Using semi-implicit representation of algebraic surfaces

AbstractIn this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real algebraic models of compact surfaces: these applications yield new insight into the geometry of the real locus, proving several surprising facts on this geometry. This geometry can be thought of as a half-way point between the biregular and birational geometries.

Download Full-text

On $$W_2$$ W 2 -lifting of Frobenius of algebraic surfaces

Collectanea mathematica ◽

10.1007/s13348-014-0130-y ◽

2015 ◽

Vol 67 (1) ◽

pp. 69-83 ◽

Cited By ~ 1

Author(s):

He Xin

Keyword(s):

Algebraic Surfaces

Download Full-text

Seshadri constants and very ample divisors on algebraic surfaces

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crll.2003.044 ◽

2003 ◽

Vol 2003 (559) ◽

Author(s):

Brian Harbourne

Keyword(s):

Algebraic Surfaces ◽

Seshadri Constants ◽

Ample Divisors

Download Full-text

Method for intersecting algebraic surfaces with rational polynomial patches

Computer-Aided Design ◽

10.1016/0010-4485(90)90011-z ◽

1990 ◽

Vol 22 (10) ◽

pp. 645-654 ◽

Cited By ~ 22

Author(s):

G.A. Kriezis ◽

P.V. Prakash ◽

N.M. Patrikalakis

Keyword(s):

Algebraic Surfaces ◽

Rational Polynomial

Download Full-text

Point set registration for assembly feature pose estimation using simulated annealing nested Gauss-Newton optimization

Assembly Automation ◽

10.1108/aa-09-2020-0130 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Kunyong Chen ◽

Yong Zhao ◽

Jiaxiang Wang ◽

Hongwen Xing ◽

Zhengjian Dong

Keyword(s):

Simulated Annealing ◽

Pose Estimation ◽

Distance Metric ◽

Implicit Representation ◽

Registration Method ◽

Content Type ◽

Point Set Registration ◽

Searching Strategy ◽

Global Robustness ◽

Point Set

Purpose This paper aims to propose a fast and robust 3D point set registration method for pose estimation of assembly features with few distinctive local features in the manufacturing process. Design/methodology/approach The distance between the two 3D objects is analytically approximated by the implicit representation of the target model. Specifically, the implicit B-spline surface is adopted as an interface to derive the distance metric. With the distance metric, the point set registration problem is formulated into an unconstrained nonlinear least-squares optimization problem. Simulated annealing nested Gauss-Newton method is designed to solve the non-convex problem. This integration of gradient-based optimization and heuristic searching strategy guarantees both global robustness and sufficient efficiency. Findings The proposed method improves the registration efficiency while maintaining high accuracy compared with several commonly used approaches. Convergence can be guaranteed even with critical initial poses or in partial overlapping conditions. The multiple flanges pose estimation experiment validates the effectiveness of the proposed method in real-world applications. Originality/value The proposed registration method is much more efficient because no feature estimation or point-wise correspondences update are performed. At each iteration of the Gauss–Newton optimization, the poses are updated in a singularity-free format without taking the derivatives of a bunch of scalar trigonometric functions. The advantage of the simulated annealing searching strategy is combined to improve global robustness. The implementation is relatively straightforward, which can be easily integrated to realize automatic pose estimation to guide the assembly process.

Download Full-text