Footvector representation of curves and surfaces

Valasek Gábor and Bálint Csaba and Leitereg András: Footvector representation of curves and surfaces. In: Acta cybernetica, (25) 2. pp. 555-573. (2021)

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Abstract

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.

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 2021
Volume: 25
Number: 2
ISSN: 0324-721X
Page Range: pp. 555-573
Language: English
Publisher: University of Szeged, Institute of Informatics
Place of Publication: Szeged
Event Title: Conference of PhD Students in Computer Science (12.) (2020) (Szeged)
Related URLs: http://acta.bibl.u-szeged.hu/75565/
DOI: 10.14232/actacyb.290145
Uncontrolled Keywords: Számítógépes grafika - geometria
Additional Information: Bibliogr.: p. 572-573. ; ill. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.02. Computer and information sciences
Date Deposited: 2022. May. 13. 08:48
Last Modified: 2022. May. 13. 08:49
URI: http://acta.bibl.u-szeged.hu/id/eprint/75623

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