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Item Procedural Interpolation of Historical City Maps(The Eurographics Association and John Wiley and Sons Ltd., 2012) Krecklau, Lars; Manthei, Christopher; Kobbelt, Leif; P. Cignoni and T. ErtlWe propose a novel approach for the temporal interpolation of city maps. The input to our algorithm is a sparse set of historical city maps plus optional additional knowledge about construction or destruction events. The output is a fast forward animation of the city map development where roads and buildings are constructed and destroyed over time in order to match the sparse historical facts and to look plausible where no precise facts are available. A smooth transition between any real-world data could be interesting for educational purposes, because our system conveys an intuition of the city development. The insertion of data, like when and where a certain building or road existed, is efficiently performed by an intuitive graphical user interface. Our system collects all this information into a global dependency graph of events. By propagating time intervals through the dependency graph we can automatically derive the earliest and latest possible date for each event which are guaranteeing temporal as well as geographical consistency (e.g. buildings can only appear along roads that have been constructed before). During the simulation of the city development, events are scheduled according to a score function that rates the plausibility of the development (e.g. cities grow along major roads). Finally, the events are properly distributed over time to control the dynamics of the city development. Based on the city map animation we create a procedural city model in order to render a 3D animation of the city development over decades.Item Efficient Enforcement of Hard Articulation Constraints in the Presence of Closed Loops and Contacts(The Eurographics Association and John Wiley and Sons Ltd., 2014) Tomcin, Robin; Sibbing, Dominik; Kobbelt, Leif; B. Levy and J. KautzIn rigid body simulation, one must distinguish between contacts (so-called unilateral constraints) and articulations (bilateral constraints). For contacts and friction, iterative solution methods have proven most useful for interactive applications, often in combination with Shock-Propagation in cases with strong interactions between contacts (such as stacks), prioritizing performance and plausibility over accuracy. For articulation constraints, direct solution methods are preferred, because one can rely on a factorization with linear time complexity for tree-like systems, even in ill-conditioned cases caused by large mass-ratios or high complexity. Despite recent advances, combining the advantages of direct and iterative solution methods wrt. performance has proven difficult and the intricacy of articulations in interactive applications is often limited by the convergence speed of the iterative solution method in the presence of closed kinematic loops (i.e. auxiliary constraints) and contacts. We identify common performance bottlenecks in the dynamic simulation of unilateral and bilateral constraints and are able to present a simulation method, that scales well in the number of constraints even in ill-conditioned cases with frictional contacts, collisions and closed loops in the kinematic graph. For cases where many joints are connected to a single body, we propose a technique to increase the sparsity of the positive definite linear system. A solution to these bottlenecks is presented in this paper to make the simulation of a wider range of mechanisms possible in real-time without extensive parameter tuning.Item Procedural Modeling of Interconnected Structures(The Eurographics Association and Blackwell Publishing Ltd., 2011) Krecklau, Lars; Kobbelt, Leif; M. Chen and O. DeussenThe complexity and detail of geometric scenes that are used in today's computer animated films and interactive games have reached a level where the manual creation by traditional 3D modeling tools has become infeasible. This is why procedural modeling concepts have been developed which generate highly complex 3D models by automatically executing a set of formal construction rules. Well-known examples are variants of L-systems which describe the bottom-up growth process of plants and shape grammars which define architectural buildings by decomposing blocks in a top-down fashion. However, none of these approaches allows for the easy generation of interconnected structures such as bridges or roller coasters where a functional interaction between rigid and deformable parts of an object is needed. Our approach mainly relies on the top-down decomposition principle of shape grammars to create an arbitrarily complex but well structured layout. During this process, potential attaching points are collected in containers which represent the set of candidates to establish interconnections. Our grammar then uses either abstract connection patterns or geometric queries to determine elements in those containers that are to be connected. The two different types of connections that our system supports are rigid object chains and deformable beams. The former type is constructed by inverse kinematics, the latter by spline interpolation. We demonstrate the descriptive power of our grammar by example models of bridges, roller coasters, and wall-mounted catenaries.Item Linear Analysis of Nonlinear