Teseo Schneider

University of Victoria | UVIC · Department of Computer Science

For a given PDE problem, three main factors affect the accuracy of FEM solutions: basis order, mesh resolution, and mesh element quality. The first two factors are easy to control, while controlling element shape quality is a challenge, with fundamental limitations on what can be achieved. We propose to use p-refinement (increasing element degree)...

Contacts weave through every aspect of our physical world, from daily household chores to acts of nature. Modeling and predictive computation of these phenomena for solid mechanics is important to every discipline concerned with the motion of mechanical systems, including engineering and animation. Nevertheless, efficiently time-stepping accurate a...

We propose a new tetrahedral meshing technique, fTetWild, to convert triangle soups into high-quality tetrahedral meshes. Our method builds upon the TetWild algorithm, inheriting its unconditional robustness, but dramatically reducing its computation cost and guaranteeing the generation of a valid tetrahedral mesh with floating point coordinates. T...

This course is a group endeavor by Sebastian Koeh, Teseo Sehneider, Francis Williams, and Daniele Panozzo. Please contact us if you have questions or comments. For troubleshooting, please post an issue on github. We are grateful to the authors of all open souree C++ libraries we are using. In particular, libigl, tetwild, polyfem, pybind11, and Jupy...

The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) and it is a staple in most engineering applications. The popularity of this approach led to the development of a large family of variants, and, while their theoretical properties (such as convergence rate, stability, etc.) are well studied, their...

Recent advances in the simulation of frictionally contacting elastodynamics with the Incremental Potential Contact (IPC) model have enabled inversion and intersection-free simulation via the application of mollified barriers, filtered line-search, and optimization-based solvers for time integration. In its current formulation the IPC model is const...

We propose In-Timestep Remeshing, a fully coupled, adaptive meshing algorithm for contacting elastodynamics where remeshing steps are tightly integrated, implicitly, within the timestep solve. Our algorithm refines and coarsens the domain automatically by measuring physical energy changes within each ongoing timestep solve. This provides consistent...

Interval computation is widely used in Computer Aided Design to certify computations that use floating point operations to avoid pitfalls related to rounding error introduced by inaccurate operations. Despite its popularity and practical benefits, support for interval arithmetic is not standardized nor available in mainstream programming languages....

Mechanical signals establish two-way communication between mammalian cells and their environment. Cells contacting a surface exert forces via contractility and transmit them at the areas of focal adhesions. External stimuli, such as compressive and pulling forces, typically affect the adhesion-free cell surface. Here, we demonstrate the collaborati...

We introduce a novel approach to describe mesh generation, mesh adaptation, and geometric modeling algorithms relying on changing mesh connectivity using a high-level abstraction. The main motivation is to enable easy customization and development of these algorithms via a declarative specification consisting of a set of per-element invariants, ope...

Background and Objective: population-based finite element analysis of hip joints allows us to understand the effect of inter-subject variability on simulation results. Developing large subject-specific population models is challenging and requires extensive manual effort. Thus, the anatomical representations are often subjected to simplification. T...

Developing computational models of the human jaw acquired from cone-beam computed tomography (CBCT) scans is time-consuming and labor-intensive. Besides, a quantitative comparison is not attainable in the literature due to the involved manual tasks and the lack of surface/volumetric meshes. We share an open-access repository of 17 patient-specific...

Background: State-of-the-art finite element studies on human jaws are mostly limited to the geometry of a single patient. In general, developing accurate patient-specific computational models of the human jaw acquired from cone-beam computed tomography (CBCT) scans is labor-intensive and non-trivial, which involves time-consuming human-in-the-loop...

The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which require a tetrahedral or hexahedral mesh to construct the basis. While the theoretical properties of FEM basis (suc...

We introduce a general differentiable solver for time-dependent deformation problems with contact. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed incremental potential contact method for handling contact and friction forces to solve PDE- and ODE-constrained optimization problem...

We introduce a high-order finite element formulation (high-order basis) for elastodynamic simulation on high-order (curved) meshes based on the recently proposed Incremental Potential Contact model. High-order meshes provide a more accurate geometrical approximation of the object boundary (where stress usually concentrates, especially in the presen...

We introduce the first exact root parity counter for continuous collision detection (CCD). That is, our algorithm computes the parity (even or odd) of the number of roots of the cubic polynomial arising from a CCD query. We note that the parity is unable to differentiate between zero (no collisions) and the rare case of two roots (collisions). Our...

We introduce a code generator that converts unoptimized C++ code operating on sparse data into vectorized and parallel CPU or GPU kernels. Our approach unrolls the computation into a massive expression graph, performs redundant expression elimination, grouping, and then generates an architecture-specific kernel to solve the same problem, assuming t...

