Variable-Radius Blending by Using Gregory Patches in Geo- metric Modeling

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Date
1991
Journal Title
Journal ISSN
Volume Title
Publisher
Eurographics Association
Abstract
Blending surfaces, which connect two curved surfaces smoothly, often appear in geometric modeling. Many of the blending surfaces are variable-radius blends. Variableradius blending surfaces are very important in the design process, but it is difficult to generate such surfaces with existing geometric modelers. This paper proposes a new method to generate variable-radius blends. Instead of the popular rolling-ball method, we adopt “sliding-circle” blending. A circle slides on two curved surfaces so that the circle is perpendicular to a specified control curve, and its trajectory defines a blending surface. A variable-radius blend can be generated if the radius of the circle changes smoothly. In our method, the shape of the variable-radius blend is represented by Gregory patches. The Gregory patch is an extension of a Bezier patch and two Gregory patches can be connected together with tangential continuity. The characteristics of the Gregory patch are suitable for representing blending surfaces with geometric modelers.
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@inproceedings{
10.2312:egtp.19911038
, booktitle = {
EG 1991-Technical Papers
}, editor = {}, title = {{
Variable-Radius Blending by Using Gregory Patches in Geo- metric Modeling
}}, author = {
Harada, T.
and
Konnoa, K.
and
Chiyokura, H.
}, year = {
1991
}, publisher = {
Eurographics Association
}, ISSN = {
1017-4656
}, ISBN = {}, DOI = {
10.2312/egtp.19911038
} }
Citation