Bilinear interpolation on a quadrilateral using Barycentric coordinates

In computer graphics, we rarely encounter continuous data. We often work with digital data, and in the context of geometric modeling, this means we typically work with polygon meshes rather than procedural surfaces like Bézier patches. The most popular technique for constructing digital three-dimensional objects in dedicated modeling software is polygon modeling. The result of the creation phase is a set of polygons (mesh), where the polygons in the mesh can share vertices and edges with other polygons. Although users can create various types of surfaces (e.g., non-manifold), the most common surface is the topological 2-manifold. In short, a 2-manifold is a mathematical concept in topology, where the space locally resembles the Euclidean plane in \mathbb{R}^2. Essentially, every point on a 2-manifold has a neighborhood that looks like a piece of the plane. Examples of 2-manifold mesh triangle-based Examples of 2-manifold mesh quad-based At the vertices of a polygon, users can store ... Read full article.