基于时序区间反转的隐式曲面动画渲染方法

doi:10.11996/JG.j.2095-302X.2025030635

图学学报 ›› 2025, Vol. 46 ›› Issue (3): 635-641.DOI: 10.11996/JG.j.2095-302X.2025030635

• 计算机图形学与虚拟现实 • 上一篇下一篇

基于时序区间反转的隐式曲面动画渲染方法

李晓丽(), 张昆, 杜振龙, 陈东, 宋爽

南京工业大学计算机与信息工程学院，江苏南京 211816

收稿日期:2024-08-30 接受日期:2024-12-24 出版日期:2025-06-30 发布日期:2025-06-13
通讯作者:杜振龙(1971-)，男，教授，博士。主要研究方向为计算机图形学、计算机视觉。E-mail：duzhl-cad@163.com
第一作者:李晓丽(1971-)，女，副教授，博士。主要研究方向为计算机图形学、计算机视觉。E-mail：lixl@njtech.edu.cn
基金资助:
国家自然科学基金(62202221);国家自然科学基金(61672279)

Implicit surface animation rendering based on temporal interval inversion

LI Xiaoli(), ZHANG Kun, DU Zhenlong, CHEN Dong, SONG Shuang

School of Computer and Information Engineering, Nanjing Tech University, Nanjing Jiangsu 211816, China

Received:2024-08-30 Accepted:2024-12-24 Published:2025-06-30 Online:2025-06-13
Contact: DU Zhenlong (1971-), professor, Ph.D. His main research interests cover computer graphics and computer vision. E-mail：duzhl-cad@163.com
First author：LI Xiaoli (1971-), associate professor, Ph.D. Her main research interests cover computer graphics and computer vision. E-mail：lixl@njtech.edu.cn
Supported by:
National Natural Science Foundation of China(62202221);National Natural Science Foundation of China(61672279)

摘要/Abstract

摘要：

动画渲染是计算机图形学中的一个重要分支，专注于生成时序动态图像。传统的动画渲染方法在时间轴进行几何场景的逐帧渲染，易造成计算资源的浪费。为了提高动画渲染效率，提出了基于时序区间反转的隐式曲面动画渲染方法。首先，用稀疏八叉树网格划分隐式场景空间，采用区间运算递归细分隐式场景，将含有隐式曲面的场景分为隐式体内部、外部和表面。然后利用区间运算对时间导数进行范围限定定位隐式场景中的变化，多个连续隐式曲面直接存在相对或绝对静止的区间，在保持全局误差不变的情况下有选择地重新评估区域，实现隐式曲面之间的消隐。最后，通过并行化线程技术渲染隐式曲面动画，显著提高渲染效率。实验结果表明，该方法与逐帧渲染方法相比，在保持渲染质量的同时，实现了几十倍的加速。

关键词: 隐式曲面, 八叉树算法, 递归细分, 区间运算, 隐式曲面消隐

Abstract:

Animation rendering is an important branch of computer graphics that focuses on generating temporal dynamic image sequences. The common animation rendering methods involves per-frame rendering of geometric scenes along the timeline, which can easily lead to the waste of computing resources. To enhance the animation rendering efficiency, an implicit surface animation rendering method based on temporal interval reversal was proposed. This method exploited a sparse octree mesh to divide the implicit scene space, employed interval arithmetic for recursive subdivision of the implicit scene, and categorized the scenes containing implicit surfaces into interior, exterior, and surface areas. Interval arithmetic was utilized to limit the range of the time derivative, thereby localizing changes within the implicit scene. There were intervals of relative or absolute stillness between multiple consecutive implicit surfaces, and by selectively re-evaluating areas while maintaining the global error, the occlusion between implicit surfaces was achieved. Finally, parallelized threads were utilized to render implicit surface animation. Experimental results showed that the proposed method, compared with the frame-by-frame rendering method, achieved an acceleration of several tens of times while maintaining the rendering quality.

Key words: implicit surface, octree algorithm, recursive subdivision, interval arithmetic, implicit surface occlusion

中图分类号:

TP391

李晓丽, 张昆, 杜振龙, 陈东, 宋爽. 基于时序区间反转的隐式曲面动画渲染方法[J]. 图学学报, 2025, 46(3): 635-641.

