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Maximum Mipmaps for Fast, Accurate, and Scalable Dynamic Height Field Rendering

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Maximum Mipmaps for Fast, Accurate, and Scalable Dynamic Height Field Rendering Maximum Mipmaps for Fast, Accurate, and Scalable Dynamic Height Field Rendering Art Tevs, Ivo Ihrke and Hans-Peter Seidel Max-Planck-Institut für Informatik Figure 1: Left: Scene rendered with around 40FPS at 1500 × 1200 screen resolution. The resolution of the height map is 10242. The height field is rendered twice since water is reflecting the environment. Right: A screenshot from the Venus scene showing a highly complex height map applied on a planar surface, height map resolution is 40962 rendered with 25 FPS at 1200x900 screen resolution. Abstract such as terrain rendering, depth-assisted light field rendering and This paper presents a GPU-based, fast, and accurate dynamic height collision detection are relying upon fast and accurate intersection field rendering technique that scales well to large scale height fields. tests. Furthermore, different advanced texture mapping techniques Current real-time rendering algorithms for dynamic height fields like displacement mapping [Cook 1984], relief mapping [Policarpo employ approximate ray-height field intersection methods, whereas et al. 2005; Policarpo and Oliveira 2006] and shell mapping [Po- accurate algorithms require pre-computation in the order of seconds rumbescu et al. 2005; Jeschke et al. 2007] use an underlying ray- to minutes and are thus not suitable for dynamic height field ren- height field intersection algorithm. Finally, GPU ray-casting ap- dering. We alleviate this problem by using maximum mipmaps, proaches e.g. for reflection/refraction rendering like [Wyman 2005; a hierarchical data structure supporting accurate and efficient ren- Szirmay-Kalos et al. 2005; Hu and Qin 2007] use ray-depth map dering while simultaneously lowering the pre-computation costs to intersections to compute refracted or reflected rays. Addition- negligible levels. Furthermore, maximum mipmaps allow for view- ally, these algorithms can benefit from depth-enhanced environment dependent level-of-detail rendering. In combination with hierarchi- look-ups [Szirmay-Kalos et al. 2005]. cal ray-stepping this results in an efficient intersection algorithm for Current state-of-the-art methods employ broadly two classes of large scale height fields. algorithms. The first class are fast, approximate methods, e.g. uni- form stepping combined with binary search. These methods are CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional not guaranteed to find the correct intersection and lead to artifacts Graphics and Realism—Raytracing; Color, shading, shadowing, in the rendering process. The second class are accurate algorithms and texture; Visible line/surface algorithms I.3.6 [Computer Graph- that rely on pre-computed information to facilitate fast traversal and ics]: Methodology and Techniques—Graphics data structures and accurate intersection computation. This comes at the cost of pre- data types computation time (seconds to minutes) and storage requirements in Keywords: graphics hardware, simplification/level of detail, spa- graphics memory. tial data structures, texturing techniques, displacement mapping, The method proposed in this paper takes an in-between ap- height field intersection, surface details, real-time rendering, GPU proach. We use a pre-computed, hierarchical data structure, the 1 Introduction maximum mipmap, to facilitate efficient intersection operations. On the other hand, this data structure is also efficient to pre- Efficient ray-height field intersections are an important tool in a compute, enabling real-time update rates. The pre-computation is range of computer graphics applications. A number of applications simple and fast since only a customized mipmap shader is neces- sary. In summary, our algorithm is usable in a wide range of graph- ics algorithms, enabling accurate height field intersections for large scale dynamic height fields with the overhead of storing a mipmap. The paper is organized as follows. In Sect. 2 we review related work and applications of height field rendering. In Sect. 3 we in- troduce our height field intersection algorithm, which we compare against existing methods in Sect. 4. In Sect. 5 we show results for a prototypical application before we conclude the paper in Sect. 6. Figure 2: Height field samples are defined at the corners of a regular grid (left), four corner points define a bilinear patch of the height field (middle), the highest resolution mipmap contains the maximumvalue of the bilinear patch (right). 