Yang Liu (刘洋)

Principal Researcher

Contact

Internet Graphics Group
Microsoft Research Asia
13130, Microsoft Tower 2,
No. 5 Dan Ling Street,
Haidian District
Beijing, P.R. China, 100080


📧: Email me

[Google Scholar]

Education and Work Experience

Research Interest

  • Geometric Computation and Optimization
  • Learning-based Geometry Processing and Synthesis
  • Mesh processing and generation

Professional Activities

Code

  • HLBFGS: A hybrid L-BFGS optimization framework which unifies L-BFGS method, Preconditioned L-BFGS method, Preconditioned Conjugate Gradient method. (Source code in C++).
  • QCVT: Fast 3D Centroidal Voronoi Tessellation for a convex domain. ( Windows executable files only)
  • 3D Voronoi Tessellation and Restricted Voronoi Diagram. Source code is available in the supplemental material of LpCVT paper.

Gallery and Models

Intern students

  • Xin-Yang Zheng (PHD candidate from Tsinghua Univ., 2021.7--now)
  • Yu-Qi Yang (PHD candidate from TSinghua Univ., 2017.7--2018.5, 2019.2--2024.1)
  • Jian-Yu Xiong (Master candidate from Tsinghua Univ., 2022.12--2023.5)
  • Siming Yan (PHD candidate from UT Austin, 2022.5--2022.11)
  • Dr. Hao-Xiang Guo (PhD candidate, from Tsinghua Univ., 2018.1--2022.9), now work at miHoYo
  • Jie Pan (Master candidate from USTC Univ., 2021.4--2022.8)
  • Dr. Chun-Yu Sun (PhD Candidate, from Tsinghua Univ., 2016.11--2022.5), now work at Momenta
  • Dr. Shi-Lin Liu (PhD Candidate, from USTC, 2014.7--2015.5, 2016.7--2021.6), now work at Momenta
  • Xin Li (Master Candidate, from PKU, 2020.9-2021.3)
  • FengYuSheng Wang (Undergraduate, from USTC, 2019.2-2019.6, 2020.5--2020.9)
  • Qian-Fang Zou (Master Candidate, from USTC, 2018.9--2020.4)
  • Xiaohan Liu (Master Candidate, from UCAS, 2018.9--2019.1), now PHD student at Univ. of Tokyo
  • Dr. Ran Zhang (PHD Candidate, from IST Austria, 2018.8--2018.11), now work at Tencent
  • Ke Qu (Master Candidate, from Zhejiang Univ., 2018.6-2018.9), now work at Microsoft
  • Dr. Chang-Jian Li (PhD Candidate, from HKU, 2016.2--2016.7, 2016.11--2018.1, 2018.5-2018.8), now assistant professor at Univ. of Edinburgh.
  • Dr. Peng-Shuai Wang (PhD candidate, from Tsinghua, 2014.2--2018.7), now assistant professor at PKU.
  • Dr. Xiao-Ming Fu (PhD Candidate, from USTC, 2012.9--2016.6), now associate professor at USTC.
  • Dr. Chong-Yang Bai (Undergraduate, from USTC, 2015.9--2016.6), now work at Microsoft.
  • Dr. Caigui Jiang (PhD Candidate, from KAUST, 2015.6--2015.8), now Professor at Xi'an Jiaotong University.
  • Dr. Shuo Jin (PhD Candidate, from CUHK, 2014.8--2015.1)
  • Dr. Shuang-Ming Chai (Undergraduate, from USTC, 2013.7--2014.5).
  • Dr. Mario Deuss (PhD Candidate, from EPFL, 2013.6--2013.9)
  • Dr. Pan Hao (PhD Candidate, from HKU, 2012.9--2013.1), now researcher at MSRA.
  • Dr. Yufei Li (PhD Candidate, from HKU, 2011.9--2012.2), now at Citadel GQS.
  • Dr. Jun Wang (PhD Candidate, from USTC, 2010.7--2011.1), now work at BaiDu.

