Negative curvature
Hyperbolic space
Pentagonal and star tilings cover geodesic planes. Square and hexagonal patterns live on horospheres. Reflections follow the same curved geometry as the camera rays.
Interactive path tracing
Explore hyperbolic space.
Follow light through a world with negative curvature, then return to familiar Euclidean geometry. Open a scene to move the camera and watch the image converge.
Zero curvature
Euclidean space
A refractive sphere, a diffuse cube, and a partly reflective plane. This familiar scene provides a reference for how materials and light behave without spatial curvature.
The images above are offline renders and work in any browser. Interactive scenes require WebGPU and a keyboard and mouse. Drag to look, use WASD to move, and scroll to zoom. Choose a lower quality setting for smoother movement.
Watch
The original walkthrough
A tour of Hypertrace from 2020 shows the project in motion. The current web renderer brings the Euclidean and hyperbolic examples into the browser.
Watch the video ↗Understand
Why do light rays curve?
Learn how the upper half-space model, complex Möbius transformations, and local material interactions fit into a path tracer. Includes the role of quaternions and the limits of floating-point precision.
Read the theory