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Conservative enclosing box construction algorithm based on implicit geometric coding with Lipschitz linear constraints
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Bingyu ZHANG1, 2, 3, Liqun KUANG1, 2, 3, Fengguang XIONG1, 2, 3, Fanshu SUN1, 2, 3, Shichao JIAO1, 2, 3
Journal of Graphics | 2026, 47(1) : 152 - 161
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Journal of Graphics | 2026, 47(1): 152-161
Computer Graphics and Virtual Reality
Conservative enclosing box construction algorithm based on implicit geometric coding with Lipschitz linear constraints
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Bingyu ZHANG1, 2, 3, Liqun KUANG1, 2, 3, Fengguang XIONG1, 2, 3, Fanshu SUN1, 2, 3, Shichao JIAO1, 2, 3
Affiliations
  • 1 School of Computer Science and Technology, North University of China, Taiyuan Shanxi 030051, China
  • 2 Shanxi Provincial Key Laboratory of Machine Vision and Virtual Reality, Taiyuan Shanxi 030051, China
  • 3 Shanxi Province’s Vision Information Processing and Intelligent Robot Engineering Research Center, Taiyuan Shanxi 030051, China
Published: 2026-02-28 doi: 10.11996/JG.j.2095-302X.2026010152
Outline
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Currently the mainstream enveloping box methods are widely used in 3D scene rendering, ray tracing, and collision detection tasks; however, these methods suffer from the problems of low space utilization and insufficient fitting accuracy in fitting complex geometries, which are difficult to ensure strict conservatism and still have room for improvement in reducing false detection rates. To address these issues, a conservative bounding-box construction method combining implicit geometric coding and Lipschitz constraints was proposed. Implicit geometric coding mapped the input coordinates to a high-dimensional space via position coding, thus capturing local and global geometric information and improving bounding-box adaptability. A trainable Lipschitz-constrained linear layer was introduced to dynamically adjust Lipschitz constants control gradient changes, and Lipschitz regularization loss was combined with dynamically weighted cross-entropy loss to reduce the FP rate while optimizing the boundary fitting. The experimental results demonstrated that the method can achieve a false-negative rate of 0 on multiple 3D models and reduce the false-detection rate by up to 3.1% compared to the benchmark method, and improve the single-ray query method by 1.7 ms, providing a highly efficient and robust solution for high-precision conservative bounding box fitting.

conservative bounding box  /  Lipschitz constraint  /  implicit geometric encoding  /  ray tracing  /  collision detection
Bingyu ZHANG, Liqun KUANG, Fengguang XIONG, Fanshu SUN, Shichao JIAO. Conservative enclosing box construction algorithm based on implicit geometric coding with Lipschitz linear constraints[J]. Journal of Graphics, 2026 , 47 (1) : 152 -161 . DOI: 10.11996/JG.j.2095-302X.2026010152
  • National Natural Science Foundation of China(62272426)
  • Shanxi Provincial Science and Technology Major Special Programs “Listed and Commanded” Project(202201150401021)
  • Basic Research Program of Shanxi Province(202303021212189)
Year 2026 volume 47 Issue 1
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Article Info
doi: 10.11996/JG.j.2095-302X.2026010152
  • Receive Date:2025-05-08
  • Online Date:2026-05-19
  • Published:2026-02-28
Article Data
Affiliations
History
  • Received:2025-05-08
  • Accepted:2025-09-17
Funding
National Natural Science Foundation of China(62272426)
Shanxi Provincial Science and Technology Major Special Programs “Listed and Commanded” Project(202201150401021)
Basic Research Program of Shanxi Province(202303021212189)
Affiliations
    1 School of Computer Science and Technology, North University of China, Taiyuan Shanxi 030051, China
    2 Shanxi Provincial Key Laboratory of Machine Vision and Virtual Reality, Taiyuan Shanxi 030051, China
    3 Shanxi Province’s Vision Information Processing and Intelligent Robot Engineering Research Center, Taiyuan Shanxi 030051, China

Corresponding:

KUANG Liqun,E-mail:
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表12种不同金属材料的力学参数

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Number of
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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