Avatar animations using green coordinates

Abstract

There are many kinds of meshes that can be used to build an avatar. In this case, we will focus on closed triangular meshes. These meshes are formed of a set of vertices, edges and faces. The way these items are connected and positioned in space is what sculpts the avatar we want to create. Closed triangular meshes restrict the faces to be triangles, meaning that each face is formed of three vertices connected by three edges and all the edges are included in exactly two triangles. This way, the mesh is entirely formed of triangles and all of them are connected to another triangle through each edge. Moreover, each face is assigned an outward normal vector which we will also use in this work. An example can be seen in Figure 1.1. As one can easily imagine, if we only had this mesh, the way to animate it would be to move all the vertices of the mesh adequately until it adopted the desired pose, and we would have to do this for each keyframe of the animation. When the mesh is very coarse, this simple methodology could be feasible; however, this is not normally the case, especially nowadays when computational power increases so drastically every year, making it possible to create and control meshes of millions of vertices. Following this need, many structures aimed to control the mesh and animate it have been built. In the following subsection I will brie y introduce the skeletons and the free-form deformations (FFD). Only these two will be mentioned, because the FFD's will be used in this work and the skeleton is the most commonly used and it's important to point out the advantages of the method proposed in the paper Green Coordinates.