On the modeling of developable Hermite patches

Kusno -

Abstract


The developable surfaces are useful in plat-metal and plywood sheet installation. For this reason, the paper discusses designing the developable Hermite patches with its boundary curves placed in different parallel planes. The steps used are in this way. Using the boundary curves data, and a developable patches’ criteria equation, we evaluate this equation to find some geometric elements of both curves that can be practically used to construct the developable pieces. Then the study makes a procedure to design the pieces. As a result, we obtain some equations and methods to model many shapes of the developable Hermite patches that can be constructed by its endpoints, intermediate points, the tangent, and acceleration vectors at the endpoints of the patches’ boundary curves. The endpoints and the intermediate control points can be applied to raise and lower the surface shape along the pieces. Moving the intermediate control points between the endpoints, and determining the tangent, and acceleration vectors are used to change the patches' surface slopes in a different form. Using this method, the surface shape of the pieces can be curved and fluctuate into more than three arches. We also numerically calculate the connection G1 between two developable Hermite pieces adjacent.


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Published: 2021-01-27

How to Cite this Article:

Kusno -, On the modeling of developable Hermite patches, J. Math. Comput. Sci., 11 (2021), 1145-1165

Copyright © 2021 Kusno -. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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