DA Wand: Distortion-Aware Selection using Neural Mesh Parameterization

We present a neural technique for learning to select a local sub-region around a point which can be used for mesh parameterization. The motivation for our framework is driven by interactive workflows used for decaling, texturing, or painting on surfaces. Our key idea is to incorporate segmentation probabilities as weights of a classical parameterization method, implemented as a novel differentiable parameterization layer within a neural network framework. We train a segmentation network to select 3D regions that are parameterized into 2D and penalized by the resulting distortion, giving rise to segmentations which are distortion-aware. Following training, a user can use our system to interactively select a point on the mesh and obtain a large, meaningful region around the selection which induces a low-distortion parameterization. Our code and project page are currently available.Comment: Project page: https://threedle.github.io/DA-Wand/ Code: https://github.com/threedle/DA-Wan

Bijective Parameterization with Free Boundaries

When displaying 3D surfaces onto computer screens, additional information is often mapped onto the surface to enhance the quality of the rendering. Surface parameterization generates a correspondence, or mapping, between the 3D surface and 2D parameterization space. This mapping has many applications in computer graphics, but in most cases cannot be performed without introducing large distortions in the 2D parameterization. Along with problems of distortion, the mapping of the 2D space to 3D for many applications can be invalidated if the property of bijectivity is violated. While there is previous research guaranteeing bijectivity, these methods must constrain or modify the boundary of the 2D parameterization. This dissertation, describes a fully automatic method for generating guaranteed bijective surface parameterizations from triangulated 3D surfaces. In particular, a new isometric distortion energy metric is introduced preventing local folds of triangles in the parameterization as well as a barrier function that prevents intersection of the 2D boundaries. By using a computationally efficient isometric metric energy, the dissertation achieves fast and comparable optimization times to previous methods. The boundary of the parameterization is free to change shape during the optimization to minimize distortion. A new optimization approach is introduced called singularity aware optimization and in conjunction with an interior point approach and barrier energy functions guarantee bijectivity. This optimization framework is then modified to allow for an importance weighting allowing for customizable and more efficient texel usage

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

Shape Animation with Combined Captured and Simulated Dynamics

We present a novel volumetric animation generation framework to create new types of animations from raw 3D surface or point cloud sequence of captured real performances. The framework considers as input time incoherent 3D observations of a moving shape, and is thus particularly suitable for the output of performance capture platforms. In our system, a suitable virtual representation of the actor is built from real captures that allows seamless combination and simulation with virtual external forces and objects, in which the original captured actor can be reshaped, disassembled or reassembled from user-specified virtual physics. Instead of using the dominant surface-based geometric representation of the capture, which is less suitable for volumetric effects, our pipeline exploits Centroidal Voronoi tessellation decompositions as unified volumetric representation of the real captured actor, which we show can be used seamlessly as a building block for all processing stages, from capture and tracking to virtual physic simulation. The representation makes no human specific assumption and can be used to capture and re-simulate the actor with props or other moving scenery elements. We demonstrate the potential of this pipeline for virtual reanimation of a real captured event with various unprecedented volumetric visual effects, such as volumetric distortion, erosion, morphing, gravity pull, or collisions

