arXiv subjects

Ryusuke Sugimoto

Publications and source records attributed to Ryusuke Sugimoto.

6 recordsLinked to original sources

arXiv2026

Monte Carlo Rendering to Diffusion Curves with Differential BEM

We present a method for generating vector graphics, in the form of diffusion curves, directly from noisy samples produced by a Monte Carlo renderer. While generating raster images from 3D geometry via Monte Carlo raytracing is commonplace, there is no corresponding practical approach for robustly and directly extracting editable vector images with shading information from 3D geometry. To fill this gap, we formulate the problem as a stochastic optimization problem over the space of geometries and colors of diffusion curve handles, and solve it with the Levenberg-Marquardt algorithm. At the core of our method is a novel differential boundary element method (BEM) framework that reconstructs colors from diffusion curve handles and computes gradients with respect to their parameters, requiring the expensive matrix factorization only once at the beginning of the optimization. Unlike triangulation-based techniques that require a clean domain decomposition, our method is robust to geometrically challenging scenarios, such as intersecting diffusion curves, and to color noise in the target image, enabling the direct use of noisy Monte Carlo samples without requiring a converged, error-free input image. We demonstrate the robustness and broad applicability of our approach across several test cases. Finally, we highlight several open questions raised by our work, which spans both theory and applications.

cs.GR↗

arXiv2024

Projected Walk on Spheres: A Monte Carlo Closest Point Method for Surface PDEs

We present projected walk on spheres (PWoS), a novel pointwise and discretization-free Monte Carlo solver for surface PDEs with Dirichlet boundaries, as a generalization of the walk on spheres method (WoS) [Muller 1956; Sawhney and Crane 2020]. We adapt the recursive relationship of WoS designed for PDEs in volumetric domains to a volumetric neighborhood around the surface, and at the end of each recursion step, we project the sample point on the sphere back to the surface. We motivate this simple modification to WoS with the theory of the closest point extension used in the closest point method. To define the valid volumetric neighborhood domain for PWoS, we develop strategies to estimate the local feature size of the surface and to compute the distance to the Dirichlet boundaries on the surface extended in their normal directions. We also design a mean value filtering method for PWoS to improve the method's efficiency when the surface is represented as a polygonal mesh or a point cloud. Finally, we study the convergence of PWoS and demonstrate its application to graphics tasks, including diffusion curves, geodesic distance computation, and wave propagation animation. We show that our method works with various types of surfaces, including a surface of mixed codimension.

math.NA↗

arXiv2024

Galerkin Method of Regularized Stokeslets for Procedural Fluid Flow with Control Curves

We present a new procedural incompressible velocity field authoring tool, which lets users design a volumetric flow by directly specifying velocity along control curves. Our method combines the Method of Regularized Stokeslets with Galerkin discretization. Based on the highly viscous Stokes flow assumption, we find the force along a given set of curves that satisfies the velocity constraints along them. We can then evaluate the velocity anywhere inside the surrounding infinite 2D or 3D domain. We also show the extension of our method to control the angular velocity along control curves. Compared to a collocation discretization, our method is not very sensitive to the vertex sampling rate along control curves and only requires a small linear system solve.

cs.GR↗

arXiv2024

Velocity-Based Monte Carlo Fluids

We present a velocity-based Monte Carlo fluid solver that overcomes the limitations of its existing vorticity-based counterpart. Because the velocity-based formulation is more commonly used in graphics, our Monte Carlo solver can be readily extended with various techniques from the fluid simulation literature. We derive our method by solving the Navier-Stokes equations via operator splitting and designing a pointwise Monte Carlo estimator for each substep. We reformulate the projection and diffusion steps as integration problems based on the recently introduced walk-on-boundary technique [Sugimoto et al. 2023]. We transform the volume integral arising from the source term of the pressure Poisson equation into a form more amenable to practical numerical evaluation. Our resulting velocity-based formulation allows for the proper simulation of scenes that the prior vorticity-based Monte Carlo method [Rioux-Lavoie and Sugimoto et al. 2022] either simulates incorrectly or cannot support. We demonstrate that our method can easily incorporate advancements drawn from conventional non-Monte Carlo methods by showing how one can straightforwardly add buoyancy effects, divergence control capabilities, and numerical dissipation reduction methods, such as advection-reflection and PIC/FLIP methods.

cs.GR↗

arXiv2023

A Practical Walk-on-Boundary Method for Boundary Value Problems

We introduce the walk-on-boundary (WoB) method for solving boundary value problems to computer graphics. WoB is a grid-free Monte Carlo solver for certain classes of second order partial differential equations. A similar Monte Carlo solver, the walk-on-spheres (WoS) method, has been recently popularized in computer graphics due to its advantages over traditional spatial discretization-based alternatives. We show that WoB's intrinsic properties yield further advantages beyond those of WoS. Unlike WoS, WoB naturally supports various boundary conditions (Dirichlet, Neumann, Robin, and mixed) for both interior and exterior domains. WoB builds upon boundary integral formulations, and it is mathematically more similar to light transport simulation in rendering than the random walk formulation of WoS. This similarity between WoB and rendering allows us to implement WoB on top of Monte Carlo ray tracing, and to incorporate advanced rendering techniques (e.g., bidirectional estimators with multiple importance sampling, the virtual point lights method, and Markov chain Monte Carlo) into WoB. WoB does not suffer from the intrinsic bias of WoS near the boundary and can estimate solutions precisely on the boundary. Our numerical results highlight the advantages of WoB over WoS as an attractive alternative to solve boundary value problems based on Monte Carlo.

cs.GR↗

arXiv2022

Water Simulation and Rendering from a Still Photograph

We propose an approach to simulate and render realistic water animation from a single still input photograph. We first segment the water surface, estimate rendering parameters, and compute water reflection textures with a combination of neural networks and traditional optimization techniques. Then we propose an image-based screen space local reflection model to render the water surface overlaid on the input image and generate real-time water animation. Our approach creates realistic results with no user intervention for a wide variety of natural scenes containing large bodies of water with different lighting and water surface conditions. Since our method provides a 3D representation of the water surface, it naturally enables direct editing of water parameters and also supports interactive applications like adding synthetic objects to the scene.

cs.GR↗