Convolution Filtering of Continuous Signed Distance Fields for Polygonal Meshes

• Published in: Computer graphics forum Vol. 34; no. 6; pp. 277 - 288
• Main Authors: Sanchez, Mathieu, Fryazinov, Oleg, Fayolle, Pierre-Alain, Pasko, Alexander
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.09.2015
• Subjects: Analysis; Approximation; Blending; distance function; Filtering; Filtration; Finite element method; geometric modelling; I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling-Geometric algorithms; Image processing systems; implicit surfaces; languages and systems; Mathematical analysis; Mathematical models; polygonal modelling; Preserving; signed distance fields; Studies; Topological manifolds
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12599

Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C1 discontinuities causing creases to appear when applying operations such as blending or metamorphosis. The focus of this work is to efficiently evaluate the signed distance function and to apply a smoothing filter to it while preserving the shape of the initial mesh. The resulting function is smooth almost everywhere, while preserving the exact shape of the polygonal mesh. Due to its low complexity, the proposed filtering technique remains fast compared to its main alternatives providing C1‐continuous distance field approximation. Several applications are presented such as blending, metamorphosis and heterogeneous modelling with polygonal meshes. Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C1 discontinuities causing creases to appear when applying operations such as blending or metamorphosis. The focus of this work is to efficiently evaluate the signed distance function and to apply a smoothing filter to it while preserving the shape of the initial mesh. The resulting function is smooth almost everywhere, while preserving the exact shape of the polygonal mesh. Due to its low complexity, the proposed filtering technique remains fast compared to its main alternatives providing C1‐continuous distance field approximation. Several applications are presented such as blending, metamorphosis and heterogeneous modelling with polygonal meshes.