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Shared utility functions\n\nimport { Vector3D, Vector4D, Vector5D } from './types.ts';\n\nexport class MathUtils {\n // Clamp a value between min and max\n static clamp(value: number, min: number, max: number): number {\n return Math.min(Math.max(value, min), max);\n }\n\n // Linear interpolation\n static lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n }\n\n // Map a value from one range to another\n static map(value: number, fromMin: number, fromMax: number, toMin: number, toMax: number): number {\n return toMin + (value - fromMin) * (toMax - toMin) / (fromMax - fromMin);\n }\n\n // Convert degrees to radians\n static degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n }\n\n // Convert radians to degrees\n static radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n }\n\n // Calculate distance between two 3D points\n static distance3D(a: Vector3D, b: Vector3D): number {\n const dx = a.x - b.x;\n const dy = a.y - b.y;\n const dz = a.z - b.z;\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n }\n\n // Calculate distance between two 4D points\n static distance4D(a: Vector4D, b: Vector4D): number {\n const dx = a.x - b.x;\n const dy = a.y - b.y;\n const dz = a.z - b.z;\n const dw = a.w - b.w;\n return Math.sqrt(dx * dx + dy * dy + dz * dz + dw * dw);\n }\n\n // Normalize a 3D vector\n static normalize3D(v: Vector3D): Vector3D {\n const length = Math.sqrt(v.x * v.x + v.y * v.y + v.z * v.z);\n if (length < 0.001) return { x: 0, y: 0, z: 0 };\n return {\n x: v.x / length,\n y: v.y / length,\n z: v.z / length\n };\n }\n\n // Normalize a 4D vector\n static normalize4D(v: Vector4D): Vector4D {\n const length = Math.sqrt(v.x * v.x + v.y * v.y + v.z * v.z + v.w * v.w);\n if (length < 0.001) return { x: 0, y: 0, z: 0, w: 0 };\n return {\n x: v.x / length,\n y: v.y / length,\n z: v.z / length,\n w: v.w / length\n };\n }\n\n // Calculate dot product of two 3D vectors\n static dot3D(a: Vector3D, b: Vector3D): number {\n return a.x * b.x + a.y * b.y + a.z * b.z;\n }\n\n // Calculate dot product of two 4D vectors\n static dot4D(a: Vector4D, b: Vector4D): number {\n return a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w;\n }\n\n // Calculate cross product of two 3D vectors\n static cross3D(a: Vector3D, b: Vector3D): Vector3D {\n return {\n x: a.y * b.z - a.z * b.y,\n y: a.z * b.x - a.x * b.z,\n z: a.x * b.y - a.y * b.x\n };\n }\n\n // Generate a random number between min and max\n static random(min: number = 0, max: number = 1): number {\n return min + Math.random() * (max - min);\n }\n\n // Generate a random integer between min and max (inclusive)\n static randomInt(min: number, max: number): number {\n return Math.floor(this.random(min, max + 1));\n }\n\n // Check if a number is approximately equal to another (within epsilon)\n static approximately(a: number, b: number, epsilon: number = 0.001): boolean {\n return Math.abs(a - b) < epsilon;\n }\n\n // Smooth step function\n static smoothstep(edge0: number, edge1: number, x: number): number {\n const t = this.clamp((x - edge0) / (edge1 - edge0), 0, 1);\n return t * t * (3 - 2 * t);\n }\n\n // Smoother step function\n static smootherstep(edge0: number, edge1: number, x: number): number {\n const t = this.clamp((x - edge0) / (edge1 - edge0), 0, 1);\n return t * t * t * (t * (t * 6 - 15) + 10);\n }\n}\n\nexport class ColorUtils {\n // Convert HSL to RGB\n static hslToRgb(h: number, s: number, l: number): { r: number; g: number; b: number } {\n h /= 360;\n s /= 100;\n l /= 100;\n\n const hue2rgb = (p: number, q: number, t: number): number => {\n if (t < 0) t += 1;\n if (t > 1) t -= 1;\n if (t < 1/6) return p + (q - p) * 6 * t;\n if (t < 1/2) return q;\n if (t < 2/3) return p + (q - p) * (2/3 - t) * 6;\n return p;\n };\n\n let r, g, b;\n\n if (s === 0) {\n r = g = b = l; // achromatic\n } else {\n const q = l < 0.5 ? l * (1 + s) : l + s - l * s;\n const p = 2 * l - q;\n r = hue2rgb(p, q, h + 1/3);\n g = hue2rgb(p, q, h);\n b = hue2rgb(p, q, h - 1/3);\n }\n\n return {\n r: Math.round(r * 255),\n g: Math.round(g * 255),\n b: Math.round(b * 255)\n };\n }\n\n // Convert RGB to hex string\n static rgbToHex(r: number, g: number, b: number): string {\n return \"#\" + ((1 << 24) + (r << 16) + (g << 8) + b).toString(16).slice(1);\n }\n\n // Generate a color based on a value (useful for visualizing dimensions)\n static valueToColor(value: number, min: number, max: number): string {\n const normalized = MathUtils.clamp((value - min) / (max - min), 0, 1);\n const hue = (1 - normalized) * 240; // Blue to red\n const { r, g, b } = this.hslToRgb(hue, 100, 50);\n return this.rgbToHex(r, g, b);\n }\n\n // Generate rainbow colors for multiple objects\n static generateRainbowColors(count: number): string[] {\n const colors: string[] = [];\n for (let i = 0; i < count; i++) {\n const hue = (i / count) * 360;\n const { r, g, b } = this.hslToRgb(hue, 70, 50);\n colors.push(this.rgbToHex(r, g, b));\n }\n return colors;\n }\n}\n\nexport class PerformanceUtils {\n // Debounce function calls\n static debounce any>(\n func: T,\n wait: number\n ): (...args: Parameters) => void {\n let timeout: number | undefined;\n return (...args: Parameters) => {\n clearTimeout(timeout);\n timeout = setTimeout(() => func(...args), wait);\n };\n }\n\n // Throttle function calls\n static throttle any>(\n func: T,\n limit: number\n ): (...args: Parameters) => void {\n let inThrottle: boolean;\n return (...args: Parameters) => {\n if (!inThrottle) {\n func(...args);\n inThrottle = true;\n setTimeout(() => inThrottle = false, limit);\n }\n };\n }\n\n // Measure execution time\n static measureTime(name: string, func: () => T): T {\n const