Geometric Constraint Solving and Engineering Geometry

Geometric Constraint Solving

• X.S. Gao, Q. Lin, and G. Zhang, A C-tree Decomposition Algorithm for 2D and 3D Geometric Constraint Solving, Computer Aided Design, 38(1), 1-13, 2006.
• X.S. Gao and S. C. Chou, Solving Geometric Constraint Systems, I. A Global Propagation Approach, Computer Aided Design, Vol. 30, No. 1, 47-54, 1998.
• X.S. Gao and S. C. Chou, Solving Geometric Constraint Systems, II. A Symbolic Computational Approach, Computer Aided Design, Vol. 30, No.2, 115-122, 1998.
• X.S. Gao, K. Jiang, and C.-C. Zhu, Geometric Constraint Solving with Conics and Linkages, Computer Aided Design,, 34(6), 421-433, 2002.
• J. Ge, S.C. Chou and X.S. Gao, Geometric Constraint Satisfaction Using Optimization Methods, Computer Aided Design, 31(14), 867-879, 2000.
• G.F. Zhang and X.S. Gao, Well-constrained Completion and Decomposition for Under-constrained Geometric Constraint Problems, 16, International Journal of Computational Geometry & Applications, 461-478, 2006.
• G.F. Zhang and X.S. Gao, Spatial Geometric Constraint Solving Based on k-connected Graph Decomposition, 973-977, Proc. of The 21st Annual ACM Symposium on Applied Computing, Dijon, France, ACM Press, 2006.
• X.S. Gao, C.M. Hoffmann and W. Yang, Solving spatial basic geometric constraint configurations with locus intersection, Computer Aided Design, 111-122, 36(2), 2004.
• X.S. Gao and G. Zhang, Geometric Constraint Solving via C-tree Decomposition, (Appendix) ACM Solid Modelling 2003, 45-55, Seattle, USA, ACM Press, New York, 2003.
• X.S. Gao, C. Zhu, S.-C. Chou, and J.-X. Ge, Automated Generation of Kempe Linkages for Algebraic Curves and Surfaces, Mechanism and Machine Theory, 36(9), 1019-1033, 2002.
• X.S. Gao, C.M. Hoffmann and W. Yang, Solving Basic Gometric Constraint Configurations with Locus Intersection, Proc. ACM Solid Modelling 2002, 95-104, ACM Press, New York, 2002.
• X.S. Gao, L. Huang, and K, Jiang, Geometric Constraint Solving with Geometric Transformation, Science in China (Series F), 44(1), 50-59, 2001.
• X.S. Gao, L. Huang, and K, Jiang, A Hybrid Method for Solving Geometric Constraint Problems in Automated Deduction in Geometry, J. Richter-Gebert and D. Wang (eds), 16-25, LNAI No. 2061, Springer-Verlag, Berlin, 2001.

Direct Kinematics of Stewart Platform

• X.S. Gao, D. Lei, Q. Liao, and G. Zhang, Generalized Stewart Platforms and their Direct Kinematics, IEEE Trans. Robotics, vol 21, 141-151, 2005.
• G.F. Zhang and X.S. Gao, Planar Generalized Stewart-Gough Platforms and their Direct Kinematics, ADG 2004, LNAI 3763, 198-211, Springer-Verlag, Berlin, 2006,.

Perspective-n-point Problem

• X.S. Gao, X. Hou, J. Tang and H. Chen, Complete Solution Classification for the Perspective-Three-Point Problem, IEEE Tran. on PAMI, 930-943, 25(8), 2003..
  Here is the appendix to this paper
• X.S. Gao and J. Tang, On the Probability of the Number of Solutions for the P4P Problem, Journal of Mathematical Imaging and Vision, 25, 79-86, 2006.