A Learned Shape-Adaptive Subsurface Scattering Model

Subsurface scattering, in which light refracts into a translucent material to interact with its interior, is the dominant mode of light transport in many types of organic materials. Accounting for this phenomenon is thus crucial for visual realism, but explicit simulation of the complex internal scattering process is often too costly. BSSRDF models based on analytic transport solutions are significantly more efficient but impose severe assumptions that are almost always violated, e.g. planar geometry, isotropy, low absorption, and spatio-directional separability. The resulting discrepancies between model and usage lead to objectionable errors in renderings, particularly near geometric features that violate planarity. This article introduces a new shape-adaptive BSSRDF model that retains the efficiency of prior analytic methods while greatly improving overall accuracy. Our approach is based on a conditional variational autoencoder, which learns to sample from a reference distribution produced by a brute-force volumetric path tracer. In contrast to the path tracer, our autoencoder directly samples outgoing locations on the object surface, bypassing a potentially lengthy internal scattering process. The distribution is conditional on both material properties and a set of features characterizing geometric variation in a neighborhood of the incident location. We use a low-order polynomial to model the local geometry as an implicitly defined surface, capturing curvature, thickness, corners, as well as cylindrical and toroidal regions. We present several examples of objects with challenging medium parameters and complex geometry and compare to ground truth simulations and prior work.

Modélisation, analyse mathématique et simulation numérique de la dynamique des glaciers

Guillaume Jouvet

We address the free boundary problem that consists in finding the shape of a three dimensional glacier over a given period and under given climatic conditions. Glacier surface moves by sliding, internal shear and external exchange of mass. Ice is modelled as a non Newtonian fluid. Given the shape of the glacier, the velocity of ice is obtained by solving a stationary non-linear Stokes problem with a sliding law along the bedrock-ice interface. The shape of the glacier is updated by computing a Volume Of Fluid (VOF) function, which satisfies a transport equation. Climatic effects (accumulation and ablation of ice) are taken into account in the source term of this equation. A decoupling algorithm with a two-grid method allows the velocity of ice and the VOF to be computed using different numerical techniques, such that a Finite Element Method (FEM) and a characteristics method. On a theoretical level, we prove the well-posedness of the non-linear Stokes problem. A priori estimates for the convergence of the FEM are established by using a quasi-norm technique. Eventually, convergence of the linearisation schemes, such that a fixed point method and a Newton method, is proved. Several applications demonstrate the potential of the numerical method to simulate the motion of a glacier during a long period. The first one consists in the simulation of Rhone et Aletsch glacier from 1880 to 2100 by using climatic data provided by glaciologists. The glacier reconstructions over the last 120 years are validated against measurements. Afterwards, several different climatic scenarios are investigated in order to predict the shape the glaciers until 2100. A dramatic retreat during the 21st century is anticipated for both glaciers. The second application is an inverse problem. It aims to find a climate parametrization allowing a glacier to fit some of its moraines. Two other aspects of glaciology are also addressed in this thesis. The first one consists in modeling and in simulating ice collapse during the calving process. The previous ice flow model is supplemented by a Damage variable which describes the presence of micro crack in ice. An additional numerical scheme allows the Damage field to be solved and a two dimensional simulation of calving to be performed. The second problem aims to prove the existence of stationary ice sheet when considering shallow ice model and a simplified geometry. Numerical investigation confirms the theoretical result and shows physical properties of the solution.

EPFL2010

Geometric Tools for Exploring Manifolds of Light Transport Paths

Wenzel Alban Jakob

Photorealistic images created using physical simulations of light have become a ubiquitous element of our everyday lives. The most successful techniques for producing such images replicate the key physical phenomena in a detailed software simulation, including the emission of light by sources, transport through space, and scattering in the atmosphere and at the surfaces of objects. Mathematically, this computation involves the approximation of many highdimensional integrals, one for each pixel of the image, usually using Monte Carlo methods. Although a great deal of progress has been made on rendering algorithms, so that physically based rendering is now routinely used in many applications, commonly occurring situations can still cause these algorithms to become impractically slow, forcing users to make unrealistic scene modifications to obtain satisfactory results. Light transport is complex because light can flow along a great variety of different paths through a scene, though only a subset of these makes relevant contributes to the final image. The simulation becomes ineffective when it is difficult to find the important paths. Commonly occurring materials like smooth metal or glass surfaces can easily lead to such situations, where only very few lighting paths participate, leading to spiky integrands and poor convergence. How to efficiently handle such cases in general has been a long-standing problem. In this paper, we provide a geometric solution to this problem by representing light paths as points in an abstract high-dimensional configuration space that is defined by a system of constraint equations. This configuration space is a differentiable manifold, which can be locally parameterized in the neighborhood of an existing path. Building on this framework, we propose Manifold Exploration, a rendering technique that efficiently explores the integration domain by taking geometrically informed steps on the manifold of light paths.

ACM2015

Adaptive analysis-aware defeaturing

Ondine Gabrielle Chanon

Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, depending on the partial differential equation that one wants to solve in the geometrical model of interest, removing some important geometrical features may greatly impact the solution accuracy. For instance, in solid mechanics simulations, such features can be holes or fillets near stress concentration regions. Unfortunately, the effect of geometrical simplification on the accuracy of the problem solution is often neglected, because its analysis is a time-consuming task that is often performed manually, based on the expertise of engineers. It is therefore important to have a better understanding of the effect of geometrical model simplification, also called defeaturing, to improve our control on the simulation accuracy along the design and analysis phase.In this thesis, we formalize the process of defeaturing, and we analyze its impact on the accuracy of solutions of some partial differential problems. To achieve this goal, we first precisely define the error between the problem solution defined in the exact geometry, and the one defined in the simplified geometry. Then, we introduce an a posteriori estimator of the energy norm of this error. This allows us to reliably and efficiently control the error coming from the addition or the removal of geometrical features. We subsequently consider a finite element approximation of the defeatured problem, and the induced numerical error is integrated to the proposed defeaturing error estimator. In particular, we address the special case of isogeometric analysis based on (truncated) hierarchical B-splines, in possibly trimmed and multipatch geometries. In this framework, we derive a reliable a posteriori estimator of the overall error, i.e., of the error between the exact solution defined in the exact geometry, and the numerical solution defined in the defeatured geometry.We then propose a two-fold adaptive strategy for analysis-aware defeaturing, which starts by considering a coarse mesh on a fully-defeatured computational domain. On the one hand, the algorithm performs classical finite element mesh refinements in a (partially) defeatured geometry. On the other hand, the strategy also allows for geometrical refinement. That is, at each iteration, the algorithm is able to choose which missing geometrical features should be added to the simplified geometrical model, in order to obtain a more accurate solution.Throughout the thesis, we validate the presented theory, the properties of the aforementioned estimators and the proposed adaptive strategies, thanks to an extensive set of numerical experiments.

EPFL2022