Efficient Terrain Triangulation and Modification Algorithms for Game Applications

An efficient terrain generation algorithm is developed, based on constrained conforming Delaunay triangulation. The density of triangulation in different regions of a terrain is determined by its flatness, as seen from a height map, and a control map. Tracks and other objects found in a game world can be applied over the terrain using the “stenciling” and “stitching” algorithms. Using user controlled parameters, varying levels of detail can be preserved when applying these objects over the terrain as well. The algorithms have been incorporated into 3dsMax as plugins, and the experimental results demonstrate the usefulness and efficiency of the developed algorithms

Differential operators on sketches via alpha contours

A vector sketch is a popular and natural geometry representation depicting a 2D shape. When viewed from afar, the disconnected vector strokes of a sketch and the empty space around them visually merge into positive space and negative space, respectively. Positive and negative spaces are the key elements in the composition of a sketch and define what we perceive as the shape. Nevertheless, the notion of positive or negative space is mathematically ambiguous: While the strokes unambiguously indicate the interior or boundary of a 2D shape, the empty space may or may not belong to the shape’s exterior. For standard discrete geometry representations, such as meshes or point clouds, some of the most robust pipelines rely on discretizations of differential operators, such as Laplace-Beltrami. Such discretizations are not available for vector sketches; defining them may enable numerous applications of classical methods on vector sketches. However, to do so, one needs to define the positive space of a vector sketch, or the sketch shape. Even though extracting this 2D sketch shape is mathematically ambiguous, we propose a robust algorithm, Alpha Contours, constructing its conservative estimate: a 2D shape containing all the input strokes, which lie in its interior or on its boundary, and aligning tightly to a sketch. This allows us to define popular differential operators on vector sketches, such as Laplacian and Steklov operators. We demonstrate that our construction enables robust tools for vector sketches, such as As-Rigid-As-Possible sketch deformation and functional maps between sketches, as well as solving partial differential equations on a vector sketch

