@holotope/core

Zero-dependency N-dimensional geometry kernel: vectors, matrices, and exterior products in 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 — the simplex and orthoplex author any requested face family via maxCellDimension, through the top simplex or the orthoplex's whole simplicial boundary; authored groups are combinatorial and unoriented, so render double-sided and derive oriented boundaries from the section path), perspective/orthographic/coordinate-subspace N→3 projection with Float64 homogeneous evaluation, explicit inverse fibres, and perspective-correct segment/triangle lifting, an injective R2→R3 plane embedding (PlaneEmbedding3D: [x, y] → [x, y, 0] exactly, a unique typed inverse on its image, no fibre — render products consume the common DisplayMap3D contract, of which Projection is the lossy specialization), and exact hyperplane slicing via marching tetrahedra with source-edge interpolation provenance. A renderer-independent representation layer adds dimension-checked map lineage, capability-sensitive hit results, auditable in-memory source-cell references, and explicit dimension-independent cell-incidence queries and source-edge coordinates plus multi-view source-parameter consensus for constrained interaction. A deterministic linear coordinate- constraint solver gives edge and barycentric source-simplex coordinates one shared vocabulary for compatibility, rank, unresolved degrees, conditioning, and residual certificates while leaving each coordinate domain explicit. Immutable named constraint-system snapshots add stable replacement/removal and keyed diagnostics without introducing editor state. The simplex path extends this to multi-view homogeneous triangulation. 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. The spectral layer provides a deterministic symmetric eigensolver plus sparse unweighted graph Laplacians, connected components, complete modal bases, and basis-independent repeated-mode projectors for any CellComplex 1-skeleton.

createHypercube() preserves its established edge/face/cube output by default. Set maxCellDimension to author higher cuboid cells explicitly; for example, a full tesseract then contains one 16-vertex 4-cell. simplexizeCuboidGroupN() applies the dimension-generic Kuhn decomposition to any binary-ordered cuboid group, returning k! simplices per k-cell plus exact parent-cell and local- permutation provenance. tetrahedralizeCuboidCells() remains the compatible three-dimensional convenience wrapper over that kernel.

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

Sections are also dimension-generic. HyperplaneSliceN is the affine chart in any RN — its ambient dimension is inferred from its normal — and sectionSimplexGroupN cuts a group of simplicial k-cells with it into (k-1)-simplices. A section is an intersection, not a projection: it is injective on what it keeps and loses dimension rather than distinctness, which is why a section point can name its source and a projected pixel often cannot. (An embedding is the third kind of display map and loses nothing at all — see PlaneEmbedding3D for R2 content.) Every output vertex carries a sparse affine combination of original source vertices, so cutting an already-sectioned complex still names the geometry a reader started from rather than the intermediate one.

MIT © Nikolay Petrov