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Jonathan Stewart
Jonathan Stewart

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During the level set inversion process, when the salt/sediments interface evolves, updating the physical model parameters near the interface becomes an issue. We propose to perform a continuous deformation of the medium while conserving the mesh topology. The interface nodes are moved consistently with the implicit level set function. Furthermore, this approach preserves a meshed representation of the interface through the inversion process allowing a more accurate seismic modeling. The mesh deformation is obtained by geostatistical kriging of node locations, constrained by the updated interface position.




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Libigl is an open source C++ library for geometry processing research and development. Dropping the heavy data structures of tradition geometry libraries, libigl is a simple header-only library of encapsulated functions. This combines the rapid prototyping familiar to Matlab or Python programmers with the performance and versatility of C++. The tutorial is a self-contained, hands-on introduction to libigl. Via interactive, step-by-step examples, we demonstrate how to accomplish common geometry processing tasks such as computation of differential quantities and operators, real-time deformation, parametrization, numerical optimization and remeshing. Each section of the lecture notes links to a cross-platform example application.


libigl provides input [output] functions to read [write] many common mesh formats.The IO functions are contained in the files read*.h and write*.h. As a generalrule each libigl function is contained in a pair of .h/.cpp files with the same name.By default, the .h files include the corresponding cpp files, making the library header-only.


Libigl can read mixed meshes stored in Gmsh .msh version 2 file format.These files can contain mixture of different meshes, as well as additional scalar and vector fields defined on element level and vertex level.


Storing normals per-corner is an efficient and convenient way of supporting bothsmooth and sharp (e.g. creases and corners) rendering. This format is common toOpenGL and the .obj mesh file format. Often such normals are tuned by the meshdesigner, but creases and corners can also be computed automatically. Libiglimplements a simple scheme which computes corner normals as averages ofnormals of faces incident on the corresponding vertex which do not deviate by more than a specified dihedral angle (e.g. 20).


Often the sum above is truncated to the first kk eigen vectors. If the lowfrequency modes are chosen, i.e. those corresponding to small \lambda_i\lambda_ivalues, then this truncation effectively regularizes \mathbff\mathbff to smooth,slowly changing functions over the mesh (e.g. 8). Modalanalysis and model subspaces have been used frequently in real-time deformation(e.g. 7).


Modern mesh-based shape deformation methods satisfy user deformationconstraints at handles (selected vertices or regions on the mesh) and propagatethese handle deformations to the rest of shape smoothly and without removingor distorting details. Libigl provides implementations of a variety ofstate-of-the-art deformation techniques, ranging from quadratic mesh-basedenergy minimizers, to skinning methods, to non-linear elasticity-inspiredtechniques.


The period of research between 2000 and 2010 produced a collection oftechniques that cast the problem of handle-based shape deformation as aquadratic energy minimization problem or equivalently the solution to a linearpartial differential equation.


This energy is not rotation invariant. If we rotate the mesh by 90 degreesthe change in edge vectors not aligned with the axis of rotation will be large,despite the overall deformation being perfectly rigid.


Taken in turn, these optimizations culminate in a method which optimizes overthe space of linear blend skinning deformations spanned by high-quality weights(i.e. manually painted ones or bounded biharmonic weights). This space is alow-dimensional subspace of all possible mesh deformations, captured by writinglinear blend skinning in matrix form:


The example FastAutomaticSkinningTransformations compares a full (slow) ARAP deformation on a detailed shape (left of middle), to ARAP with grouped rotation edge sets (right of middle), to the very fast subpsace method (right).


The algorithm can be implemented reusing the functions discussed in thedeformation chapter: igl::arap_precomputation and igl::arap_solve. The onlydifference is that the optimization has to be done in 2D instead of 3D and thatwe need to compute a starting point. While for 3D deformation the optimizationis bootstrapped with the original mesh, this is not the case for ARAPparametrization since the starting point must be a 2D mesh. In Example503, we initialize the optimization with harmonicparametrization. Similarly to LSCM, the boundary is free to deform to minimizethe distortion.


Anisotropic and non-uniform quad remeshing is important to concentrate theelements in the regions with more details. It is possible to extend the MIQquad meshing framework to generate anisotropic quad meshes using a meshdeformation approach 33.