Publications and Manuscripts

2023
Jiepeng Wang, Hao Pan, Yang Liu, Xin Tong, Taku Komura and Wenping Wang: StructRe: Rewriting for Structured Shape Modeling, preprint, 2023.
Mutian Xu, Xingyilang Yin, Lingteng Qiu, Yang Liu, Xin Tong, Xiaoguang Han: SAMPro3D: Locating SAM Prompts in 3D for Zero-Shot Scene Segmentation, preprint, 2023.
Siming Yan, Yu-Qi Yang, Yu-Xiao Guo, Hao Pan, Peng-Shuai Wang, Xin Tong, Yang Liu, Qixing Huang: 3D Feature Prediction for Masked-AutoEncoder-Based Point Cloud Pretraining, accept to International Conference on Learning Representations (ICLR) 2024.
Yu-Qi Yang, Yu-Xiao Guo, Jian-Yu Xiong, Yang Liu, Hao Pan, Peng-Shuai Wang, Xin Tong, Baining Guo: Swin3D: A Pretrained Transformer Backbone for 3D Indoor Scene Understanding, accepted to Computational Visual Media, 2023. Project Page
Xin-Yang Zheng, Hao Pan, Peng-Shuai Wang, Xin Tong, Yang Liu, Heung-Yeung Shum: Locally Attentional SDF Diffusion for Controllable 3D Shape Generation, ACM Transactions on Graphics(SIGGRAPH), Journal version, 2023. Project Page

2022
Hao-Xiang Guo, Yang Liu, Hao Pan, Baining Guo: Implicit Conversion of Manifold B-Rep Solids by Neural Halfspace Representation, ACM Transactions on Graphics(SIGGRAPH ASIA), 2022. [Project page] [Code] [Surface Extraction Code]
Chun-Yu Sun, Xin Tong, Yang Liu: Semantic Segmentation-assisted Instance Feature Fusion for Multilevel 3D part Instance Segmentation, Computational Visual Media, 2022. [Project page]
Xin-Yang Zheng, Yang Liu, Peng-Shuai Wang, Xin Tong: SDF-StyleGAN: Implicit SDF-Based StyleGAN for 3D Shape Generation, Computer Graphics Forum (SGP), 2022. [Supplemental] [Project page]
Peng-Shuai Wang, Xin Tong, Yang Liu: Dual Octree Graph Networks for Learning Adaptive Volumetric Shape Representations, ACM Transactions on Graphics(SIGGRAPH), 2022. [Project page]
Hao-Xiang Guo, Shi-Lin Liu, Hao Pan, Yang Liu, Xin Tong, Baining Guo: ComplexGen: CAD Reconstruction by B-Rep Chain Complex Generation, ACM Transactions on Graphics(SIGGRAPH), 2022. [Project page]
Chun-Yu Sun, Yu-Qi Yang, Hao-Xiang Guo, Peng-Shuai Wang, Xin Tong, Yang Liu, Heung-Yeung Shum: Semi-Supervised 3D Shape Segmentation with Multilevel Consistency and Part Substitution, Computational Visual Media. [Project page]
Zhi Deng, Yang Liu, Hao Pan, Wassim Jabi, Juyong Zhang, Bailin Deng: Sketch2PQ: Freeform Planar Quadrilateral Mesh Design via a Single Sketch, IEEE Transactions on Visualization & Computer Graphics. [video].

2021
Long Ma, Sidan Yao, Jianming Zheng, Yang Liu, Yuanfeng Zhou, Shiqing Xin, Ying He: Constructing Self-Supporting Surfaces with Planar Quadrilateral Elements, Computational Visual Media, 2022.
Yu-Qi Yang, Peng-Shuai Wang, Yang Liu: Interpolation-Aware Padding for 3D Sparse Convolutional Neural Networks, ICCV 2021. [Project page]
Peng-Shuai Wang, Yang Liu, Yu-Qi Yang, Xin Tong: Spline Positional Encoding for Learning 3D Implicit Signed Distance Fields, IJCAI 2021. [Project page]
Shi-Lin Liu, Hao-Xiang Guo, Hao Pan, Peng-Shuai Wang, Xin Tong, Yang Liu: Deep Implicit Moving Least-Squares Functions for 3D Reconstruction, CVPR 2021. [Code]

