Non-smooth developable geometry for interactively animating paper crumpling

International audienceWe present the first method to animate sheets of paper at interactive rates, while automatically generating a plausible set of sharp features when the sheet is crumpled. The key idea is to interleave standard physically-based simulation steps with procedural generation of a piecewise continuous developable surface. The resulting hybrid surface model captures new singular points dynamically appearing during the crumpling process, mimicking the effect of paper fiber fracture. Although the model evolves over time to take these irreversible damages into account, the mesh used for simulation is kept coarse throughout the animation, leading to efficient computations. Meanwhile, the geometric layer ensures that the surface stays almost isometric to its original 2D pattern. We validate our model through measurements and visual comparison with real paper manipulation, and show results on a variety of crumpled paper configurations

Robotic manipulation of cloth: mechanical modeling and perception

(Eng) In this work we study various mathematical problems arising from the robotic manipulation of cloth. First, we develop a locking-free continuous model for the physical simulation of inextensible textiles. We present a novel 'finite element' discretization of our inextensibility constraints which results in a unified treatment of triangle and quadrilateral meshings of the cloth. Next, we explain how to incorporate contacts, self-collisions and friction into the equations of motion, so that frictional forces and inextensibility and collision constraints may be integrated implicitly and without any decoupling. We develop an efficient 'active-set' solver tailored to our non-linear problem which takes into account past active constraints to accelerate the resolution of unresolved contacts and moreover can be initialized from any non-necessarily feasible point. Then, we embark ourselves in the empirical validation of the developed model. We record in a laboratory setting --with depth cameras and motion capture systems-- the motions of seven types of textiles (including e.g. cotton, denim and polyester) of various sizes and at different speeds and end up with more than 80 recordings. The scenarios considered are all dynamic and involve rapid shaking and twisting of the textiles, collisions with frictional objects and even strong hits with a long stick. We then, compare the recorded textiles with the simulations given by our inextensible model, and find that on average the mean error is of the order of 1 cm even for the largest sizes (DIN A2) and the most challenging scenarios. Furthermore, we also tackle other problems relevant to robotic cloth manipulation, such as cloth perception and classification of its states. We present a reconstruction algorithm based on Morse theory that proceeds directly from a point-cloud to obtain a cellular decomposition of a surface with or without boundary: the results are a piecewise parametrization of the cloth surface as a union of Morse cells. From the cellular decomposition the topology of the surface can be then deduced immediately. Finally, we study the configuration space of a piece of cloth: since the original state of a piece of cloth is flat, the set of possible states under the inextensible assumption is the set of developable surfaces isometric to a fixed one. We prove that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. Inspired on this result we introduce the dGLI cloth coordinates, a low-dimensional representation of the state of a piece of cloth based on a directional derivative of the Gauss Linking Integral. These coordinates --computed from the position of the cloth's boundary-- allow to distinguish key qualitative changes in folding sequences.(Esp) En este trabajo estudiamos varios problemas matemáticos relacionados con la manipulación robótica de textiles. En primer lugar, desarrollamos un modelo continuo libre de 'locking' para la simulación física de textiles inextensibles. Presentamos una novedosa discretización usando 'elementos finitos' de nuestras restricciones de inextensibilidad resultando en un tratamiento unificado de mallados triangulares y cuadrangulares de la tela. A continuación, explicamos cómo incorporar contactos, autocolisiones y fricción en las ecuaciones de movimiento, de modo que las fuerzas de fricción y las restricciones de inextensibilidad y colisiones puedan integrarse implícitamente y sin ningún desacoplamiento. Desarrollamos un 'solver' de tipo 'conjunto-activo' adaptado a nuestro problema no lineal que tiene en cuenta las restricciones activas pasadas para acelerar la resolución de los contactos no resueltos y, además, puede inicializarse desde cualquier punto no necesariamente factible. Posteriormente, nos embarcamos en la validación empírica del modelo desarrollado. Grabamos en un entorno de laboratorio -con cámaras de profundidad y sistemas de captura de movimiento- los movimientos de siete tipos de textiles (entre los que se incluyen, por ejemplo, algodón, tela vaquera y poliéster) de varios tamaños y a diferentes velocidades, terminando con más de 80 grabaciones. Los escenarios considerados son todos dinámicos e implican sacudidas y torsiones rápidas de los textiles, colisiones con obstáculos e incluso golpes con una varilla cilíndrica. Finalmente, comparamos las grabaciones con las simulaciones dadas por nuestro modelo inextensible, y encontramos que, de media, el error es del orden de 1 cm incluso para las telas más grandes (DIN A2) y los escenarios más complicados. Además, también abordamos otros problemas relevantes para la manipulación robótica de telas, como son la percepción y la clasificación de sus estados. Presentamos un algoritmo de reconstrucción basado en la teoría de Morse que procede directamente de una nube de puntos para obtener una descomposición celular de una superficie con o sin borde: los resultados son una parametrización a trozos de la superficie de la tela como una unión de celdas de Morse. A partir de la descomposición celular puede deducirse inmediatamente la topología de la superficie. Por último, estudiamos el espacio de configuración de un trozo de tela: dado que el estado original de la tela es plano, el conjunto de estados posibles bajo la hipótesis de inextensibilidad es el conjunto de superficies desarrollables isométricas a una fija. Demostramos que una curva genérica simple, cerrada y regular a trozos en el espacio puede ser el borde de un número finito de superficies desarrollables con curvatura media no nula. Inspirándonos en este resultado, introducimos las coordenadas dGLI, una representación de dimensión baja del estado de un pedazo de tela basada en una derivada direccional de la integral de enlazamiento de Gauss. Estas coordenadas -calculadas a partir de la posición del borde de la tela- permiten distinguir cambios cualitativos clave en distintas secuencias de plegado