Because libigl (purposefully) does not center its implementations around adynamic mesh data structure (e.g. half-edge datastructure), support fortopology changes are limited. Nonetheless, libigl has support for isolated edgecollapses, sequences of edge-collapses (each in O(log) time) and priority queuebased decimation.


The version we implement in libigl is the general version described by 27, and is in two files: and . A demo implementing regularity constraints (creating a mesh in which each face is as regular as possible) is in Example 713.


Although the advantages can be game-changing, there are practical limits that still remain. For example, instance counts, triangles per mesh, material complexity, output resolution, and performance should be carefully measured for any combination of content and hardware. Nanite will continue to expand its capabilities and improve performance in future releases of Unreal Engine.


Nanite is currently limited to rigid meshes, which represent greater than 90% of the geometry in any typical scene. Nanite supports dynamic translation, rotation, and non-uniform scaling of rigid meshes, but does not support general mesh deformation, whether it is dynamic or static. This means any position of a Nanite mesh in a way that is more complex than can be expressed in a single 4x3 matrix multiply applied to the entire mesh.


Sets the percentage of triangles that remain when reducing the source mesh for Nanite. This becomes the coarse representation (or Fallback Mesh) used when the full detail Nanite data cannot be, such as platforms which do not support Nanite rendering, or when it is impractical to use Nanite data like with complex collision.


Many parts of Unreal Engine need access to the traditional vertex buffer provided by traditionally rendered meshes. When Nanite is enabled for a Static Mesh, it generates a coarse representation of the highly detailed mesh that is accessible and used where Nanite data cannot be. The Fallback Mesh is the generated mesh used when Nanite rendering is not supported. It is also used in situations where it wouldn't be ideal to use the full-detail mesh, like when complex collision is needed, using lightmaps for baked lighting is required, and for hardware ray tracing reflections with Lumen.


In the Static Mesh Editor, you can toggle between the fully detailed Nanite mesh and the Nanite Fallback Mesh using the viewports Nanite Fallback option in the Show dropdown menu. Alternatively, you can use the hotkey Ctrl + N to quickly toggle between the two visualization options.


Because of the micro detail that Nanite is able to achieve, it might be assumed that it means a large increase in geometry data resulting in larger game package sizes and downloads for players. However, the reality isn't that dire. In fact, Nanite's mesh format is significantly smaller than the standard Static Mesh format because of Nanite's specialized mesh encoding.


The optimization is not to be done in the rig, but with the deformation technique, that's why if you use mesh deform, you should always create a proxy version of the character. I'll cover that in one of the last chapters of the tutorials I'm publishing.


I find the new depsgraph does drop speed initially, but if you up the subdivision levels it doesn't drop per level like it does in the old graph. In the rig file, the proxy mesh is on layer 2. If you link the rig, you'll link the group "vincent_low" into the new scene.


JP is right in regards to optimizations; the rig is not the issue; it's the deformations. I get about 60 FPS with just the rig, 35 with the proxy mesh, 24 on the high-res mesh without subdivisions, 9 with one level. In the new depsgraph I get 26 FPS on just the rig, 19 with the proxy mesh, and 15 with the high-res mesh without subdivisions.


Thank you for your response, but sadly it didn't help.As far as I know, mesh didn't move. I suppose it isjust a bug. I managed to find a solution by appendingall of the objects in the file to another file, linking Vincentagain and applying his animation (action) from previous file.It solved the problem as Vincent is back to normal.


Now that you have the basics covered, download the project using the Download Materials button at the top or bottom of this page, then unpack the files and open the starter project in Unity. Check out the folder structure in the Project view:


Save the file and return to Unity. Select the Sphere and look at its HeartMesh component. Make sure you've checked Is Edit Mode so you can see the mesh's vertices in the Scene view. Then click on the arrow icon next to Selected Indices to show the array.


Vega FEM 4.0 provides virtual tet meshing for nearly self-collidingand colliding triangle meshes [LB18]. It alsoimproves the multi-threading efficiency of elasticforce and stiffness matrix computations (via "stencil force models").We also replaced pthreads with Intel TBB for multi-threading, andadded support for cubic meshes to corotationalLinearFEM.We also provide an as-rigid-as-possible (ARAP) deformation implementation,and improved meshing with exact predicates. 041b061a72


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