As‐Rigid‐AsPossible Distance Field Metamorphosis

Widely used for morphing between objects with arbitrary topology, distance field interpolation (DFI) handles topological transition naturally without the need for correspondence or remeshing, unlike surface‐based interpolation approaches. However, lack of correspondence in DFI also leads to ineffective control over the morphing process. In particular, unless the user specifies a dense set of landmarks, it is not even possible to measure the distortion of intermediate shapes during interpolation, let alone control it. To remedy such issues, we introduce an approach for establishing correspondence between the interior of two arbitrary objects, formulated as an optimal mass transport problem with a sparse set of landmarks. This correspondence enables us to compute non‐rigid warping functions that better align the source and target objects as well as to incorporate local rigidity constraints to perform as‐rigid‐aspossible DFI. We demonstrate how our approach helps achieve flexible morphing results with a small number of landmarks.     

Table‐driven Adaptive Importance Sampling

Monte Carlo rendering algorithms generally rely on some form of importance sampling to evaluate the measurement equation. Most of these importance sampling methods only take local information into account, however, so the actual importance function used may not closely resemble the light distribution in the scene. In this paper, we present Table‐driven Adaptive Importance Sampling (TAIS), a sampling technique that augments existing importance functions with tabular importance maps that direct sampling towards undersampled regions of path space. The importance maps are constructed lazily, relying on information gathered during the course of sampling. During sampling the importance maps act either in parallel with or as a preprocess to existing importance sampling methods. We show that our adaptive importance maps can be effective at reducing variance in a number of rendering situations.     

Time‐Discrete Geodesics in the Space of Shells

Building on concepts from continuum mechanics, we offer a computational model for geodesics in the space of thin shells, with a metric that reflects viscous dissipation required to physically deform a thin shell. Different from previous work, we incorporate bending contributions into our deformation energy on top of membrane distortion terms in order to obtain a physically sound notion of distance between shells, which does not require additional smoothing. Our bending energy formulation depends on the so‐called relative Weingarten map, for which we provide a discrete analogue based on principles of discrete differential geometry. Our computational results emphasize the strong impact of physical parameters on the evolution of a shell shape along a geodesic path.     

On Discrete Killing Vector Fields and Patterns on Surfaces

Symmetry is one of the most important properties of a shape, unifying form and function. It encodes semantic information on one hand, and affects the shape's aesthetic value on the other. Symmetry comes in many flavors, amongst the most interesting being intrinsic symmetry, which is defined only in terms of the intrinsic geometry of the shape. Continuous intrinsic symmetries can be represented using infinitesimal rigid transformations, which are given as tangent vector fields on the surface – known as Killing Vector Fields. As exact symmetries are quite rare, especially when considering noisy sampled surfaces, we propose a method for relaxing the exact symmetry constraint to allow for approximate symmetries and approximate Killing Vector Fields, and show how to discretize these concepts for generating such vector fields on a triangulated mesh. We discuss the properties of approximate Killing Vector Fields, and propose an application to utilize them for texture and geometry synthesis.     

A Data‐driven Segmentation for the Shoulder Complex

The human shoulder complex is perhaps the most complicated joint in the human body being comprised of a set of three bones, muscles, tendons, and ligaments. Despite this anatomical complexity, computer graphics models for motion capture most often represent this joint as a simple ball and socket. In this paper, we present a method to determine a shoulder skeletal model that, when combined with standard skinning algorithms, generates a more visually pleasing animation that is a closer approximation to the actual skin deformations of the human body. We use a data‐driven approach and collect ground truth skin deformation data with an optical motion capture system with a large number of markers (200 markers on the shoulder complex alone). We cluster these markers during movement sequences and discover that adding one extra joint around the shoulder improves the resulting animation qualitatively and quantitatively yielding a marker set of approximately 70 markers for the complete skeleton. We demonstrate the effectiveness of our skeletal model by comparing it with ground truth data as well as with recorded video. We show its practicality by integrating it with the conventional rendering/animation pipeline.     

ProcDef: Local‐to‐global Deformation for Skeleton‐free Character Animation

Animations of characters with flexible bodies such as jellyfish, snails, and, hearts are difficult to design using traditional skeleton‐based approaches. A standard approach is keyframing, but adjusting the shape of the flexible body for each key frame is tedious. In addition, the character cannot dynamically adjust its motion to respond to the environment or user input. This paper introduces a new procedural deformation framework (ProcDef) for designing and driving animations of such flexible objects. Our approach is to synthesize global motions procedurally by integrating local deformations. ProcDef provides an efficient design scheme for local deformation patterns; the user can control the orientation and magnitude of local deformations as well as the propagation of deformation signals by specifying line charts and volumetric fields. We also present a fast and robust deformation algorithm based on shape‐matching dynamics and show some example animations to illustrate the feasibility of our framework.     

