rotatsioonijärjekorra

Rotatsioonijärjekord, or rotation order, is a concept used in various fields, most notably in computational geometry and computer graphics. It refers to a way of ordering the neighbors of a vertex in a planar graph or a polygon. In essence, when you stand at a vertex and look outwards, the rotation order defines the sequence in which the adjacent vertices appear as you sweep around the vertex in a consistent direction, typically counter-clockwise.

This ordering is crucial for algorithms that process geometric structures. For example, in triangulating a polygon, understanding the rotation order of vertices around an interior point or along the polygon's boundary helps determine which triangles can be formed without crossing edges. Similarly, in mesh processing, the rotation order of vertices around a face is essential for operations like edge collapsing or face extrusion, ensuring that the topological structure remains consistent.

The implementation of rotation order often involves sorting adjacent vertices based on their polar angle relative to the current vertex. This sorting allows algorithms to efficiently traverse the local neighborhood of a vertex in a predictable manner. Without a well-defined rotation order, algorithms might produce incorrect results or struggle to maintain the geometric integrity of the data. The concept is fundamental to many geometric algorithms that rely on the local connectivity of vertices.