The mathematic basics of developing a 3d shoe last shape using the reverse engineering method.

Abstract

A shoe making industry which can offer shoes that fit consumer needs has a decided advantage over its competitors. Next to fashion, shoe fitness and foot comfort is an important selection criterion. The shoe last is the main element that provides the of comfort shoes. Most of the scientific researches devoted to the topic of computer-aided design of lasts, are focused on finding the optimal ratio of the foot and shoe shape, on the selection of the most suitable last. However, the features of tailor made shoe production often require the creation of a new shoe last shape based on the customer's foot parameters. This paper is devoted to the development of an algorithm for the method of а new last shape designing for the tailor made shoes in a graphical 3D CAD environment and a mathematic model of its deformation in accordance with the basic parameters of the foot and the last style. The modeling of the last by reverse engineering involves scanning the original last, which is the basis for creating a new shape by performing some deformations of the original shape. Such deformations can be described mathematically as geometric transformation matrices: displacement, rotation, scale, etc. In the article for designing a new last shape, the method of calculating the parameters of deformation of the base last shape in accordance with the style and theoretical parameters of the last, obtained based on the foot sizes of the consumer, is proposed. Based on these calculations, an algorithm for the method of modeling a new shoe last using the reverse engineering method was developed and a mathematical model of the geometric deformation of its complex 3d shape, which is performed in the 3d CAD designing process, was calculated.

Keywords

• взуттєва колодка
• математична модель
• геометрична деформація
• зворотній інжиніринг
• стопа
• взуття за індивідуальним замовленням
• хмара точок
• 3д середовище
• сапр