A Condition Number for Non‐Rigid Shape Matching

Despite the large amount of work devoted in recent years to the problem of non‐rigid shape matching, practical methods that can successfully be used for arbitrary pairs of shapes remain elusive. In this paper, we study the hardness of the problem of shape matching, and introduce the notion of the shape condition number, which captures the intuition that some shapes are inherently more difficult to match against than others. In particular, we make a connection between the symmetry of a given shape and the stability of any method used to match it while optimizing a given distortion measure. We analyze two commonly used classes of methods in deformable shape matching, and show that the stability of both types of techniques can be captured by the appropriate notion of a condition number. We also provide a practical way to estimate the shape condition number and show how it can be used to guide the selection of landmark correspondences between shapes. Thus we shed some light on the reasons why general shape matching remains difficult and provide a way to detect and mitigate such difficulties in practice.     

Fast Particle‐based Visual Simulation of Ice Melting

The visual simulation of natural phenomena has been widely studied. Although several methods have been proposed to simulate melting, the flows of meltwater drops on the surfaces of objects are not taken into account. In this paper, we propose a particle‐based method for the simulation of the melting and freezing of ice objects and the interactions between ice and fluids. To simulate the flow of meltwater on ice and the formation of water droplets, a simple interfacial tension is proposed, which can be easily incorporated into common particle‐based simulation methods such as Smoothed Particle Hydrodynamics. The computations of heat transfer, the phase transition between ice and water, the interactions between ice and fluids, and the separation of ice due to melting are further accelerated by implementing our method using CUDA. We demonstrate our simulation and rendering method for depicting melting ice at interactive frame‐rates.     

Designing Quad‐dominant Meshes with Planar Faces

We study the combined problem of approximating a surface by a quad mesh (or quad‐dominant mesh) which on the one hand has planar faces, and which on the other hand is aesthetically pleasing and has evenly spaced vertices. This work is motivated by applications in freeform architecture and leads to a discussion of fields of conjugate directions in surfaces, their singularities and indices, their optimization and their interactive modeling. The actual meshing is performed by means of a level set method which is capable of handling combinatorial singularities, and which can deal with planarity, smoothness, and spacing issues.     

Flexible Splicing of Upper‐Body Motion Spaces on Locomotion

This paper presents an efficient technique for synthesizing motions by stitching, or splicing, an upper‐body motion retrieved from a motion space on top of an existing lower‐body locomotion of another motion. Compared to the standard motion splicing problem, motion space splicing imposes new challenges as both the upper and lower body motions might not be known in advance. Our technique is the first motion (space) splicing technique that propagates temporal and spatial properties of the lower‐body locomotion to the newly generated upper‐body motion and vice versa. Whereas existing techniques only adapt the upper‐body motion to fit the lower‐body motion, our technique also adapts the lower‐body locomotion based on the upper body task for a more coherent full‐body motion. In this paper, we will show that our decoupled approach is able to generate high‐fidelity full‐body motion for interactive applications such as games.     

Implicit Integration for Particle‐based Simulation of Elasto‐Plastic Solids

We present a novel particle‐based method for stable simulation of elasto‐plastic materials. The main contribution of our method is an implicit numerical integrator, using a physically‐based model, for computing particles that undergo both elastic and plastic deformations. The main advantage of our implicit integrator is that it allows the use of large time steps while still preserving stable and physically plausible simulation results. As a key component of our algorithm, at each time step we compute the particle positions and velocities based on a sparse linear system, which we solve efficiently on the graphics hardware. Compared to existing techniques, our method allows for a much wider range of stiffness and plasticity settings. In addition, our method can significantly reduce the computation cost for certain range of material types. We demonstrate fast and stable simulations for a variety of elasto‐plastic materials, ranging from highly stiffelastic materials to highly plastic ones.     

Synthesizing Two‐character Interactions by Merging Captured Interaction Samples with their Spacetime Relationships

Existing synthesis methods for closely interacting virtual characters relied on user‐specified constraints such as the reaching positions and the distance between body parts. In this paper, we present a novel method for synthesizing new interacting motion by composing two existing interacting motion samples without the need to specify the constraints manually. Our method automatically detects the type of interactions contained in the inputs and determines a suitable timing for the interaction composition by analyzing the spacetime relationships of the input characters. To preserve the features of the inputs in the synthesized interaction, the two inputs will be aligned and normalized according to the relative distance and orientation of the characters from the inputs. With a linear optimization method, the output is the optimal solution to preserve the close interaction of two characters and the local details of individual character behavior. The output animations demonstrated that our method is able to create interactions of new styles that combine the characteristics of the original inputs.     