LI Xiaoli, ZHANG Kun, DU Zhenlong, CHEN Dong, SONG Shuang. Implicit surface animation rendering based on temporal interval inversion[J]. Journal of Graphics, 2025, 46(3): 635-641.

图/表 9

图1 算法总体流程

Fig. 1 Overview of approach

图2 运动小球平滑融合到复杂静态环境中((a) 230帧；(b) 350帧；(c) 445帧；(d) 560帧)

Fig. 2 Moving ball blends smoothly into a complex static environment ((a) 230 frame; (b) 350 frame; (c) 445 frame; (d) 560 frame)

图3 小球在扭曲线圈中滚动((a) 230帧；(b) 350帧；(c) 445帧；(d) 560帧)

Fig. 3 The small ball moves along a twisted coil ((a) 230 frame; (b) 350 frame; (c) 445 frame; (d) 560 frame)

图4 小球在摇篮式场景中摆动((a) 230帧；(b) 350帧；(c) 445帧；(d) 560帧)

Fig. 4 The ball swings in a cradle-like scenario ((a) 230 frame; (b) 350 frame; (c) 445 frame; (d) 560 frame)

图5 滑动钢琴块运动((a) 230帧；(b) 350帧；(c) 445帧；(d) 560帧)

Fig. 5 Sliding piano block ((a) 230 frame; (b) 350 frame; (c) 445 frame; (d) 560 frame)

图6 与逐帧MPR方法精度对比((a) 230帧；(b) 230帧；(c) 445帧；(d) 445帧)

Fig. 6 Precision comparison with per-frame MPR ((a) 230 frame; (b) 230 frame; (c) 445 frame; (d) 445 frame)

图7 与逐帧MPR方法在不同δ值场景渲染帧时长对比((a)复杂静态环境；(b)扭曲线圈)

Fig. 7 Comparison with the per-frame and ours ((a) Complex static environment; (b) Twisting coils)

表1 改变δ和ε的定量比较

Table 1 Quantitative results comparison with changing δ and ε within different scenarios

场景	ε	δ	平均帧时间/ms	总加速	平均帧加速
融球建筑	1024³	0.01	66.17	19.71	71.95
		0.03	31.47	41.44	126.01
		0.06	19.56	66.68	193.99
	256³	0.01	7.03	12.19	16.02
		0.03	4.70	18.25	22.16
		0.06	3.58	23.92	28.33
扭曲线圈	1024³	0.01	224.82	3.05	3.10
		0.03	120.34	5.70	5.92
		0.06	55.02	17.48	13.38
	256³	0.01	12.06	3.14	3.16
		0.03	10.73	3.52	3.55
		0.06	8.28	4.57	4.63
摆动小球	1024³	0.01	35.76	6.09	6.66
		0.03	26.86	8.11	9.19
		0.06	21.67	10.05	11.63
	256³	0.01	5.64	3.61	3.72
		0.03	4.99	4.09	4.20
		0.06	4.66	4.38	4.51
滑动琴块	1024³	0.01	18.86	28.68	87.84
		0.03	17.08	31.67	92.37
		0.06	14.05	38.50	98.42
	256³	0.01	2.92	13.48	14.86
		0.03	2.96	13.29	14.59
		0.06	2.90	13.54	14.94

表2 与逐帧MPR方法的对比(以δ=0.06，ε=10243)

Table 2 Comparison with per-frame MPR and ours in different scenes (δ=0.06, ε=10243)

场景	方法	平均帧时间/ms	总加速	平均帧加速
融球建筑	Per-frame	1304.05	1.00	1.00
融球建筑	Ours	19.56	66.68	193.99
扭曲线圈	Per-frame	686.04	1.00	1.00
扭曲线圈	Ours	55.02	17.48	13.38
摆动小球	Per-frame	217.85	1.00	1.00
摆动小球	Ours	21.67	10.05	11.63
滑动琴块	Per-frame	540.87	11.00	1.00
滑动琴块	Ours	14.05	38.50	98.42

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基于时序区间反转的隐式曲面动画渲染方法

Implicit surface animation rendering based on temporal interval inversion

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