Euclidean space

A glass sphere, a diffuse cube, and a partly reflective square-tiled backdrop.

cargo run --release -p hypertrace-examples --bin euclidean

Browser viewer

A yellow glass sphere and turquoise cube in front of a tiled reflective backdrop.

Optional. Requires WebGPU; starts only when requested.

Native requirements and instructions

Technical details

Drag to look; Tab locks the mouse. WASD moves; Space/C moves up/down; Q/E rolls. Scroll zooms; R resets. The viewer pauses when hidden or outside the page’s visible area. Open viewer separately.

What to observe

Look through the glass sphere at the cube and backdrop, then compare the backdrop’s reflection with the direct view.

As in every geometry, free rays follow intrinsic straight lines (geodesics). In Euclidean Cartesian coordinates these also appear as straight lines; the distortion through the yellow sphere comes from refraction.
The backdrop combines diffuse and specular reflection. Its tiles use physical cell dimensions, shared with the horosphere patterns in the hyperbolic example.
The sphere and cube have the same approximate scale as objects in the curved examples, making camera movement comparable.

Geometry of the three spaces · Scene construction

Screenshots

Click an image to open its full-resolution PNG.

A closer view of refraction and the tiled backdrop. 1600 × 1200 · 4096 samples per pixel · 4 path events.
Camera and settings · Render source