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geometry 4d

Perspective, stereographic and orthographic projections compared

Project one rotated 4D polytope three ways side by side (stereographic edges as true circular arcs) and measure what each map keeps: straight lines, circles, parallels and angles. Reads built-in polytopes or any fourd_polytope/v1 JSON record.

Recorded render of Perspective, stereographic and orthographic projections compared

What this component contains

  • ATTRIBUTION.md
  • LICENSE
  • README.md
  • component.json
  • example.gltf
  • fourd.py
  • preview.png
  • projection_comparison.py
  • test_package.py
  • verification/native.json

How it works

Entry points
make_polytope, load_polytope, arc, stereographic_derivative, tangent_on_sphere, angle_errors, is_concyclic, meshes and 4 more
Outputs
example.gltf
Coordinates
x, y, z, w; the three views sit along glTF x (perspective, stereographic, orthographic), +Y up

Recorded checks

godot 4.7.2.stable.official.ed1daf0bf

  • cli_rebuilds_example
  • gltf_structure_example
  • cli_example_runs
  • cli_example_gltf_structure
  • godot_loads_example
  • godot_loads_cli_24cell_three_views
  • preview_render

Limits to consider

Each view is scaled so its farthest vertex sits at the circumradius, which hides the real size differences between the projections. Stereographic arcs are polylines of a few segments (6 by default), so they approximate the circular images. Angle errors are measured at vertices only. The stereographic view refuses a vertex at the projection pole; choose a rotation that moves it. Input records must be convex polytopes centred near the origin for the circumsphere to make sense.