start = performance.now();\n const result = func();\n const end = performance.now();\n console.log(`${name} took ${end - start} milliseconds`);\n return result;\n }\n\n // Create a simple object pool for performance\n static createObjectPool(\n createFn: () => T,\n resetFn: (obj: T) => void,\n initialSize: number = 10\n ) {\n const pool: T[] = [];\n \n // Pre-populate the pool\n for (let i = 0; i < initialSize; i++) {\n pool.push(createFn());\n }\n\n return {\n get(): T {\n return pool.pop() || createFn();\n },\n \n release(obj: T): void {\n resetFn(obj);\n pool.push(obj);\n },\n \n size(): number {\n return pool.length;\n }\n };\n }\n}\n\nexport class ValidationUtils {\n // Validate that a value is a finite number\n static isValidNumber(value: any): value is number {\n return typeof value === 'number' && isFinite(value);\n }\n\n // Validate a 3D vector\n static isValid3DVector(v: any): v is Vector3D {\n return v && \n typeof v === 'object' &&\n this.isValidNumber(v.x) &&\n this.isValidNumber(v.y) &&\n this.isValidNumber(v.z);\n }\n\n // Validate a 4D vector\n static isValid4DVector(v: any): v is Vector4D {\n return v && \n typeof v === 'object' &&\n this.isValidNumber(v.x) &&\n this.isValidNumber(v.y) &&\n this.isValidNumber(v.z) &&\n this.isValidNumber(v.w);\n }\n\n // 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Higher Dimensional Geometry Visualizer\n\nA Next.js application for visualizing and interacting with 4D and 5D geometric shapes and their transformations.\n\n## Features\n\n- **4D/5D Shape Visualization**: Render hypercubes, pentachorons, and other higher-dimensional primitives\n- **Real-time Transformations**: Rotate, scale, and translate shapes in higher dimensions\n- **3D Projections**: View how higher-dimensional objects project into 3D space\n- **Interactive Controls**: Intuitive UI for manipulating shapes and camera perspectives\n- **Cross-sections**: Explore slices through higher-dimensional objects\n- **Performance Optimized**: Efficient calculations and rendering for complex geometry\n- **Responsive Design**: Works across desktop and mobile devices\n\n## Supported Shapes\n\n- **4D Shapes**: Tesseract (4D cube), 16-cell, 600-cell, 120-cell\n- **5D Shapes**: Penteract (5D cube), 5-simplex, 5-orthoplex\n- **Custom Primitives**: User-defined higher-dimensional objects\n\n## Technology Stack\n\n- Next.js with TypeScript\n- Three.js for 3D rendering\n- React Three Fiber for React integration\n- Custom mathematical libraries for higher-dimensional calculations\n- Tailwind CSS for styling\n\n## Project Structure\n\n```\n├── backend/\n│ ├── index.ts # API endpoints\n│ └── routes/\n│ └── calculations.ts # Mathematical computation endpoints\n├── frontend/\n│ ├── components/\n│ │ ├── App.tsx # Main application component\n│ │ ├── GeometryViewer.tsx # 3D visualization component\n│ │ ├── ControlPanel.tsx # User interface controls\n│ │ ├── ShapeSelector.tsx # Shape selection interface\n│ │ └── CrossSection.tsx # Cross-section visualization\n│ ├── index.html # Main HTML template\n│ ├── index.tsx # Frontend entry point\n│ └── style.css # Global styles\n├── shared/\n│ ├── math/\n│ │ ├── geometry4d.ts # 4D geometric calculations\n│ │ ├── geometry5d.ts # 5D geometric calculations\n│ │ ├── projections.ts # Projection algorithms\n│ │ └── transformations.ts # Transformation matrices\n│ ├── types.ts # Shared TypeScript types\n│ └── utils.ts # Utility functions\n└── README.md\n```\n\n## Getting Started\n\n1. The application runs as an HTTP val\n2. Navigate to the main page to start exploring higher-dimensional geometry\n3. Use the control panel to select shapes, adjust transformations, and modify viewing parameters\n4. Interact with the 3D viewport to explore projections and cross-sections\n\n## Mathematical Background\n\nThis application implements advanced concepts from higher-dimensional geometry:\n- Orthogonal projections from nD to 3D space\n- Rotation matrices in 4D and 5D spaces\n- Cross-sectional analysis of higher-dimensional objects\n- Real-time transformation calculations optimized for 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Shared types for higher-dimensional geometry visualization\n\nexport interface Vector4D {\n x: number;\n y: number;\n z: number;\n w: number;\n}\n\nexport interface Vector5D {\n x: number;\n y: number;\n z: number;\n w: number;\n v: number;\n}\n\nexport interface Vector3D {\n x: number;\n y: number;\n z: number;\n}\n\nexport interface Matrix4D {\n elements: number[][]; // 4x4 matrix\n}\n\nexport interface Matrix5D {\n elements: number[][]; // 5x5 matrix\n}\n\nexport interface Edge {\n start: number;\n end: number;\n}\n\nexport interface Face {\n vertices: number[];\n}\n\nexport interface Cell {\n faces: number[];\n}\n\nexport interface Shape4D {\n vertices: Vector4D[];\n edges: Edge[];\n faces: Face[];\n cells: Cell[];\n name: string;\n}\n\nexport interface Shape5D {\n vertices: Vector5D[];\n edges: Edge[];\n faces: Face[];\n cells: Cell[];\n hypercells: Cell[];\n name: string;\n}\n\nexport interface ProjectionSettings {\n distance: number;\n perspective: boolean;\n viewAngle: number;\n}\n\nexport interface TransformationState {\n rotation4D: {\n xy: number;\n xz: number;\n xw: number;\n yz: number;\n yw: number;\n zw: number;\n };\n rotation5D?: {\n xy: number;\n xz: number;\n xw: number;\n xv: number;\n yz: number;\n yw: number;\n yv: number;\n zw: number;\n zv: number;\n wv: number;\n };\n scale: number;\n translation: Vector4D | Vector5D;\n}\n\nexport interface CameraState {\n position: Vector3D;\n target: Vector3D;\n up: Vector3D;\n fov: number;\n}\n\nexport interface LightingState {\n ambient: number;\n directional: {\n intensity: number;\n