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 is said to be acute. The immediate benefits of having a nonobtuse or acute mesh include more efficient and more accurate geodesic computation on meshes using fast marching, and guaranteed validity for planar mesh embeddings via discrete harmonic maps.
The first guaranteed nonobtuse mesh generation in 3D was introduced in Eurographics Symposium on Geometry Processing 2006 by Li and Zhang.
