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23 June 1993 Single valuedness, parameterization, and approximating 3D surfaces using B-splines
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Abstract
In this paper we provide a very simple, yet efficient, scheme for modeling volume boundaries using patches which are B-spline surfaces. Given a noisy three dimensional cloud of points, we use constrained minimization using B-splines as basis functions to smooth the data and create a three dimensional model of the surface of the object. Such a method is useful for representing complete free-form surface models of objects. Instead of fitting one B-spline surface to the complete data set, the data is segmented into smaller sub-clouds that are single valued in a local frame of reference. This work builds upon our earlier work on surface fitting in a rectangular domain, and extends it to arbitrary domains. We divide the problem into three stages: (1) segmentation of the sensor data from 3-D world coordinates into data patches, (2) approximation of the data in this space to create B-spline surface patches, and (3) reconversion into the world coordinate system. We also describe a complete system, Surfacer, built around these ideas which includes a comprehensive set of tools to manipulate point sets and surfaces in a CAD framework.
© (1993) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Saravajit Sahay Sinha and Pradeep Seneviratne "Single valuedness, parameterization, and approximating 3D surfaces using B-splines", Proc. SPIE 2031, Geometric Methods in Computer Vision II, (23 June 1993); https://doi.org/10.1117/12.146625
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