Surface Deformation Potentials on Meshes for Computer Graphics and Visualization

Shape deformation models have been used in computer graphics primarily to describe the dynamics of physical deformations like cloth draping, collisions of elastic bodies, fracture, or animation of hair. Less frequent is their application to problems not directly related to a physical process. In this thesis we apply deformations to three problems in computer graphics that do not correspond to physical deformations. To this end, we generalize the physical model by modifying the energy potential. Originally, the energy potential amounts to the physical work needed to deform a body from its rest state into a given configuration and relates material strain to internal restoring forces that act to restore the original shape. For each of the three problems considered, this potential is adapted to reflect an application specific notion of shape. Under the influence of further constraints, our generalized deformation results in shapes that balance preservation of certain shape properties and application specific objectives similar to physical equilibrium states. The applications discussed in this thesis are surface parameterization, interactive shape editing and automatic design of panorama maps. For surface parameterization, we interpret parameterizations over a planar domain as deformations from a flat initial configuration onto a given surface. In this setting, we review existing parameterization methods by analyzing properties of their potential functions and derive potentials accounting for distortion of geometric properties. Interactive shape editing allows an untrained user to modify complex surfaces, be simply grabbing and moving parts of interest. A deformation model interactively extrapolates the transformation from those parts to the rest of the surface. This thesis proposes a differential shape representation for triangle meshes leading to a potential that can be optimized interactively with a simple, tailored algorithm. Although the potential is not physically accurate, it results in intuitive deformation behavior and can be parameterized to account for different material properties. Panorama maps are blends between landscape illustrations and geographic maps that are traditionally painted by an artist to convey geographic surveyknowledge on public places like ski resorts or national parks. While panorama maps are not drawn to scale, the shown landscape remains recognizable and the observer can easily recover details necessary for self location and orientation. At the same time, important features as trails or ski slopes appear not occluded and well visible. This thesis proposes the first automatic panorama generation method. Its basis is again a surface deformation, that establishes the necessary compromise between shape preservation and feature visibility.Potentiale zur Flächendeformation auf Dreiecksnetzen für Anwendungen in der Computergrafik und Visualisierung Deformationsmodelle werden in der Computergrafik bislang hauptsächlich eingesetzt, um die Dynamik physikalischer Deformationsprozesse zu modellieren. Gängige Beispiele sind Bekleidungssimulationen, Kollisionen elastischer Körper oder Animation von Haaren und Frisuren. Deutlich seltener ist ihre Anwendung auf Probleme, die nicht direkt physikalischen Prozessen entsprechen. In der vorliegenden Arbeit werden Deformationsmodelle auf drei Probleme der Computergrafik angewandt, die nicht unmittelbar einem physikalischen Deformationsprozess entsprechen. Zu diesem Zweck wird das physikalische Modell durch eine passende Änderung der potentiellen Energie verallgemeinert. Die potentielle Energie entspricht normalerweise der physikalischen Arbeit, die aufgewendet werden muss, um einen Körper aus dem Ruhezustand in eine bestimmte Konfiguration zu verformen. Darüber hinaus setzt sie die aktuelle Verformung in Beziehung zu internen Spannungskräften, die wirken um die ursprüngliche Form wiederherzustellen. In dieser Arbeit passen wir für jedes der drei betrachteten Problemfelder die potentielle Energie jeweils so an, dass sie eine anwendungsspezifische Definition von Form widerspiegelt. Unter dem Einfluss weiterer Randbedingungen führt die so verallgemeinerte Deformation zu einer Fläche, die eine Balance zwischen der Erhaltung gewisser Formeigenschaften und Zielvorgaben der Anwendung findet. Diese Balance entspricht dem Equilibrium einer physikalischen Deformation. Die drei in dieser Arbeit diskutierten Anwendungen sind Oberflächenparameterisierung, interaktives Bearbeiten von Flächen und das vollautomatische Erzeugen von Panoramakarten im Stile von Heinrich Berann. Zur Oberflächenparameterisierung interpretieren wir Parameterisierungen über einem flachen Parametergebiet als Deformationen, die ein ursprünglich ebenes Flächenstück in eine gegebene Oberfläche verformen. Innerhalb dieses Szenarios vergleichen wir dann existierende Methoden zur planaren Parameterisierung, indem wir die resultierenden potentiellen Energien analysieren, und leiten weitere Potentiale her, die die Störung geometrischer Eigenschaften wie Fläche und Winkel erfassen. Verfahren zur interaktiven Flächenbearbeitung ermöglichen schnelle und intuitive Änderungen an einer komplexen Oberfläche. Dazu wählt der Benutzer Teile der Fläche und bewegt diese durch den Raum. Ein Deformationsmodell extrapoliert interaktiv die Transformation der gewählten Teile auf die restliche Fläche. Diese Arbeit stellt eine neue differentielle Flächenrepräsentation für diskrete Flächen vor, die zu einem einfach und interaktiv zu optimierendem Potential führt. Obwohl das vorgeschlagene Potential nicht physikalisch korrekt ist, sind die resultierenden Deformationen intuitiv. Mittels eines Parameters lassen sich außerdem bestimmte Materialeigenschaften einstellen. Panoramakarten im Stile von Heinrich Berann sind eine Verschmelzung von Landschaftsillustration und geographischer Karte. Traditionell werden sie so von Hand gezeichnet, dass bestimmt Merkmale wie beispielsweise Skipisten oder Wanderwege in einem Gebiet unverdeckt und gut sichtbar bleiben, was große Kunstfertigkeit verlangt. Obwohl diese Art der Darstellung nicht maßstabsgetreu ist, sind Abweichungen auf den ersten Blick meistens nicht zu erkennen. Dadurch kann der Betrachter markante Details schnell wiederfinden und sich so innerhalb des Gebietes orientieren. Diese Arbeit stellt das erste, vollautomatische Verfahren zur Erzeugung von Panoramakarten vor. Grundlage ist wiederum eine verallgemeinerte Oberflächendeformation, die sowohl auf Formerhaltung als auch auf die Sichtbarkeit vorgegebener geographischer Merkmale abzielt

Studying Changes in the Cryosphere Using Radar Interferometry: Permafrost Surface Subsidence and Glacial Unloading Deformation

