---
res:
  bibo_abstract:
  - "Isomanifolds are the generalization of isosurfaces to arbitrary dimension and
    codimension, i.e. submanifolds of ℝ^d defined as the zero set of some multivariate
    multivalued smooth function f: ℝ^d → ℝ^{d-n}, where n is the intrinsic dimension
    of the manifold. A natural way to approximate a smooth isomanifold M is to consider
    its Piecewise-Linear (PL) approximation M̂ based on a triangulation \U0001D4AF
    of the ambient space ℝ^d. In this paper, we describe a simple algorithm to trace
    isomanifolds from a given starting point. The algorithm works for arbitrary dimensions
    n and d, and any precision D. Our main result is that, when f (or M) has bounded
    complexity, the complexity of the algorithm is polynomial in d and δ = 1/D (and
    unavoidably exponential in n). Since it is known that for δ = Ω (d^{2.5}), M̂
    is O(D²)-close and isotopic to M, our algorithm produces a faithful PL-approximation
    of isomanifolds of bounded complexity in time polynomial in d. Combining this
    algorithm with dimensionality reduction techniques, the dependency on d in the
    size of M̂ can be completely removed with high probability. We also show that
    the algorithm can handle isomanifolds with boundary and, more generally, isostratifolds.
    The algorithm for isomanifolds with boundary has been implemented and experimental
    results are reported, showing that it is practical and can handle cases that are
    far ahead of the state-of-the-art. @eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Jean-Daniel
      foaf_name: Boissonnat, Jean-Daniel
      foaf_surname: Boissonnat
  - foaf_Person:
      foaf_givenName: Siargey
      foaf_name: Kachanovich, Siargey
      foaf_surname: Kachanovich
  - foaf_Person:
      foaf_givenName: Mathijs
      foaf_name: Wintraecken, Mathijs
      foaf_surname: Wintraecken
      foaf_workInfoHomepage: http://www.librecat.org/personId=307CFBC8-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-7472-2220
  bibo_doi: 10.4230/LIPIcs.SoCG.2021.17
  bibo_volume: 189
  dct_date: 2021^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/1868-8969
  - http://id.crossref.org/issn/978-3-95977-184-9
  dct_language: eng
  dct_publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik@
  dct_title: Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn
    triangulations@
...