VOLMAP: a Large Scale Benchmark for Volume Mappings to Simple Base Domains

Correspondences between geometric domains (mappings) are ubiquitous in computer graphics and engineering, both for a variety of downstream applications and as core building blocks for higher level algorithms. In particular, mapping a shape to a convex or star-shaped domain with simple geometry is a fundamental module in existing pipelines for mesh generation, solid texturing, generation of shape correspondences, advanced manufacturing etc. For the case of surfaces, computing such a mapping with guarantees of injectivity is a solved problem. Conversely, robust algorithms for the generation of injective volume mappings to simple polytopes are yet to be found, making this a fundamental open problem in volume mesh processing. VOLMAP is a large scale benchmark aimed to support ongoing research in volume mapping algorithms. The dataset contains 4.7K tetrahedral meshes, whose boundary vertices are mapped to a variety of simple domains, either convex or star-shaped. This data constitutes the input for candidate algorithms, which are then required to position interior vertices in the domain to obtain a volume map. Overall, this yields more than 22K alternative test cases. VOLMAP also comprises tools to process this data, analyze the resulting maps, and extend the dataset with new meshes, boundary maps and base domains. This article provides a brief overview of the field, discussing its importance and the lack of effective techniques. We then introduce both the dataset and its major features. An example of comparative analysis between two existing methods is also present

A Dataset and Benchmark for Mesh Parameterization

UV parameterization is a core task in computer graphics, with applications in mesh texturing, remeshing, mesh repair, mesh editing, and more. It is thus an active area of research, which has led to a wide variety of parameterization methods that excel according to different measures of quality. There is no single metric capturing parameterization quality in practice, since the quality of a parameterization heavily depends on its application; hence, parameterization methods can best be judged by the actual users of the computed result. In this paper, we present a dataset of meshes together with UV maps collected from various sources and intended for real-life use. Our dataset can be used to test parameterization methods in realistic environments. We also introduce a benchmark to compare parameterization methods with artist-provided UV parameterizations using a variety of metrics. This strategy enables us to evaluate the performance of a parameterization method by computing the quality indicators that are valued by the designers of a mesh.Comment: Supplemental material available at odedstein.com/projects/benchmark-for-parameterizatio

A Survey of Spatial Deformation from a User-Centered Perspective

The spatial deformation methods are a family of modeling and animation techniques for indirectly reshaping an object by warping the surrounding space, with results that are similar to molding a highly malleable substance. They have the virtue of being computationally efficient (and hence interactive) and applicable to a variety of object representations. In this paper we survey the state of the art in spatial deformation. Since manipulating ambient space directly is infeasible, deformations are controlled by tools of varying dimension - points, curves, surfaces and volumes - and it is on this basis that we classify them. Unlike previous surveys that concentrate on providing a single underlying mathematical formalism, we use the user-centered criteria of versatility, ease of use, efficiency and correctness to compare techniques

Napodobení a výroba vzhledu pomocí diferencovatelných materiálových modelů

Výpočetní deriváty kódu - s kódem - jsou jedním z klíčových aktivátorů revoluce strojového učení. V počítačové grafice umožňuje automatická diferenciace řešit problémy s inverzním renderingem, kde se z jednoho nebo několika vstupních snímků získávají parametry jako je odrazovost objektu, poloha nebo koeficienty rozptylu a absorpce ob- jemu. V této práci zvažujeme problémy s přizpůsobením vzhledu a s výrobou, které lze uvést jako příklady problémů s inverzním renderingem. Zatímco optimalizace založená na gradientu, kterou umožňují diferencovatelné programy, má potenciál přinést velmi dobré výsledky, vyžaduje správné využití. Diferenciovatelný rendering není řešením problémů typu brokovnice. Diskutujeme jak teoretické koncepty, tak praktickou implementaci dife- rencovatelných renderingových algoritmů a ukazujeme, jak se spojují s různými problémy s přizpůsobením vzhledu. 1Computing derivatives of code - with code - is one of the key enablers of the machine learning revolution. In computer graphics, automatic differentiation allows to solve in- verse rendering problems. There, parameters such as an objects reflectance, position, or the scattering- and absorption coefficients of a volume, are recovered from one or several input images. In this work, we consider appearance matching and fabrication problems, that can be cast as instances of inverse rendering problems. While gradient-based opti- mization that is enabled by differentiable programs has the potential to yield very good results, it requires proper handling - differentiable rendering is not a shotgun-type prob- lem solver. We discuss both theoretical concepts and the practical implementation of differentiable rendering algorithms, and show how they connect to different appearance matching problems. 1Katedra softwaru a výuky informatikyDepartment of Software and Computer Science EducationMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

Virtual prototyping with surface reconstruction and freeform geometric modeling using level-set method

More and more products with complex geometries are being designed and manufactured by computer aided design (CAD) and rapid prototyping (RP) technologies. Freeform surface is a geometrical feature widely used in modern products like car bodies, airfoils and turbine blades as well as in aesthetic artifacts. How to efficiently design and generate digital prototypes with freeform surfaces is an important issue in CAD. This paper presents the development of a Virtual Sculpting system and addresses the issues of surface reconstruction from dexel data structures and freeform geometric modeling using the level-set method from distance field structure. Our virtual sculpting method is based on the metaphor of carving a solid block into a 3D freeform object using a 3D haptic input device integrated with the computer visualization. This dissertation presents the result of the study and consists primarily of four papers --Abstract, page iv