2020
Peng-Shuai Wang, Yu-Qi Yang, Qian-Fang Zou, Zhirong Wu, Yang Liu, Xin Tong: Unsupervised 3D Learning for Shape Analysis via Multiresolution Instance Discrimination, AAAI 2021. [Project page]
Peng-Shuai Wang, Yang Liu, Xin Tong: Deep Octree-based CNNs with Output-Guided Skip Connections for 3D Shape and Scene Completion, CVPR 2020 Workshop. [Code]
Qian-Fang Zou, Ligang Liu, Yang Liu: Instance-level 3D shape retrieval from a single image by hybrid-representation-assisted joint embedding, The Visual Computer, 2020.
Hao-Xiang Guo, Xiaohan Liu, Dong-Ming Yan, Yang Liu: Cut-enhanced PolyCube-Maps for Feature-aware All-Hex Meshing, ACM Transactions on Graphics(SIGGRAPH), 2020. [supplemental], [Project page].
Yu-Qi Yang, Shi-Lin Liu, Hao Pan, Yang Liu, Xin Tong: PFCNN: Convolutional Neural Networks on 3D Surfaces Using Parallel Frames, IEEE CVPR, 2020. [Project page].
Changjian Chen, Jun Yuan, Yafeng Lu, Yang Liu, Hang Su, Songtao Yuan, Shixia Liu: OoDAnalyzer: Interactive Analysis of Out-of-Distribution Samples, IEEE TVCG, 2020. [Videos]
Shi-Lin Liu, Yang Liu, Lan-Fang Dong, Xin Tong: RAS: A Data-driven Rigidity-Aware Skinning Model for 3D Facial Animation, Computer Graphics Forum, 39(1), 581--594, 2020. [Videos]

2019
Lei Chu, Hao Pan, Yang Liu, Wenping Wang: Repairing Man-Made Meshes via Visual Driven Global Optimization with Minimum Intrusion, ACM Transactions on Graphics(SIGGRAPH Asia), 38(6), Article 158, 2019. [Project page].
Chun-yu Sun, Qian-fang Zou, Xin Tong, Yang Liu: Learning Adaptive Hierarchical Cuboid Abstractions of 3D Shape Collections, ACM Transactions on Graphics(SIGGRAPH Asia) , 38(6), Article 241, 2019. [Project page].
Lei Chu, Pengbo Bo, Yang Liu, Wenping Wang: Surface Fairing towards Regular Principal Curvature Line Networks, Computer Graphics Forum (Pacific Graphics), 2019.
Jie Zhu, Yunfeng Zhang, Jie Guo, Huikun Liu, Mingming Liu, Yang Liu, Yanwen Guo: Label Transfer between Images and 3D Shapes via Local Correspondence Encoding, Geometric Modeling and Processing - GMP 2019, Computer Aided Geometric Design, 71, 255-266.

2018
Hao Pan, Shi-Lin Liu, Yang Liu, Xin Tong: Convolutional Neural Networks on 3D Surfaces Using Parallel Frames, arXiv:1808.04952, 2018.
Changjian Li, Hao Pan, Yang Liu, Xin Tong, Alla Sheffer, Wenping Wang: Robust Flow-Guided Neural Prediction for Sketch-Based Freeform Surface Modeling, ACM Transactions on Graphics(SIGGRAPH Asia) , 37(6), 2018. [Project page]
Peng-Shuai Wang, Chun-Yu Sun, Yang Liu, Xin Tong: Adaptive O-CNN: A Patch-based Deep Representation of 3D Shapes, ACM Transactions on Graphics(SIGGRAPH Asia), 37(6), 2018. [Project page], Open source code.

2017
Li-Ke Ma, Yizhong Zhang, Yang Liu, Kun Zhou, Xin Tong: Computational Design and Fabrication of Soft Pneumatic Objects with Desired Deformations, ACM Transactions on Graphics(SIGGRAPH Asia), 36(6), 2017. [Video], [Project page].
Peng-Shuai Wang, Yang Liu, Yu-Xiao Guo, Chun-Yu Sun, Xin Tong: O-CNN: Octree-based Convolutional Neural Networks for 3D Shape Analysis, ACM Transactions on Graphics(SIGGRAPH), 36(4), 2017. [Project page], Open source code.
Changjian Li, Hao Pan, Yang Liu, Xin Tong, Alla Sheffer, Wenping Wang: BendSketch: Modeling Freeform Surfaces Through 2D Sketching, ACM Transactions on Graphics(SIGGRAPH) , 36(4), 2017. [Project page]
Shuo Jin, Chengkai Dai, Yang Liu, Charlie C.L. Wang: Motion Imitation Based on Sparsely Sampled Correspondence, Journal of Computing and Information Science in Engineering, 2017. [Video]
Saifeng Ni, Zichun Zhong, Yang Liu, Wenping Wang, Zhonggui Chen and Xiaohu Guo: Sliver-Suppressing Tetrahedral Mesh Optimization with Gradient-Based Shape Matching Energy, Geometric Modeling and Processing - GMP 2017, Computer Aided Geometric Design, 52-53, 247-261. [DOI]

