Abstract
A Gregory patch and a rational boundary Gregory patch have characteristics such that any n-sided loop is interpolated smoothly and that many patches can be generated to connect smoothly with each other. However, since the mathematical form of these patches is different from conventional surface patches such as the Bézier patch, no algorithm was known to subdivide them. The subdivision algorithm that could be applied to other surface patches could not be applied to them.
This paper proves that the bicubic Gregory patch can be converted to a bi-7th degree rational Bézier patch and moreover, that the bicubic rational boundary Gregory patch can be converted to a bi-11th degree rational Bézier patch. Because these rational Bézier patches can be subdivided, by using this conversion algorithm, we have developed a method to get the intersection curves between a Gregory patch or a rational boundary Gregory patch and a plane. The rational Bézier patch is also a good medium for transferring Gregory patch data to other systems.
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© 1990 Springer-Verlag Tokyo
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Takamura, T., Ohta, M., Toriya, H., Chiyokura, H. (1990). A Method to Convert a Gregory Patch and a Rational Boundary Gregory Patch to a Rational Bézier Patch and Its Applications. In: Chua, TS., Kunii, T.L. (eds) CG International ’90. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68123-6_32
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DOI: https://doi.org/10.1007/978-4-431-68123-6_32
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-68125-0
Online ISBN: 978-4-431-68123-6
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