Composing quadrilateral meshes for animation

The modeling-by-composition paradigm can be a powerful tool in modern animation pipelines. We propose two novel interactive techniques to compose 3D assets that enable the artists to freely remove, detach and combine components of organic models. The idea behind our methods is to preserve most of the original information in the input characters and blend accordingly where necessary. The first method, QuadMixer, provides a robust tool to compose the quad layouts of watertight pure quadrilateral meshes, exploiting the boolean operations defined on triangles. Quad Layout is a crucial property for many applications since it conveys important information that would otherwise be destroyed by techniques that aim only at preserving the shape. Our technique keeps untouched all the quads in the patches which are not involved in the blending. The resulting meshes preserve the originally designed edge flows that, by construction, are captured and incorporated into the new quads. SkinMixer extends this approach to compose skinned models, taking into account not only the surface but also the data structures for animating the character. We propose a new operation-based technique that preserves and smoothly merges meshes, skeletons, and skinning weights. The retopology approach of QuadMixer is extended to work on quad-dominant and arbitrary complex surfaces. Instead of relying on boolean operations on triangle meshes, we manipulate signed distance fields to generate an implicit surface. The results preserve most of the information in the input assets, blending accordingly in the intersection regions. The resulting characters are ready to be used in animation pipelines. Given the high quality of the results generated, we believe that our methods could have a huge impact on the entertainment industry. Integrated into current software for 3D modeling, they would certainly provide a powerful tool for the artists. Allowing them to automatically reuse parts of their well-designed characters could lead to a new approach for creating models, which would significantly reduce the cost of the process

Retopology: a comprehensive study of current automation solutions from an artist’s workflow perspective

Dissertação de mestrado em Engenharia InformáticaTopology (the density, organization and flow of a 3D mesh’s connectivity) constrains the suitability of a 3D model for any given purpose, be it surface showcasing through renders, use in real-time engines, posing or animation. While some of these use cases might not have very strict topology requirements, others may demand optimized polygon counts for performance reasons, or even specific geometry distribution in order to take deformation directions into account. Many processes for creating 3D models such as sculpting try to make the user unaware of the inner workings of geometry, by providing flexible levels of surface detailing through dynamic geometry allocation. The resulting models have a dense, unorganized topology that is inefficient and unfit for most use cases, with the additional drawback of being hard to work with manually. Retopology is the process of providing a new topology to a model such as these, while maintaining the shape of its surface. It’s a technical and time-consuming process that clashes with the rest of the artist’s workflow, which is mainly composed of creative processes. While there’s abundant research in this area focusing on polygon distribution quality based on surface shape, artists are still left with no options but to resort to manual work when it comes to deformation-optimized topology. This document exposes this disconnect, along with a proposed framework that attempts to provide a more complete retopology solution for 3D artists. This framework combines traditional mesh extraction algorithms with adapting manually-made meshes in a pipeline that tries to understand the input on a higher level, in order to solve deficiencies that are present in current retopology tools. Our results are very positive, presenting an improvement over state of the art solutions, which could possibly steer discussion and research in this area to be more in line with the needs of 3D artists.A topologia (a densidade, organização e direções tomadas pela conectividade de uma mesh 3D) limita a adequação de um modelo 3D para um leque variado de usos, entre os quais, visualização da superfície através de renders, uso em motores real-time, poses ou animações. Embora muitos destes usos não possuam requerimentos de topologia muito rigorosos, outros podem exigir número de polígonos mais baixos por questões de performance, ou até distribuição de geometria específica para acomodar direções de deformação corretamente. Muitos processos de criação de modelos 3D, como escultura, permitem que o utilizador não esteja ciente do que se passa em termos de funcionamento da geometria por debaixo da utilização. Isto é conseguido oferecendo níveis de detalhe flexíveis, alocando geometria de forma dinâmica. Os modelos resultantes têm uma topologia densa e desorganizada, que é ineficiente e pouco apropriada para a maior parte dos casos de uso, com a desvantagem adicional de ser difícil de trabalhar com a mesma manualmente. A retopologia é o processo de gerar uma nova topologia para um modelo, ao mesmo tempo que se mantém a forma da superfície. É um processo técnico e demorado, que entra em conflito com o resto do fluxo de trabalho do artista, que é composto maioritariamente por processos artísticos. Apesar de haver investigação abundante nesta área focada na qualidade da distribuição de polígonos baseada na forma da superfície, os artistas continuam a ter de recorrer ao trabalho manual quando se trata de topologia otimizada para deformações. Este documento expõe esta divergência, propondo, em conjunto, uma framework que tenta oferecer uma solução mais completa para os artistas 3D. Esta framework combina algoritmos de extração de meshes tradicionais com adaptação de meshes feitas manualmente, numa pipeline que tenta compreender o input a um nível superior, resolvendo as deficiências presentes nas ferramentas de retopologia atuais. Os nossos resultados são bastante positivos, apresentando melhorias em relação a soluções de estado da arte, facto que poderá mudar o rumo da discussão e investigação neste campo, para melhor se adequar às necessidades dos artistas 3D

