NDLI: Exact and approximate representations of trimmed surfaces with NURBS and Bézier surfaces

Content Provider	IEEE Xplore Digital Library
Author	Xin Li Falai Chen
Copyright Year	2009
Description	Author affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, China, 230026 (Xin Li; Falai Chen)
Abstract	A trimmed surface is usually represented as a parametric surface with a set of trimming curves. However, many CAD processes and algorithms cannot be applied to trimmed surfaces directly because of the complexity in manipulating trimmed surfaces. Moreover, trimmed surfaces will create gaps between different trimmed surfaces. Thus it is desirable to represent a trimmed surface by a group of regular surfaces, such as NURBS or Bézier surfaces. The present paper provides an algorithm to split a trimmed NURBS surface into several NURBS or Bézier surfaces. The surface patches which domains are far away from the trimming curves coincide with the given trimmed NURBS surface and the patches which domains are close to the trimming curves are represented with high degree Bézier surface patches (exact) or bi-cubic B-spline surfaces (approximate). The algorithm is simple, efficient and easy to implement. Compared with previous approaches ([1] and [3]), the new algorithm doesn't change the parameterization of most regions and is easy to maintain the continuity. Since our algorithm can keep most of the patches unchanged, most of the surface patches will be $C^{2}$ continuous. Furthermore, the surface patches can be locally merged to be $G^{1}$ in the neighbor of trimming curves which is very difficult for those in [1] and [3].
Starting Page	286
Ending Page	291
File Size	306960
Page Count	6
File Format	PDF
ISBN	9781424436996
DOI	10.1109/CADCG.2009.5246888
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-08-19
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	CADCAM Solid modeling Computer aided manufacturing Mathematics Surface topography Application software Spline NURBS Surface reconstruction topologically inconsistent Computer graphics intersection Bézier surface Surface cracks Trimmed surface
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
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