@holotope/core

Zero-dependency N-dimensional geometry kernel: vectors and matrices of any dimension, plane rotations and the so(n) exponential map, a paired-quaternion Rotor4 fast path with slerp, N-D rigid transforms and cameras, cell complexes, polytope builders (n-cube, simplex, orthoplex, all six regular polychora, duoprisms), perspective/orthographic N→3 projection, and exact hyperplane slicing via marching tetrahedra. Its structured-space layer also includes the exact 240-root E8 orbit and the icosian folding into conjugate 4-spaces, plus exact cut-and-project lattices, flats, convex windows, and finite model-set patches, including complete-shell Elser–Sloane sections. The implicit-field layer adds inspectable quaternion and bicomplex Julia families, deterministic packed-point and affine-slice sampling, and an approximate isosurface extractor whose full evaluation records remain available. Exact Airbrot, Firebrot, and Earthbrot specifications independently cover the Platonic parameter slices of the tricomplex Mandelbrot set. The coupling layer adds provenance-driven parameter decorations, including the canonical Elser–Sloane internal-coordinate map and an exact finite-orbit equivariance checker for its H4 action. SkewProductFlow adds state-dependent SO(4) fiber dynamics with periodic-orbit closure and holonomy reports.

Renderable coordinates run in Float64 on the CPU, while supported lattice, window, and group decisions stay in exact quadratic rings. The kernel is renderer-agnostic; pair it with @holotope/three to render with three.js.

Live showcase · Repository & docs

import { HyperplaneSlice4, create600Cell, sliceTetrahedra } from '@holotope/core';

const cell600 = create600Cell({ radius: 1.5 });
const slice = HyperplaneSlice4.axisAligned(3, 0); // the w = 0 hyperplane
// ...march its tetrahedra into an exact 3D cross-section

MIT © Nikolay Petrov