Geometry images

Geometry images
Xianfeng Gu, Steven Gortler, Hugues Hoppe.
ACM Trans. Graphics (SIGGRAPH), 21(3), 2002.
Connectivity-free resampling of an arbitrary shape into a regular 2D grid.
Abstract: Surface geometry is often modeled with irregular triangle meshes. The process of remeshing refers to approximating such geometry using a mesh with (semi)-regular connectivity, which has advantages for many graphics applications. However, current techniques for remeshing arbitrary surfaces create only semi-regular meshes. The original mesh is typically decomposed into a set of disk-like charts, onto which the geometry is parametrized and sampled. In this paper, we propose to remesh an arbitrary surface onto a completely regular structure we call a geometry image. It captures geometry as a simple 2D array of quantized points. Surface signals like normals and colors are stored in similar 2D arrays using the same implicit surface parametrization — texture coordinates are absent. To create a geometry image, we cut an arbitrary mesh along a network of edge paths, and parametrize the resulting single chart onto a square. Geometry images can be encoded using traditional image compression algorithms, such as wavelet-based coders.
Hindsights: Geometry images have the potential to simplify the rendering pipeline, since they eliminate the "gather" operations associated with vertex indices and texture coordinates. Although the paper emphasizes the exciting possibilities of resampling mesh geometry into an image, the same parametrization scheme can also be used to construct single-chart parametrizations over irregular meshes, for seam-free texture mapping. The irregular "cruft" present in several of the parametrizations is addressed by the inverse-stretch regularization term described in the 2003 Spherical Parametrization paper.