Implementation of efficient surface discretisation algorithms adapted to geometric models specific to the footwear industry

In 3D modelling, a surface mesh is a collection of vertices, edges, and faces that define the shape of a 3D object. The surface mesh is typically used to represent the outer surface of an object, as opposed to the internal structure. A surface mesh is usually defined as a polygon mesh, which is a collection of polygons (triangles or quadrilaterals are the most common) that are connected at their vertices. The vertices of the mesh define the shape of the object, and the edges and faces provide the topological information that describes how the vertices are connected. Surface meshes are often used in 3D modelling software to create 3D objects for animation, video games, and other purposes. Although triangular meshes are the most widely used in various fields, they have a series of disadvantages that quad meshes solve in most cases. This article presents a set of algorithms capable of generating quad meshes from any type of input triangular mesh, preserving the geometric characteristics of the initial model. This process is known as 'remeshing'. The results obtained by these algorithms on a large number of models related to the footwear industry have been compared, as well as analysing the advantages and disadvantages of each one of them applied to geometric models commonly used in footwear industry.