Abstract We present edge‐friend, a data structure for quad meshes with access to neighborhood information required for Catmull‐Clark subdivision surface refinement. Edge‐friend enables efficient real‐time subdivision surface rendering. In particular, the resulting algorithm is deterministic, does not require hardware support for atomic floating‐point arithmetic, and is optimized for efficient rendering on GPUs. Edge‐friend exploits that after one subdivision step, two edges can be uniquely and implicitly assigned to each quad. Additionally, edge‐friend is a compact data structure, adding little overhead. Our algorithm is simple to implement in a single compute shader kernel, and requires minimal synchronization which makes it particularly suited for asynchronous execution. We easily extend our kernel to support relevant Catmull‐Clark subdivision surface features, including semi‐smooth creases, boundaries, animation and attribute interpolation. In case of topology changes, our data structure requires little preprocessing, making it amendable for a variety of applications, including real‐time editing and animations. Our method can process and render billions of triangles per second on modern GPUs. For a sample mesh, our algorithm generates and renders 2.9 million triangles in 0.58ms on an AMD Radeon RX 7900 XTX GPU.

Abstract In this paper, we introduce a novel technique for pre‐filtering multi‐layer shadow maps. The occluders in the scene are stored as variable‐length lists of fragments for each texel. We show how this representation can be filtered by progressively merging these lists. In contrast to previous pre‐filtering techniques, our method better captures the distribution of depth values, resulting in a much higher shadow quality for overlapping occluders and occluders with different depths. The pre‐filtered maps are generated and evaluated directly on the GPU, and provide efficient queries for shadow tests with arbitrary filter sizes. Accurate soft shadows are rendered in real‐time even for complex scenes and difficult setups. Our results demonstrate that our pre‐filtered maps are general and particularly scalable.

Hardware tessellation is one of the latest GPU features. Triangle or quad meshes are tessellated on-the-fly, where the tessellation level is chosen adaptively in a separate shader. The hardware tessellator only generates topology; attributes such as positions or texture coordinates of the newly generated vertices are determined in a domain shader. Typical applications of hardware tessellation are view dependent tessellation of parametric surfaces and displacement mapping. Often, the attributes for the newly generated vertices are stored in textures, which requires uv unwrapping, chartification, and atlas generation of the input mesh--a process that is time consuming and often requires manual intervention. In this paper, we present an alternative representation that directly stores optimized attribute values for typical hardware tessellation patterns and simply assigns these attributes to the generated vertices at render time. Using a multilevel fitting approach, the attribute values are optimized for several resolutions. Thereby, we require no parameterization, save memory by adapting the density of the samples to the content, and avoid discontinuities by construction. Our representation is optimally suited for displacement mapping: it automatically generates seamless, view-dependent displacement mapped models. The multilevel fitting approach generates better low-resolution displacement maps than simple downfiltering. By properly blending levels, we avoid artifacts such as popping or swimming surfaces. We also show other possible applications such as signal-optimized texturing or light baking. Our representation can be evaluated in a pixel shader, resulting in signal adaptive, parameterization-free texturing, comparable to PTex or Mesh Colors. Performance evaluation shows that our representation is on par with standard texture mapping and can be updated in real time, allowing for application such as interactive sculpting.

We present a novel representation for storing sub-triangle signals, such as colors, normals, or displacements directly with the triangle mesh. Signal samples are stored as guided by hardware-tessellation patterns. Thus, we can directly render from our representation by assigning signal samples to attributes of vertices generated by the hardware tessellator.

Abstract We propose a lossless, single‐rate triangle mesh topology codec tailored for fast data‐parallel GPU decompression. Our compression scheme coherently orders generalized triangle strips in memory. To unpack generalized triangle strips efficiently, we propose a novel parallel and scalable algorithm. We order vertices coherently to further improve our compression scheme. We use a variable bit‐length code for additional compression benefits, for which we propose a scalable data‐parallel decompression algorithm. For a set of standard benchmark models, we obtain (min: 3.7, med: 4.6, max: 7.6) bits per triangle. Our CUDA decompression requires only about 15% of the time it takes to render the model even with a simple shader.

Abstract In this paper we analyze normal vector representations. We derive the error of the most widely used representation, namely 3D floating‐point normal vectors. Based on this analysis, we show that, in theory, the discretization error inherent to single precision floating‐point normals can be achieved by 2 50.2 uniformly distributed normals, addressable by 51 bits. We review common sphere parameterizations and show that octahedron normal vectors perform best: they are fast and stable to compute, have a controllable error, and require only 1 bit more than the theoretical optimal discretization with the same error.

Abstract In this paper we address the problem of optimal centre placement for scattered data approximation using radial basis functions (RBFs) by introducing the concept of floating centres. Given an initial least‐squares solution, we optimize the positions and the weights of the RBF centres by minimizing a non‐linear error function. By optimizing the centre positions, we obtain better approximations with a lower number of centres, which improves the numerical stability of the fitting procedure. We combine the non‐linear RBF fitting with a hierarchical domain decomposition technique. This provides a powerful tool for surface reconstruction from oriented point samples. By directly incorporating point normal vectors into the optimization process, we avoid the use of off‐surface points which results in less computational overhead and reduces undesired surface artefacts. We demonstrate that the proposed surface reconstruction technique is as robust as recent methods, which compute the indicator function of the solid described by the point samples. In contrast to indicator function based methods, our method computes a global distance field that can directly be used for shape registration.

Figure 1: We adaptively subdivide rational Bézier patches until a view-dependent error metric is satisfied. For a 1600x1200 image of the car model (right) we render 192k quads at 143 fps on a NVIDIA GTX 280 – including CUDA transfer overheads, texturing, Phong shading, and 16x multisampling. We propose a view-dependent adaptive subdivision algorithm for rendering parametric surfaces on parallel hardware. Our framework allows us to bound the screen space error of a piecewise linear approximation. We naturally assign more primitives to curved areas while keeping quads large for flatter parts of the model and avoid cracks resulting from the polygonal approximation of nonuniform patch subdivision. The overall algorithm is simple, fits current GPUs extremely well, and is surprisingly fast while producing little to no artifacts.