Algorithm for approximation transitional developable surfaces between two polygons

Abstract

The paper describes and explains the computational geometry method that simulates the physical model of transitional pipeline parts whose cross sections have polygonal form and are made of materials that cannot be wrinkled or stretched. This geometrical concept is taken from the classical line geometry and can be directly applied to the creation of computer algorithm that generates the transitional surfaces between two polygons. Mathematical concept of the solution for this problem is based on approximation of the boundary surface triangulation and is presented in MATLAB program. Solutions are given in the form of three-dimensional surface models from which the necessary technical documentation can quickly be made using standard CAD/CAM tools thus shortening the time necessary to prepare the construction and production. In particular, the paper presents the basic computer graphics theory of ruled and developable surfaces, the concept of a geometrical solution for the problem, and the algorithm for generation of transitional surface between two polygons.