The question of what are good views of a 3D object has been addressed by numerous researchers in perception, computer vision, and computer graphics. This has led to a large variety of measures for the goodness of views as well as some special-case viewpoint selection algorithms. In this article, we leverage the results of a large user study to optimize the parameters of a general model for viewpoint goodness, such that the fitted model can predict people's preferred views for a broad range of objects. Our model is represented as a combination of attributes known to be important for view selection, such as projected model area and silhouette length. Moreover, this framework can easily incorporate new attributes in the future, based on the data from our existing study. We demonstrate our combined goodness measure in a number of applications, such as automatically selecting a good set of representative views, optimizing camera orbits to pass through good views and avoid bad views, and trackball controls that gently guide the viewer towards better views.

In this paper, we describe a design methodology that we have termed Minimalist Game Design. Minimalist games have small rulesets, narrow decision spaces, and abstract audiovisual representations, yet they do not compromise on depth of play or possibility space. We begin with a motivation for and definition of minimalist games, including terms such as "rules," "mechanics," "control," and "interface," and illustrate the importance of artificial design constraints. Using a number of examples, we show the strengths of minimalist game elements in systems, controls, visuals, and audio. Adhering to these constraints, these games feature a small set of mechanics and one core mechanic, while still being sufficiently deep and allowing for player exploration and performance. This depth comes from procedural methods, combinatorial complexity, probability, obfuscation, challenge, or any combination thereof. Our methodology embraces principles of holistic design, where there is no "filler," and where every element of the game contributes to the play experience in some meaningful, deliberate way.

The modeling of volumetric objects is still a difficult problem. Solid texture synthesis methods enable the design of volumes with homogeneous textures, but global features such as smoothly varying colors seen in vegetables and fruits are difficult to model. In this paper, we propose a representation called diffusion surfaces (DSs) to enable modeling such objects. DSs consist of 3D surfaces with colors defined on both sides, such that the interior colors in the volume are obtained by diffusing colors from nearby surfaces. A straightforward way to compute color diffusion is to solve a volumetric Poisson equation with the colors of the DSs as boundary conditions, but it requires expensive volumetric meshing which is not appropriate for interactive modeling. We therefore propose to interpolate colors only locally at user-defined cross-sections using a modified version of the positive mean value coordinates algorithm to avoid volumetric meshing. DSs are generally applicable to model many different kinds of objects with internal structures. As a case study, we present a simple sketch-based interface for modeling objects with rotational symmetries that can also generate random variations of models. We demonstrate the effectiveness of our approach through various DSs models with simple non-photorealistic rendering techniques enabled by DSs.

Surface-based deformation and cage-based deformation are two popular shape editing paradigms. Surface-based methods are easy to use and produce high-quality results by preserving differential properties of the surface mesh, but are limited by their computational requirements. Cage-based methods produce results quickly but at the expense of usability and realism, and typically require manual construction of suitable cages. We introduce a hybrid approach that combines the two methods. The user can perform edits on an automatically-generated simplified version of an input shape using As-rigid-as-possible surface modeling, and the edit is propagated to the original shape by a precomputed space deformation based on Mean value coordinates. We analyze deformation quality and running time for a variety of cage sizes. High-quality results are obtained for meshes on the order of 100K vertices at interactive rates by using cages with ~5% of the vertices of the original shape.

Shape deformation and editing are important for animation and game design. Based on as-rigid-as-possible (ARAP) surface modeling, an efficient approach is proposed to approximately preserve the volume of an object with large-scale deformations. The classical ARAP surface modeling uses two-stage iterations to recover rotations and preserve edge lengths. However, there is no volume preserving constraint, which may cause undesired artifacts. We show that the volume can be roughly kept by leveraging the skeleton information. First a skeleton is selected, and points are evenly generated on the skeleton. Then each point is correlated with several vertices on the surface of the object. The connectivity between the skeleton and the surface is defined as skeleton edges, which can be easily added into the linear system of the ARAP method as additional rows without breaking the manifoldness or sacrificing speed. Since this linear system is able to preserve the lengths of both the surface and skeleton edges, the area of cross sections and the volume between cross sections can be approximately preserved.

In this paper we present an algorithm for watertight meshing of closed, sketched curves. The sketch is resampled as a piecewise linear (PWL) curve and placed onto a triangular grid. A small boundary (seed) that describes a closed path along grid points is placed inside the sketch and grown until it resembles the sketch. Vertices of the evolved grid boundary are projected onto the stroke to establish a bijective, ordered mapping. Finally, valences along the boundary are optimized while retaining the previously established mapping. The resulting mesh patch can be duplicated, stitched and inflated to generate a new shape, or used to fill a hole in an existing shape. We have implemented our algorithm in FiberMesh, an interactive sketch based interface for designing freeform surfaces, where it is used for the all mesh generation processes. The triangulation generated with our algorithm improves the quality of the model by reducing the number of irregular vertices, while running at real time rates.