2 Related Work fine the result. Dummer [2006] uses cone ratios to define empty space regions. Policarpo and Oliveira [2007] improve this method Ray-height field intersection is a pervasive tool in graphics algo- by allowing exactly one ray-height field intersection for any ray in- rithms. The classical application of direct height field rendering side the cone. Again, a binary search follows the ray traversal to is terrain rendering. Terrain rendering is usually performed us- refine the result. ing level-of-detail techniques that analyze the height field data in In contrast to recent GPU-based ray-height field intersection an online or offline step and compute an optimized triangulation methods we propose to borrow from the earlier CPU-based accurate which is then ray-traced or rendered by rasterization-based ap- ray tracing methods to perform scalable and efficient height field in- proaches, e.g. [Lindstrom et al. 1996; Roettger et al. 1998; Hoppe tersections. The maximum mipmap is a data structure equivalent to 1998]. Direct ray tracing of height fields is often based on 2D a fully sub-divided quad-tree [Samet 1990] and thus allows for hier- rasterization [Musgrave 1988; Cohen and Shaked 1993; Cohen-Or archical traversal of the height map which in practice results in near et al. 1996; Qu et al. 2003; Henning and Stephenson 2004]. The logarithmic traversal complexity. Minimum-Maximum Mipmaps ray’s projection into the texture domain is rasterized and the cells have been used lately for soft shadow rendering [Guennebaud et al. corresponding to height map pixels are checked for intersections. 2006] and geometry image intersection [Carr et al. 2006]. Guen- These algorithms use different acceleration methods. Cohen and nebaud et al. [2006] use a hierarchical mipmap structure to effi- Shaked [1993] use a pyramidal data stucture to perform hierarchi- ciently determine the occluded region between a point and an area cal ray tracing. Cohen-Or et al. [1996] use an incremental uni- light source. Carr et al. [2006] use minimum-maximum mipmaps form traversal where each pixel column of an image is traced incre- to define a hierarchy of axis-aligned bounding boxes for deform- mentally. Whereas the previous methods use a constant height ap- ing triangle meshes. Once the lowest mipmap level is reached they proximation inside a height field cell, Qu et al. [2003] use different perform ray-triangle intersections. primitives, i.e. planes or polygonal approximations, yielding higher quality renderings for low resolution height fields. Henning and Our algorithm is mainly inspired by the work of Cohen and Stephenson [2004] use the run-length’s of the discretized lines to Shaked [1993], who use discrete line traversal of a quad-tree to intersect larger bounding volumes with the height field data. Smits render height fields on a parallel computer, whereas we employ et al. [2000] directly intersect displacement mapped triangles using current graphics hardware and a parametric line description. We barycentric coordinate hierarchies instead of regular sampling on a also use parametric surface patches for the description of a height two-dimensional grid. field within one voxel, whereas [Cohen and Shaked 1993] assume a piecewise constant height field. In GPU-based real-time rendering algorithms these ray-tracing methods have not become popular. Instead, approximate methods A similar approach as taken in this paper is presented by Oh et like uniform stepping combined with binary search are dominantly al. [2006]. However, their work has several shortcomings which being used [Oliveira and Policarpo 2005; Policarpo and Oliveira we improve upon. The major improvements are a truly hierar- 2006]. Alternatively, Newton iterations [Ohbuchi 2003; Wyman chical traversal of the maximum mipmap data structure, a view- 2005; Hu and Qin 2007] or the secant method [Risser et al. 2005; dependent, adaptive, per-pixel level-of-detail selection and an ac- Szirmay-Kalos et al. 2005] are performed either by themselves or curate bilinear patch intersection at the lowest level of the mipmap. combined with uniform search. The former approach is usually 3 Algorithm being taken when accuracy is not too much of an issue, like in re- fraction rendering or nearby geometry lookup after refraction or Our ray-height-field intersection algorithm is based on an accel- reflection, or when the height map is simple. eration data structure, the maximum mipmap. This data structure In case correct intersections are required, intersection methods is fast to pre-compute and allows for efficient empty space skip- based on safety zones are being used, e.g. [Donnelly 2005; Baboud ping. In using a mipmap-like data structure for empty-space skip- and Decoret 2006; Jeschke et al. 2007]. All safety zone tech- ping we balance the complexity of pre-computing the acceleration niques known today require off-line pre-computation of the ac- data structure with that of the ray traversal phase. celeration structure. Donnelly [2005] uses distance maps which The maximum mipmap represents an implicit bounding volume require a 3D texture and significant pre-computation
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