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257 freeform: A Tool for Teaching the Mathematics of Curves and Surfaces

By James R. Miller

Abstract

We describe the structure and use of an interactive modeling and visualization tool used to help students understand various important concepts in curve and surface design. This paper describes those aspects of the tool related to NURBS curves, but Bezier and Hermite curves are also supported as are Bezier and B-Spline surfaces. The focus of this paper is almost exclusively on those features of the tool used to visualize the mathematics of NURBS curves and surfaces, especially focusing on an integrated visualization of how weights and knots affect the blending functions and, through them, the curve. It is currently packaged as a standalone C++ program using OpenGL, running on Macintosh and linux operating systems. A port to Windows is underway, but as a part of a larger effort to redesign and better package a Java-JOGL-Swing version, access to which will be placed in the public domain using Java Web Start

Topics: CAD education, visualizing B-Spline functions, curve & surface design. DOI, 10.3722/cadaps.2010.257-267
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.297.5669
Provided by: CiteSeerX
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