A nonobtuse triangle mesh is composed of a set of triangles in which every angle is less than or equal to 90° we call these triangles nonobtuse triangles. If each (triangle) face angle is strictly less than 90^◦, then the triangle mesh

Triangle mesh

A triangle mesh is a type of polygon mesh in computer graphics. It comprises a set of triangles that are connected by their common edges or corners....

 is said to be acute. The immediate benefits of having a nonobtuse or acute mesh include more efficient and more accurate geodesic

Geodesic

In mathematics, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In the presence of a Riemannian metric, geodesics are defined to be the shortest path between points in the space...

 computation on meshes using fast marching

Fast marching method

The fast marching method is introduced by James A. Sethian as a numerical method for solving boundary value problems of the Eikonal equation:Typically, such a problem describes the evolution of a closed curve as a function of time T with speed F in the normal direction at a point x on the curve...

, and guaranteed validity for planar mesh embeddings via discrete harmonic maps.

The first guaranteed nonobtuse mesh generation

Mesh generation

Mesh generation is the practice of generating a polygonal or polyhedral mesh that approximates a geometric domain. The term "grid generation" is often used interchangeably. Typical uses are for rendering to a computer screen or for physical simulation such as finite element analysis or...

in 3D was introduced in Eurographics Symposium on Geometry Processing 2006 by Li and Zhang.