See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/220853059 Generalized Displacement Maps. Conference Paper · January 2004 DOI: 10.2312/EGWR/EGSR04/227-233 · Source: DBLP CITATIONS READS 77 66 6 authors, including: Xin Tong Shi-Min Hu Microsoft Tsinghua University 93 PUBLICATIONS 2,322 CITATIONS 198 PUBLICATIONS 4,662 CITATIONS SEE PROFILE SEE PROFILE Baining Guo Heung-Yeung Shum Microsoft Microsoft 166 PUBLICATIONS 5,366 CITATIONS 301 PUBLICATIONS 18,616 CITATIONS SEE PROFILE SEE PROFILE All content following this page was uploaded by Shi-Min Hu on 26 March 2014. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately. Eurographics Symposium on Rendering (2004) H. W. Jensen, A. Keller (Editors) Generalized Displacement Maps † ∗ ∗ ∗ ∗ Xi Wang Xin Tong Stephen Lin Shimin Hu Baining Guo Heung-Yeung Shum Tsinghua University ∗ Microsoft Research Asia Abstract In this paper, we introduce a real-time algorithm to render the rich visual effects of general non-height-field geo- metric details, known as mesostructure. Our method is based on a five-dimensional generalized displacement map (GDM) that represents the distance of solid mesostructure along any ray cast from any point within a volumetric sample. With this GDM information, we propose a technique that computes mesostructure visibility jointly in ob- ject space and texture space which enables both control of texture distortion and efficient computation of texture coordinates and shadowing. GDM can be rendered with either local or global illumination as a per-pixel process in graphics hardware to achieve real-time rendering of general mesostructure. 1. Introduction Fine scale surface geometry, known as mesostructure, is an integral component in the appearance of many real-world materials and objects. The rendering of mesostructure pro- vides not only fine resolution form to a surface, but also rich visual details such as fine-scale shading, shadows, occlu- sions and silhouettes. To enhance the realism of synthesized images, much attention has been focused on efficient and comprehensive methods for rendering mesostructure and its detailed appearance features. The two most common approaches to mesostructure ren- dering are by mapping images and by mapping geome- try onto a surface. Bidirectional texture functions (BTFs) [DNvGK99] record images of a mesostructure sample under different lighting and viewing directions, but since this rep- resentation contains no 3D geometric information, silhou- ettes and the effects of surface curvature cannot be rendered. These problems can be handled by mapping mesostructure Figure 1: Mesostructure rendering with GDM. Left column: geometry onto a surface to form a detailed object model, under local illumination. Right column: under global illumi- as done with displacement maps [Coo84] and volumet- nation. ric textures [KK89, Ney98]. Although the visual effects of mesostructure can be rendered from such a model, the large amount of detailed geometry mapped into the object space ject space can be avoided by precomputing the visibility can lead to considerable processing. of mesostructure points and storing it in texture space, as proposed in view-dependent displacement mapping (VDM) The burdens of handling directly mapped geometry in ob- ∗ [WWT 03]. With this information, VDM achieves real-time rendering of mesostructure visual effects including silhou- † This work was done while Xi Wang was a visiting student at Mi- ettes. This method, however, suffers from two significant crosoft Research Asia. drawbacks. One is that it can be applied only to height-field c The Eurographics Association 2004. X. Wang, X. Tong, S. Lin, S. Hu, B. Guo & H.-Y. Shum / Generalized Displacement Maps geometry on closed surfaces. The other is that VDM can mesostructure sample, the 2D geometric structure inherent be practically precomputed for only a limited class of sur- in images precludes rendering of mesostructure silhouettes. face shapes, e.g., with respect to a single surface curvature ∗ Most prior techniques assume that mesostructures have parameter as in [WWT 03]. As a result, the precomputed the form of height fields on a mesh, a 2-1/2 D repre- VDM lacks the specificity to accurately represent surfaces sentation. For rendering mesostructures that have height with curvature variations and texture warping, which can field geometry, bump mapping [Bli78] and its exten- consequently lead to significant texture distortions. sions [Max88, SC00, BM93, HDKS00] offer an efficient ap- In this paper, we present a general mesostructure render- proach, but do not account for silhouettes. Silhouettes can be ing technique based on a proposed generalized