On Prism-based Motion Blur and Locking-proof Tetrahedra

Motion blur is an important visual effect in computer graphics for both real-time, interactive, and offline applications. Current methods offer either slow and accurate solutions for offline ray tracing applications, or fast and inaccurate solutions for real-time applications. This thesis is a collection of three papers, two of which address the need for motion blur solutions that cater to applications that need to be accurate and as well as interactive, and a third that addresses the problem of locking in standard FEM simulations. In short, this thesis deals with the problem of representing continuous motion in a discrete setting.In Paper I, we implement a GPU based fast analytical motion blur renderer. Using ray/triangular prism intersections to determine triangle visibility and shading, we achieve interactive frame rates.In Paper II, we show and address the limitations of using prisms as approximations of the triangle swept volume. A hybrid method of prism intersections and time-dependent edge equations is used to overcome the limitations of Paper I.In Paper III, we provide a solution that alleviates volumetric locking in standard Neo-Hookean FEM simulations without resorting to higher order interpolation

Fast Analytical Motion Blur with Transparency

We introduce a practical parallel technique to achieve real-time motion blur for textured and semi-transparent triangles with high accuracy using modern commodity GPUs. In our approach, moving triangles are represented as prisms. Each prism is bounded by the initial and final position of the triangle during one animation frame and three bilinear patches on the sides. Each prism covers a number of pixels for a certain amount of time according to its trajectory on the screen. We efficiently find, store and sort the list of prisms covering each pixel including the amount of time the pixel is covered by each prism. This information, together with the color, texture, normal, and transparency of the pixel, is used to resolve its final color. We demonstrate the performance, scalability, and generality of our approach in a number of test scenarios, showing that it achieves a visual quality practically indistinguishable from the ground truth in a matter of just a few milliseconds, including rendering of textured and transparent objects. A supplementary video has been made available online

Locking-Proof Tetrahedra

The simulation of incompressible materials suffers from locking when using the standard finite element method (FEM) and coarse linear tetrahedral meshes. Locking increases as the Poisson ratio gets close to 0.5 and often lower Poisson ratio values are used to reduce locking, affecting volume preservation. We propose a novel mixed FEM approach to simulating incompressible solids that alleviates the locking problem for tetrahedra. Our method uses linear shape functions for both displacements and pressure, and adds one scalar per node. It can accommodate nonlinear isotropic materials described by a Young\u27s modulus and any Poisson ratio value by enforcing a volumetric constitutive law. The most realistic such material is Neo-Hookean, and we focus on adapting it to our method. For , we can obtain full volume preservation up to any desired numerical accuracy. We show that standard Neo-Hookean simulations using tetrahedra are often locking, which, in turn, affects accuracy. We show that our method gives better results and that our Newton solver is more robust. As an alternative, we propose a dual ascent solver that is simple and has a good convergence rate. We validate these results using numerical experiments and quantitative analysis

Improved Accuracy for Prism-Based Motion Blur

For motion blur of dynamic triangulated objects, it is common to construct a prism-like shape for each triangle, from the linear trajectories of its three edges and the triangle’s start and end position during the delta time step. Such a prism can be intersected with a primary ray to find the time points where the triangle starts and stops covering the pixel center. These intersections are paired into time intervals for the triangle and pixel. Then, all time intervals, potentially from many prisms, are used to aggregate a motion-blurred color contribution to the pixel.For real-time rendering purposes, it is common to linearly interpolate the ray-triangle intersection and uv coordinates over the time interval. This approximation often works well, but the true path in 3D and uv space for the ray-triangle intersection, as a function of time, is in general nonlinear.In this article, we start by noting that the path of the intersection point can even partially reside outside of the prism volume itself: i.e., the prism volume is not always identical to the volume swept by the triangle. Hence, we must first show that the prisms still work as bounding volumes when finding the time intervals with primary rays, as that may be less obvious when the volumes differ. Second, we show a simple and potentially common class of cases where\ua0this happens, such as when a triangle undergoes a wobbling- or swinging-like motion during a time step. Third, when the volumes differ, linear interpolation between two points on the prism surfaces for triangle properties works particularly poorly, which leads to visual artifacts. Therefore, we finally modify a prism-based real-time motion-blur algorithm to use adaptive sampling along the correct paths regarding the triangle location and uv coordinates over which we want to compute a filtered color. Due to being adaptive, the algorithm has a negligible performance penalty on pixels where linear interpolation is sufficient, while being able to significantly improve the visual quality where needed, for a very small additional cost