direction: Vector3D;\n };\n point: {\n intensity: number;\n position: Vector3D;\n };\n}\n\nexport interface CrossSectionSettings {\n enabled: boolean;\n dimension: number;\n position: number;\n normal: Vector4D | Vector5D;\n}\n\nexport interface RenderSettings {\n showVertices: boolean;\n showEdges: boolean;\n showFaces: boolean;\n wireframe: boolean;\n opacity: number;\n color: string;\n edgeColor: string;\n vertexColor: string;\n}\n\nexport type ShapeType = \n | 'tesseract' \n | '16-cell' \n | '600-cell' \n | '120-cell'\n | 'penteract'\n | '5-simplex'\n | '5-orthoplex'\n | 'custom';\n\nexport interface AppState {\n currentShape: ShapeType;\n dimension: 4 | 5;\n transformations: TransformationState;\n camera: CameraState;\n lighting: LightingState;\n projection: ProjectionSettings;\n crossSection: CrossSectionSettings;\n rendering: RenderSettings;\n isAnimating: boolean;\n animationSpeed: number;\n}",[],[139,173],"1757a83c-59a2-11f0-952b-f69ea79377d9","transformations.ts","1757a904-59a2-11f0-952b-f69ea79377d9","10e2870c-b7b7-48c6-9e40-545c61d33aa9",6,["D",1751721315964],"// Transformation utilities for higher-dimensional geometry\n\nimport { Vector4D, Vector5D, Matrix4D, Matrix5D, TransformationState } from '../types.ts';\nimport { Geometry4D } from './geometry4d.ts';\nimport { Geometry5D } from './geometry5d.ts';\n\nexport class TransformationEngine {\n // Apply all transformations to a 4D point\n static transform4D(point: Vector4D, state: TransformationState): Vector4D {\n let result = { ...point };\n \n // Apply scaling\n result.x *= state.scale;\n result.y *= state.scale;\n result.z *= state.scale;\n result.w *= state.scale;\n \n // Apply rotations\n const rotationMatrix = Geometry4D.createCompositeRotation(state.rotation4D);\n result = Geometry4D.transformVector(result, rotationMatrix);\n \n // Apply translation\n const translation = state.translation as Vector4D;\n result.x += translation.x;\n result.y += translation.y;\n result.z += translation.z;\n result.w += translation.w;\n \n return result;\n }\n\n // Apply all transformations to a 5D point\n static transform5D(point: Vector5D, state: TransformationState): Vector5D {\n let result = { ...point };\n \n // Apply scaling\n result.x *= state.scale;\n result.y *= state.scale;\n result.z *= state.scale;\n result.w *= state.scale;\n result.v *= state.scale;\n \n // Apply rotations\n if (state.rotation5D) {\n const rotationMatrix = Geometry5D.createCompositeRotation(state.rotation5D);\n result = Geometry5D.transformVector(result, rotationMatrix);\n }\n \n // Apply translation\n const translation = state.translation as Vector5D;\n result.x += translation.x;\n result.y += translation.y;\n result.z += translation.z;\n result.w += translation.w;\n result.v += translation.v;\n \n return result;\n }\n\n // Create animation interpolation between two transformation states\n static interpolateTransformations(\n from: TransformationState, \n to: TransformationState, \n t: number\n ): TransformationState {\n const lerp = (a: number, b: number, t: number) => a + (b - a) * t;\n \n // Interpolate 4D rotations\n const rotation4D = {\n xy: lerp(from.rotation4D.xy, to.rotation4D.xy, t),\n xz: lerp(from.rotation4D.xz, to.rotation4D.xz, t),\n xw: lerp(from.rotation4D.xw, to.rotation4D.xw, t),\n yz: lerp(from.rotation4D.yz, to.rotation4D.yz, t),\n yw: lerp(from.rotation4D.yw, to.rotation4D.yw, t),\n zw: lerp(from.rotation4D.zw, to.rotation4D.zw, t)\n };\n\n // Interpolate 5D rotations if they exist\n let rotation5D = undefined;\n if (from.rotation5D && to.rotation5D) {\n rotation5D = {\n xy: lerp(from.rotation5D.xy, to.rotation5D.xy, t),\n xz: lerp(from.rotation5D.xz, to.rotation5D.xz, t),\n xw: lerp(from.rotation5D.xw, to.rotation5D.xw, t),\n xv: lerp(from.rotation5D.xv, to.rotation5D.xv, t),\n yz: lerp(from.rotation5D.yz, to.rotation5D.yz, t),\n yw: lerp(from.rotation5D.yw, to.rotation5D.yw, t),\n yv: lerp(from.rotation5D.yv, to.rotation5D.yv, t),\n zw: lerp(from.rotation5D.zw, to.rotation5D.zw, t),\n zv: lerp(from.rotation5D.zv, to.rotation5D.zv, t),\n wv: lerp(from.rotation5D.wv, to.rotation5D.wv, t)\n };\n }\n\n // Interpolate translation\n const fromTrans = from.translation as any;\n const toTrans = to.translation as any;\n const translation: any = {\n x: lerp(fromTrans.x, toTrans.x, t),\n y: lerp(fromTrans.y, toTrans.y, t),\n z: lerp(fromTrans.z, toTrans.z, t),\n w: lerp(fromTrans.w, toTrans.w, t)\n };\n \n if (fromTrans.v !== undefined && toTrans.v !== undefined) {\n translation.v = lerp(fromTrans.v, toTrans.v, t);\n }\n\n return {\n rotation4D,\n rotation5D,\n scale: lerp(from.scale, to.scale, t),\n translation\n };\n }\n\n // Generate smooth rotation animation keyframes\n static generateRotationKeyframes(\n dimension: 4 | 5,\n duration: number,\n rotationSpeed: { [key: string]: number }\n ): TransformationState[] {\n const keyframes: TransformationState[] = [];\n const steps = Math.max(60, duration * 60); // 60 FPS\n \n for (let i = 0; i <= steps; i++) {\n const t = i / steps;\n const time = t * duration;\n \n const rotation4D = {\n xy: rotationSpeed.xy ? rotationSpeed.xy * time : 0,\n xz: rotationSpeed.xz ? rotationSpeed.xz * time : 0,\n xw: rotationSpeed.xw ? rotationSpeed.xw * time : 0,\n yz: rotationSpeed.yz ? rotationSpeed.yz * time : 0,\n yw: rotationSpeed.yw ? rotationSpeed.yw * time : 0,\n zw: rotationSpeed.zw ? rotationSpeed.zw * time : 0\n };\n\n let rotation5D = undefined;\n if (dimension === 5) {\n rotation5D = {\n xy: rotationSpeed.xy ? rotationSpeed.xy * time : 0,\n xz: rotationSpeed.xz ? rotationSpeed.xz * time : 0,\n xw: rotationSpeed.xw ? rotationSpeed.xw * time : 0,\n xv: rotationSpeed.xv ? rotationSpeed.xv * time : 0,\n yz: rotationSpeed.yz ? rotationSpeed.yz * time : 0,\n yw: rotationSpeed.yw ? rotationSpeed.yw * time : 0,\n yv: rotationSpeed.yv ? rotationSpeed.yv * time : 0,\n zw: rotationSpeed.zw ? rotationSpeed.zw * time : 0,\n zv: rotationSpeed.zv ? rotationSpeed.zv * time : 0,\n wv: rotationSpeed.wv ? rotationSpeed.wv * time : 0\n };\n }\n\n const translation = dimension === 5 \n ? { x: 0, y: 0, z: 0, w: 0, v: 0 }\n : { x: 0, y: 0, z: 0, w: 0 };\n\n keyframes.push({\n rotation4D,\n rotation5D,\n scale: 1,\n translation\n });\n }\n \n return keyframes;\n }\n\n // Apply perspective correction for better visualization\n static applyPerspectiveCorrection(points: Vector4D[], viewDistance: number): Vector4D[] {\n return points.map(point => {\n // Adjust w-coordinate based on distance from viewer\n const distance = Math.sqrt(point.x * point.x + point.y * point.y + point.z * point.z);\n const correctedW = point.w + distance / viewDistance;\n \n return {\n x: point.x,\n y: point.y,\n z: point.z,\n w: correctedW\n };\n });\n }\n\n // Create transformation matrix for arbitrary axis rotation in 4D\n static createAxisRotation4D(axis1: Vector4D, axis2: Vector4D, angle: number): Matrix4D {\n // Normalize the axes\n const normalize = (v: Vector4D): Vector4D => {\n const length = Math.sqrt(v.x * v.x + v.y * v.y + v.z * v.z + v.w * v.w);\n return length > 0.001 ? {\n x: v.x / length,\n y: v.y / length,\n z: v.z / length,\n w: v.w / length\n } : { x: 1, y: 0, z: 0, w: 0 };\n };\n\n const u = normalize(axis1);\n const v = normalize(axis2);\n \n // Create rotation matrix using Rodrigues' rotation formula extended to 4D\n const cos = Math.cos(angle);\n const sin = Math.sin(angle);\n \n const matrix = [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1]\n ];\n\n // This is a simplified version - full implementation would be more complex\n for (let i = 0; i < 4; i++) {\n for (let j = 0; j < 4; j++) {\n const uComponent = [u.x, u.y, u.z, u.w][i] * [u.x, u.y, u.z, u.w][j];\n const vComponent = [v.x, v.y, v.z, v.w][i] * [v.x, v.y, v.z, v.w][j];\n \n matrix[i][j] = (i === j ? 1 : 0) + \n (cos - 1) * (uComponent + vComponent) +\n sin * (i === j ? 0 : (uComponent - vComponent));\n }\n }\n\n return { elements: matrix };\n }\n\n // Decompose a transformation matrix into its components\n static decompose4DMatrix(matrix: Matrix4D): {\n scale: Vector4D;\n rotation: { [key: string]: number };\n translation: Vector4D;\n } {\n const m = matrix.elements;\n \n // Extract translation (assuming it's in the last column)\n const translation: Vector4D = {\n x: m[0][3] || 0,\n y: m[1][3] || 0,\n z: m[2][3] || 0,\n w: m[3][3] || 0\n };\n\n // Extract scale\n const scaleX = Math.sqrt(m[0][0] * m[0][0] + m[1][0] * m[1][0] + m[2][0] * m[2][0] + m[3][0] * m[3][0]);\n const scaleY = Math.sqrt(m[0][1] * m[0][1] + m[1][1] * m[1][1] + m[2][1] * m[2][1] + m[3][1] * m[3][1]);\n const scaleZ = Math.sqrt(m[0][2] * m[0][2] + m[1][2] * m[1][2] + m[2][2] * m[2][2] + m[3][2] * m[3][2]);\n const scaleW = Math.sqrt(m[0][3] * m[0][3] + m[1][3] * m[1][3] + m[2][3] * m[2][3] + m[3][3] * m[3][3]);\n\n const scale: Vector4D = { x: scaleX, y: scaleY, z: scaleZ, w: scaleW };\n\n // Extract rotation (simplified - full implementation would be more complex)\n const rotation = {\n xy: Math.atan2(m[1][0], m[0][0]),\n xz: Math.atan2(m[2][0], m[0][0]),\n xw: Math.atan2(m[3][0], m[0][0]),\n yz: Math.atan2(m[2][1], m[1][1]),\n yw: Math.atan2(m[3][1], m[1][1]),\n zw: Math.atan2(m[3][2], m[2][2])\n };\n\n return { scale, rotation, translation };\n }\n\n // Create smooth easing functions for animations\n static easeInOutCubic(t: number): number {\n return t < 0.5 ? 4 * t * t * t : 1 - Math.pow(-2 * t + 2, 3) / 2;\n }\n\n static easeInOutQuart(t: number): number {\n return t < 0.5 ? 8 * t * t * t * t : 1 - Math.pow(-2 * t + 2, 4) / 2;\n }\n\n static easeInOutSine(t: number): number {\n return -(Math.cos(Math.PI * t) - 1) / 2;\n }\n}",[],[139,188,180],"math","f8e4ba70-59a1-11f0-bc55-f69ea79377d9","projections.ts","f8e4bb2e-59a1-11f0-bc55-f69ea79377d9",5,["D",1751721264877],"// Projection algorithms for higher-dimensional geometry\n\nimport { Vector3D, Vector4D, Vector5D, ProjectionSettings } from '../types.ts';\n\nexport class ProjectionEngine {\n // Orthogonal projection from 4D to 3D\n static orthogonal4DTo3D(point: Vector4D): Vector3D {\n return {\n x: point.x,\n y: point.y,\n z: point.z\n };\n }\n\n // Perspective projection from 4D to 3D\n static perspective4DTo3D(point: Vector4D, settings: ProjectionSettings): Vector3D {\n const { distance, viewAngle } = settings;\n const factor = distance / (distance - point.w);\n \n return {\n x: point.x * factor,\n y: point.y * factor,\n z: point.z * factor\n };\n }\n\n // Stereographic projection from 4D to 3D\n static stereographic4DTo3D(point: Vector4D, radius: number = 1): Vector3D {\n const denominator = radius - point.w;\n if (Math.abs(denominator) < 0.001) {\n // Point at infinity, return a large value\n return { x: point.x * 1000, y: point.y * 1000, z: point.z * 1000 };\n }\n \n const factor = radius / denominator;\n return {\n x: point.x * factor,\n y: point.y * factor,\n z: point.z * factor\n };\n }\n\n // Double perspective projection from 5D to 3D\n static perspective5DTo3D(point: Vector5D, settings: ProjectionSettings): Vector3D {\n const { distance } = settings;\n \n // First projection: 5D to 4D\n const factor1 = distance / (distance - point.v);\n const point4D: Vector4D = {\n x: point.x * factor1,\n y: point.y * factor1,\n z: point.z * factor1,\n w: point.w * factor1\n };\n \n // Second projection: 4D to 3D\n return this.perspective4DTo3D(point4D, settings);\n }\n\n // Orthogonal projection from 5D to 3D (dropping two dimensions)\n static