🔷 幾何学

TessellationsInteractive tessellation explorer. Regular tilings (triangular, square, hexagonal) and… Quaternion RotationInteractive side-by-side Euler angles vs quaternion rotation comparison. See gimbal lock in… Parametric SurfacesInteractive parametric surface explorer. Render torus, Klein bottle, Möbius strip, sphere… Origami FoldingInteractive origami folding simulator. Explore Miura-ori, Yoshimura and Kresling crease… Minimal Surfaces — Catenoid, Helicoid, Soap FilmExplore minimal surfaces: catenoid, helicoid, Enneper surface and soap-film simulation.… Sphere Projections — Mercator, Stereographic & MoreCompare 6 map projections of a sphere onto a flat plane: Mercator, Stereographic,… Tesseract — 4D Hypercube Rotation VisualiserVisualise a 4-dimensional hypercube (tesseract) projected into 2D. Rotate in 6 independent… Polyhedra ExplorerExplore all 5 Platonic solids and 13 Archimedean solids in interactive 3D. Drag to rotate,… Topology SurfacesNewTopological surfaces: genus, Euler characteristic, Klein bottle and Mobius strip… Gyroid & Minimal SurfacesNewExplore triply-periodic minimal surfaces in 3D — Gyroid, Schwarz P, Diamond and Neovius —… Sphere & Circle PackingNewHow densely can equal circles and spheres fill space? Compare square, hexagonal and random… Geodesic DomeNewBuild Buckminster Fuller geodesic spheres by subdividing an icosahedron and projecting onto… Bézier, B-Spline & NURBSNewThe parametric curves behind every vector graphic and font. Drag control points, watch the… Delaunay & VoronoiNewCompute the Delaunay triangulation (Bowyer–Watson) of a draggable point set live, with the… Menger SpongeNewThe canonical 3D fractal: subdivide each cube into 27 children and keep 20, recurse.… Torus KnotNewReshape a (p,q) torus knot with iridescent fresnel shading — change p, q and tube thickness. Superellipse — Lamé Curves & the SquircleNewSweep the exponent n in |x/a|ⁿ + |y/b|ⁿ = 1 and watch it morph from astroid to diamond,… Sierpiński Tetrahedron — 3D FractalNewExplore the Sierpiński tetrahedron — a 3D fractal built by replacing a tetrahedron with four… Archimedean SolidsNewInteractive Archimedean solids explorer. Rotate the truncated tetrahedron, cuboctahedron,… Compass & Straightedge ConstructionsNewAnimated, mathematically real compass-and-straightedge constructions: perpendicular… Conic SectionsNewInteractive conic sections simulator. Slice a double cone with an adjustable plane and watch… Euler's Formula (V-E+F=2)NewRotate eight polyhedra, from the tetrahedron to a truncated cube, and watch live vertex,… Gaussian Curvature ExplorerNewCompare a sphere, plane, saddle, cylinder and torus rendered as rotatable shaded meshes,… Golden Ratio SpiralNewInteractive golden ratio spiral simulator. Watch the golden rectangle subdivide into… Kepler-Poinsot Star PolyhedraNewInteractive Kepler-Poinsot star polyhedra simulator. Rotate the small stellated… Pentagon TilingNewExplore convex pentagon tilings of the plane. See why regular pentagons alone can never tile… Perspective Projection & Vanishing PointsNewA floor grid and 3D boxes are projected onto the picture plane using real camera math, the… Poincare Disk (Hyperbolic Geometry)NewDrag points inside the unit disk to draw real hyperbolic geodesic arcs via circle-inversion… Polyhedron Nets (Unfolding 3D Solids)NewWatch the five Platonic solids unfold into flat 2D nets and fold back into 3D, using a real… 4D Regular PolytopesNewRotate genuine 4-dimensional regular polytopes, the 5-cell, 16-cell and 24-cell, plus a… Reuleaux PolygonsNewBuild genuine curves of constant width from odd-sided regular polygons (3-11 sides). Watch a… Spherical TrigonometryNewPlace three points on a rotatable globe to form a great-circle triangle. Live arc lengths,… Symmetry Groups & Wallpaper PatternsNewTile the plane with an asymmetric flag motif under eight real wallpaper-group generators… Voronoi Diagrams & Lloyd's RelaxationNewGenerate random sites and watch a raster-computed Voronoi diagram relax toward a centroidal…