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2009•Journal of Engineering GraphicsRequires access

Quick Approach for Finding Parametric Values of 3D Points on NURBS Surface Curve

Yiduo Wang

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Abstract

First the NUBRS surface is adaptively tessellated into a strip of triangle mesh along the given curve,on which a set of discrete points is adaptively taken and using the mean parametric values of the nearest triangle vertices as the first approximation of the parameters for each discrete point,iteratively.Refine them to the projection of the 3D points onto the parameter plane coincide with its 2D image on the given curve.Tests verified the effectiveness of such an approach.

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What this paper is about

First the NUBRS surface is adaptively tessellated into a strip of triangle mesh along the given curve,on which a set of discrete points is adaptively taken and using the mean parametric values of the nearest triangle vertices as the first approximation of the parameters for each discrete point,iteratively.Refine them to the projection of the 3D points onto the parameter plane coincide with its 2D image on the given curve.Tests verified the effectiveness of such an approach.

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Available abstract

First the NUBRS surface is adaptively tessellated into a strip of triangle mesh along the given curve,on which a set of discrete points is adaptively taken and using the mean parametric values of the nearest triangle vertices as the first approximation of the parameters for each discrete point,iteratively.Refine them to the projection of the 3D points onto the parameter plane coincide with its 2D image on the given curve.Tests verified the effectiveness of such an approach.

Key concepts: Parametric statistics, Mathematics, Surface (topology), Parametric equation, Parametric surface, Projection (relational algebra), Point (geometry), Set (abstract data type)

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