On the modeling of developable Hermite patches

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.