VR Mathipia is an immersive VR learning experience where users visualize and interact with 3D coordinate geometry and space physics.
You explore mathematical concepts through gameplay by navigating a spaceship, assisted by a companion AI named Phobo, while tracking and eliminating incoming meteorites using real-world mathematical models.
- Smooth VR locomotion for immersive exploration
- Natural controller-based movement
- Full interaction inside spaceship environment
- AI companion inside the spaceship
- Guides player through missions
- Explains spatial concepts using dialogue
- Helps understand math visually in VR
- Ray is cast from player/camera direction
- Detects meteor collision in real time
- Computes exact 3D hit position
- Visualizes spatial vector direction
d = (c × Δt) / 2
Where:
- c = Speed of light (299,792,458 m/s)
- Δt = Signal travel time
- d = Distance to object
Used to simulate real-world radar-based distance calculation.
P = A + tD
Where:
- P = Target point (meteor position)
- A = Origin (spaceship position)
- D = Direction vector (normalized)
- t = Distance scalar
- Px = Ax + tDx
- Py = Ay + tDy
- Pz = Az + tDz
d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)
Used to compute:
- Distance between spaceship and meteor
- Ray travel length
D = (M - A) / |M - A|
Where:
- M = Meteor position
- A = Ship position
Ensures accurate directional targeting in 3D space.
Used to approximate meteor shape:
- Width (X), Height (Y), Depth (Z) extracted from spatial bounds
- Forms an axis-aligned bounding box around scanned points
|X - Y| < ε AND |Y - Z| < ε
If dimensions are approximately equal → Sphere
Else → Irregular Shape
V = (4/3)πabc
Where:
- a, b, c = Semi-axes (half of width, height, depth)
Used to estimate meteor size and physical mass volume.
A ≈ 4π (( (ab)^p + (ac)^p + (bc)^p ) / 3)^(1/p)
Where:
- p ≈ 1.6
Provides a highly accurate surface estimation for irregular 3D bodies.
VR Mathipia supports importing real-world scanned objects into the VR environment using iPhone LiDAR-based scanning tools such as Luma 3D.
- Scan real-world object using Luma 3D (iPhone LiDAR scan)
- Export model as 3D file (OBJ / GLB)
- Import into VR Mathipia at runtime
- Select scanned object inside VR file browser
- Spawn object into VR space
- Apply bounding and mesh analysis
Once imported, the system automatically:
- Computes approximate bounding box
- Estimates:
- 📦 Surface Area
- ⚖️ Volume (using ellipsoid approximation)
- Detects shape classification (sphere / irregular / complex mesh)
- Allows real-time scaling & inspection inside VR
This system helps users:
- Understand real-world geometry
- Compare scanned objects with mathematical models
- Visualize how abstract formulas apply to physical objects
- Enter spaceship with Phobo
- Explore VR environment
- Receive mission briefing
- Detect incoming meteorites
- Scan meteor shape using ray system
- Analyze geometry using bounding + physics formulas
- Import real-world scanned objects (Luma 3D)
- Compute surface area + volume of scanned models
- Calculate exact coordinates using vector math
- Lock target and destroy meteor
- Complete mission
- Unity (VR Development)
- Blender (3D Modeling)
- Meta XR (VR Integration)
- Luma 3D (Real-world scanning pipeline)
- Rishav Goswami — VR Developer
- Rahul Singla — UI Designer
VR Mathipia transforms abstract mathematics into a visual + interactive VR experience, combining geometry, vector mathematics, and real-world physics + scanning to make learning intuitive, immersive, and engaging.