PSCC: Parallel Self-Collision Culling with Spatial Hashing on GPUs

Min Tang, Zhongyuan Liu,, Ruofeng Tong, Dinesh Manocha

We present a GPU-based self-collision culling method (PSCC) based on a combination of normal cone culling and spatial hashing techniques. We first describe a normal cone test front (NCTF) based parallel algorithm that maps well to GPU architectures. We use sprouting and shrinking operators to maintain compact NCTFs. Moreover, we use the NCTF nodes to efficient build an enhanced spatial hashing for triangles meshes and use that for inter-object and intra-object collisions. Compared with conventional spatial hashing, our approach provides higher culling efficiency and reduces the cost of narrow phrase culling. As compared to prior GPU-based parallel collision detection algorithm, our approach demonstrates 6?8X speedup. We also present an efficient approach for GPU-based cloth simulation based on PSCC. In practice, our GPU-based cloth simulation takes about one second per frame on complex scenes with tens or hundreds of thousands of triangles, and is about 4-6X faster than prior GPU-based simulation algorithms.

PSCC: Parallel Self-Collision Culling with Spatial Hashing on GPUs

Real-Time Virtual Pipes Simulation and Modeling for Small-Scale Shallow Water

François Dagenais, Julián Guzmán, Valentin Vervondel, Alexander Hay, Sébastien Delorme, David Mould, and Eric Paquette

We propose an approach for real-time shallow water simulation, building upon the virtual pipes model with multi-layered heightmaps. Our approach introduces the use of extended pipes which resolve flow through fully-flooded passages, which is not possible using current multi-layered techniques. We extend the virtual pipe method with a physically-based viscosity model that is both fast and stable. Our viscosity model is integrated implicitly without the expense of solving a large linear system. The liquid is rendered as a triangular mesh surface built from a heightmap. We propose a novel surface optimization approach that prevents interpenetrations of the liquid surface with the underlying terrain geometry. To improve the realism of small-scale scenarios, we present a meniscus shading approach that adjusts the liquid surface normals based on a distance field. Our approach runs in real time on various scenarios of roughly 10×10 cm at a resolution of 0.5 mm with up to five layers.

Real-Time Virtual Pipes Simulation and Modeling for Small-Scale Shallow Water

Pressure Boundaries for Implicit Incompressible SPH

Stefan Band, Christoph Gissler, Markus Ihmsen, Jens Cornelis, Andreas Peer, Matthias Teschner

Implicit incompressible SPH (IISPH) solves a pressure Poisson equation (PPE). While the solution of the PPE provides pressure at fluid samples, the embedded boundary handling does not compute pressure at boundary samples. Instead, IISPH uses various approximations to remedy this deficiency. In this paper, we illustrate the issues of these IISPH approximations. We particularly derive Pressure Boundaries, a novel boundary handling that overcomes previous IISPH issues by the computation of physically meaningful pressure values at boundary samples. This is basically achieved with an extended PPE. We provide a detailed description of the approach that focuses on additional technical challenges due to the incorporation of boundary samples into the PPE. We therefore use volume-centric SPH discretizations instead of typically used density-centric ones. We further analyze the properties of the proposed boundary handling and compare it to the previous IISPH boundary handling. In addition to the fact that the proposed boundary handling provides physically meaningful pressure and pressure gradients at boundary samples, we show further benefits such as reduced pressure oscillations, improved solver convergence and larger possible time steps. The memory footprint of fluid samples is reduced and performance gain factors of up to five compared to IISPH are presented.

Pressure Boundaries for Implicit Incompressible SPH

An Implicit SPH Formulation for Incompressible Linearly Elastic Solids

Andreas Peer, Christoph Gissler, Stefan Band, Matthias Teschner
We propose a novel SPH formulation for deformable solids. Key aspects of our method are implicit elastic forces and an adapted SPH formulation for the deformation gradient that—in contrast to previous work—allows a rotation extraction directly from the SPH deformation gradient. The proposed implicit concept is entirely based on linear formulations. As a linear strain tensor is used, a rotation-aware computation of the deformation gradient is required. In contrast to existing work, the respective rotation estimation is entirely realized within the SPH concept using a novel formulation with incorporated kernel gradient correction for first-order consistency. The proposed implicit formulation and the adapted rotation estimation allow for significantly larger time steps and higher stiffness compared to explicit forms. Performance gain factors of up to one hundred are presented. Incompressibility of deformable solids is accounted for with an ISPH pressure solver. This further allows for a pressure-based boundary handling and a unified processing of deformables interacting with SPH fluids and rigids. Self-collisions are implicitly handled by the pressure solver.

An Implicit SPH Formulation for Incompressible Linearly Elastic Solids

SIGGRAPH 2018

SIGGRAPH:

 

TOG presentations:

Controllable Dendritic Crystal Simulation Using Orientation Field

Bo Ren, Jiahui Huang, Ming C. Lin, Shi-Min Hu

Real world dendritic growths show charming structures by their exquisite balance between the symmetry and randomness in the crystal formation. Other than the variety in the natural crystals, richer visual appearance of crystals can benefit from artificially controlling of the crystal growth on its growing directions and shapes. In this paper, by introducing one extra dimension of freedom, i.e. the orientation field, into the simulation, we propose an efficient algorithm for dendritic crystal simulation that is able to reproduce arbitrary symmetry patterns with different levels of asymmetry breaking effect on general grids or meshes including spreading on curved surfaces and growth in 3D. Flexible artistic control is also enabled in a unified manner by exploiting and guiding the orientation field in the visual simulation. We show the effectiveness of our approach by various demonstrations of simulation results.

