Surface Fairing towards Regular Principal Curvature Line Networks

Freeform surfaces whose principal curvature line network is regularly distributed, are essential to many real applications like CAD modeling, architecture design, and industrial fabrication. However, most designed surfaces do not hold this nice property because it is hard to enforce such constraints...

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Bibliographic Details
Published in:Computer graphics forum Vol. 38; no. 7; pp. 115 - 125
Main Authors: Chu, Lei, Bo, Pengbo, Liu, Yang, Wang, Wenping
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.10.2019
Subjects:
Architecture
CCS Concepts
Computing methodologies → Mesh geometry models
Curvature
Finite element method
Machine shops
Mathematical analysis
Modelling
Networks
Parametric curve and surface models
Quadrilaterals
Shape analysis
Surface geometry
Tensors
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:Freeform surfaces whose principal curvature line network is regularly distributed, are essential to many real applications like CAD modeling, architecture design, and industrial fabrication. However, most designed surfaces do not hold this nice property because it is hard to enforce such constraints in the design process. In this paper, we present a novel method for surface fairing which takes a regular distribution of the principal curvature line network on a surface as an objective. Our method first removes the high‐frequency signals from the curvature tensor field of an input freeform surface by a novel rolling guidance tensor filter, which results in a more regular and smooth curvature tensor field, then deforms the input surface to match the smoothed field as much as possible. As an application, we solve the problem of approximating freeform surfaces with regular principal curvature line networks, discretized by quadrilateral meshes. By introducing the circular or conical conditions on the quadrilateral mesh to guarantee the existence of discrete principal curvature line networks, and minimizing the approximate error to the original surface and improving the fairness of the quad mesh, we obtain a regular discrete principal curvature line network that approximates the original surface. We evaluate the efficacy of our method on various freeform surfaces and demonstrate the superiority of the rolling guidance tensor filter over other tensor smoothing techniques. We also utilize our method to generate high‐quality circular/conical meshes for architecture design and cyclide spline surfaces for CAD modeling.
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.13821