Examples

This page demonstrates a few examples of scenes in the Thurston geometries. Items flagged with (VR) are working with virtual reality (just hit the "Enter VR" button). Items flagged with (PR) incorporate a path tracer. Hit 'p' to launch the path tracer.

Basics

• Automatic window resize
• Minimal global scene
• Minimal local scene
• Materials
• Fog
• Reflections
• Simple animated object
• Fly controls (french keyboard)
• Boolean algebra on shapes (with fly controls)
• Virtual Reality (with fly controls)

Euclidean space $\mathbb E^3$

• Inside a three-torus
• Inside a three-torus (VR)
• Animating a light
• Animating a light (VR)
• Complement of a local ball with UV material
• Nearest neighbors
• Creeping
• Dehn twist
• Half space
• Ball lattice (with a directed SDF)
• Shooting (VR)
• Rotating earth
• Cylinder (global)
• Cylinder (local)
• Path tracer (PT)
• Translucent Tiling (PT)
• Lens (PT)
• Displacement shape modifier (for fun, nothing rigorous)
• Box shape
• Debugging example

Hyperbolic space $\mathbb H^3$

• Basic scene
• Horoballs
• Local cylinder
• Local capped cylinder
• Tourist view (VR)
• Native view (VR)
• Right angled hexagon (VR)
• Using a quadratic ring for the lattice
• Exponential map (VR) Light beam on the controller
• Exponential map (VR) Torch attached to the controller
• Shooting (VR)
• Creeping
• Path tracer (PT)
• Translucent Tiling (PT)
• Scattering Material (PT)
• Realistic Fog (Scattering) (PT)
• Fog and Spherical Lens (PT)
• Birthday cake lattice
• Debugging example

Three-sphere $S^3$

• Quaternion group
• Quaternion group (VR)
• Quaternion group (ball version)
• Cylinder

Product geometry $S^2 \times \mathbb E$

• Line of balls along the $\mathbb E$-direction
• Balls in a lattice
• Point Light (shortest ray only)
• Lattice
• Debugging example

Product geometry $\mathbb H^2 \times \mathbb E$

• Lattice: Cusped Torus $\times\ S^1$
• Lattice: Orbi-Torus $\times\ S^1$ (cone point with angle $\pi$)
• Lattice with balls: Orbi-Torus $\times\ S^1$ (cone point with angle $\pi$)
• Orbi-Torus (VR)
• Point lights
• Debugging example

Nil

• Single ball (VR)
• Mapping torus by a Dehn twist
• Mapping torus by a Dehn twist (VR)
• Quotient of the mapping torus by a Dehn twist (VR)
• Contact distribution
• Lattice of balls
• Vertical plane (with an animated reflecting checkerboard texture)
• Vertical plane (with a directed SDF)
• Fibers of the projection to the euclidean space (VR)
• Shooting (VR)
• Path tracer (PT)
• Debugging in Nil
• Debugging in Nil (bis)

The universal cover of ${\rm SL}(2, \mathbb R)$

• Lattice of balls (orbi-torus)
• Lattice of balls (genus 2 surface)
• Lattice (genus 2 surface)
• Debugging example

Sol

• Balls!
• X/Y-halfspaces
• Z-halfspace
• A lattice of balls in the XY-plane
• A cube (made with boolean operations)
• A lattice of balls
• A lattice of cubes
• Debugging example

PathTracer

• First example
• Volumetric Light
• Switch between two renderers (use the key 'p' to switch between the two renderers)
• Debugging example

Sandbox

• A page for JS experimentation
• A dialogue box
• Imports