Output details

Optimized surface discretization of functionally defined multi-material objects

One of the open problems in computer-aided design is representation and handling of multi-material heterogeneous object models. This is important for emerging multi-material 3D printing. One of the promising approaches is based on implicit surfaces, which are surfaces in space with a specific given real function value. This representation is popular because of its ability to describe complicated shapes and to handle topological changes during simulation. We deal with models for complex objects built step by step in a constructive manner from simple primitives with predefined implicit surfaces by applying set operations (union, intersection, difference) to the primitives. Visualization of such objects can be done by ray-tracing or by polygonization. The polygonization procedure generates an approximation of the surface by a set of triangles. It is usually done by sampling the function on a regular grid and inspecting each cell in the grid to check if it intersects with the surface.

Originality

The original contribution of this work is an algorithm for the approximation of an implicit surface, which is a boundary of a multi-material heterogeneous object, by a good quality optimized triangular mesh.

Rigour

We show that the mesh generated by the proposed algorithm satisfies the following criteria: regularized shape and size of mesh triangles, optimized connectivity, retrieved sharp features, minimized approximation error (to the implicit surface) and mesh edges aligned with material boundaries for multi-material objects.

Significance

We illustrate the algorithm by several practical examples, including complex surfaces with several disconnected components and sharp features, and freeform objects that appear in both artistic and industrial design. The generated meshes with above properties are required in object analysis using boundary-element and finite-element methods, object fabrication especially using multi-material 3D printing and other critical applications.