orthogonal5DTo3D(point: Vector5D, dropDimensions: [number, number] = [3, 4]): Vector3D {\n const coords = [point.x, point.y, point.z, point.w, point.v];\n const result = [0, 0, 0];\n let resultIndex = 0;\n \n for (let i = 0; i < 5; i++) {\n if (!dropDimensions.includes(i) && resultIndex < 3) {\n result[resultIndex] = coords[i];\n resultIndex++;\n }\n }\n \n return {\n x: result[0] || 0,\n y: result[1] || 0,\n z: result[2] || 0\n };\n }\n\n // Schlegel projection for 4D polytopes\n static schlegel4DTo3D(point: Vector4D, center: Vector4D, projectionPoint: Vector4D): Vector3D {\n // Vector from projection point to the point\n const direction = {\n x: point.x - projectionPoint.x,\n y: point.y - projectionPoint.y,\n z: point.z - projectionPoint.z,\n w: point.w - projectionPoint.w\n };\n \n // Find intersection with the 3D hyperplane (w = 0)\n if (Math.abs(direction.w) < 0.001) {\n return { x: point.x, y: point.y, z: point.z };\n }\n \n const t = -projectionPoint.w / direction.w;\n return {\n x: projectionPoint.x + t * direction.x,\n y: projectionPoint.y + t * direction.y,\n z: projectionPoint.z + t * direction.z\n };\n }\n\n // Parallel projection with custom direction\n static parallelProjection4D(point: Vector4D, direction: Vector4D, plane: Vector4D): Vector3D {\n // Project point onto the 3D plane perpendicular to the direction\n const dot = point.x * direction.x + point.y * direction.y + \n point.z * direction.z + point.w * direction.w;\n const planeDot = plane.x * direction.x + plane.y * direction.y + \n plane.z * direction.z + plane.w * direction.w;\n \n if (Math.abs(planeDot) < 0.001) {\n return { x: point.x, y: point.y, z: point.z };\n }\n \n const t = dot / planeDot;\n return {\n x: point.x - t * plane.x,\n y: point.y - t * plane.y,\n z: point.z - t * plane.z\n };\n }\n\n // Fisheye projection for wide-angle viewing\n static fisheye4DTo3D(point: Vector4D, fov: number = Math.PI / 2): Vector3D {\n const r = Math.sqrt(point.x * point.x + point.y * point.y + point.z * point.z + point.w * point.w);\n if (r < 0.001) return { x: 0, y: 0, z: 0 };\n \n const theta = Math.acos(Math.abs(point.w) / r);\n const phi = Math.atan2(point.y, point.x);\n const psi = Math.atan2(Math.sqrt(point.x * point.x + point.y * point.y), point.z);\n \n const fisheyeR = (2 * theta / fov) * Math.sin(fov / 2);\n \n return {\n x: fisheyeR * Math.cos(phi) * Math.sin(psi),\n y: fisheyeR * Math.sin(phi) * Math.sin(psi),\n z: fisheyeR * Math.cos(psi)\n };\n }\n\n // Adaptive projection that chooses the best method based on the data\n static adaptiveProjection(points: Vector4D[], settings: ProjectionSettings): Vector3D[] {\n // Analyze the distribution of w-coordinates\n const wValues = points.map(p => p.w);\n const minW = Math.min(...wValues);\n const maxW = Math.max(...wValues);\n const wRange = maxW - minW;\n \n // Choose projection method based on w-distribution\n if (wRange < 0.1) {\n // Points are mostly in the same w-plane, use orthogonal\n return points.map(p => this.orthogonal4DTo3D(p));\n } else if (minW > -settings.distance * 0.9) {\n // No points too close to the projection center, use perspective\n return points.map(p => this.perspective4DTo3D(p, settings));\n } else {\n // Some points might cause issues with perspective, use stereographic\n return points.map(p => this.stereographic4DTo3D(p));\n }\n }\n\n // Cross-section projection: project a 4D cross-section to 2D\n static crossSection4DTo2D(point: Vector4D, normal: Vector4D): { x: number; y: number } {\n // Find two orthogonal vectors in the 3D subspace perpendicular to normal\n const u = this.findOrthogonalVector4D(normal);\n const v = this.crossProduct4D(normal, u);\n \n // Project point onto the 2D plane spanned by u and v\n const uDot = point.x * u.x + point.y * u.y + point.z * u.z + point.w * u.w;\n const vDot = point.x * v.x + point.y * v.y + point.z * v.z + point.w * v.w;\n \n return { x: uDot, y: vDot };\n }\n\n // Helper function to find an orthogonal vector in 4D\n private static findOrthogonalVector4D(v: Vector4D): Vector4D {\n // Find the component with the smallest absolute value\n const abs = [Math.abs(v.x), Math.abs(v.y), Math.abs(v.z), Math.abs(v.w)];\n const minIndex = abs.indexOf(Math.min(...abs));\n \n const result = { x: 0, y: 0, z: 0, w: 0 };\n switch (minIndex) {\n case 0: result.x = 1; break;\n case 1: result.y = 1; break;\n case 2: result.z = 1; break;\n case 3: result.w = 1; break;\n }\n \n // Make it orthogonal using Gram-Schmidt\n const dot = result.x * v.x + result.y * v.y + result.z * v.z + result.w * v.w;\n const vLengthSq = v.x * v.x + v.y * v.y + v.z * v.z + v.w * v.w;\n \n if (vLengthSq > 0.001) {\n const factor = dot / vLengthSq;\n result.x -= factor * v.x;\n result.y -= factor * v.y;\n result.z -= factor * v.z;\n result.w -= factor * v.w;\n }\n \n // Normalize\n const length = Math.sqrt(result.x * result.x + result.y * result.y + \n result.z * result.z + result.w * result.w);\n if (length > 0.001) {\n result.x /= length;\n result.y /= length;\n result.z /= length;\n result.w /= length;\n }\n \n return result;\n }\n\n // Helper function for 4D cross product (returns a vector orthogonal to both inputs)\n private static crossProduct4D(a: Vector4D, b: Vector4D): Vector4D {\n // This is a simplified version - true 4D cross product is more complex\n return {\n x: a.y * b.z - a.z * b.y,\n y: a.z * b.x - a.x * b.z,\n z: a.x * b.y - a.y * b.x,\n w: 0 // Simplified\n };\n }\n}",[],[139,188,190],"dbfdd892-59a1-11f0-a68e-f69ea79377d9","geometry5d.ts","dbfdd950-59a1-11f0-a68e-f69ea79377d9",4,["D",1751721216383],"// 5D Geometry calculations and shape generation\n\nimport { Vector5D, Vector3D, Shape5D, Edge, Face, Cell, Matrix5D } from '../types.ts';\n\nexport