1 ].clone();
binormals[ i ] = binormals[ i - 1 ].clone();
vec.crossVectors( tangents[ i - 1 ], tangents[ i ] );
if ( vec.length() > Number.EPSILON ) {
vec.normalize();
const theta = Math.acos( MathUtils.clamp( tangents[ i - 1 ].dot( tangents[ i ] ), - 1, 1 ) ); // clamp for floating pt errors
normals[ i ].applyMatrix4( mat.makeRotationAxis( vec, theta ) );
}
binormals[ i ].crossVectors( tangents[ i ], normals[ i ] );
}
// if the curve is closed, postprocess the vectors so the first and last normal vectors are the same
if ( closed === true ) {
let theta = Math.acos( MathUtils.clamp( normals[ 0 ].dot( normals[ segments ] ), - 1, 1 ) );
theta /= segments;
if ( tangents[ 0 ].dot( vec.crossVectors( normals[ 0 ], normals[ segments ] ) ) > 0 ) {
theta = - theta;
}
for ( let i = 1; i <= segments; i ++ ) {
// twist a little...
normals[ i ].applyMatrix4( mat.makeRotationAxis( tangents[ i ], theta * i ) );
binormals[ i ].crossVectors( tangents[ i ], normals[ i ] );
}
}
return {
tangents: tangents,
normals: normals,
binormals: binormals
};
}
clone() {
return new this.constructor().copy( this );
}
copy( source ) {
this.arcLengthDivisions = source.arcLengthDivisions;
return this;
}
toJSON() {
const data = {
metadata: {
version: 4.6,
type: 'Curve',
generator: 'Curve.toJSON'
}
};
data.arcLengthDivisions = this.arcLengthDivisions;
data.type = this.type;
return data;
}
fromJSON( json ) {
this.arcLengthDivisions = json.arcLengthDivisions;
return this;
}
}
export { Curve };