Building plane and solid modeling using NURBS
Cid Alexandre Santos Péret Sant'Ana1; Fernando Morais de Loyola1; Lucas Silveira Campos2; Éder Lima de Albuquerque1
1 Universidade de Brasília; 2 Universidade Federal do Espírito Santo
doi:10.20906/CPS/CILAMCE2017-0649
Resumo
This work presents a reimplementation of the programs 𝑃𝑟𝑜𝑝𝐺𝑒𝑜𝑖𝑠𝑜, which calculates the geometric properties of solid and flat figures applying the radial integration method in conjunction with the NURBS. The reimplementation aims to make the program accessible to an individual with basic knowledge in programming, without the need for prior knowledge of NURBS. The 𝑒𝑥𝑡𝑟𝑢𝑑𝑒 command was also developed from the program 𝑃𝑟𝑜𝑝𝐺𝑒𝑜𝑖𝑠𝑜3𝐷, which is capable of extruding solids from user defined curves. First, a brief historical introduction is made indicating the relevance of the study of isogeometric modeling. The curves and Bézier surfaces, B-splines, and finally the NURBS are presented. Following, the steps for the implementation of the algorithm based on the radial integration method are described. The programs were developed using 𝑀𝐴𝑇𝐿𝐴𝐵® which were tested, whenever possible, on problems whose analytical solutions were known. Otherwise, results from the 𝑆𝑜𝑙𝑖𝑑𝑊𝑜𝑟𝑘𝑠®2016 program were used for comparisons. Numerical results show good agreement to the analytical ones.
Palavras-chave: CAD; Isogeometric Formulation; NURBS; Radial Integration Method; Geometric properties