Figure 1: Reproducing fine surface detail using our method for signal optimal displacement mapping. From left to right: Augustus model and close-ups of the full resolution model (366 MB GPU memory, 19.3 ms rendering time), and our reconstructions with fitting errors εmax = 0.1 (90 MB, 11.9 ms) and εmax = 0.5 (28 MB, 3.7 ms), respectively. AbstractWe 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.Contrary to texture mapping, our approach does not require any atlas generation, chartification, or uv-unwrapping. Thus, it does not suffer from texture-related artifacts, such as discontinuities across chart boundaries or distortion. Moreover, our approach allows specifying the optimal sampling rate adaptively on a per triangle basis, resulting in significant memory savings for most signal types.We propose a signal optimal approach for converting arbitrary signals, including existing assets with textures or mesh colors, into our representation. Further, we provide efficient algorithms for mipmapping, bi-and tri-linear interpolation directly in our representation. Our approach is optimally suited for displacement mapping: it automatically generates crack-free, view-dependent displacement mapped models enabling continuous level-of-detail.

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.

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