We introduce an over-sketching interface for feature-preserving surface mesh editing. The user sketches a stroke that is the suggested position of part of a silhouette of the displayed surface. The system then segments all image-space silhouettes of the pro jected surface, identifies among all silhouette segments the best matching part, derives vertices in the surface mesh corresponding to the silhouette part, selects a sub-region of the mesh to be modified, and feeds appropriately modified vertex positions together with the sub-mesh into a mesh deformation tool. The overall algorithm has been designed to enable interactive modification of the surface - yielding a surface editing system that comes close to the experience of sketching 3D models on paper.

This paper presents an interface for designing freeform surfaces with a collection of 3D curves. The user first creates a rough 3D model by using a sketching interface. Unlike previous sketching systems, the user-drawn strokes stay on the model surface and serve as handles for controlling the geometry. The user can add, remove, and deform these control curves easily, as if working with a 2D line drawing. The curves can have arbitrary topology; they need not be connected to each other. For a given set of curves, the system automatically constructs a smooth surface embedding by applying functional optimization. Our system provides realtime algorithms for both control curve deformation and the subsequent surface optimization. We show that one can create sophisticated models using this system, which have not yet been seen in previous sketching or functional optimization systems.

We introduce an over-sketching interface for feature-preserving surface mesh editing. The user sketches a stroke that is the suggested position of part of a silhouette of the displayed surface. The system then segments all image-space silhouettes of the projected surface, identifies among all silhouette segments the best matching part, derives vertices in the surface mesh corresponding to the silhouette part, selects a sub-region of the mesh to be modified, and feeds appropriately modified vertex positions together with the sub-mesh into a mesh deformation tool. The overall algorithm has been designed to enable interactive modification of the surface -- yielding a surface editing system that comes close to the experience of sketching 3D models on paper.

We introduce a framework for triangle shape optimization and feature preserving smoothing of triangular meshes that is guided by the vertex Laplacians, specifically, the uniformly weighted Laplacian and the discrete mean curvature normal. Vertices are relocated so that they approximate prescribed Laplacians and positions in a weighted least-squares sense; the resulting linear system leads to an efficient, non-iterative solution. We provide different weighting schemes and demonstrate the effectiveness of the framework on a number of detailed and highly irregular meshes; our technique successfully improves the quality of the triangulation while remaining faithful to the original surface geometry, and it is also capable of smoothing the surface while preserving geometric features.

In this paper we present a method for the intuitive editing of surface meshes by means of view-dependent sketching. In most existing shape deformation work, editing is carried out by selecting and moving a handle, usually a set of vertices. Our system lets the user easily determine the handle, either by silhouette selection and cropping, or by sketching directly onto the surface. Subsequently, an edit is carried out by sketching a new, view-dependent handle position or by indirectly influencing differential properties along the sketch. Combined, these editing and handle metaphors greatly simplify otherwise complex shape modeling tasks. We come to the conclusion that sketching a shape is inverse NPR. Consequently, we design a sketch-based modeling interface using silhouettes and sketches as input, and producing contours, or suggestive contours, and ridges/ravines. The user can sketch a curve, and the system adapts the shape so that the sketch becomes a feature line on the model, while preserving global and local geometry as much as possible [Sorkine et. al 2004]. As the requested properties of the sketch cannot or should not always be accommodated exactly, users only suggest feature lines.

Physically based deformable models have been widely embraced by the Computer Graphics community. Many problems outlined in a previous survey by Gibson and Mirtich [GM97] have been addressed, thereby making these models interesting and useful for both offline and real-time applications, such as motion pictures and video games. In this paper, we present the most significant contributions of the past decade, which produce such impressive and perceivably realistic animations and simulations: finite element/difference/volume methods, mass-spring systems, meshfree methods, coupled particle systems and reduced deformable models based on modal analysis. For completeness, we also make a connection to the simulation of other continua, such as fluids, gases and melting objects. Since time integration is inherent to all simulated phenomena, the general notion of time discretization is treated separately, while specifics are left to the respective models. Finally, we discuss areas of application, such as elastoplastic deformation and fracture, cloth and hair animation, virtual surgery simulation, interactive entertainment and fluid/smoke animation, and also suggest areas for future research.