2016
Yiqi Cai, Xiaohu Guo, Yang Liu, Wenping Wang, Weihua Mao, and Zichun Zhong : Surface Approximation via Asymptotic Optimal Geometric Partition, IEEE Transactions on Visualization & Computer Graphics , 23(12), 2613-2626, 2016. supplement material, video. [DOI]
Xiao-Ming Fu, Chong-Yang Bai and Yang Liu: Efficient Volumetric PolyCube-Map Construction, Computer Graphics Forum (Pacific Graphics) 35(7), 2016. Project page, supplement material. [DOI]
Xiao-Ming Fu and Yang Liu: Computing Inversion-Free Mappings by Simplex Assembly, ACM Transactions on Graphics(SIGGRAPH Asia), 35(6), 2016. Project page, supplement material, code. [DOI]
Peng-Shuai Wang, Yang Liu and Xin Tong: Mesh Denoising via Cascaded Normal Regression, ACM Transactions on Graphics(SIGGRAPH Asia) , 35(6), 2016. Project page(code and data). [DOI]
Pengbo Bo, Yang Liu, Changhe Tu, Caiming Zhang and Wenping Wang: Surface Fitting with Cyclide Splines, Geometric Modeling and Processing - GMP 2016, Computer Aided Geometric Design, 43(1), 2--15. [DOI]

2015
Peng-Shuai Wang, Xiao-Ming Fu, Yang Liu, Xin Tong, Shi-Lin Liu and Baining Guo: Rolling Guidance Normal Filter for Geometric Processing, ACM Transactions on Graphics(SIGGRAPH Asia), 34(6), 2015. Data, Program, slides. [DOI]
Xiao-Ming Fu, Yang Liu and Baining Guo: Computing Locally Injective Mappings by Advanced MIPS, ACM Transactions on Graphics(SIGGRAPH) 34(4), 2015. Data. [DOI]
Pan Hao, Yang Liu, Alla Sheffer, Nicholas Vining, Chang-Jian Li and Wenping Wang: Flow Aligned Surfacing of Curve Networks, ACM Transactions on Graphics(SIGGRAPH) 34(4), 2015. data, Project page. [DOI]
Yufei Li, Yang Liu and Wenping Wang: Planar Hexagonal Meshing for Architecture, IEEE Transactions on Visualization & Computer Graphics , 95-106, 2015. IEEE TVCG spotlight article for Jan. 2015. Appendix. [DOI]