class Geometry5D {\n // Create a 5D rotation matrix for the given plane and angle\n static createRotationMatrix(plane: string, angle: number): Matrix5D {\n const cos = Math.cos(angle);\n const sin = Math.sin(angle);\n const matrix = Array(5).fill(null).map(() => Array(5).fill(0));\n \n // Initialize as identity matrix\n for (let i = 0; i < 5; i++) {\n matrix[i][i] = 1;\n }\n\n switch (plane) {\n case 'xy':\n matrix[0][0] = cos; matrix[0][1] = -sin;\n matrix[1][0] = sin; matrix[1][1] = cos;\n break;\n case 'xz':\n matrix[0][0] = cos; matrix[0][2] = -sin;\n matrix[2][0] = sin; matrix[2][2] = cos;\n break;\n case 'xw':\n matrix[0][0] = cos; matrix[0][3] = -sin;\n matrix[3][0] = sin; matrix[3][3] = cos;\n break;\n case 'xv':\n matrix[0][0] = cos; matrix[0][4] = -sin;\n matrix[4][0] = sin; matrix[4][4] = cos;\n break;\n case 'yz':\n matrix[1][1] = cos; matrix[1][2] = -sin;\n matrix[2][1] = sin; matrix[2][2] = cos;\n break;\n case 'yw':\n matrix[1][1] = cos; matrix[1][3] = -sin;\n matrix[3][1] = sin; matrix[3][3] = cos;\n break;\n case 'yv':\n matrix[1][1] = cos; matrix[1][4] = -sin;\n matrix[4][1] = sin; matrix[4][4] = cos;\n break;\n case 'zw':\n matrix[2][2] = cos; matrix[2][3] = -sin;\n matrix[3][2] = sin; matrix[3][3] = cos;\n break;\n case 'zv':\n matrix[2][2] = cos; matrix[2][4] = -sin;\n matrix[4][2] = sin; matrix[4][4] = cos;\n break;\n case 'wv':\n matrix[3][3] = cos; matrix[3][4] = -sin;\n matrix[4][3] = sin; matrix[4][4] = cos;\n break;\n }\n\n return { elements: matrix };\n }\n\n // Apply transformation matrix to a 5D vector\n static transformVector(vector: Vector5D, matrix: Matrix5D): Vector5D {\n const { x, y, z, w, v } = vector;\n const m = matrix.elements;\n \n return {\n x: m[0][0] * x + m[0][1] * y + m[0][2] * z + m[0][3] * w + m[0][4] * v,\n y: m[1][0] * x + m[1][1] * y + m[1][2] * z + m[1][3] * w + m[1][4] * v,\n z: m[2][0] * x + m[2][1] * y + m[2][2] * z + m[2][3] * w + m[2][4] * v,\n w: m[3][0] * x + m[3][1] * y + m[3][2] * z + m[3][3] * w + m[3][4] * v,\n v: m[4][0] * x + m[4][1] * y + m[4][2] * z + m[4][3] * w + m[4][4] * v\n };\n }\n\n // Project 5D point to 3D using double perspective projection\n static projectTo3D(point: Vector5D, distance1: number = 2, distance2: number = 2): Vector3D {\n // First project from 5D to 4D\n const factor1 = distance1 / (distance1 - point.v);\n const point4D = {\n x: point.x * factor1,\n y: point.y * factor1,\n z: point.z * factor1,\n w: point.w * factor1\n };\n \n // Then project from 4D to 3D\n const factor2 = distance2 / (distance2 - point4D.w);\n return {\n x: point4D.x * factor2,\n y: point4D.y * factor2,\n z: point4D.z * factor2\n };\n }\n\n // Generate penteract (5D cube) vertices and structure\n static createPenteract(): Shape5D {\n const vertices: Vector5D[] = [];\n \n // Generate all 32 vertices of a penteract\n for (let i = 0; i < 32; i++) {\n vertices.push({\n x: (i & 1) ? 1 : -1,\n y: (i & 2) ? 1 : -1,\n z: (i & 4) ? 1 : -1,\n w: (i & 8) ? 1 : -1,\n v: (i & 16) ? 1 : -1\n });\n }\n\n // Generate edges\n const edges: Edge[] = [];\n for (let i = 0; i < 32; i++) {\n for (let j = i + 1; j < 32; j++) {\n // Two vertices are connected if they differ in exactly one coordinate\n const diff = [\n vertices[i].x !== vertices[j].x ? 1 : 0,\n vertices[i].y !== vertices[j].y ? 1 : 0,\n vertices[i].z !== vertices[j].z ? 1 : 0,\n vertices[i].w !== vertices[j].w ? 1 : 0,\n vertices[i].v !== vertices[j].v ? 1 : 0\n ].reduce((sum, val) => sum + val, 0);\n \n if (diff === 1) {\n edges.push({ start: i, end: j });\n }\n }\n }\n\n // Generate faces (simplified)\n const faces: Face[] = [];\n for (let dim1 = 0; dim1 < 5; dim1++) {\n for (let dim2 = dim1 + 1; dim2 < 5; dim2++) {\n for (let val1 = -1; val1 <= 1; val1 += 2) {\n for (let val2 = -1; val2 <= 1; val2 += 2) {\n for (let val3 = -1; val3 <= 1; val3 += 2) {\n const faceVertices: number[] = [];\n for (let i = 0; i < 32; i++) {\n const coords = [vertices[i].x, vertices[i].y, vertices[i].z, vertices[i].w, vertices[i].v];\n let matches = 0;\n if (coords[dim1] === val1) matches++;\n if (coords[dim2] === val2) matches++;\n if (matches === 2) {\n faceVertices.push(i);\n }\n }\n if (faceVertices.length === 4) {\n faces.push({ vertices: faceVertices });\n }\n }\n }\n }\n }\n }\n\n // Generate cells and hypercells (simplified)\n const cells: Cell[] = [];\n const hypercells: Cell[] = [];\n \n // This is a simplified version - full implementation would be much more complex\n for (let i = 0; i < Math.min(faces.length, 40); i += 6) {\n if (i + 5 < faces.length) {\n cells.push({ faces: [i, i + 1, i + 2, i + 3, i + 4, i + 5] });\n }\n }\n\n for (let i = 0; i < Math.min(cells.length, 10); i += 8) {\n if (i + 7 < cells.length) {\n hypercells.push({ faces: [i, i + 1, i + 2, i + 3, i + 4, i + 5, i + 6, i + 7] });\n }\n }\n\n return {\n vertices,\n edges,\n faces,\n cells,\n hypercells,\n name: 'Penteract'\n };\n }\n\n // Generate 5-simplex (5D tetrahedron)\n static create5Simplex(): Shape5D {\n const vertices: Vector5D[] = [\n { x: 1, y: 0, z: 0, w: 0, v: 0 },\n { x: 0, y: 1, z: 0, w: 0, v: 0 },\n { x: 0, y: 0, z: 1, w: 0, v: 0 },\n { x: 0, y: 0, z: 0, w: 1, v: 0 },\n { x: 0, y: 0, z: 0, w: 0, v: 1 },\n { x: -1/5, y: -1/5, z: -1/5, w: -1/5, v: -1/5 }\n ];\n\n const edges: Edge[] = [];\n // Connect all vertices to each other\n for (let i = 0; i < 6; i++) {\n for (let j = i + 1; j < 6; j++) {\n edges.push({ start: i, end: j });\n }\n }\n\n // Generate triangular faces\n const faces: Face[] = [];\n for (let i = 0; i < 6; i++) {\n for (let j = i + 1; j < 6; j++) {\n for (let k = j + 1; k < 6; k++) {\n faces.push({ vertices: [i, j, k] });\n }\n }\n }\n\n // Generate tetrahedral cells\n const cells: Cell[] = [];\n for (let