Skip to content
Shape3d
See the figures

Shape3d - pure C# mesh renderer

A renderer that draws figures which cannot exist.

Twenty primitives and a short cast of impossible figures - the Penrose staircase, the tribar, an Escher loop - each one a real list of 3D triangles that only reads as impossible from a single camera. Rotate it and the illusion pulls itself apart. No engine, no WebGL, no packages outside the .NET base library: the whole thing rasterises to a 2D canvas.

Start with the stairs Why it works
Penrose staircase rendered from the one viewpoint where its four flights close into a single loop that appears to climb forever.
penrose-stairs - the one camera where the loop closes - orthographic - 224 verts / 336 tris
20
shapes in the catalog
4
C# projects, 1,214 lines
0
dependencies beyond the BCL
2D
canvas raster, no shaders

The main act

Impossible figures

Real meshes that lie about their geometry - valid from one angle, broken from every other.

Animated turntable of the Penrose staircase: as it spins, the four flights briefly line up into a closed climbing loop, then separate into four disconnected staircases at different heights.
Turntable - the trick in motion
The loop that comes apart

For a few frames each turn the four flights meet in a square that seems to climb without end. Spin a little further and they spring into four ordinary staircases stranded at different heights - the hidden riser that resets the loop to the ground swings into view.

penrose-stairs - 18-frame turntable - orthographic - 224 verts / 336 tris
Penrose staircase seen from an ordinary angle, showing two separate flights of stairs sitting at clearly different heights.
Penrose staircase - exposed
Same stairs, honest angle

Off the magic viewpoint the cheat is plain: the flights never meet. One arm quietly drops its whole height at the corner the canonical camera keeps hidden.

penrose-stairs - orthographic - 224 verts / 336 tris
The three bars of the Penrose tribar, shown apart so the gaps between their ends are visible.
The tribar
Three bars that never touch

The impossible triangle cannot be built in real space - so the mesh is three square bars that only line up in a flat drawing. Here the renderer shows the gap the printed illusion depends on hiding.

penrose-triangle - orthographic - 24 verts / 36 tris
A solid cube with the looping Penrose staircase set on its roof, echoing Escher's Ascending and Descending.
Ascending and descending
Escher's rooftop loop

A plain block with the staircase loop dropped onto its roof, after M.C. Escher's 1960 lithograph. The building is ordinary; only the stairs break the rules.

escher - orthographic - 296 verts / 444 tris

The honest half

Primitives and attractors

The same rasteriser on shapes that play fair - parametric surfaces, a Platonic solid, a fractal, a chaotic orbit.

A trefoil knot swept as a smooth tube.
Trefoil knot
The simplest real knot

The smallest knot you cannot undo, swept as a tube along a (2,3) torus curve.

trefoil - perspective - 3,360 verts / 6,720 tris
A UV torus, a donut ring of quads.
Torus
A ring of quads

A UV donut, each ring sampled around a second ring - the textbook parametric surface.

torus - perspective - 512 verts / 1,024 tris
A Menger sponge, level 2, an isometric cube riddled with square holes.
Menger sponge - level 2
A cube, hollowed twice

Remove the middle of a cube, then do the same to each of the 400 pieces left behind.

menger - orthographic - 3,200 verts / 4,800 tris
A regular icosahedron, the 20-faced Platonic solid.
Icosahedron
Twenty faces, twelve points

The largest Platonic solid, built straight from the golden-ratio vertex coordinates.

icosahedron - perspective - 12 verts / 20 tris
The Lorenz attractor traced as a ribbon tube, its two looping lobes forming a butterfly.
Lorenz attractor
Chaos as a ribbon

The 1963 toy weather system, integrated step by step and drawn as a tube - two lobes, never quite repeating.

lorenz - perspective - 48,000 verts / 95,984 tris

Under the hood

Why the impossible ones work

01 Honest geometry

Every figure is a genuine set of 3D vertices and triangles. Nothing is drawn in 2D and nothing is faked - you can export any of them to OBJ or STL and open them in a modeller.

02 The camera does the lying

Orthographic projection throws away depth, so a corner sitting far behind another lands on exactly the same pixels. Line the pieces up that way and a broken loop looks whole. Add perspective, or turn a few degrees, and the gap returns.

03 A 2D rasteriser

Faces are depth-sorted back to front, back-faces culled, lit by one directional light, and painted onto a plain canvas. No GPU, no shader, no matrix library - just arithmetic from the base class library.