TY - JOUR AU - Gábor Valasek AU - Csaba Bálint AU - András Leitereg PY - 2021/08/04 Y2 - 2024/03/29 TI - Footvector Representation of Curves and Surfaces JF - Acta Cybernetica JA - Acta Cybern VL - 25 IS - 2 SE - Special Issue of the 12th Conference of PhD Students in Computer Science DO - 10.14232/actacyb.290145 UR - https://cyber.bibl.u-szeged.hu/index.php/actcybern/article/view/4205 AB - 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. ER -