displace- rendered by displacement maps [Coo84, CCC87], which ex- ment map (GDM), which represents the distance of solid plicitly model the geometric details of height fields. While mesostructure along any ray cast from any point within techniques based on height fields benefit from relative ease a volumetric texture. Unlike previous displacement map in processing, they lack the generality to describe a range of methods which model surfaces using one offset value per surface geometries that includes weave patterns and slanted texel, generalized displacement maps can handle arbitrary protrusions. non-height-field mesostructures. Furthermore, the GDM ap- Volumetric textures provide a general 3D representation proach overcomes both the texture distortion problems of of mesostructure as volumetric data sampled on 3D regu- VDM and the computational expense of directly mapped ge- lar grids [KK89, Ney98]. Traditionally, volumetric textures ometry by computing visibility jointly in texture space and are rendered by tracing rays through a shell volume mapped object space. The precomputed GDM values facilitate tex- on a surface, which is expensive for real time applications. ture coordinate computation of viewing rays whose piece- Recently, a set of slice-based approaches have been devel- wise linear trajectory in texture space is determined in object oped for volumetric texture rendering. Meyer et al. [MN98] space according to the shape of the base mesh. By account- rendered the volume prism extruded from each triangle as a ing for curvature variations and texture warping in object stack of axis-aligned textured slices. Lensch et al. [LDS02] space, ray intersections in texture space are more accurately used a set of slices parallel to the projection plane to ren- established, resulting in less texture distortion. der the shell volume. In [LPFH01], volumetric fur mapped The GDM can similarly be used to quickly determine on a surface is rendered as concentric layers from the skin whether the intersection point is shadowed from local illumi- outwards, and extruded fins from triangle edges near the sil- nation, and can moreover be efficiently employed for scenes houette are also rendered to reduce artifacts. Daubert et al. with global illumination. With a simple per-pixel implemen- [DS02] applied a precomputed visibility map to render shad- tation in graphics hardware, GDM can render complex volu- owing effects of thin knitwear. In these slice-based methods, metric textures including silhouettes in real time to produce the number of slices used for each triangle increases with detailed mesostructure appearance as shown in Fig. 1. The volumetric resolution. This encumbers the rendering process contributions of this work are summarized as follows: with additional overhead that is magnified when sophisti- cated per-pixel shading is incorporated. To our knowledge, • the generalized displacement map for rendering of general no previous work has been able to render volumetric textures non-height-field mesostructure on both open and closed with global illumination in real time. surfaces • visibility computation in texture and object spaces to re- Related methods for rapid software rendering include the duce texture distortion and increase efficiency work of Arvo and Kirk [AK87], which uses view-dependent • a hardware implementation of GDM for real-time render- distance data in volumes to accelerate ray tracing. Dischler ing with either local and global illumination [Dis98] used ray tracing in texture space to map mesostruc- tures onto base geometry. He also proposed a special data structure to accelerate the software rendering. Daubert et 2. Related Work ∗ al. [DKS 03] precomputed visibility information and then Previous methods for mesostructure rendering can be cate- reused it for shadow computation and indirect illumination. gorized by the dimensionality of their geometric represen- In GDM, visibility information is used for rendering both tations. Highly realistic mesostructure appearance can be silhouettes and shadows in real time. modelled from collections of 2D images such as BTFs. Poly- nomial texture maps [MGW01] represent mesostructure ap- 3. GDM Modeling and Rendering pearance of each surface point under different lighting di- rections by fitting a biquadric polynomial. For non-diffuse Our mesostructure rendering method takes mesostructure surfaces, this approach models only a fixed viewpoint. Re- geometry as input and computes its GDM. After the GDM cently, [SLSS03] integrated the BTF with precomputed radi- texture is mapped to a surface, rendering is performed by a ance transfer of macro-scale geometry, and then rendered the