Budget sampling of parametric surface patches

Author(s):  
Jatin Chhugani ◽  
Subodh Kumar
Author(s):  
Yu Wang

Abstract In this paper, we present a new method to calculate intersection curve of offset surfaces of two parametric surface patches. This method is based on the concept of normal projection and the intersection problem is formulated with a set of tensorial differential equations. The intersection is represented in the parametric spaces of the base surfaces and no offset surface approximation is needed. Numerical examples are presented for non-uniform rational b-spline (NURBS) surfaces to illustrate the effectiveness and efficiency of the proposed approach.


Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1304
Author(s):  
Wenchao Wu ◽  
Yongguang Hu ◽  
Yongzong Lu

Plant leaf 3D architecture changes during growth and shows sensitive response to environmental stresses. In recent years, acquisition and segmentation methods of leaf point cloud developed rapidly, but 3D modelling leaf point clouds has not gained much attention. In this study, a parametric surface modelling method was proposed for accurately fitting tea leaf point cloud. Firstly, principal component analysis was utilized to adjust posture and position of the point cloud. Then, the point cloud was sliced into multiple sections, and some sections were selected to generate a point set to be fitted (PSF). Finally, the PSF was fitted into non-uniform rational B-spline (NURBS) surface. Two methods were developed to generate the ordered PSF and the unordered PSF, respectively. The PSF was firstly fitted as B-spline surface and then was transformed to NURBS form by minimizing fitting error, which was solved by particle swarm optimization (PSO). The fitting error was specified as weighted sum of the root-mean-square error (RMSE) and the maximum value (MV) of Euclidean distances between fitted surface and a subset of the point cloud. The results showed that the proposed modelling method could be used even if the point cloud is largely simplified (RMSE < 1 mm, MV < 2 mm, without performing PSO). Future studies will model wider range of leaves as well as incomplete point cloud.


1997 ◽  
Vol 119 (2) ◽  
pp. 275-283 ◽  
Author(s):  
Takashi Maekawa ◽  
Wonjoon Cho ◽  
Nicholas M. Patrikalakis

Self-intersection of offsets of regular Be´zier surface patches due to local differential geometry and global distance function properties is investigated. The problem of computing starting points for tracing self-intersection curves of offsets is formulated in terms of a system of nonlinear polynomial equations and solved robustly by the interval projected polyhedron algorithm. Trivial solutions are excluded by evaluating the normal bounding pyramids of the surface subpatches mapped from the parameter boxes computed by the polynomial solver with a coarse tolerance. A technique to detect and trace self-intersection curve loops in the parameter domain is also discussed. The method has been successfully tested in tracing complex self-intersection curves of offsets of Be´zier surface patches. Examples illustrate the principal features and robustness characteristics of the method.


2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Esra Betul Koc Ozturk

With the help of the Frenet frame of a given pseudo null curve, a family of parametric surfaces is expressed as a linear combination of this frame. The necessary and sufficient conditions are examined for that curve to be an isoparametric and asymptotic on the parametric surface. It is shown that there is not any cylindrical and developable ruled surface as a parametric surface. Also, some interesting examples are illustrated about these surfaces.


2021 ◽  
pp. 103090
Author(s):  
Guillaume Coiffier ◽  
Justine Basselin ◽  
Nicolas Ray ◽  
Dmitry Sokolov

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