Generative modeling: a symbolic system for geometric modeling
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Curve and surface fitting with splines
Curve and surface fitting with splines
Dynamic NURBS with geometric constraints for interactive sculpting
ACM Transactions on Graphics (TOG) - Special issue on interactive sculpting
The NURBS book (2nd ed.)
Creating generative models from range images
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Computational Geometry in C
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
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In this paper we present an efficient method for smooth surface generation from unorganised points using NURBS. This is a preferred alternative to using triangular meshes, which are expensive to store, transmit, render and are difficult to manipulate. The proposed method does not require triangulation prior to surface fitting because it generates NURBS directly. Two fundamental problems must be addressed to accomplish this task: parameterisation of measured data and overcoming ill-conditioning of the least squares surface fitting. We propose to solve the parameterisation problem by employing a suitable base surface, automatically generated from the data points, or provided as a CAD model if available. Ill-conditioning was solved by introducing additional fitting criteria in the minimisation functional, which constrain the fitted surface in the regions with insufficient number of data points. Surface fitting is performed by treating the surface as a whole without the need to either identify or re-measure the regions with insufficient data. The accuracy of fitting is dictated by the number of control points. The improvements in data compression, shape analysis and rendering are presented. The realised computational speed and the quality of the results were found to be highly encouraging.