11 Modeling surfaces with boundary representations and triangle meshes

 

This chapter covers

  • Understanding the pros and cons of boundary representation modeling
  • Seeing the triangle mesh as a particular case of a boundary representation
  • Understanding the downsides of triangle mesh modeling
  • Confidently using contouring algorithms: Marching cubes and dual contouring
  • Understanding the trade-off between the model precision and model size

With signed distance functions, we model a 2D shape or a 3D body by introducing a rule. The function is negative inside the shape, positive outside, and 0 on the border. Most of the time, we’re not interested in anything apart from the border, which alone is enough to model a shape. So why bother modeling anything else?

With boundary representation, we model only the boundary of a body or shape. In 2D, we model a set of contours that represents the shape’s border. In 3D, we model a set of surfaces that represents the border of a body.

In computer-aided design (CAD) applications, the smoothness of surfaces is an important property for modeling, so we usually model our things with smooth pieces of curves and surfaces. The surface pieces are in turn bound by their own boundaries in UV space.

11.1 Smooth curves and surfaces

11.1.1 Data representation

11.1.2 Operations are also data

11.1.3 Section 11.1 summary

11.2 Segments and triangles

11.2.1 Vertices and triangles vs. the half-edge representation

11.2.2 Pros and cons of triangle meshes

11.2.3 Section 11.2 summary

11.3 Practical example: Contouring with marching cubes and dual contouring algorithms

11.3.1 Marching cubes

11.3.2 Dual contouring

11.3.3 Is it that simple in practice, too?

11.3.4 Section 11.3 summary