Optimal design of morphing structures

Morphing structures change their geometric configuration to achieve a wide range of performance goals. For morphing aircraft these include alleviating drag, or altering aerofoil lift. The design of structures capable of realising these goals is a highly multidisciplinary problem. Optimally morphing a compliant structure involves finding the distribution of actuation which best achieves a desired configuration change. In this work, the location and magnitude of discrete actuators are optimised, to minimise both aerodynamic and geometric objective functions. A range of optimisation methods, including differential and stochastic techniques, has been implemented to search optimally the large, nonlinear, and often discontinuous design spaces associated with such problems. The optimal design of morphing systems is investigated through consideration of a morphing shock control bump and an adaptive leading edge. CFD is implemented to evaluate the aerodynamic performance of optimiser-controlled morphing structures. A bespoke grid-generation algorithm is developed, capable of producing a mesh for all possible geometries, with low levels of cell skewness and orthogonality at the fluid-structure boundaries. Structural compliance – a prerequisite for morphing – allows significant displacement of the structure to occur, but simultaneously enables the possibility of detrimental aeroelastic effects. Static aeroelasticity is catered for, at significant computational expense, via coupling of the structural and aerodynamic models within individual optimisation function evaluations. Morphing geometry is investigated to reduce computational design requirements, and provide an objective starting point for an aeroelastic optimisation. The requirements of morphing between aerodynamic shapes are evaluated using geometry-based objective functions. Displacements and curvatures are compared between an optimiser-controlled structure and the target morph, and the differences minimised to effect the required shape change. In addition to enabling optimal problem definition, these geometric objective functions allow conclusions on the feasibility of a morph to be drawn a priori

A Parametrization-Based Surface Reconstruction System for Triangular Mesh Simplification with Application to Large Scale Scenes

The laser scanner is nowadays widely used to capture the geometry of art, animation maquettes, or large architectural, industrial, and land form models. It thus poses specific problems depending on the model scale. This thesis provides a solution for simplification of triangulated data and for surface reconstruction of large data sets, where feature edges provide an obvious segmentation structure. It also explores a new method for model segmentation, with the goal of applying multiresolution techniques to data sets characterized by curvy areas and the lack of clear demarcation features. The preliminary stage of surface segmentation, which takes as input single or multiple scan data files, generates surface patches which are processed independently. The surface components are mapped onto a two-dimensional domain with boundary constraints, using a novel parametrization weight coefficient. This stage generates valid parameter domain points, which can be fed as arguments to parametric modeling functions or surface approximation schemes. On this domain, our approach explores two types of remeshing. First, we generate points in a regular grid pattern, achieving multiresolution through a flexible grid step, which nevertheless is designed to produce a globally uniform resampling aspect. In this case, for reconstruction, we attempt to solve the open problem of border reconciliation across adjacent domains by retriangulating the border gap between the grid and the fixed irregular border. Alternatively, we straighten the domain borders in the parameter domain and coarsely triangulate the resulting simplified polygons, resampling the base domain triangles in a 1-4 subdivision pattern, achieving multiresolution from the number of subdivision steps. For mesh reconstruction, we use a linear interpolation method based on the original mesh triangles as control points on local planes, using a saved triangle correspondence between the original mesh and the parametric domain. We also use a region-wide approximation method, applied to the parameter grid points, which first generates data-trained control points, and then uses them to obtain the reconstruction values at the resamples. In the grid resampling scheme, due to the border constraints, the reassembly of the segmented, sequentially processed data sets is seamless. In the subdivision scheme, we align adjacent border fragments in the parameter space, and use a region-to-fragment map to achieve the same border reconstruction across two neighboring components. We successfully process data sets up to 1,000,000 points in one pass of our program, and are capable of assembling larger scenes from sequential runs. Our program consists of a single run, without intermediate storage. Where we process large input data files, we fragment the input using a nested application of our segmentation algorithm to reduce the size of the input scenes, and our pipeline reassembles the reconstruction output from multiple data files into a unique view