Detail preserving continuum simulation of straight hair

Hou

Computer Animation & Virtual

2023

Poisson's equation is one of the most popular partial differential equation (PDE), which is widely used in image processing, computer graphics and other fields. However, solving a large‐scale Poisson's equation always costs huge computational resources. Fast Fourier transform (FFT) is an efficient Poisson solver but it only works in rectangular domain. In this paper, we propose a FFT‐based Poisson solver in nonrectangular domain on regular grids combined with algebraic multigrid (AMG). We extend the original Poisson's equation to a rectangular domain to construct an equivalent equation, so that it can use FFT algorithm to accelerate the solving to Poisson's equation. Experiments show that the FFT‐based Poisson solver can improve the solving speed of large‐scale Poisson's equations in nonrectangular domain. We demonstrate the solver in applications of image processing and fluid simulation.

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

FFT‐based efficient Poisson solver in nonrectangular domain

Hou

Computer Animation & Virtual

2023

“…These methods partly inspire our work on collision handling for cohesive wet strands. Also, a few authors have treated strands or other deformable thin structures as a fluid-like material and hence adopted continuumbased collision handling [Fei et al 2018;Hadap and Magnenat-Thalmann 2001;Lee et al 2019;McAdams et al 2009], where contact and friction are solved globally on a uniform grid. These methods either need an extra pass of traditional penalty-based collision handling or can be numerically difficult for simulating stiff strands.…”

Section: Strand Simulationmentioning

confidence: 99%

A multi-scale model for coupling strands with shear-dependent liquid

et al. 2019

Fig. 1. Left: A rotating brush splashing through thick oil paint. The inset shows a zoomed view of paint on the bristles. Middle: Melted chocolate poured onto a hair-covered cylinder that rotates to mimic the shaking behavior of mammals. Right: Soba noodles covered with oyster sauce pulled upwards by a fork.We propose a framework for simulating the complex dynamics of strands interacting with compressible, shear-dependent liquids, such as oil paint, mud, cream, melted chocolate, and pasta sauce. Our framework contains three main components: the strands modeled as discrete rods, the bulk liquid represented as a continuum (material point method), and a reduced-dimensional flow of liquid on the surface of the strands with detailed elastoviscoplastic behavior. These three components are tightly coupled together. To enable discrete strands interacting with continuum-based liquid, we develop models that account for the volume change of the liquid as it passes through strands and the momentum exchange between the strands and the liquid. We also develop an extended constraint-based collision handling method that supports cohesion between strands. Furthermore, we present a principled method to preserve the total momentum of a strand and its surface flow, as well as an analytic plastic flow approach for Herschel-Bulkley fluid that enables stable semi-implicit integration at larger time steps. We explore a series of challenging scenarios, involving splashing, shaking, and agitating the liquid which causes the strands to stick together and become entangled.

“…Foster and Metaxas used particles for tracking liquids in [Foster and Metaxas 1996]. Most applications in computer graphics are for incompressible flows using a MAC-grid [Harlow and Welch 1965] pressure projection to enforce incompressibility in the grid momentum update [Batty et al 2007;Batty and Bridson 2008;Boyd and Bridson 2012;Larionov et al 2017;McAdams et al 2009;Zhang et al 2016]. Unilateral incompressibility, where a divergence-inequality constraint replaces the divergence-free constraint, has been used with FLIP for a wide range of applications.…”

Section: Previous Workmentioning

confidence: 99%

A polynomial particle-in-cell method

et al. 2017

Self Cite

Fig. 1. Ink drop. We compare from left to right FLIP, APIC, and PolyPIC for an inkjet in an ambient incompressible fluid. PolyPIC more effectively resolves the vorticial details.Recently the Affine Particle-In-Cell (APIC) Method was proposed by 2017b] to improve the accuracy of the transfers in Particle-In-Cell (PIC) [Harlow 1964] techniques by augmenting each particle with a locally affine, rather than locally constant description of the velocity. This reduced the dissipation of the original PIC without suffering from the noise present in the historic alternative, Fluid-Implicit-Particle (FLIP) [Brackbill and Ruppel 1986]. We present a generalization of APIC by augmenting each particle with a more general local function. By viewing the grid-to-particle transfer as a linear and angular momentum conserving projection of the particle-wise local grid velocities onto a reduced basis, we greatly improve the energy and vorticity conservation over the original APIC. Furthermore, we show that the cost of the generalized projection is negligible over APIC when using a particular class of local polynomial functions. Lastly, we note that our method retains the filtering property of APIC and PIC and thus has similar robustness to noise.