During animal embryogenesis, homeostasis and disease, tissues push and pull on their surroundings to move forward. Although the force-generating machinery is known, it is unknown how tissues exert physical stresses on their substrate to generate motion in vivo. Here, we identify the force transmission machinery, the substrate and the stresses that...

The computation of first and second-order derivatives is a staple in many computing applications, ranging from machine learning to scientific computing. We propose an algorithm to automatically differentiate algorithms written in a subset of C99 code and its efficient implementation as a Python script. We demonstrate that our algorithm enables auto...

We introduce a collection of benchmark problems in 2D and 3D (geometry description and boundary conditions), including simple cases with known analytic solution, classical experimental setups, and complex geometries with fabricated solutions for evaluation of numerical schemes for incompressible Navier-Stokes equations in laminar flow regime. We co...

We introduce a broad-phase contrinuous collision detection algorithms designed to take advantage of modern GPU hardware. Our apporoach is based on a simple and suprising experimental observation that brute force checking all collision pairs is, surprisingly, much faster than competing approaches when executed on a modern GPU, due to the massive com...

We introduce a collection of benchmark problems in 2D and 3D (geometry description and boundary conditions), including simple cases with known analytic solution, classical experimental setups, and complex geometries with fabricated solutions for evaluation of numerical schemes for incompressible Navier-Stokes equations in laminar flow regime. We co...

In this paper, we present a new posteriori method to generate high order curved meshes directly from linear meshes through a recently developed poly-spline isogeometric (IGA) method. Given an input structured or unstructured linear quadrilateral or hexahedral mesh, our method constructs quadratic poly-spline IGA bases for each element and ensures c...

We introduce a large-scale benchmark for continuous collision detection (CCD) algorithms, composed of queries manually constructed to highlight challenging degenerate cases and automatically generated using existing simulators to cover common cases. We use the benchmark to evaluate the accuracy, correctness, and efficiency of state-of-the-art conti...

We introduce a code generator that converts unoptimized C++ code operating on sparse data into vectorized and parallel CPU or GPU kernels. Our approach unrolls the computation into a massive expression graph, performs redundant expression elimination, grouping, and then generates an architecture-specific kernel to solve the same problem, assuming t...

Interval computation is widely used to certify computations that use floating point operations to avoid pitfalls related to rounding error introduced by inaccurate operations. Despite its popularity and practical benefits, support for interval arithmetic is not standardized nor available in mainstream programming languages. We propose the first ben...

Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications. Recently, there has been a surge in data-driven methods to complement traditional numerical simulations methods, motivated by the opportunity to reduce computational costs and/or learn new physical models leveragi...

During animal embryogenesis, homeostasis and disease, tissues push and pull on their surroundings to move forward. Although the force-generating machinery is known, it is unknown how tissues exert physical stresses on their substrate to generate motion in vivo . Here, we identify the force transmission machinery, the substrate, and the stresses tha...

We introduce the first implicit time-stepping algorithm for rigid body dynamics, with contact and friction, that guarantees intersection-free configurations at every time step. Our algorithm explicitly models the curved trajectories traced by rigid bodies in both collision detection and response. For collision detection, we propose a conservative n...

We introduce a robust and automatic algorithm to convert linear triangle meshes with feature annotated into coarse tetrahedral meshes with curved elements. Our construction guarantees that the high-order meshes are free of element inversion or self-intersection. A user-specified maximal geometrical error from the input mesh controls the faithfulnes...

We introduce an algorithm to convert a self-intersection free, orientable, and manifold triangle mesh T into a generalized prismatic shell equipped with a bijective projection operator to map T to a class of discrete surfaces contained within the shell whose normals satisfy a simple local condition. Properties can be robustly and efficiently transf...

Generating locally optimal UAV-trajectories is challenging due to the non-convex constraints of collision avoidance and actuation limits. We present the first local, optimization-based UAV-trajectory generator that simultaneously guarantees validity and asymptotic optimality. \textit{Validity:} Given a feasible initial guess, our algorithm guarante...

We introduce a large scale benchmark for continuous collision detection (CCD) algorithms, composed of queries manually constructed to highlight challenging degenerate cases and automatically generated using existing simulators to cover common cases. We use the benchmark to evaluate the accuracy, correctness, and efficiency of state-of-the-art conti...

Sparse matrix computations are among the most important computational patterns, commonly used in geometry processing, physical simulation, graph algorithms, and other situations where sparse data arises. In many cases, the structure of a sparse matrix is known a priori, but the values may change or depend on inputs to the algorithm. We propose a ne...

The computation of first and second-order derivatives is a staple in many computing applications, ranging from machine learning to scientific computing. We propose an algorithm to automatically differentiate algorithms written in a subset of C99 code and its efficient implementation as a Python script. We demonstrate that our algorithm enables auto...

