In this dissertation, we first introduce an equal-area spherical map, HEALPix, which is borrowed from astrophysics. Its associated sample pattern is uniformly distributed over the sphere surface. Then we discuss its application in environment mapping. Although the HEALPix representation is more balanced than the traditional cubemap, it cannot utilize the built-in hardware operations like cubemap, and the mipmapping construction is more complicated. Therefore, its rendering speed is not comparable to that of the cubemap. This motivates us to invent a new six-face spherical map, called isocube. Unlike cubemap, isocube is an equal-area mapping, i.e., each texel spans the same area and is equally important. Due to the six-face representation, isocube can fit nicely into the cubemap hardware and hence can fully exploit the hardware operations tailored for cubemap. In addition, its mapping computation only involves a small overhead. Therefore the look-up speed for isocube is very fast. / Next we discuss another application of HEALPix map, the dynamic environment sequence sampling. Previous work only considers the static case where the environment map is approximated by finite directional light sources. In the dynamic case, the individual regeneration of samples for each frame may introduce abrupt, changes in the rendering animation. To handle this temporal inconsistency problem, we propose spherical q2-tree based on IIEALPix map. The adaptiveness of the quadtree can suppress the abrupt changes between consecutive frames, and hence a rather smooth rendering can be produced. This method, however, generates sample pattern independently for each environment frame, and therefore it may still cause unexpected, lumps in some situations. To fully utilize the temporal coherence in the sequence, we present a global sampling approach which treats the dynamic environment sequence as a all volume and performs sampling in the volume. The volumetric sampling adapts the sample number according to each frame and restricts the temporal/spatial changes within small subdivided volumes, and hence ensures a smooth sampling sequence. Within the framework, we present a volumetric importance metric and develop a binary-quad tree to perform stratification. Experimental results show that our volumetric sampling method can generate light samples with a better temporal consistency. / Spherical map is the foundation for many applications in computer graphics, such as environment mapping, precomputed radiance transfer, radiosity and image-based rendering. For these applications that involve intensive computation on spherical domain, it is generally desirable to employ equal-area and uniform spherical maps as the underlying parameterization. However, equal-area spherical maps are less exploited in graphics. / Wan, Liang. / "August 2007." / Adviser: Tien-Tsin Wong. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1121. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 118-123). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

No description available.