Controllable Dendritic Crystal Simulation Using Orientation Field

A Skinned Tetrahedral Mesh for Hair Animation and Hair-Water Interaction

Minjae Lee, David Hyde, Michael Bao, Ronald Fedkiw

We propose a novel framework for hair animation as well as hair-water interaction that supports millions of hairs. First, we develop a hair animation framework that embeds hair into a tetrahedralized volume mesh that we kinematically skin to deform and follow the exterior of an animated character. Allowing the hairs to follow their precomputed embedded locations in the kinematically deforming skinned mesh already provides visually plausible behavior. Creating a copy of the tetrahedral mesh, endowing it with springs, and attaching it to the kinematically skinned mesh creates more dynamic behavior. Notably, the springs can be quite weak and thus efficient to simulate because they are structurally supported by the kinematic mesh. If independent simulation of individual hairs or guide hairs is desired, they too benefit from being anchored to the kinematic mesh dramatically increasing efficiency as weak springs can be used while still supporting interesting and dramatic hairstyles. Furthermore, we explain how to embed these dynamic simulations into the kinematically deforming skinned mesh so that they can be used as part of a blendshape system where an artist can make many subsequent iterations without requiring any additional simulation. Although there are many applications for our newly proposed approach to hair animation, we mostly focus on the particularly challenging problem of hair-water interaction. While doing this, we discuss how porosities are stored in the kinematic mesh, how the kinematically deforming mesh can be used to apply drag and adhesion forces to the water, etc.

A Skinned Tetrahedral Mesh for Hair Animation and Hair-Water Interaction

Exponential Rosenbrock-Euler Integrators for Elastodynamic Simulation

Yu Ju Chen, Uri M. Ascher, Dinesh K. Pai

High quality simulations of the dynamics of soft flexible objects can be rather costly, because the assembly of internal forces through an often nonlinear stiffness at each time step is expensive. Many standard implicit integrators introduce significant, time-step dependent artificial damping. Here we propose and demonstrate the effectiveness of an exponential Rosenbrock-Euler (ERE) method which avoids discretization-dependent artificial damping. The method is relatively inexpensive and works well with the large time steps used in computer graphics. It retains correct qualitative behaviour even in challenging circumstances involving non-convex elastic energies. Our integrator is designed to handle and perform well even in the important cases where the symmetric stiffness matrix is not positive definite at all times. Thus we are able to address a wider range of practical situations than other related solvers. We show that our system performs efficiently for a wide range of soft materials.

Exponential Rosenbrock-Euler Integrators for Elastodynamic Simulation

Efficient BVH-based Collision Detection Scheme with Ordering and Restructuring

X. L. Wang, M. Tang, D. Manocha, Ruo-Feng Tong

Bounding volume hierarchy (BVH) has been widely adopted as the acceleration structure in broad-phase collision detection. Previous state-of-the-art BVH-based collision detection approaches exploited the spatio-temporal coherence of simulations by maintaining a bounding volume test tree (BVTT) front. A major drawback of these algorithms is that large deformations in the scenes decrease culling efficiency and slow down collision queries. Moreover, for front-based methods, the inefficient caching on GPU caused by the arbitrary layout of BVH and BVTT front nodes becomes a critical performance issue. We present a fast and robust BVH-based collision detection scheme on GPU that addresses the above problems by ordering and restructuring BVHs and BVTT fronts. Our techniques are based on the use of histogram sort and an auxiliary structure BVTT front log, through which we analyze the dynamic status of BVTT front and BVH quality. Our approach efficiently handles inter- and intra-object collisions and performs especially well in simulations where there is considerable spatio-temporal coherence. The benchmark results demonstrate that our approach is significantly faster than the previous BVH-based method, and also outperforms other state-of-the-art spatial subdivision schemes in terms of speed.

Efficient BVH-based Collision Detection Scheme with Ordering and Restructuring

Stabilizing Integrators for Real-Time Physics

Dimitar Dinev, Tiantian Liu, Ladislav Kavan

We present a new time integration method featuring excellent stability and energy conservation properties, making it particularly suitable for real-time physics. The commonly used backward Euler method is stable but introduces artificial damping. Methods such as implicit midpoint do not suffer from artificial damping but are unstable in many common simulation scenarios. We propose an algorithm that blends between the implicit midpoint and forward/backward Euler integrators such that the resulting simulation is stable while introducing only minimal artificial damping. We achieve this by tracking the total energy of the simulated system, taking into account energy-changing events: damping and forcing. To facilitate real-time simulations, we propose a local/global solver, similar to Projective Dynamics, as an alternative to Newton’s method. Compared to the original Projective Dynamics, which is derived from backward Euler, our final method introduces much less numerical damping at the cost of minimal computing overhead. Stability guarantees of our method are derived from the stability of backward Euler, whose stability is a widely accepted empirical fact. However, to our knowledge, theoretical guarantees have so far only been proven for linear ODEs. We provide preliminary theoretical results proving the stability of backward Euler also for certain cases of nonlinear potential functions.

Stabilizing Integrators for Real-Time Physics