As‐Conformal‐As‐Possible Surface Registration

We present a non‐rigid surface registration technique that can align surfaces with sizes and shapes that are different from each other, while avoiding mesh distortions during deformation. The registration is constrained locally as conformal as possible such that the angles of triangle meshes are preserved, yet local scales are allowed to change. Based on our conformal registration technique, we devise an automatic registration and interactive registration technique, which can reduce user interventions during template fitting. We demonstrate the versatility of our technique on a wide range of surfaces.     

Enhancing Bounding Volumes using Support Plane Mappings for Collision Detection

In this paper we present a new method for improving the performance of the widely used Bounding Volume Hierarchies for collision detection. The major contribution of our work is a culling algorithm that serves as a generalization of the Separating Axis Theorem for non parallel axes, based on the well‐known concept of support planes. We also provide a rigorous definition of support plane mappings and implementation details regarding the application of the proposed method to commonly used bounding volumes. The paper describes the theoretical foundation and an overall evaluation of the proposed algorithm. It demonstrates its high culling efficiency and in its application, significant improvement of timing performance with different types of bounding volumes and support plane mappings for rigid body simulations.     

Topology‐based Smoothing of 2D Scalar Fields with C1‐Continuity

Data sets coming from simulations or sampling of real‐world phenomena often contain noise that hinders their processing and analysis. Automatic filtering and denoising can be challenging: when the nature of the noise is unknown, it is difficult to distinguish between noise and actual data features; in addition, the filtering process itself may introduce “artificial” features into the data set that were not originally present. In this paper, we propose a smoothing method for 2D scalar fields that gives the user explicit control over the data features. We define features as critical points of the given scalar function, and the topological structure they induce (i.e., the Morse‐Smale complex). Feature significance is rated according to topological persistence. Our method allows filtering out spurious features that arise due to noise by means of topological simplification, providing the user with a simple interface that defines the significance threshold, coupled with immediate visual feedback of the remaining data features. In contrast to previous work, our smoothing method guarantees a C¹‐continuous output scalar field with the exact specified features and topological structures.     

Editing and Synthesizing Two‐Character Motions using a Coupled Inverted Pendulum Model

This study aims to develop a controller for use in the online simulation of two interacting characters. This controller is capable of generalizing two sets of interaction motions of the two characters based on the relationships between the characters. The controller can exhibit similar motions to a captured human motion while reacting in a natural way to the opponent character in real time. To achieve this, we propose a new type of physical model called a coupled inverted pendulum on carts that comprises two inverted pendulum on a cart models, one for each individual, which are coupled by a relationship model. The proposed framework is divided into two steps: motion analysis and motion synthesis. Motion analysis is an offline preprocessing step, which optimizes the control parameters to move the proposed model along a motion capture trajectory of two interacting humans. The optimization procedure generates a coupled pendulum trajectory which represents the relationship between two characters for each frame, and is used as a reference in the synthesis step. In the motion synthesis step, a new coupled pendulum trajectory is planned reflecting the effects of the physical interaction, and the captured reference motions are edited based on the planned trajectory produced by the coupled pendulum trajectory generator. To validate the proposed framework, we used a motion capture data set showing two people performing kickboxing. The proposed controller is able to generalize the behaviors of two humans to different situations such as different speeds and turning speeds in a realistic way in real time.     

Non‐iterative Second‐order Approximation of Signed Distance Functions for Any Isosurface Representation

Signed distance functions (SDF) to explicit or implicit surface representations are intensively used in various computer graphics and visualization algorithms. Among others, they are applied to optimize collision detection, are used to reconstruct data fields or surfaces, and, in particular, are an obligatory ingredient for most level set methods. Level set methods are common in scientific visualization to extract surfaces from scalar or vector fields. Usual approaches for the construction of an SDF to a surface are either based on iterative solutions of a special partial differential equation or on marching algorithms involving a polygonization of the surface. We propose a novel method for a non‐iterative approximation of an SDF and its derivatives in a vicinity of a manifold. We use a second‐order algebraic fitting scheme to ensure high accuracy of the approximation. The manifold is defined (explicitly or implicitly) as an isosurface of a given volumetric scalar field. The field may be given at a set of irregular and unstructured samples. Stability and reliability of the SDF generation is achieved by a proper scaling of weights for the Moving Least Squares approximation, accurate choice of neighbors, and appropriate handling of degenerate cases. We obtain the solution in an explicit form, such that no iterative solving is necessary, which makes our approach fast.