i = 0; i < 6; i++) {\n for (let j = i + 1; j < 6; j++) {\n for (let k = j + 1; k < 6; k++) {\n for (let l = k + 1; l < 6; l++) {\n cells.push({ faces: [i, j, k, l] }); // Simplified\n }\n }\n }\n }\n\n const hypercells: Cell[] = [\n { faces: [0, 1, 2, 3, 4] } // Single 5-cell\n ];\n\n return {\n vertices,\n edges,\n faces,\n cells,\n hypercells,\n name: '5-Simplex'\n };\n }\n\n // Calculate cross-section of 5D shape with a 4D hyperplane\n static calculateCrossSection(shape: Shape5D, vValue: number): Vector3D[] {\n const crossSectionPoints: Vector3D[] = [];\n \n // Find intersections of edges with the hyperplane v = vValue\n for (const edge of shape.edges) {\n const v1 = shape.vertices[edge.start];\n const v2 = shape.vertices[edge.end];\n \n // Check if edge crosses the hyperplane\n if ((v1.v <= vValue && v2.v >= vValue) || (v1.v >= vValue && v2.v <= vValue)) {\n if (Math.abs(v1.v - v2.v) > 0.001) {\n // Calculate intersection point\n const t = (vValue - v1.v) / (v2.v - v1.v);\n const intersection4D = {\n x: v1.x + t * (v2.x - v1.x),\n y: v1.y + t * (v2.y - v1.y),\n z: v1.z + t * (v2.z - v1.z),\n w: v1.w + t * (v2.w - v1.w)\n };\n \n // Project 4D intersection to 3D\n const factor = 2 / (2 - intersection4D.w);\n crossSectionPoints.push({\n x: intersection4D.x * factor,\n y: intersection4D.y * factor,\n z: intersection4D.z * factor\n });\n }\n }\n }\n \n return crossSectionPoints;\n }\n\n // Multiply two 5D matrices\n static multiplyMatrices(a: Matrix5D, b: Matrix5D): Matrix5D {\n const result = Array(5).fill(null).map(() => Array(5).fill(0));\n \n for (let i = 0; i < 5; i++) {\n for (let j = 0; j < 5; j++) {\n for (let k = 0; k < 5; k++) {\n result[i][j] += a.elements[i][k] * b.elements[k][j];\n }\n }\n }\n \n return { elements: result };\n }\n\n // Create composite rotation matrix from multiple rotations\n static createCompositeRotation(rotations: { [key: string]: number }): Matrix5D {\n let result: Matrix5D = { \n elements: Array(5).fill(null).map((_, i) => \n Array(5).fill(null).map((_, j) => i === j ? 1 : 0)\n )\n };\n\n for (const [plane, angle] of Object.entries(rotations)) {\n if (angle !== 0) {\n const rotMatrix = this.createRotationMatrix(plane, angle);\n result = this.multiplyMatrices(result, rotMatrix);\n }\n }\n\n return result;\n }\n}",[],[139,188,198],"c358fc86-59a1-11f0-9b50-f69ea79377d9","geometry4d.ts","c358fd62-59a1-11f0-9b50-f69ea79377d9",3,["D",1751721175037],"// 4D Geometry calculations and shape generation\n\nimport { Vector4D, Vector3D, Shape4D, Edge, Face, Cell, Matrix4D } from '../types.ts';\n\nexport class Geometry4D {\n // Create a 4D rotation matrix for the given plane and angle\n static createRotationMatrix(plane: string, angle: number): Matrix4D {\n const cos = Math.cos(angle);\n const sin = Math.sin(angle);\n const matrix = [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1]\n ];\n\n switch (plane) {\n case 'xy':\n matrix[0][0] = cos; matrix[0][1] = -sin;\n matrix[1][0] = sin; matrix[1][1] = cos;\n break;\n case 'xz':\n matrix[0][0] = cos; matrix[0][2] = -sin;\n matrix[2][0] = sin; matrix[2][2] = cos;\n break;\n case 'xw':\n matrix[0][0] = cos; matrix[0][3] = -sin;\n matrix[3][0] = sin; matrix[3][3] = cos;\n break;\n case 'yz':\n matrix[1][1] = cos; matrix[1][2] = -sin;\n matrix[2][1] = sin; matrix[2][2] = cos;\n break;\n case 'yw':\n matrix[1][1] = cos; matrix[1][3] = -sin;\n matrix[3][1] = sin; matrix[3][3] = cos;\n break;\n case 'zw':\n matrix[2][2] = cos; matrix[2][3] = -sin;\n matrix[3][2] = sin; matrix[3][3] = cos;\n break;\n }\n\n return { elements: matrix };\n }\n\n // Apply transformation matrix to a 4D vector\n static transformVector(vector: Vector4D, matrix: Matrix4D): Vector4D {\n const { x, y, z, w } = vector;\n const m = matrix.elements;\n \n return {\n x: m[0][0] * x + m[0][1] * y + m[0][2] * z + m[0][3] * w,\n y: m[1][0] * x + m[1][1] * y + m[1][2] * z + m[1][3] * w,\n z: m[2][0] * x + m[2][1] * y + m[2][2] * z + m[2][3] * w,\n w: m[3][0] * x + m[3][1] * y + m[3][2] * z + m[3][3] * w\n };\n }\n\n // Project 4D point to 3D using perspective projection\n static projectTo3D(point: Vector4D, distance: number = 2): Vector3D {\n const factor = distance / (distance - point.w);\n return {\n x: point.x * factor,\n y: point.y * factor,\n z: point.z * factor\n };\n }\n\n // Generate tesseract (4D cube) vertices and structure\n static createTesseract(): Shape4D {\n const vertices: Vector4D[] = [];\n \n // Generate all 16 vertices of a tesseract\n for (let i = 0; i < 16; i++) {\n vertices.push({\n x: (i & 1) ? 1 : -1,\n y: (i & 2) ? 1 : -1,\n z: (i & 4) ? 1 : -1,\n w: (i & 8) ? 1 : -1\n });\n }\n\n // Generate edges (32 edges total)\n const edges: Edge[] = [];\n for (let i = 0; i < 16; i++) {\n for (let j = i + 1; j < 16; j++) {\n // Two vertices are connected if they differ in exactly one coordinate\n const diff = [\n vertices[i].x !== vertices[j].x ? 1 : 0,\n vertices[i].y !== vertices[j].y ? 1 : 0,\n vertices[i].z !== vertices[j].z ? 1 : 0,\n vertices[i].w !== vertices[j].w ? 