Interactive decal compositing with discrete exponential maps
ACM SIGGRAPH 2006 Papers
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3D modeling systems form the basis for many of the most widely used graphics applications. Although interfaces have long provided the ability to paint directly on a 3D model, the colors are usually stored in a 2D domain, such as in a texture map. Despite its widespread use and several advantages, texture mapping has several shortcomings in the context of 3D painting. 3D painting usually requires only a local surface parameterization, while many parameterization methods are global and cannot be applied directly for 3D paints. The computing cost can be too high for realtime parameterization and obvious texture distortions can arise. One of the key works to address these shortcomings is by Schmidt et al. [Schmidt et al. 2006] on decal compositing, who provided an efficient local parameterization for 3D painting. They try to minimize the distortion of textures by approximating the exponential map. However, their work still has many limitations on 3D paintings. Their local parameterization method relies on the topology of the local mesh structure, which implies that this method is not stable on different mesh topologies that represent the same geometric shape. Experimental examples showed particular problems when models include large numbers of sliver triangles. Due to the sensitivity to the mesh topology, there is not an error bound between their approximation and the exponential mapping. While their method works well in many standard situations, the limitations can cause significant texture distortion in other cases.