In past decades, cryospheric components such as glaciers, ice sheets, sea ice, and frozen ground have been undergoing significant and rapid changes, associated with changes in the global climate system. In this research, I present two case studies on how geodetic tools, especially Radar Interferometry (InSAR), can be used to monitor and to advance our understanding of the changing cryosphere. First, I measure seasonal and long-term surface subsidence on the North Slope of Alaska near Prudhoe Bay using InSAR. I detect a long-term surface subsidence of 1 to 4 cm per decade, which is probably caused by melting of ground ice within the permafrost, as ground temperatures have increased by 2 to 3°C in northern Alaska since the early 1980s. I also find a seasonal subsidence of 1 to 4 cm during summer thaw seasons, which is caused by the volume decrease of the top soil layer (the active layer) undergoing annual thawing-freezing cycles. A retrieval algorithm is developed to estimate the active layer thickness (ALT) using the InSAR-measured seasonal subsidence. The estimated ALT values match in situ measurements at Circumpolar Active Layer Monitoring sites within the uncertainties. I estimate an ALT of 30 to 50 cm over moist tundra areas, and a larger thickness of 50 to 80 cm over wet tundra areas. Second, I use InSAR and Global Positioning System data to measure the crustal elastic uplift near Jakobshavn Glacier in west-central Greenland caused by its rapid ice loss since 1997. These geodetic measurements place valuable constraints on the ice mass balance estimation based on altimetry measurements from NASA\u27s Airborne Topographic Mapper (ATM), as I find good agreement between the observed crustal rebound rates and the predicted rates using the ATM measurements. I also directly invert for the spatial pattern of ice thinning from the InSAR-measured crustal deformation. Overall, this research suggests that InSAR-measured surface deformation complements traditional in situ monitoring of the active layer and the permafrost, extends ALT estimates over large areas at high spatial resolution, provides new insights into the dynamics of permafrost systems and changes in permafrost conditions, and helps to study the ice mass loss of a rapidly thinning glacier and its surrounding region and to better understand a glacier\u27s rapid response to a warming climate

Les squelettes : structures d'interaction directe et intuitive avec des formes 3D

The interactions in shape creation graphic applications are far from natural. The user tends to avoid as much as possible such applications and prefer to sketch or model his/her shape.To bridge this widening gap between computer and the general public, we focus on skeletons. They are intuitive shape representation models that we propose to use as direct and intuitive interaction structures.All skeletons suffer from very low quality as shape representation models, concerning the geometry of the shape they capture, the quantity of skeletal noise they contain or the lack of useful organization of their elements. Moreover, some functionalities that must be granted to skeletons are only partially solved. Those solutions make use of additional data computed thanks to the shape during the skeletonization. Thus, when the skeleton is modified by an interaction, we cannot update those data to make use of such functionalities.Thanks to a practical observation of skeletons, we built a set of algorithmic solutions to those problems.We make an optimal use of skeleton data to visualize the shape described by a skeleton, to remove skeletal noise and to structure skeleton elements. With our methods, we build the meso-skeleton, a hierarchical structure that captures and controls all characteristic parts of a shape.The meso-skeleton is adapted to be used as a direct and intuitive interaction structure, which allows us to bridge the gap aforementioned. Also, our work can lead to further researches to enhance skeletonization techniques and thus produce skeletons that are good quality shape representation models.Dans les applications graphiques, les interactions avec les formes sont peu naturelles. L'utilisateur repousse autant que possible l'usage de ces applications, préférant dessiner ou sculpter une forme. Pour combler ce fossé qui se creuse entre l'informatique et le grand public, nous nous tournons vers les squelettes. Ce sont des modèles de représentation des formes intuitifs que nous proposons d'utiliser comme structure d'interaction directe et intuitive.Tous les squelettes souffrent d'un problème de qualité, que ce soit au niveau de la géométrie qu'ils capturent, de leurs quantité de bruit ou encore de l'absence d'organisation utile de leurs éléments. De plus, certaines fonctionnalités nécessaires des squelettes ne sont que partiellement résolues, et ceci grâce à des données additionnelles calculées à partir de la forme lors de la squelettisation. Ainsi, lorsque le squelette est modifié par une interaction, nous sommes dans l'incapacité de mettre à jour ces données et d'utiliser ces fonctionnalités.Nous avons construit un ensemble de solutions algorithmiques à ces problèmes. Nous faisons un usage optimal des données contenues dans le squelette pour visualiser la forme qu'il décrit, supprimer son bruit et structurer ses éléments. Nous construisons un squelette hiérarchique qui capture et contrôle toutes les zones caractéristiques d'une forme.Ce squelette est adapté pour une interaction directe et intuitive, ce qui permet de combler le fossé dont nous faisions mention. Nos travaux permettent également d'améliorer les méthodes de squelettisation et produire des squelettes qui sont déjà de bonne qualité