1. A computer-implemented method, comprising: accessing, by a computing device, data representing a surface mesh model of a three-dimensional object; assigning, by the computing device, initial two-dimensional texture coordinates to each node within the surface mesh using a mapping technique in which computing the texture coordinates of each node other than an origin node is dependent on a distance and direction of a vector formed between the node and a neighbor node within the surface mesh to which texture coordinates have previously been assigned, the assigning including computing texture coordinates for each given node other than the origin node and a nearest neighbor of the origin node by: identifying a nearest neighbor of the given node to which texture coordinates have been assigned; identifying a nearest neighbor of the nearest neighbor to which texture coordinates have also been assigned; and computing the texture coordinates of the given node dependent on the texture coordinates of the nearest neighbor and the texture coordinates of the nearest neighbor of the nearest neighbor; computing, by the computing device, a conformal mapping solution to generate revised two-dimensional coordinates for each node within the surface mesh, wherein said computing is based on the assigned initial two-dimensional texture coordinates; and storing the revised two-dimensional texture coordinates for subsequent use in a graphics application.