A Parametric Simplicial Formulation of Houthakker\u27s Capacity Method

The paper reformulates Houthakker’s capacity method for quadratic programming in the framework of the Simplex and dual methods for quadratic programming, thereby greatly reducing the conceptual and computational complexities of the method. It is shown that the method is applicable for all convex quadratic programming problems, including the case of a semi-definite matrix of the quadratic form and that of constraints in equality form. The method reduces in the linear programming case to a parametric version of the dual method

Vector Graphics Complexes

International audienceBasic topological modeling, such as the ability to have several faces share a common edge, has been largely absent from vector graphics. We introduce the vector graphics complex (VGC) as a simple data structure to support fundamental topological modeling operations for vector graphics illustrations. The VGC can represent any arbitrary non-manifold topology as an immersion in the plane, unlike planar maps which can only represent embeddings. This allows for the direct representation of incidence relationships between objects and can therefore more faithfully capture the intended semantics of many illustrations, while at the same time keeping the geometric flexibility of stacking-based systems. We describe and implement a set of topological editing operations for the VGC, including glue, unglue, cut, and uncut. Our system maintains a global stacking order for all faces, edges, and vertices without requiring that components of an object reside together on a single layer. This allows for the coordinated editing of shared vertices and edges even for objects that have components distributed across multiple layers. We introduce VGC-specific methods that are tailored towards quickly achieving desired stacking orders for faces, edges, and vertices

Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree

The contour tree is an abstraction of a scalar field that encodes the nesting relationships of isosurfaces. We show how to use the contour tree to represent individual contours of a scalar field, how to simplify both the contour tree and the topology of the scalar field, how to compute and store geometric properties for all possible contours in the contour tree, and how to use the simplified contour tree as an interface for exploratory visualization

OPT-Mimic: Imitation of Optimized Trajectories for Dynamic Quadruped Behaviors

Reinforcement Learning (RL) has seen many recent successes for quadruped robot control. The imitation of reference motions provides a simple and powerful prior for guiding solutions towards desired solutions without the need for meticulous reward design. While much work uses motion capture data or hand-crafted trajectories as the reference motion, relatively little work has explored the use of reference motions coming from model-based trajectory optimization. In this work, we investigate several design considerations that arise with such a framework, as demonstrated through four dynamic behaviours: trot, front hop, 180 backflip, and biped stepping. These are trained in simulation and transferred to a physical Solo 8 quadruped robot without further adaptation. In particular, we explore the space of feed-forward designs afforded by the trajectory optimizer to understand its impact on RL learning efficiency and sim-to-real transfer. These findings contribute to the long standing goal of producing robot controllers that combine the interpretability and precision of model-based optimization with the robustness that model-free RL-based controllers offer