1 : 0\n ].reduce((sum, val) => sum + val, 0);\n \n if (diff === 1) {\n edges.push({ start: i, end: j });\n }\n }\n }\n\n // Generate faces (24 square faces)\n const faces: Face[] = [];\n // Each face is defined by 4 vertices that form a square\n // This is a simplified version - full implementation would be more complex\n for (let dim1 = 0; dim1 < 4; dim1++) {\n for (let dim2 = dim1 + 1; dim2 < 4; dim2++) {\n for (let val1 = -1; val1 <= 1; val1 += 2) {\n for (let val2 = -1; val2 <= 1; val2 += 2) {\n const faceVertices: number[] = [];\n for (let i = 0; i < 16; i++) {\n const coords = [vertices[i].x, vertices[i].y, vertices[i].z, vertices[i].w];\n if (coords[dim1] === val1 && coords[dim2] === val2) {\n faceVertices.push(i);\n }\n }\n if (faceVertices.length === 4) {\n faces.push({ vertices: faceVertices });\n }\n }\n }\n }\n }\n\n // Generate cells (8 cubic cells)\n const cells: Cell[] = [];\n for (let w = -1; w <= 1; w += 2) {\n cells.push({ faces: faces.map((_, i) => i).slice(0, 6) }); // Simplified\n }\n\n return {\n vertices,\n edges,\n faces,\n cells,\n name: 'Tesseract'\n };\n }\n\n // Generate 16-cell (4D cross-polytope)\n static create16Cell(): Shape4D {\n const vertices: Vector4D[] = [\n { x: 1, y: 0, z: 0, w: 0 },\n { x: -1, y: 0, z: 0, w: 0 },\n { x: 0, y: 1, z: 0, w: 0 },\n { x: 0, y: -1, z: 0, w: 0 },\n { x: 0, y: 0, z: 1, w: 0 },\n { x: 0, y: 0, z: -1, w: 0 },\n { x: 0, y: 0, z: 0, w: 1 },\n { x: 0, y: 0, z: 0, w: -1 }\n ];\n\n const edges: Edge[] = [];\n // Connect vertices that are not opposite to each other\n for (let i = 0; i < 8; i++) {\n for (let j = i + 1; j < 8; j++) {\n const v1 = vertices[i];\n const v2 = vertices[j];\n // Check if they're not opposite (dot product != -1)\n const dot = v1.x * v2.x + v1.y * v2.y + v1.z * v2.z + v1.w * v2.w;\n if (Math.abs(dot + 1) > 0.001) {\n edges.push({ start: i, end: j });\n }\n }\n }\n\n // Generate triangular faces\n const faces: Face[] = [];\n for (let i = 0; i < 8; i++) {\n for (let j = i + 1; j < 8; j++) {\n for (let k = j + 1; k < 8; k++) {\n // Check if these three vertices form a valid triangular face\n const v1 = vertices[i];\n const v2 = vertices[j];\n const v3 = vertices[k];\n \n // Simplified check - in a real implementation, this would be more sophisticated\n const sum = Math.abs(v1.x + v2.x + v3.x) + \n Math.abs(v1.y + v2.y + v3.y) + \n Math.abs(v1.z + v2.z + v3.z) + \n Math.abs(v1.w + v2.w + v3.w);\n \n if (Math.abs(sum - 1) < 0.001) {\n faces.push({ vertices: [i, j, k] });\n }\n }\n }\n }\n\n const cells: Cell[] = [];\n // Each cell is a tetrahedron\n for (let i = 0; i < faces.length; i += 4) {\n if (i + 3 < faces.length) {\n cells.push({ faces: [i, i + 1, i + 2, i + 3] });\n }\n }\n\n return {\n vertices,\n edges,\n faces,\n cells,\n name: '16-Cell'\n };\n }\n\n // Calculate cross-section of 4D shape with a 3D hyperplane\n static calculateCrossSection(shape: Shape4D, wValue: number): Vector3D[] {\n const crossSectionPoints: Vector3D[] = [];\n \n // Find intersections of edges with the hyperplane w = wValue\n for (const edge of shape.edges) {\n const v1 = shape.vertices[edge.start];\n const v2 = shape.vertices[edge.end];\n \n // Check if edge crosses the hyperplane\n if ((v1.w <= wValue && v2.w >= wValue) || (v1.w >= wValue && v2.w <= wValue)) {\n if (Math.abs(v1.w - v2.w) > 0.001) {\n // Calculate intersection point\n const t = (wValue - v1.w) / (v2.w - v1.w);\n const intersection = {\n x: v1.x + t * (v2.x - v1.x),\n y: v1.y + t * (v2.y - v1.y),\n z: v1.z + t * (v2.z - v1.z)\n };\n crossSectionPoints.push(intersection);\n }\n }\n }\n \n return crossSectionPoints;\n }\n\n // Multiply two 4D matrices\n static multiplyMatrices(a: Matrix4D, b: Matrix4D): Matrix4D {\n const result = Array(4).fill(null).map(() => Array(4).fill(0));\n \n for (let i = 0; i < 4; i++) {\n for (let j = 0; j < 4; j++) {\n for (let k = 0; k < 4; k++) {\n result[i][j] += a.elements[i][k] * b.elements[k][j];\n }\n }\n }\n \n return { elements: result };\n }\n\n // Create composite rotation matrix from multiple rotations\n static createCompositeRotation(rotations: { [key: string]: number }): Matrix4D {\n let result: Matrix4D = { elements: [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1]\n ]};\n\n for (const [plane, angle] of Object.entries(rotations)) {\n if (angle !== 0) {\n const rotMatrix = this.createRotationMatrix(plane, angle);\n result = this.multiplyMatrices(result, rotMatrix);\n }\n }\n\n return result;\n }\n}",[],[139,188,206],"c3591a90-59a1-11f0-9b50-f69ea79377d9",["D",1751721175037],[157,158,159,160],[139,188],["D",1751721129544],[156,161,162],[139],["D",1751721027052],{"_96":95,"_103":99},{"_96":95,"_97":-5,"_98":99,"_18":54,"_100":101,"_102":24},{"_13":85,"_31":86,"_42":41,"_87":43,"_88":-5,"_89":-5,"_90":-5,"_91":-5,"_92":-5,"_93":44,"_94":95},"ctx",{"_78":-5,"_123":257,"_258":259,"_260":261,"_262":24,"_263":24,"_264":24,"_265":58,"_266":-5,"_267":-7,"_268":-7,"_269":62,"_270":24,"_271":24,"_272":-5,"_273":24,"_274":24,"_275":24,"_276":-5},"ENV",{"_228":229,"_230":231,"_232":86,"_233":234,"_235":236,"_237":238,"_239":240,"_241":242,"_243":244,"_245":246,"_247":248,"_249":250,"_251":252,"_253":254,"_255":256},"REACT_APP_SENTRY_DSN","https://586020d86f05489db63a554690acf1e9@o1398359.ingest.sentry.io/6724499","RENDER_GIT_COMMIT","c73f21da490985bff19c279eb0e09db24d688e4f","RENDER_GIT_BRANCH","POSTHOG_API_TOKEN","phc_nmoyuAkStEZuUp69rYlg1DZgrIt19Gx0Y4Hwf8tGgJP","POSTHOG_API_HOST","https://wart.val.town","WEB_API_TEMPLATE","https://{val}.web.val.run","APP_URL","https://www.val.town","MODULE_URL","https://esm.town","VANITY_WEB_API_TEMPLATE","https://{label}.val.run/","DENOLS_URL","https://lsp.val.town","NODE_ENV","production","CLOUDFLARE_TURNSTILE_SITE_KEY","0x4AAAAAACtaIZJH7s9rBMZ6","GOOGLE_CLIENT_ID","875989696899-jtsqkhlbdv5jrlsk8631p7ipjg3c6o62.apps.googleusercontent.com","STRIPE_PUBLISHABLE_KEY","pk_live_51N2zvWEpZTTLipIkVEwXrUG9AT0yeOOEYxszarZT1jpsZV58Ly6wlg3SltZpHN26CUalOBmUSY7adQRQiSkCZz2500qSXNkf8Y","API_URL","https://api.val.town",[],"preferencesKeybindings","default","preferencesTheme","light","preferencesFixers","preferencesCopilot","preferencesSelectionAi","preferencesCloseBrackets","preferencesChatPanelState","preferencesDprint","preferencesDenofmt","notificationCount","flagDenols","isBusinessOrgMember","businessOrgHandle","isBusinessOrgAdmin","isHigherTownieTier","navCollapsed","currentOrgId"]

Diff · v7