We present a sampling strategy and rendering framework for intersect-able models, whose surface is implicitly defined by a black box intersection test that provides the location and normal of the closest intersection of a ray with the surface. To speed up image generation despite potentially slow intersection tests, our method exploits spatial coherence by adjusting the sampling resolution in image space to the surface variation in object space. The result is a set of small, view-dependent bilinear surface approximations, which are rendered as quads using conventional graphics hardware. The advantage of this temporary rendering representation is two-fold: First, rendering is performed on the GPU, leaving CPU time for ray intersection computation. Second, bilinear surface approximations are derived from the geometry and can be reused in other views. Here, graphics hardware is exploited to determine the subset of image space in need of re-sampling. We demonstrate our system by ray casting an implicit surface defined from point samples, for which current ray-surface intersection computations are usually too slow to generate images at interactive rates.

We present a method for modeling and animating a wide spectrum of volumetric objects, with material properties anywhere in the range from stiff elastic to highly plastic. Both the volume and the surface representation are point based, which allows arbitrarily large deviations form the original shape. In contrast to previous point based elasticity in computer graphics, our physical model is derived from continuum mechanics, which allows the specification of common material properties such as Young's Modulus and Poisson's Ratio. In each step, we compute the spatial derivatives of the discrete displacement field using a Moving Least Squares (MLS) procedure. From these derivatives we obtain strains, stresses and elastic forces at each simulated point. We demonstrate how to solve the equations of motion based on these forces, with both explicit and implicit integration schemes. In addition, we propose techniques for modeling and animating a point-sampled surface that dynamically adapts to deformations of the underlying volumetric model.

Patch-based texture synthesis has proven to produce high quality textures faster than pixel-based approaches. Previous algorithms differ in how the regions of overlap between neighboring patches are treated. We present an approach that produces higher quality overlap regions than simple blending of patches or computing good boundaries, however, that is faster than re-synthesizing invalid pixels using a classical per-pixel synthesis algorithm: we use a k-nearest neighbor (knn) data structure, obtained from the input texture in a precomputation step. Results from our implementation show that the algorithm produces high-quality textures, where the time complexity of the synthesis stage is linear in the number of re-synthesized pixels and, therefore, scales well with the size of the input texture.

Patch-based texture synthesis algorithms produce reasonable results for a wide variety of texture classes. They preserve global structure, but often introduce unwanted visual artifacts along patch boundaries. Pixel-based synthesis algorithms, on the other hand, tend to blur out small objects while maintaining a consistent texture impression, which in return doesn't necessarily resemble the input texture. In this paper, we propose an adaptive and hybrid algorithm. Our algorithm adaptively splits patches so as to use as large as possible patches while staying within a user-defined error tolerance for the mismatch in the overlap region. Using large patches improves the reproduction of global structure. The remaining errors in the overlap regions are eliminated using pixel-based re-synthesis. We introduce an optimized ordering for the re-synthesis of these erroneous pixels using morphological operators, which ensures that every pixel has enough valid (i.e., error-free) neighboring pixels. Examples and comparisons with existing techniques demonstrate that our approach improves over previous texture synthesis algorithms, especially for textures with well-visible, possibly anisotropic structure, such as natural stone wall or scales.

Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. This intrinsic representation could be derived from differential properties of the mesh, i.e. its Laplacian [...]

PhD thesis: Interfaces and Algorithms for the Creation, Modification, and Optimization of Surface Meshes (oct 2007)

my phd thesis summarizes my work on sketch based mesh editing and creation, as well as some work on mesh smoothing and triangle shape optimization. all proposed algorithms are based on discrete Laplace operators and least squares solvers. the thesis summarizes four of my previous publications, but also gives some more insight into various design decisions and mathematical subtleties.

MSc thesis: hybrid texture synthesis (june 2003)

my masters thesis topic was the development of a novel, hybrid texture synthesis algorithm, which combines the strengths of existing pixel- and patch-based synthesis methods. the thesis is partially summarized in our egsr 2003 paper above, but also contains a more detailed description of the core algorithm. We furthermore explore efficiency enhancement and an augmented error metric, both listed as future work in the paper.

An As-Short-As-Possible Introduction to the Least Squares, Weighted Least Squares and Moving Least Squares Methods for Scattered Data Approximation and Interpolation (may 2004)

Shadow Mapping and Shadow Volumes: Recent Developments in Real-Time Shadow Rendering (2002)

Physically Based Simulation and Animation of Gaseous Phenomena in a Periodic Domain (2002)

for the algorithmic animation course project i implemented and experimented with computational fluid dynamics and smoke-like animations. my project report, the source code and precompiled binaries for windows and linux can be downloaded below. the codebase is taken from jos stams stable fluids paper, which i presented in class (the presentation can be downloaded below).

the six videos from the project report (click on image to download mpeg video)