We introduce a new technique to check containment of a triangle within an envelope built around a given triangle mesh. While existing methods conservatively check containment within a Euclidean envelope, our approach makes use of a non-Euclidean envelope where containment can be checked both exactly and efficiently. Exactness is crucial to address...

We propose a new tetrahedral meshing method, fTetWild, to convert triangle soups into high-quality tetrahedral meshes. Our method builds on the TetWild algorithm, replacing the rational triangle insertion with a new incremental approach to construct and optimize the output mesh, interleaving triangle insertion and mesh optimization. Our approach ma...

Traction Force Microscopy (TFM) derives maps of cell-generated forces, typically in the nN range, transmitted to the extracellular environment upon actuation of complex biological processes. In traditional approaches, force rendering requires a terminal, time-consuming step of cell deadhesion to obtain a reference image. A conceptually opposite app...

We propose a robust 2D meshing algorithm, TriWild, to generate curved triangles reproducing smooth feature curves, leading to coarse meshes designed to match the simulation requirements necessary by applications and avoiding the geometrical errors introduced by linear meshes. The robustness and effectiveness of our technique are demonstrated by bat...

The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for surface reconstruction. Specifically, we overfit a neural network representing a local chart parameterization to...

Barycentric coordinates provide a convenient way to represent a point inside a triangle as a convex combination of the triangle's vertices and to linearly interpolate data given at these vertices. Due to their favourable properties, they are commonly applied in geometric modelling, finite element methods, computer graphics, and many other fields. I...

We introduce an integrated meshing and finite element method pipeline enabling black-box solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which contains a small number of star-shaped polyhedra, and build a set of high-order basis on its elements, combinin...

We present a parallel algorithm for multivariate Radial Basis Function Partition of Unity Method (RBF-PUM) interpolation. The concurrent nature of the RBF-PUM enables designing parallel algorithms for dealing with a large number of scattered data-points in high space dimensions. To efficiently exploit this concurrency, our algorithm makes use of sh...

Barycentric mappings allow to naturally warp a source polygon to a corresponding target polygon, or, more in general, to create mappings between closed curves or polyhedra. Unfortunately, bijectivity of such barycentric mappings can only be guaranteed for the special case of warping between convex polygons. In fact, for any barycentric coordinates...

The discretization of the computational domain plays a central role in the finite element method. In the standard discretization the domain is triangulated with a mesh and its boundary is approximated by a polygon. The boundary approximation induces a geometry-related error which influences the accuracy of the solution. To control this geometry-rel...

Winter sports like skiing and snowboarding are often group activities. Groups of skiers and snowboarders traditionally use paper maps or board-mounted larger-scale maps near ski lifts to aid decision making: which slope to take next, where to have lunch, or what hazards to avoid when going off-piste. To enrich those static maps with personal conten...

Static and dynamic evolution of software systems may be described in terms of connection additions and removals in a graph. Due to the inherent complexity of software, navigating through such a dynamic network is a non-trivial task and extracting relevant information typically involves sophisticated queries. We explore the notion of space-time cube...

Static and dynamic evolution of software systems may be described in terms of connection additions and removals in a graph. Due to the inherent complexity of software, navigating through such a dynamic network is a non-trivial task and extracting relevant information typically involves sophisticated queries. We explore the notion of space-time cube...

Geometry-related software is increasingly important in computational science and visual computing. Engineering such software is particularly challenging due to the size and complexity of the data it operates on. In this paper we present VESTIGE, a framework that employs visualization to address that challenge. VESTIGE targets four software engineer...

Mapping from one planar polygonal domain to another is a fundamental problem in computer graphics and geometric modelling. Exploiting the properties of harmonic maps, we define smooth and bijective maps with prescribed behaviour along the domain boundary. These maps can be approximated in different ways, and we discuss the respective advantages and...

A common way of blending between two planar curves is to linearly interpolate their signed curvature functions and to reconstruct the intermediate curve from the interpolated curvature values. But if both input curves are closed, this strategy can lead to open intermediate curves. We present a new algorithm for solving this problem, which finds the...

We introduce the novel concept of composite barycentric mappings and give theoretical conditions under which they are guaranteed to be bijective. We then focus on mean value mappings and derive a simple procedure for computing their Jacobians, leading to an efficient GPU‐assisted implementation for interactively designing composite mean value mappi...

With the wide support for serialization in objectoriented programming languages, persistent objects have become common place. Retrieving previously “persisted” objects from classes whose schema changed is however difficult, and may lead to invalidating the consistency of the application. The ESCHER framework addresses this issues through an IDE-bas...