Open Access

ARTICLE

A Fast and Memory-Efficient Direct Rendering Method for Polynomial-Based Implicit Surfaces

by Jiayu Ren^1,*, Susumu Nakata²

1 Graduate School of Information Science and Engineering, Ritsumeikan University, Ibaraki, Osaka, 567-8570, Japan
2 College School of Information Science and Engineering, Ritsumeikan University, Ibaraki, Osaka, 567-8570, Japan

* Corresponding Author: Jiayu Ren. Email:

Computer Modeling in Engineering & Sciences 2024, 141(2), 1033-1046. https://doi.org/10.32604/cmes.2024.054238

Received 22 May 2024; Accepted 12 August 2024; Issue published 27 September 2024

Abstract

Three-dimensional surfaces are typically modeled as implicit surfaces. However, direct rendering of implicit surfaces is not simple, especially when such surfaces contain finely detailed shapes. One approach is ray-casting, where the field of the implicit surface is assumed to be piecewise polynomials defined on the grid of a rectangular domain. A critical issue for direct rendering based on ray-casting is the computational cost of finding intersections between surfaces and rays. In particular, ray-casting requires many function evaluations along each ray, severely slowing the rendering speed. In this paper, a method is proposed to achieve direct rendering of polynomial-based implicit surfaces in real-time by strategically narrowing the search range and designing the shader to exploit the structure of piecewise polynomials. In experiments, the proposed method achieved a high framerate performance for different test cases, with a speed-up factor ranging from 1.1 to 218.2. In addition, the proposed method demonstrated better efficiency with high cell resolution. In terms of memory consumption, the proposed method saved between 90.94% and 99.64% in different test cases. Generally, the proposed method became more memory-efficient as the cell resolution increased.

---

Keywords

---