Mesh Slicing Along Isolines of Surface-Based Functions

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Date
2024
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
Abstract
There are numerous practical scenarios where the surface of a 3D object is equipped with varying properties. The process of slicing the surface along the isoline of the property field is a widely utilized operation. While the geometry of the 3D object can typically be approximated with a piecewise linear triangle mesh, the property field f might be too intricate to be linearly approximated at the same resolution. Arbitrarily reducing the isoline within a triangle into a straight-line segment could result in noticeable artifacts. In this paper, we delve into the precise extraction of the isoline of a surface-based function f for slicing the surface apart, allowing the extracted isoline to be curved within a triangle. Our approach begins by adequately sampling Steiner points on mesh edges. Subsequently, for each triangle, we categorize the Steiner points into two groups based on the signs of their function values. We then trace the bisector between these two groups of Steiner points by simply computing a 2D power diagram of all Steiner points. It's worth noting that the weight setting of the power diagram is derived from the first-order approximation of f . Finally, we refine the polygonal bisector by adjusting each vertex to the closest point on the actual isoline. Each step of our algorithm is fully parallelizable on a triangle level, making it highly efficient. Additionally, we provide numerous examples to illustrate its practical applications.
Description

CCS Concepts: Computing methodologies → Shape modeling; Mesh models

        
@inproceedings{
10.2312:pg.20241283
, booktitle = {
Pacific Graphics Conference Papers and Posters
}, editor = {
Chen, Renjie
and
Ritschel, Tobias
and
Whiting, Emily
}, title = {{
Mesh Slicing Along Isolines of Surface-Based Functions
}}, author = {
Wang, Lei
and
Wang, Xudong
and
Wang, Wensong
and
Chen, Shuangmin
and
Xin, Shiqing
and
Tu, Changhe
and
Wang, Wenping
}, year = {
2024
}, publisher = {
The Eurographics Association
}, ISBN = {
978-3-03868-250-9
}, DOI = {
10.2312/pg.20241283
} }
Citation