before 2015
Xiao-Ming Fu, Yang Liu, John Snyder and Baining Guo: Anisotropic Simplicial Meshing Using Local Convex Functions, ACM Transactions on Graphics(SIGGRAPH Asia) 33(6), 2014. [DOI], Anisotropic Mesh results, slides.
Mario Deuss, Daniele Panozzo, Emily Whiting, Yang Liu, Philippe Block, Olga Sorkine-Hornung and Mark Pauly: Assembling Self-Supporting Structures, ACM Transactions on Graphics(SIGGRAPH Asia) 33(6), 2014. [DOI], Video and data. Project page.
Lei Liu, Yongjie Zhang, Yang Liu and Wenping Wang: Feature-Preserving T-mesh Construction Using Skeleton-based Polycubes, Computer Aided Design (SPM 2014), 162-172. [DOI]
Shixia Liu, Yingcai Wu, Enxun Wei, Mengchen Liu and Yang Liu : StoryFlow: Tracking the Evolution of Stories, IEEE InfoVis 2013 , IEEE Transactions on Visualization & Computer Graphics 19(12), 2436-2445, 2013. Project page [DOI]
Yupeng Zhang, Teng Han, Zhimin Ren, Nobuyuki Umetani, Xin Tong, Yang Liu, Takaaki Shiratori and Xiang Cao: BodyAvatar: Creating Freeform 3D Avatars using First-Person Body Gestures, UIST 2013, 387-396. Project page(Demo). [DOI]
Yang Liu, Pan Hao, John Snyder, Wenping Wang and Baining Guo: Computing Self-Supporting Surfaces by Regular Triangulation, ACM Transactions on Graphics(SIGGRAPH) 32(4), 2013. Supplemental material, slides. [DOI]
Yufei Li, Yang Liu, Weiwei Xu, Wenping Wang and Baining Guo: All-Hex Meshing using Singularity-Restricted Field, ACM Transactions on Graphics(SIGGRAPH Asia) 31(6), 177:1-177:11, 2012. Supplemental material (videos and data), slides. [DOI]
Lifeng Zhu, Weiwei Xu, John Snyder, Yang Liu, Guoping Wang and Baining Guo: Motion-Guided Mechanical Toy Modeling, ACM Transactions on Graphics(SIGGRAPH Asia) 31(6), 127:1-127:10, 2012. Supplemental material. [DOI]
Dong-Ming Yan, Wenping Wang, Yang Liu and Zhouwang Yang: Variational Mesh Segmentation via Quadric Surface Fitting, Computer-Aided Design , 44(11), 1072-1082, 2012. [DOI]
Hao Pan, Yi-King Choi, Yang Liu, Wenchao Hu, Qiang Du, Konrad Polthier, Robust Modeling of Constant Mean Curvature Surfaces, ACM Transactions on Graphics(SIGGRAPH) 31(4), 85:1-85:11, 2012. [Supplemental material, slides. [DOI]
Wenni Zheng, Pengbo Bo, Yang Liu, Wenping Wang: Fast B-spline Curve Fitting by L-BFGS, Geometric Modeling and Processing - GMP 2012, Computer Aided Geometric Design, 29(7), 448-462, 2012. [DOI]
Feng Sun, Yi-King Choi, Wenping Wang, Dong-Ming Yan, Yang Liu, Bruno Lévy: Obtuse Triangle Suppression in Anisotropic Meshes, Computer Aided Geometric Design , 28(9), 537-548, 2011. [DOI]
Yang Liu, Weiwei Xu, Jun Wang, Lifeng Zhu, Baining Guo, Falai Chen, Guoping Wang : General Planar Quadrilateral Mesh Design Using Conjugate Direction Field, ACM Transactions on Graphics(SIGGRAPH Asia) , 30(6), 140:1-140:10, 2011. [Errata: a term in Eqn.4 is missing in the published version, please check the corrected version.][DOI]Supplemental material, slides.
Dong-Ming Yan, Wenping Wang, Bruno Lévy and Yang Liu: Efficient Computation of Clipped Voronoi Diagram and Applications, Computer Aided Design. This is a journal version of our GMP2010 paper. [DOI]
Bruno Lévy and Yang Liu: Lp Centroidal Voronoi Tessellation and its Applications, ACM Transactions on Graphics (SIGGRAPH), 29(4), 119:1-119:11, 2010. [DOI][Supplemental material: data, sourcecode, videos and supplemental examples], slides
Dong-Ming Yan, Wenping Wang, Bruno Lévy and Yang Liu: Efficient Computation of 3D Clipped Voronoi Diagram, Geometric Modeling and Processing - GMP 2010, 269-282. [DOI]
Guodong Rong, Yang Liu, Wenping Wang, Xiaotian Yin, Xianfeng Gu and Xiaohu Guo: GPU-Assisted Computation of Centroidal Voronoi Tessellation, IEEE Transactions on Visualization & Computer Graphics, 17(3), 345-356, 2011. [DOI][video and code]
Dong-Ming Yan, Bruno Lévy, Yang Liu, Feng Sun and Wenping Wang: Isotropic Remeshing with Fast and Exact Computation of Restricted Voronoi Diagram, Computer Graphics Forum (Symposium on Geometry Processing 2009), 28(5), 1445-1454. [errata] [DOI][videos: 3_holes fandisk joint vhull topo_control ]
Yang Liu, Wenping Wang, Bruno Lévy, Feng Sun, Dong-Ming Yan, Lin Lu and Chenglei Yang: On Centroidal Voronoi Tessellation Energy Smoothness and Fast Computation, ACM Transactions on Graphics, 28(4), 1-17. [DOI] [software]
