feat: initialize project with core dependencies and game entry point

node_modules/three/examples/jsm/geometries/ParametricFunctions.js

@@ -0,0 +1,100 @@
+
+/**
+ * @module ParametricFunctions
+ * @three_import import * as ParametricFunctions from 'three/addons/geometries/ParametricFunctions.js';
+ */
+
+/**
+ * A parametric function representing the Klein bottle.
+ *
+ * @param {number} v - The `v` coordinate on the surface in the range `[0,1]`.
+ * @param {number} u - The `u` coordinate on the surface in the range `[0,1]`.
+ * @param {Vector3} target - The target vector that is used to store the method's result.
+ */
+function klein( 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 );
+
+}
+
+/**
+ * A parametric function representing a flat plane.
+ *
+ * @param {number} u - The `u` coordinate on the surface in the range `[0,1]`.
+ * @param {number} v - The `v` coordinate on the surface in the range `[0,1]`.
+ * @param {Vector3} target - The target vector that is used to store the method's result.
+ */
+function plane( u, v, target ) {
+
+	target.set( u, 0, v );
+
+}
+
+/**
+ * A parametric function representing a flat mobius strip.
+ *
+ * @param {number} u - The `u` coordinate on the surface in the range `[0,1]`.
+ * @param {number} t - The `v` coordinate on the surface in the range `[0,1]`.
+ * @param {Vector3} target - The target vector that is used to store the method's result.
+ */
+function mobius( u, t, target ) {
+
+	// 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 );
+
+}
+
+/**
+ * A parametric function representing a volumetric mobius strip.
+ *
+ * @param {number} u - The `u` coordinate on the surface in the range `[0,1]`.
+ * @param {number} t - The `v` coordinate on the surface in the range `[0,1]`.
+ * @param {Vector3} target - The target vector that is used to store the method's result.
+ */
+function mobius3d( u, t, target ) {
+
+	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 );
+
+}
+
+export { klein, plane, mobius, mobius3d };