three 基础库
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import {
Curve,
ParametricGeometry,
Vector3
} from '../../../build/three.module.js';
/**
* Experimenting of primitive geometry creation using Surface Parametric equations
*/
const ParametricGeometries = {
klein: function ( v, u, target ) {
u *= Math.PI;
v *= 2 * Math.PI;
u = u * 2;
let x, z;
if ( u < Math.PI ) {
x = 3 * Math.cos( u ) * ( 1 + Math.sin( u ) ) + ( 2 * ( 1 - Math.cos( u ) / 2 ) ) * Math.cos( u ) * Math.cos( v );
z = - 8 * Math.sin( u ) - 2 * ( 1 - Math.cos( u ) / 2 ) * Math.sin( u ) * Math.cos( v );
} else {
x = 3 * Math.cos( u ) * ( 1 + Math.sin( u ) ) + ( 2 * ( 1 - Math.cos( u ) / 2 ) ) * Math.cos( v + Math.PI );
z = - 8 * Math.sin( u );
}
const y = - 2 * ( 1 - Math.cos( u ) / 2 ) * Math.sin( v );
target.set( x, y, z );
},
plane: function ( width, height ) {
return function ( u, v, target ) {
const x = u * width;
const y = 0;
const z = v * height;
target.set( x, y, z );
};
},
mobius: function ( u, t, target ) {
// flat mobius strip
// http://www.wolframalpha.com/input/?i=M%C3%B6bius+strip+parametric+equations&lk=1&a=ClashPrefs_*Surface.MoebiusStrip.SurfaceProperty.ParametricEquations-
u = u - 0.5;
const v = 2 * Math.PI * t;
const a = 2;
const x = Math.cos( v ) * ( a + u * Math.cos( v / 2 ) );
const y = Math.sin( v ) * ( a + u * Math.cos( v / 2 ) );
const z = u * Math.sin( v / 2 );
target.set( x, y, z );
},
mobius3d: function ( u, t, target ) {
// volumetric mobius strip
u *= Math.PI;
t *= 2 * Math.PI;
u = u * 2;
const phi = u / 2;
const major = 2.25, a = 0.125, b = 0.65;
let x = a * Math.cos( t ) * Math.cos( phi ) - b * Math.sin( t ) * Math.sin( phi );
const z = a * Math.cos( t ) * Math.sin( phi ) + b * Math.sin( t ) * Math.cos( phi );
const y = ( major + x ) * Math.sin( u );
x = ( major + x ) * Math.cos( u );
target.set( x, y, z );
}
};
/*********************************************
*
* Parametric Replacement for TubeGeometry
*
*********************************************/
ParametricGeometries.TubeGeometry = class TubeGeometry extends ParametricGeometry {
constructor( path, segments = 64, radius = 1, segmentsRadius = 8, closed = false ) {
const numpoints = segments + 1;
const frames = path.computeFrenetFrames( segments, closed ),
tangents = frames.tangents,
normals = frames.normals,
binormals = frames.binormals;
const position = new Vector3();
function ParametricTube( u, v, target ) {
v *= 2 * Math.PI;
const i = Math.floor( u * ( numpoints - 1 ) );
path.getPointAt( u, position );
const normal = normals[ i ];
const binormal = binormals[ i ];
const cx = - radius * Math.cos( v ); // TODO: Hack: Negating it so it faces outside.
const cy = radius * Math.sin( v );
position.x += cx * normal.x + cy * binormal.x;
position.y += cx * normal.y + cy * binormal.y;
position.z += cx * normal.z + cy * binormal.z;
target.copy( position );
}
super( ParametricTube, segments, segmentsRadius );
// proxy internals
this.tangents = tangents;
this.normals = normals;
this.binormals = binormals;
this.path = path;
this.segments = segments;
this.radius = radius;
this.segmentsRadius = segmentsRadius;
this.closed = closed;
}
};
/*********************************************
*
* Parametric Replacement for TorusKnotGeometry
*
*********************************************/
ParametricGeometries.TorusKnotGeometry = class TorusKnotGeometry extends ParametricGeometries.TubeGeometry {
constructor( radius = 200, tube = 40, segmentsT = 64, segmentsR = 8, p = 2, q = 3 ) {
class TorusKnotCurve extends Curve {
getPoint( t, optionalTarget = new Vector3() ) {
const point = optionalTarget;
t *= Math.PI * 2;
const r = 0.5;
const x = ( 1 + r * Math.cos( q * t ) ) * Math.cos( p * t );
const y = ( 1 + r * Math.cos( q * t ) ) * Math.sin( p * t );
const z = r * Math.sin( q * t );
return point.set( x, y, z ).multiplyScalar( radius );
}
}
const segments = segmentsT;
const radiusSegments = segmentsR;
const extrudePath = new TorusKnotCurve();
super( extrudePath, segments, tube, radiusSegments, true, false );
this.radius = radius;
this.tube = tube;
this.segmentsT = segmentsT;
this.segmentsR = segmentsR;
this.p = p;
this.q = q;
}
};
/*********************************************
*
* Parametric Replacement for SphereGeometry
*
*********************************************/
ParametricGeometries.SphereGeometry = class SphereGeometry extends ParametricGeometry {
constructor( size, u, v ) {
function sphere( u, v, target ) {
u *= Math.PI;
v *= 2 * Math.PI;
var x = size * Math.sin( u ) * Math.cos( v );
var y = size * Math.sin( u ) * Math.sin( v );
var z = size * Math.cos( u );
target.set( x, y, z );
}
super( sphere, u, v );
}
};
/*********************************************
*
* Parametric Replacement for PlaneGeometry
*
*********************************************/
ParametricGeometries.PlaneGeometry = class PlaneGeometry extends ParametricGeometry {
constructor( width, depth, segmentsWidth, segmentsDepth ) {
function plane( u, v, target ) {
const x = u * width;
const y = 0;
const z = v * depth;
target.set( x, y, z );
}
super( plane, segmentsWidth, segmentsDepth );
}
};
export { ParametricGeometries };