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Boundry Determination for Trivariate Solids

@inproceedings{Joy:1999:BDF,
title="Boundry Determination for Trivariate Solids",
booktitle="Proceedings of the 1999 Pacific Graphics Conference",
author="Ken Joy AND Mark A. Duchaineau ",
year="1999",
keywords="splines; boundary surface determination; trivariate B-Spline solids; Jacobian determinant.",
pages="82--91",
location="Seoul, Korea",
eventtime="October 5--7, 1999",
abstract="The trivariate tensor-product B-spline solid is a direct extension of the B-spline patch and has been shown to be useful in the creation and visualization of free-form geometric solids. Visualizing these solid objects requires the determination of the boundary surface of the solid, which is a combination of parametric and implicit surfaces. This paper presents a method that determines the implicit boundary surface by examination of the Jacobian determinant of the defining B-spline function. Using an approximation to this determinant, the domain space is adaptively subdivided until a mesh can be determined such that the boundary surface is close to linear in the cells of the mesh. A variation of the marching cubes algorithm is then used to draw the surface. Interval approximation techniques are used to approximate the Jacobian determinant and to approximate the Jacobian determinant gradient for use in the adaptive subdivision methods. This technique can be used to create free-form solid objects, useful in geometric modeling applications.",
}
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