https://github.com/WWBN/AVideo/issues/8713

node_modules/three/examples/js/geometries/ParametricGeometries.js

@@ -0,0 +1,252 @@
+/**
+ * Experimenting of primitive geometry creation using Surface Parametric equations
+ */
+
+THREE.ParametricGeometries = {
+
+	klein: function ( v, u, target ) {
+
+		u *= Math.PI;
+		v *= 2 * Math.PI;
+
+		u = u * 2;
+		var x, y, 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 );
+
+		}
+
+		y = - 2 * ( 1 - Math.cos( u ) / 2 ) * Math.sin( v );
+
+		target.set( x, y, z );
+
+	},
+
+	plane: function ( width, height ) {
+
+		return function ( u, v, target ) {
+
+			var x = u * width;
+			var y = 0;
+			var 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;
+		var v = 2 * Math.PI * t;
+
+		var x, y, z;
+
+		var a = 2;
+
+		x = Math.cos( v ) * ( a + u * Math.cos( v / 2 ) );
+		y = Math.sin( v ) * ( a + u * Math.cos( v / 2 ) );
+		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;
+		var phi = u / 2;
+		var major = 2.25, a = 0.125, b = 0.65;
+
+		var x, y, z;
+
+		x = a * Math.cos( t ) * Math.cos( phi ) - b * Math.sin( t ) * Math.sin( phi );
+		z = a * Math.cos( t ) * Math.sin( phi ) + b * Math.sin( t ) * Math.cos( phi );
+		y = ( major + x ) * Math.sin( u );
+		x = ( major + x ) * Math.cos( u );
+
+		target.set( x, y, z );
+
+	}
+
+};
+
+
+/*********************************************
+ *
+ * Parametric Replacement for TubeGeometry
+ *
+ *********************************************/
+
+THREE.ParametricGeometries.TubeGeometry = function ( path, segments, radius, segmentsRadius, closed ) {
+
+	this.path = path;
+	this.segments = segments || 64;
+	this.radius = radius || 1;
+	this.segmentsRadius = segmentsRadius || 8;
+	this.closed = closed || false;
+
+	var scope = this, numpoints = this.segments + 1;
+
+	var frames = path.computeFrenetFrames( segments, closed ),
+		tangents = frames.tangents,
+		normals = frames.normals,
+		binormals = frames.binormals;
+
+	// proxy internals
+
+	this.tangents = tangents;
+	this.normals = normals;
+	this.binormals = binormals;
+
+	var position = new THREE.Vector3();
+
+	var ParametricTube = function ( u, v, target ) {
+
+		v *= 2 * Math.PI;
+
+		var i = u * ( numpoints - 1 );
+		i = Math.floor( i );
+
+		path.getPointAt( u, position );
+
+		var normal = normals[ i ];
+		var binormal = binormals[ i ];
+
+		var cx = - scope.radius * Math.cos( v ); // TODO: Hack: Negating it so it faces outside.
+		var cy = scope.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 );
+
+	};
+
+	THREE.ParametricGeometry.call( this, ParametricTube, segments, segmentsRadius );
+
+};
+
+THREE.ParametricGeometries.TubeGeometry.prototype = Object.create( THREE.BufferGeometry.prototype );
+THREE.ParametricGeometries.TubeGeometry.prototype.constructor = THREE.ParametricGeometries.TubeGeometry;
+
+
+/*********************************************
+  *
+  * Parametric Replacement for TorusKnotGeometry
+  *
+  *********************************************/
+THREE.ParametricGeometries.TorusKnotGeometry = function ( radius, tube, segmentsT, segmentsR, p, q ) {
+
+	this.radius = radius || 200;
+	this.tube = tube || 40;
+	this.segmentsT = segmentsT || 64;
+	this.segmentsR = segmentsR || 8;
+	this.p = p || 2;
+	this.q = q || 3;
+
+	function TorusKnotCurve() {
+
+		THREE.Curve.call( this );
+
+	}
+
+	TorusKnotCurve.prototype = Object.create( THREE.Curve.prototype );
+	TorusKnotCurve.prototype.constructor = TorusKnotCurve;
+
+	TorusKnotCurve.prototype.getPoint = function ( t, optionalTarget ) {
+
+		var point = optionalTarget || new THREE.Vector3();
+
+		t *= Math.PI * 2;
+
+		var r = 0.5;
+
+		var x = ( 1 + r * Math.cos( q * t ) ) * Math.cos( p * t );
+		var y = ( 1 + r * Math.cos( q * t ) ) * Math.sin( p * t );
+		var z = r * Math.sin( q * t );
+
+		return point.set( x, y, z ).multiplyScalar( radius );
+
+	};
+
+	var segments = segmentsT;
+	var radiusSegments = segmentsR;
+	var extrudePath = new TorusKnotCurve();
+
+	THREE.ParametricGeometries.TubeGeometry.call( this, extrudePath, segments, tube, radiusSegments, true, false );
+
+};
+
+THREE.ParametricGeometries.TorusKnotGeometry.prototype = Object.create( THREE.BufferGeometry.prototype );
+THREE.ParametricGeometries.TorusKnotGeometry.prototype.constructor = THREE.ParametricGeometries.TorusKnotGeometry;
+
+
+/*********************************************
+  *
+  * Parametric Replacement for SphereGeometry
+  *
+  *********************************************/
+THREE.ParametricGeometries.SphereGeometry = function ( 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 );
+
+	}
+
+	THREE.ParametricGeometry.call( this, sphere, u, v );
+
+};
+
+THREE.ParametricGeometries.SphereGeometry.prototype = Object.create( THREE.BufferGeometry.prototype );
+THREE.ParametricGeometries.SphereGeometry.prototype.constructor = THREE.ParametricGeometries.SphereGeometry;
+
+
+/*********************************************
+  *
+  * Parametric Replacement for PlaneGeometry
+  *
+  *********************************************/
+
+THREE.ParametricGeometries.PlaneGeometry = function ( width, depth, segmentsWidth, segmentsDepth ) {
+
+	function plane( u, v, target ) {
+
+		var x = u * width;
+		var y = 0;
+		var z = v * depth;
+
+		target.set( x, y, z );
+
+	}
+
+	THREE.ParametricGeometry.call( this, plane, segmentsWidth, segmentsDepth );
+
+};
+
+THREE.ParametricGeometries.PlaneGeometry.prototype = Object.create( THREE.BufferGeometry.prototype );
+THREE.ParametricGeometries.PlaneGeometry.prototype.constructor = THREE.ParametricGeometries.PlaneGeometry;