Abstract We present a method for accelerating the convergence of continuous non‐linear shape optimization algorithms. We start with a general method for constructing gradient vector fields on a manifold, and we analyse this method from a signal processing viewpoint. This analysis reveals that we can construct various filters using the Laplace–Beltrami operator of the shape that can effectively separate the components of the gradient at different scales. We use this idea to adaptively change the scale of features being optimized to arrive at a solution that is optimal across multiple scales. This is in contrast to traditional descent‐based methods, for which the rate of convergence often stalls early once the high frequency components have been optimized. We demonstrate how our method can be easily integrated into existing non‐linear optimization frameworks such as gradient descent, Broyden–Fletcher–Goldfarb–Shanno (BFGS) and the non‐linear conjugate gradient method. We show significant performance improvement for shape optimization in variational shape modelling and parameterization, and we also demonstrate the use of our method for efficient physical simulation.

Recent 3D sketch tools produce networks of three-space curves that suggest the contours of shapes. The shapes may be non-manifold, closed three-dimensional, open two-dimensional, or mixed. Our video demonstrates a system that automatically generates intuitively appealing, piecewise-smooth surface patches from such a curve network, and an intelligent user interface for modifying the automatically chosen surface patches. Both parts of the system use a linear algebra representation of the set of surface patches to track the topology.

Abstract Recent 3D sketch tools produce networks of three‐space curves that suggest the contours of shapes. The shapes may be non‐manifold, closed three‐dimensional, open two‐dimensional, or mixed. We describe a system that automatically generates intuitively appealing piecewise‐smooth surfaces from such a curve network, and an intelligent user interface for modifying the automatically chosen surface patches. Both the automatic and the semi‐automatic parts of the system use a linear algebra representation of the set of surface patches to track the topology. On complicated inputs from ILoveSketch [ BBS08 ], our system allows the user to build the desired surface with just a few mouse‐clicks.

Abstract We present a linear system for modelling 3D surfaces from curves. Our system offers better performance, stability and precision in control than previous non‐linear systems. By exploring the direct relationship between a standard higher‐order Laplacian editing framework and Hermite spline curves, we introduce a new form of Cauchy constraint that makes our system easy to both implement and control. We introduce novel workflows that simplify the construction of 3D models from sketches. We show how to convert existing 3D meshes into our curve‐based representation for subsequent editing and modelling, allowing our technique to be applied to a wide range of existing 3D content.

In this paper we consider the problem of creating and controlling volume deformations used to articulate characters for use in high-end applications such as computer generated feature films. We introduce a method we call harmonic coordinates that significantly improves upon existing volume deformation techniques. Our deformations are controlled using a topologically flexible structure, called a cage, that consists of a closed three dimensional mesh. The cage can optionally be augmented with additional interior vertices, edges, and faces to more precisely control the interior behavior of the deformation. We show that harmonic coordinates are generalized barycentric coordinates that can be extended to any dimension. Moreover, they are the first system of generalized barycentric coordinates that are non-negative even in strongly concave situations, and their magnitude falls off with distance as measured within the cage.

No abstract available.