Hardware‐Assisted Projected Tetrahedra

Abstract

We present a flexible and highly efficient hardware-assisted volume renderer grounded on the original Projected Tetrahedra (PT) algorithm. Unlike recent similar approaches, our method is exclusively based on the rasterization of simple geometric primitives and takes full advantage of graphics hardware. Both vertex and geometry shaders are used to compute the tetrahedral projection, while the volume ray integral is evaluated in a fragment shader; hence, volume rendering is performed entirely on the GPU within a single pass through the pipeline. We apply a CUDA-based visibility ordering achieving rendering and sorting performance of over 6 M Tet/s for unstructured datasets. Furthermore, as each tetrahedron is processed independently, we employ a data-parallel solution which is neither bound by GPU memory size nor does it rely on auxiliary volume information. In addition, iso-surfaces can be readily extracted during the rendering process, and time-varying data are handled without extra burden.

Volumetric Real-Time Particle-Based Representation of Large Unstructured Tetrahedral Polygon Meshes

“…The depicted results and frame rates were recorded on an NVIDIA GeForce GTX470 using CUDA 4.1, rendered at a resolution of 1200x800 pixels. Figure 2 shows a comparison of projected tetrahedrons [5] and our algorithm. The scalar values depict the flow inside the tissue.…”

“…Sorting is known to be in O(n log n), inducing a super-linear increase in computational effort. Approaches like projected tetrahedrons have already been implemented on the GPU [5]. The authors exploit the capabilities of shaders and CUDA to perform depth sorting of the tetrahedrons.…”

Volume rendering dark matter simulations using cell projection and order-independent transparency

“…Shirley and Tuchman introduced Projected Tetrahedra (PT) [Shirley and Tuchman 1990] to compute the rendering contribution of each tetrahedra as it is splatted to the screen. Numerous improvements have been made to the original algorithm since then, such as removing artifacts [Kraus et al 2004], adding hardware acceleration [Wylie et al 2002], and accelerating the render-order sort via the GPU [Maximo et al 2010]. PT has been shown to scale well for distributed rendering of large-scale data [Ma and Crockett 1997].…”

Out-of-core visualization of time-varying hybrid-grid volume data

“…The PT algorithm needs a visibility ordering of the cells. A variety of sorting approaches have been developed [4] [16]. However, for rasterization-based GPU techniques, interactivity degrades significantly for large datasets.…”