SIGGRAPH

The current state of the art in real-time two-dimensional water wave simulation requires developers to choose between efficient Fourier-based methods, which lack interactions with moving obstacles, and finite-difference or finite element methods, which handle environmental interactions but are significantly more expensive. This paper attempts to bridge this long-standing gap between complexity and performance, by proposing a new wave simulation method that can faithfully simulate wave interactions with moving obstacles in real time while simultaneously preserving minute details and accommodating very large simulation domains. Previous methods for simulating 2D water waves directly compute the change in height of the water surface, a strategy which imposes limitations based on the CFL condition (fast moving waves require small time steps) and Nyquist's limit (small wave details require closely-spaced simulation variables). This paper proposes a novel wavelet transformation that discretizes the liquid motion in terms of amplitude-like functions that vary over space, frequency, and direction, effectively generalizing Fourier-based methods to handle local interactions. Because these new variables change much more slowly over space than the original water height function, our change of variables drastically reduces the limitations of the CFL condition and Nyquist limit, allowing us to simulate highly detailed water waves at very large visual resolutions. Our discretization is amenable to fast summation and easy to parallelize. We also present basic extensions like pre-computed wave paths and two-way solid fluid coupling. Finally, we argue that our discretization provides a convenient set of variables for artistic manipulation, which we illustrate with a novel wave-painting interface

Water wave packets

This paper presents a method for simulating water surface waves as a displacement field on a 2D domain. Our method relies on Lagrangian particles that carry packets of water wave energy; each packet carries information about an entire group of wave trains, as opposed to only a single wave crest. Our approach is unconditionally stable and can simulate high resolution geometric details. This approach also presents a straightforward interface for artistic control, because it is essentially a particle system with intuitive parameters like wavelength and amplitude. Our implementation parallelizes well and runs in real time for moderately challenging scenarios

Power Diagrams and Sparse Paged Grids for High Resolution Adaptive Liquids

© ACM, 2017. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Aanjaneya, M., Gao, M., Liu, H., Batty, C., & Sifakis, E. (2017). Power Diagrams and Sparse Paged Grids for High Resolution Adaptive Liquids. ACM Trans. Graph., 36(4), 140:1–140:12. https://doi.org/10.1145/3072959.3073625We present an efficient and scalable octree-inspired fluid simulation framework with the flexibility to leverage adaptivity in any part of the computational domain, even when resolution transitions reach the free surface. Our methodology ensures symmetry, definiteness and second order accuracy of the discrete Poisson operator, and eliminates numerical and visual artifacts of prior octree schemes. This is achieved by adapting the operators acting on the octree's simulation variables to reflect the structure and connectivity of a power diagram, which recovers primal-dual mesh orthogonality and eliminates problematic T-junction configurations. We show how such operators can be efficiently implemented using a pyramid of sparsely populated uniform grids, enhancing the regularity of operations and facilitating parallelization. A novel scheme is proposed for encoding the topology of the power diagram in the neighborhood of each octree cell, allowing us to locally reconstruct it on the fly via a lookup table, rather than resorting to costly explicit meshing. The pressure Poisson equation is solved via a highly efficient, matrix-free multigrid preconditioner for Conjugate Gradient, adapted to the power diagram discretization. We use another sparsely populated uniform grid for high resolution interface tracking with a narrow band level set representation. Using the recently introduced SPGrid data structure, sparse uniform grids in both the power diagram discretization and our narrow band level set can be compactly stored and efficiently updated via streaming operations. Additionally, we present enhancements to adaptive level set advection, velocity extrapolation, and the fast marching method for redistancing. Our overall framework gracefully accommodates the task of dynamically adapting the octree topology during simulation. We demonstrate end-to-end simulations of complex adaptive flows in irregularly shaped domains, with tens of millions of degrees of freedom.National Science FoundationNational Sciences and Engineering Research Council of Canad

Interactive Simulation of Surgical Needle Insertion and Steering

We present algorithms for simulating and visualizing the insertion and steering of needles throughdeformable tissues for surgical training and planning. Needle insertion is an essential component ofmany clinical procedures such as biopsies, injections, neurosurgery, and brachytherapy cancer treatment.The success of these procedures depends on accurate guidance of the needle tip to a clinicaltarget while avoiding vital tissues. Needle insertion deforms body tissues, making accurate placementdifficult. Our interactive needle insertion simulator models the coupling between a flexibleneedle and deformable tissue. We introduce (1) a novel algorithm for local remeshing that quicklyenforces the conformity of a tetrahedral mesh to a curvilinear needle path, enabling accurate computationof contact forces, (2) an efficient method for coupling a 3D finite element simulation with a1D inextensible rod with stick-slip friction, and (3) optimizations that reduce the computation timefor physically based simulations. We can realistically and interactively simulate needle insertioninto a prostate mesh of 13,375 tetrahedra and 2,763 vertices at a 25 Hz frame rate on an 8-core 3.0GHz Intel Xeon PC. The simulation models prostate brachytherapy with needles of varying stiffness,steering needles around obstacles, and supports motion planning for robotic needle insertion.We evaluate the accuracy of the simulation by comparing against real-world experiments in whichflexible, steerable needles were inserted into gel tissue phantoms