Constraints for Interactive Geometric Modeling(The Eurographics Association and John Wiley and Sons Ltd., 2012) Habbecke, Martin; Kobbelt, Leif; P. Cignoni and T. ErtlThanks to its flexibility and power to handle even complex geometric relations, 3D geometric modeling with nonlinear constraints is an attractive extension of traditional shape editing approaches. However, existing approaches to analyze and solve constraint systems usually fail to meet the two main challenges of an interactive 3D modeling system: For each atomic editing operation, it is crucial to adjust as few auxiliary vertices as possible in order to not destroy the user's earlier editing effort. Furthermore, the whole constraint resolution pipeline is required to run in real-time to enable a fluent, interactive workflow. To address both issues, we propose a novel constraint analysis and solution scheme based on a key observation: While the computation of actual vertex positions requires nonlinear techniques, under few simplifying assumptions the determination of the minimal set of to-be-updated vertices can be performed on a linearization of the constraint functions. Posing the constraint analysis phase as the solution of an under-determined linear system with as few non-zero elements as possible enables us to exploit an efficient strategy for the Cardinality Minimization problem known from the field of Compressed Sensing, resulting in an algorithm capable of handling hundreds of vertices and constraints in real-time. We demonstrate at the example of an image-based modeling system for architectural models that this approach performs very well in practical applications.Item Improved Surface Quality in 3D Printing by Optimizing the Printing Direction(The Eurographics Association and John Wiley & Sons Ltd., 2016) Wang, Weiming; Zanni, Cédric; Kobbelt, Leif; Joaquim Jorge and Ming LinWe present a pipeline of algorithms that decomposes a given polygon model into parts such that each part can be 3D printed with high (outer) surface quality. For this we exploit the fact that most 3D printing technologies have an anisotropic resolution and hence the surface smoothness varies significantly with the orientation of the surface. Our pipeline starts by segmenting the input surface into patches such that their normals can be aligned perpendicularly to the printing direction. A 3D Voronoi diagram is computed such that the intersections of the Voronoi cells with the surface approximate these surface patches. The intersections of the Voronoi cells with the input model's volume then provide an initial decomposition. We further present an algorithm to compute an assembly order for the parts and generate connectors between them. A post processing step further optimizes the seams between segments to improve the visual quality. We run our pipeline on a wide range of 3D models and experimentally evaluate the obtained improvements in terms of numerical, visual, and haptic quality.Item Exact and Robust (Self-)Intersections for Polygonal Meshes(The Eurographics Association and Blackwell Publishing Ltd, 2010) Campen, Marcel; Kobbelt, LeifWe present a new technique to implement operators that modify the topology of polygonal meshes at intersections and self-intersections. Depending on the modification strategy, this effectively results in operators for Boolean combinations or for the construction of outer hulls that are suited for mesh repair tasks and accurate mesh-based front tracking of deformable materials that split and merge. By combining an adaptive octree with nested binary space partitions (BSP), we can guarantee exactness (= correctness) and robustness (= completeness) of the algorithm while still achieving higher performance and less memory consumption than previous approaches. The efficiency and scalability in terms of runtime and memory is obtained by an operation localization scheme. We restrict the essential computations to those cells in the adaptive octree where intersections actually occur. Within those critical cells, we convert the input geometry into a plane-based BSP-representation which allows us to perform all computations exactly even with fixed precision arithmetics. We carefully analyze the precision requirements of the involved geometric data and predicates in order to guarantee correctness and show how minimal input mesh quantization can be used to safely rely on computations with standard floating point numbers. We properly evaluate our method with respect to precision, robustness, and efficiency.Item View-Dependent Realtime Rendering of Procedural Facades with High Geometric Detail(The Eurographics Association and Blackwell Publishing Ltd., 2013) Krecklau, Lars; Born, Janis; Kobbelt, Leif; I. Navazo, P. PoulinWe present an algorithm for realtime rendering of large-scale city models with procedurally generated facades. By using highly detailed assets like windows, doors, and decoration such city models can provide an extremely high geometric level of detail but on the downside they also consist of billions of polygons which makes it infeasible to even store them as explicit polygonal meshes. Moreover, when rendering urban scenes usually only a very small fraction of the city is actually visible which calls for effective culling mechanisms. For procedural textures there are efficient screen space techniques that evaluate, e.g., a split grammar on a per-pixel basis in the fragment shader and