Demos

pathtracer early

Early GPU pathtracer with diffuse and specular materials in Euclidean space

spectral pathtracer glass ring

Spectral pathtracer rendering a glass ring with wavelength-dependent dispersion and chromatic effects

Code: Mirage

Atmospheric mirage simulated by raymarching through a temperature-dependent refractive index gradient

Code: Sol Euclidean Planes

Code: Air Lens

Light bending through a varying refractive index gradient in Euclidean space, producing a lens effect

Square Orbit

Nested tube-shaped orbits interpolating between circles and squares

Code: Schwarzschild Earth

Gravitational lensing of an earth-textured sphere by a Schwarzschild black hole, producing multiple images

Schwarzschild Black Hole

Gravitational lensing near a Schwarzschild black hole, with Einstein rings and the photon sphere

Code: Rendering Cocktail

GPU path-traced cocktail glass with caustics and glass refraction

Code: Rendering Cocktail 1

GPU path-traced cocktail glass variant with alternate scene configuration

Code: Rendering Cocktail 3

GPU path-traced cocktail glass variant with third scene arrangement

Code: Rendering Cocktail 2

GPU path-traced cocktail glass variant with alternate viewing angle

Code: Sl2 Balloons

Colored balloons in $\widetilde{\mathrm{SL}(2,\mathbb{R})}$, related to the unit tangent bundle of the hyperbolic plane

Code: Hyp Whitehead Complement

Inside the Whitehead link complement, a cusped hyperbolic 3-manifold of finite volume

Code: Hyp Whitehead Complement Earth

Inside the Whitehead link complement with earth-textured spheres near the cusps

Code: Sl2 Vertplane

A vertical plane in $\widetilde{\mathrm{SL}(2,\mathbb{R})}$ geometry, fibered over the hyperbolic plane

Code: Sol Balloons

Colored balloons in Sol geometry, stretched by exponential expansion and contraction

Code: Sol Euclidean Planes

Planes in Sol geometry, distorted by the anisotropic metric

Code: Sol Hyperbolic Planes

Totally geodesic hyperbolic planes in Sol, forming two orthogonal foliations

Code: Nil Horizontal Plane Lights

Horizontal geodesic plane in Nil geometry with non-Euclidean lighting

Code: Nil Vertical Plane Lights

Vertical plane in Nil geometry with non-Euclidean lighting

Code: Nil Tiling Lights

Nil geometry tiling with non-Euclidean lighting from multiple sources

Code: Nil Balls Lights

Spheres in Nil geometry with non-Euclidean lighting from multiple sources

Code: Nil Balls Light

Spheres in Nil geometry lit by a single point source, showing twisted shadow patterns

Code: Nil Horizontal Plane

Horizontal totally geodesic plane in Nil geometry

Code: Nil Vertical Plane

Vertical plane in Nil geometry, distorted by the twisted metric

Code: Nil Tiling

Discrete isometry group tiling of Nil geometry

Code: Nil Balloons

Colored balloons in Nil geometry, distorted by the helical geodesic structure

Code: Nil Earth Moon

Earth and moon in Nil geometry, with viewpoint-dependent distortion from non-commutative translations

Code: Nil Earth Moon Lattice

Earth and moon arranged in a discrete lattice in Nil geometry

Code: Nil Earth Moon Row

Row of earth and moon spheres in Nil geometry, twisting as they recede

Code: Nil Earth

Earth-textured sphere in Nil geometry, distorted by the non-commutative Heisenberg metric

Code: Nil 2ball

Two spheres in Nil geometry, with helical geodesic distortion

Code: Hyp Coxeter Dodecahedron

Coxeter group tiling of $\mathbb{H}^3$ by right-angled regular dodecahedra

Code: Hyp Seifertweber Dodecahedron

Inside the Seifert–Weber dodecahedral space, a compact hyperbolic 3-manifold

Code: Hyp Balloons

Colored balloons in hyperbolic 3-space, distorted by the negative curvature

Code: Hyp Coxeter Cubes

Coxeter group tiling of $\mathbb{H}^3$ by right-angled hyperbolic cubes

Code: Hyp Planes

Totally geodesic planes (copies of $H^2$) in hyperbolic 3-space

Code: S2e Balloons

Colored balloons in $S^2 \times E$, focused by the positive curvature of the spherical factor

Code: S2e Earth S2xs1

Earth sphere in $S^2 \times S^1$, the compact product of a 2-sphere with a circle

rendering-glass

GPU path-traced glass object with refraction and caustics

Code: S2e Earth S2factor

Earth sphere viewed along the $S^2$ factor of $S^2 \times E$, where geodesics are great circles

Code: S2e Earth Moon

Earth and moon in $S^2 \times E$ geometry, visible from both sides of the sphere

Code: S2e Cube Tiling

Spherical cube tiling extruded along the Euclidean factor in $S^2 \times E

Code: H2e Lattice Earth

Earth spheres arranged in a discrete lattice in $H^2 \times E$ geometry

Code: H2e Planes

Totally geodesic planes in $H^2 \times E$, including vertical, horizontal, and mixed surfaces

Code: H2e Balloons

Colored balloons in $H^2 \times E$, distorted by the mixed-curvature product metric

Code: H2e Tiling

Hyperbolic tiling extruded along the Euclidean factor in $H^2 \times E

Code: Sph Rectangle Torus

Clifford torus in $S^3$, a flat torus dividing the 3-sphere into two congruent solid tori

Code: Sph Hopf Link

A Hopf link (two linked great circles) rendered inside $S^3$

Code: Sph Earth Moon

Earth and moon in $S^3$, with antipodal images visible from light wrapping around the sphere

Code: Sph Earth

Earth-textured sphere in $S^3$, with the antipodal image visible from behind

Code: Sph Hopf

Hopf fibers in $S^3$, showing the fibration of the 3-sphere by linked great circles

Code: Sph Balloons

Colored balloons in $S^3$, where all geodesics reconverge at the antipodal point

Code: Sph Ball Collection

Collection of balls in the 3-sphere $S^3$, visible from multiple directions via great circle geodesics

Code: Sph Quaternion

Inside a quotient of $S^3$ by the quaternion group $Q_8$, a spherical space form

Code: Euc Earth Moon

Earth and moon in Euclidean 3-space, a baseline flat geometry scene

Code: Euc 3torus Earth

Earth-textured sphere in the 3-torus, with an infinite lattice of copies visible through the identifications

Code: Euc Hopf Complement

Complement of a Hopf link in Euclidean 3-space, showing tubular neighborhoods of linked circles

Code: Euc 3torus Balloons

Colored balloons in the 3-torus, with copies visible through periodic face identifications

Code: Euc 3torus Generators

The three generating translations of the 3-torus lattice in Euclidean space

Code: Euc 3torus Ball

Inside the 3-torus, a flat Euclidean manifold with periodic boundary conditions

Code: Euc R2xs1

Inside $\mathbb{R}^2 \times S^1$, a Euclidean product geometry with one periodic direction