Efficient multi-bounce lightmap creation using GPU forward mapping

Computer graphics can nowadays produce images in realtime that are hard to distinguish from photos of a real scene. One of the most important aspects to achieve this is the interaction of light with materials in the virtual scene. The lighting computation can be separated in two different parts. The first part is concerned with the direct illumination that is applied to all surfaces lit by a light source; algorithms related to this have been greatly improved over the last decades and together with the improvements of the graphics hardware can now produce realistic effects. The second aspect is about the indirect illumination which describes the multiple reflections of light from each surface. In reality, light that hits a surface is never fully absorbed, but instead reflected back into the scene. And even this reflected light is then reflected again and again until its energy is depleted. These multiple reflections make indirect illumination very computationally expensive. The first problem regarding indirect illumination is therefore, how it can be simplified to compute it faster. Another question concerning indirect illumination is, where to compute it. It can either be computed in the fixed image that is created when rendering the scene or it can be stored in a light map. The drawback of the first approach is, that the results need to be recomputed for every frame in which the camera changed. The second approach, on the other hand, is already used for a long time. Once a static scene has been set up, the lighting situation is computed regardless of the time it takes and the result is then stored into a light map. This is a texture atlas for the scene in which each surface point in the virtual scene has exactly one surface point in the 2D texture atlas. When displaying the scene with this approach, the indirect illumination does not need to be recomputed, but is simply sampled from the light map. The main contribution of this thesis is the development of a technique that computes the indirect illumination solution for a scene at interactive rates and stores the result into a light atlas for visualizing it. To achieve this, we overcome two main obstacles. First, we need to be able to quickly project data from any given camera configuration into the parts of the texture that are currently used for visualizing the 3D scene. Since our approach for computing and storing indirect illumination requires a huge amount of these projections, it needs to be as fast as possible. Therefore, we introduce a technique that does this projection entirely on the graphics card with a single draw call. Second, the reflections of light into the scene need to be computed quickly. Therefore, we separate the computation into two steps, one that quickly approximates the spreading of the light into the scene and a second one that computes the visually smooth final result using the aforementioned projection technique. The final technique computes the indirect illumination at interactive rates even for big scenes. It is furthermore very flexible to let the user choose between high quality results or fast computations. This allows the method to be used for quickly editing the lighting situation with high speed previews and then computing the final result in perfect quality at still interactive rates. The technique introduced for projecting data into the texture atlas is in itself highly flexible and also allows for fast painting onto objects and projecting data onto it, considering all perspective distortions and self-occlusions

Signal Processing on Textured Meshes

In this thesis we extend signal processing techniques originally formulated in the context of image processing to techniques that can be applied to signals on arbitrary triangles meshes. We develop methods for the two most common representations of signals on triangle meshes: signals sampled at the vertices of a finely tessellated mesh, and signals mapped to a coarsely tessellated mesh through texture maps. Our first contribution is the combination of Lagrangian Integration and the Finite Elements Method in the formulation of two signal processing tasks: Shock Filters for texture and geometry sharpening, and Optical Flow for texture registration. Our second contribution is the formulation of Gradient-Domain processing within the texture atlas. We define a function space that handles chart discontinuities, and linear operators that capture the metric distortion introduced by the parameterization. Our third contribution is the construction of a spatiotemporal atlas parameterization for evolving meshes. Our method introduces localized remeshing operations and a compact parameterization that improves geometry and texture video compression. We show temporally coherent signal processing using partial correspondences

Lagrangian-on-Lagrangian Garment Design

Since the discovery of elastomeric materials, such as spandex or lycra, skintight clothing has revolutionized many different areas of the clothing industry, such as body-shaping clothing, athletic wear, and medical garments, among others. Often, this kind of clothing is designed to fulfill a given purpose, such as providing comfort, mobility, or improving recovery in the case of an athlete, provide support or exert some desired pressure in the case of medical garments, or actively deform the body to acquire some desired shape. Additionally, some designs aim to improve the life of the garment by, for example, minimizing tractions across the seams. While many tight-skin garments are sold in the market for generic body shapes, many of the purposes here mentioned are only achievable through a personalized fitting. To this end, we introduce a novel model, where the cloth is modeled as a membrane, parameterized as a function of the body. The cloth, is then able to slide on the body and deform it while staying always in contact. We call this model Lagrangian-on-Lagrangian. Based on this model, we develop an optimization framework, based on sensitivity analysis, capable of developing sewable patterns such that, when worn by a person, satisfy a given design target. With the framework, we include several design targets such as, body shape, stretch, pressure, sliding under motion, and seam traction. We evaluate our method on a variety of applications, as well as body shapes