Boundary rigidity of 3D CAT(0) cube complexes

The boundary rigidity problem is a classical question from Riemannian geometry: if $(M, g)$ is a Riemannian manifold with smooth boundary, is the geometry of $M$ determined up to isometry by the metric $d_g$ induced on the boundary $\partial M$? In this paper, we consider a discrete version of this problem: can we determine the combinatorial type of a finite cube complex from its boundary distances? As in the continuous case, reconstruction is not possible in general, but one expects a positive answer under suitable contractibility and non-positive curvature conditions. Indeed, in two dimensions Haslegrave gave a positive answer to this question when the complex is a finite quadrangulation of the disc with no internal vertices of degree less than $4$. We prove a $3$-dimensional generalisation of this result: the combinatorial type of a finite CAT(0) cube complex with an embedding in $\mathbb{R}^3$ can be reconstructed from its boundary distances. Additionally, we prove a direct strengthening of Haslegrave's result: the combinatorial type of any finite 2-dimensional CAT(0) cube complex can be reconstructed from its boundary distances.Comment: 30 pages, 10 figure

SHREC'20: Shape correspondence with non-isometric deformations

Estimating correspondence between two shapes continues to be a challenging problem in geometry processing. Most current methods assume deformation to be near-isometric, however this is often not the case. For this paper, a collection of shapes of different animals has been curated, where parts of the animals (e.g., mouths, tails & ears) correspond yet are naturally non-isometric. Ground-truth correspondences were established by asking three specialists to independently label corresponding points on each of the models with respect to a previously labelled reference model. We employ an algorithmic strategy to select a single point for each correspondence that is representative of the proposed labels. A novel technique that characterises the sparsity and distribution of correspondences is employed to measure the performance of ten shape correspondence methods

Data-driven shape analysis and processing

Data-driven methods serve an increasingly important role in discovering geometric, structural, and semantic relationships between shapes. In contrast to traditional approaches that process shapes in isolation of each other, data-driven methods aggregate information from 3D model collections to improve the analysis, modeling and editing of shapes. Through reviewing the literature, we provide an overview of the main concepts and components of these methods, as well as discuss their application to classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing

Numerical and Geometric Optimizations for Surface and Tolerance Modeling

Optimization techniques are widely used in many research and engineering areas. This dissertation presents numerical and geometric optimization methods for solving geometric and solid modeling problems. Geometric optimization methods are designed for manufacturing process planning, which optimizes the process by changing dependency relationships among geometric primitives from the original design diagram. Geometric primitives are used to represent part features, and dependencies in the dimensions between parts are represented by a topological graph. The ordering of these dependencies can have a significant effect on the tolerance zones in the part. To obtain tolerance zones from the dependencies, the conventional parametric method of tolerance analysis is de-composed into a set of geometric computations, which are combined and cascaded to obtain the tolerance zones in the geometric representations. Geometric optimization is applied to the topological graph in order to find a solution that provides not only an optimal dimensioning scheme but also an optimal plan for manufacturing the physical part. The applications of our method include tolerance analysis, dimension scheme optimization, and process planning. Two numerical optimization methods are proposed for local and global surface parameterizations. One is the nonlinear optimization, which is used for building the local field-aware parameterization. Given a local chart of the surface, a two-phase method is proposed, which generates a folding-free parameterization while still being aware of the geodesic metric. The parameterization method is applied in a view-dependent 3D painting system, which constitutes a local, adaptive and interactive painting environment. The other is the mixed-integer quadratic optimization, which is used for generating a quad mesh from a given triangular mesh. With a given cross field, the computation of parametric coordinates is formulated to be a mixed-integer optimization problem, which parameterizes the surface with good quality by adding redundant integer variables. The mixed integer system is solved more efficiently by an improved adaptive rounding solver. To obtain the final quadrangular mesh, an isoline tracing method and a breadth-first traversal mesh generation method are proposed so that the final mesh result has face information, which is useful for further model processing