Two novel spherical representations and their applications

Abstract

In this thesis, two novel spherical representations are introduced for two different applications in computer graphics, one for environment mapping and the other for pre-computed radiance transfer approaches. The first novel representation is unicube mapping, and the second one is vectorized visibility. Unicube mapping Cube mapping is widely used in many graphics applications due to the availability of hardware support. However, it does not sample the spherical surface evenly. A recent uniform spherical mapping, isocube mapping, samples the spherical surface evenly and exploits the six-face structure. Unfortunately, some texels in isocube mapping are not rectilinear in shape which can degrade the filtering quality. This thesis proposes a novel spherical mapping, namely unicube mapping, that has the advantages of cube mapping (exploitation of hardware and rectilinear structure) and isocube mapping (uniform sampling). Unicube mapping uses a simple function to modify the look-up vector before the conventional cube map look-up process. Hence, unicube mapping fully exploits the cube map hardware for real-time filtering and look-up. More importantly, its rectilinear partition structure allows a direct and realtime acquisition of environment maps via perspectively projecting a 3D scene on the faces of unicube map. This property facilitates dynamic environment mapping. Vectorized visibility Most existing pre-computed radiance transfer approaches for geometric relighting are vertex based. To preserve the fidelity of high frequency effects, a 3D model must be highly tessellated, otherwise artifacts due to interpolation will appear. This thesis presents a novel spherical representation for visibility representation, namely vectorized visibility, along with its geometric relighting algorithm. As vectorized visibility is also a form vector graphics, we can interpolate vectorized visibilities to synthesize the vectorized visibility of an on-screen pixel for the lighting evaluations, analogous to the morphing of vector graphics. Therefore, the artifacts due to interpolation are eliminated while preserving the high frequency shadows, even for the coarsely tessellated 3D models. In addition, our geometric relighting algorithm allows rotating lighting environment, changing viewing, and adjusting the shininess during rendering in an interactive manner. For isotropic reflection, the specular level can be adjusted from blurry to mirror reflection. Our geometric relighting algorithm can also be combined with some existing rendering algorithms to provide a better realism, e.g. dynamic bump mapping and the doubly-projected SH approach.