Detailed Voxel-Based Implicit Modeling With Local Boolean Composition of Discrete Level Sets

Zhongxiang Duan,Qin Yang,Jigang Li,Xianhai Meng

doi:10.1109/access.2020.2979571

Zhongxiang Duan, Qin Yang + Show 2 more

Open Access

https://doi.org/10.1109/access.2020.2979571

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Abstract

Compared with the functionally-based implicit models, the level set models are usually defined by discretely sampling the implicit function values over the volume grid to represent the shapes, which are suitable for scientific computing and engineering. However, the voxel-based level set methods usually lose some features and details to represent the solids due to the finite grid resolutions. In this paper, we propose a more accurate voxel-based implicit modeling method based on discrete level sets. Compared with the traditional level set methods, more than one level set function can be defined in an implicit model with our approach by classifying the cells of the volume grid. The local Boolean compositions conducted over the compound cells are used to depict the interactions of different implicit surfaces represented by corresponding level set functions, and the sharp and thin details caused by Boolean operations are preserved owing to the definition of the compound cells. We show in our experiments that our method is robust to provide the more detailed implicit description of the shapes with less loss of the features than the conventional voxel-based level set methods.

Highlights

In the field of computer graphics and scientific computing, the techniques for shape description of the objects are essential for modeling, animation, visualization and simulation
Our implicit modeling method is inspired by all these previous works, and introduces the local Boolean composition of the level set functions to depict the local features where different implicit surfaces meet over a voxel-based implicit model
In this paper, we propose a new means for implicit surface modeling based on discrete level sets

Summary

INTRODUCTION

In the field of computer graphics and scientific computing, the techniques for shape description of the objects are essential for modeling, animation, visualization and simulation. The explicit modeling approaches currently represent the boundary with mesh or parametric surfaces, while the implicit models tend to employ an implicit function to distinguish the inside and outside of the object [1]–[3]. Compared with the functional representations of shapes such as skeleton-based implicit surfaces [11], the level set method is another typical implicit representation of the solids, which is widely used in scientific computing and engineering [12]–[14]. Our method of implicit modeling, which is called compound implicit modeling in this paper, classifies the cells of the volume grid, and introduces the local Boolean compositions of level set functions over the defined compound cells. We show that our method maintains the robustness of Boolean operation as the traditional implicit models, yet present a more exact way for voxel-based shape description in computer graphics and engineering

PREVIOUS WORK

COMPOUND IMPLICIT MODELING

NUMERICAL EXPERIMENTS

CONCLUSION