thus render a textured facade in a view dependent manner. We take this idea further by introducing 3D geometric detail in addition to flat textures. Our approach is a two-pass procedure that first renders a flat procedural facade. During rasterization the fragment shader triggers the instantiation of a detailed asset whenever a geometric facade element is potentially visible. The set of instantiated detail models are then rendered in a second pass. The major challenges arise from the fact that geometric details belonging to a facade can be visible even if the base polygon of the facade itself is not visible. Hence we propose measures to conservatively estimate visibility without introducing excessive redundancy. We further extend our technique by a simple level of detail mechanism that switches to baked textures (of the assets) depending on the distance to the camera. We demonstrate that our technique achieves realtime frame rates for large-scale city models with massive detail on current commodity graphics hardware.Item A Practical Guide to Polygon Mesh Repairing(The Eurographics Association, 2012) Campen, Marcel; Attene, Marco; Kobbelt, Leif; Renato Pajarola and Michela SpagnuoloDigital 3D models are key components in many industrial and scientific sectors. In numerous domains polygonmeshes have become a de facto standard for model representation. In practice meshes often have a number ofdefects and flaws that make them incompatible with quality requirements of specific applications. Hence, repairingsuch defects in order to achieve compatibility is a highly important task - in academic as well as industrial applications. In this tutorial we first systematically analyze typical application contexts together with their requirementsand issues, as well as the various types of defects that typically play a role. Subsequently, we considerexisting techniques to process, repair, and improve the structure, geometry, and topology of imperfect meshes,aiming at making them appropriate to case-by-case requirements. We present seminal works and key algorithms,discuss extensions and improvements, and analyze the respective advantages and disadvantages depending onthe application context. Furthermore, we outline directions where further research is particularly important orpromising.Item Walking On Broken Mesh: Defect-Tolerant Geodesic Distances and Parameterizations(The Eurographics Association and Blackwell Publishing Ltd., 2011) Campen, Marcel; Kobbelt, Leif; M. Chen and O. DeussenEfficient methods to compute intrinsic distances and geodesic paths have been presented for various types of surface representations, most importantly polygon meshes. These meshes are usually assumed to be well-structured and manifold. In practice, however, they often contain defects like holes, gaps, degeneracies, non-manifold configurations - or they might even be just a soup of polygons. The task of repairing these defects is computationally complex and in many cases exhibits various ambiguities demanding tedious manual efforts. We present a computational framework that enables the computation of meaningful approximate intrinsic distances and geodesic paths on raw meshes in a way which is tolerant to such defects. Holes and gaps are bridged up to a user-specified tolerance threshold such that distances can be computed plausibly even across multiple connected components of inconsistent meshes. Further, we show ways to locally parameterize a surface based on geodesic distance fields, easily facilitating the application of textures and decals on raw meshes. We do all this without explicitly repairing the input, thereby avoiding the costly additional efforts. In order to enable broad applicability we provide details on two implementation variants, one optimized for performance, the other optimized for memory efficiency. Using the presented framework many applications can readily be extended to deal with imperfect meshes. Since we abstract from the input applicability is not even limited to meshes, other representations can be handled as well.Item Adapting Feature Curve Networks to a Prescribed Scale(The Eurographics Association and John Wiley & Sons Ltd., 2016) Gehre, Anne; Lim, Isaak; Kobbelt, Leif; Joaquim Jorge and Ming LinFeature curves on surface meshes are usually defined solely based on local shape properties such as dihedral angles and principal curvatures. From the application perspective, however, the meaningfulness of a network of feature curves also depends on a global scale parameter that takes the distance between feature curves into account, i.e., on a coarse scale, nearby feature curves should be merged or suppressed if the surface region between them is not representable at the given scale/resolution. In this paper, we propose a computational approach to the intuitive notion of scale conforming feature curve networks where the density of feature curves on the surface adapts to a global scale parameter. We present a constrained global optimization algorithm that computes scale conforming feature curve networks by eliminating curve segments that represent surface features, which are not compatible to the prescribed scale. To demonstrate the usefulness of our approach we apply isotropic and anisotropic remeshing schemes that take our feature curve networks as input. For a number of example meshes, we thus generate high quality shape approximations at various levels of detail.