Yang Liu and Wenping Wang: On Vertex Offsets of Polyhedral Surfaces, Advances in Architectural Geometry , 61-64, 2008.
Wenping Wang, Yang Liu, Dong-Ming Yan, Bin Chan, Ruotian Ling and Feng Sun, Hexagonal Meshes with Planar Faces, Technical Report, Dept. of CS, HKU, 2008.
Wenping Wang and Yang Liu: A Note on Planar Hexagonal Meshes, In I.Z. Emiris, F. Sottile and T. Theobald, editors, IMA Volume 151: Nonlinear Computational Geometry , 221-233, Springer-Verlag, 2009. [DOI][relevant talk: Slides in Workshop on Polyhedral Surfaces and Industrial Applications 2007]
Yang Liu and Wenping Wang: A Revisit to Least Squares Orthogonal Distance Fitting of Parametric Curves and Surfaces, Geometric Modeling and Processing - GMP 2008, 384-397, Springer. [DOI]
Wenping Wang, Johannes Wallner and Yang Liu : An Angle Criterion for Conical Mesh Vertices, Journal for Geometry and Graphics 11(2), 199-208, 2007.
Falai Chen, Wenping Wang and Yang Liu: Computing Singular Points of Plane Rational Curves, Journal of Symbolic Computation, 43(2), 92-117, 2008. [DOI]
Wenping Wang, Bert Jüttler, Dayue Zheng and Yang Liu: Computation of Rotation Minimizing Frame, ACM Transactions on Graphics, 27(1), Article No. 2, 2008. [DOI]
Helmut Pottmann and Yang Liu: Discrete Surfaces in Isotropic Geometry, In R. Martin, M. Sabin and J. Winkler, editors, Mathematics of Surfaces XII, volume 4647 of LNCS, 431-363. Springer, 2007. [DOI] [Gallery and Models]
Helmut Pottmann, Yang Liu, Johannes Wallner, Alexander Bobenko and Wenping Wang: Geometry of Multi-layer Freeform Structures for Architecture, ACM Transactions on Graphics(SIGGRAPH) 26(3), Article No. 65, 2007. [DOI]
Kin-Shing D. Cheng, Wenping Wang, Hong Qin, Kwan-Yee K. Wong, Huaiping Yang and Yang Liu: Design and Analysis of Optimization Methods for Subdivision Surface Fitting, IEEE Transactions on Visualization and Computer Graphics, 13(5), 878-890, 2007. [DOI]
Dong-Ming Yan, Yang Liu and Wenping Wang: Quadric Surface Extraction by Variational Shape Approximation, Geometric Modeling and Processing - GMP 2006: 4th International Conference, 73-86, 2006. [Errata][ DOI]
Yang Liu, Helmut Pottmann, Johannes Wallner, Yong-Liang Yang and Wenping Wang: Geometric Modeling with Conical Meshes and Developable Surfaces, ACM Transactions on Graphics(SIGGRAPH), 25(3), 681-689, 2006. [DOI]
Yang Liu, Helmut Pottmann and Wenping Wang: Constrained 3D Shape Reconstruction Using a Combination of Surface Fitting and Registration, Computer Aided Design, 38(6), 572-583, 2006. [DOI]
Yi-King Choi, Wenping Wang, Yang Liu and Myung-Soo Kim: Continuous Collision Detection for Two Moving Elliptic Disks, IEEE Transactions on Robotics, 22(2), 213-224, 2006. [DOI]
Wenping Wang, Helmut Pottmann and Yang Liu: Fitting B-spline Curves to Point Clouds by Curvature-Based Squared Distance Minimization, ACM Transactions on Graphics 25(2), 214-238, 2006. [DOI]
Yang Liu, Huaiping Yang and Wenping Wang: Reconstructing B-spline Curves from Point Clouds A Tangential Flow Approach Using Least Squares Minimization, International Conference on Shape Modeling and Applications 2005, 4-12. [DOI]

Falai Chen, David Cox and Yang Liu: The μ-basis and Implicitization of a Rational Parametric Surface, Journal of Symbolic Computation , 39(6)689-706, 2005. [DOI]
Kin-Shing D. Cheng, Wenping Wang, Hong Qin, Kwan-Yee K. Wong, Huaiping Yang and Yang Liu: Fitting Subdivision Surfaces to Unorganized Point Data Using SDM, Proceedings. 12th Pacific Conference on Computer Graphics and Applications , 16-24, 2004. [DOI]
Yang Liu and Falai Chen: Algebraic Conditions for Classifying the Positional Relationships between Two Conics and Their Applications, J. Comput. Sci. Tech. 19(4), 665-673, 2004. [DOI]

Liyong Shen and Yang Liu: An Algebraic Condition for the Positional Relationship of an Ellipse and a Parabola(Hyperbola), Journal of System Simulation (In Chinese), 1208－1211, 2002.

Yang Liu and Liyong Shen: An Algebraic Condition for Classifying the Positional Relationship of Two Planar Ellipses, Journal of Computer Aided Design and Computer Graphics (In Chinese), 555－560, 2003.

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Updated on Dec. 2023