Open AccessFootvector Representation of Curves and Surfaces
Author(s) -
Gábor Valasek,
Csaba Bálint,
András Leitereg
Publication year - 2021
Publication title -
acta cybernetica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.143
H-Index - 18
eISSN - 2676-993X
pISSN - 0324-721X
DOI - 10.14232/actacyb.290145
Subject(s) - representation (politics) , computer science , code (set theory) , offset (computer science) , signed distance function , generalization , algorithm , hessian matrix , geometric design , function (biology) , set (abstract data type) , mathematics , geometry , mathematical analysis , evolutionary biology , politics , political science , law , biology , programming language
This paper proposes a foot mapping-based representation of curves and surfaces which is a geometric generalization of signed distance functions. We present a first-order characterization of the footvector mapping in terms of the differential geometric invariants of the represented shape and quantify the dependence of the spatial partial derivatives of the footvector mapping with respect to the principal curvatures at the footpoint. The practical applicability of foot mapping representations is highlighted by several fast iterative methods to compute the exact footvector mapping of the offset surface of CSG trees. The set operations for footpoint mappings are higher-order functions that map a tuple of functions to a single function, which poses a challenge for GPU implementations. We propose a code generation framework to overcome this that transforms CSG trees to the GLSL shader code.