We present the new procedural modeling language G 2 (Generalized Grammar), which adapts various concepts from general purpose programming languages to provide high descriptive power with well-defined semantics and a simple syntax which is easily readable even by non-programmers. The term 'Generalized' reflects two kinds of generalization. On the one hand, we extend the scope of previous architectural modeling languages by allowing for multiple types of non-terminal objects with domain-specific operators and attributes. On the other hand, the language accepts non-terminal symbols as parameters in modeling rules and thus enables the definition of abstract structure templates for flexible re-use within the grammar. By deriving G 2 from the well-established programming language Python, we can make sure that our modeling language has a well-defined semantics. For illustration, we apply G 2 to architectural as well as plant modeling to demonstrate its descriptive power with some complex examples.

The 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.

Procedural modeling is a promising approach to create complex and detailed 3D objects and scenes. Based on the concept of split grammars, e.g., construction rules can be defined textually in order to describe a hierarchical buildup of a scene. Unfortunately, creating or even just reading such grammars can become very challenging for nonprogrammers. Recent approaches have demonstrated ideas to interactively control basic split operations for boxes, however, designers need to have a deep understanding of how to express a certain object by just using box splitting. Moreover, the degrees of freedom of a certain model are typically very high and thus the adjustment of parameters remains more or less a trial-and-error process. In our paper, we therefore present novel concepts for the intuitive and interactive handling of complex procedural grammars allowing even amateurs and non-programmers to easily modify and combine existing procedural models that are not limited to the subdivision of boxes. In our grammar 3D manipulators can be defined in order to spawn a visual representation of adjustable parameters directly in model space to reveal the influence of a parameter. Additionally, modules of the procedural grammar can be associated with a set of camera views which draw the user's attention to a specific subset of relevant parameters and manipulators. All these concepts are encapsulated into procedural high-level primitives that effectively support the efficient creation of complex procedural 3D scenes. Since our target group are mainly users without any experience in 3D modeling, we prove the usability of our system by letting some untrained students perform a modeling task from scratch.Keywords: procedural modeling, interactive shape editing, shape grammars Figure 1: By creating complex manipulator objects like a stick figure and mapping it to another procedural object like a chair, we can achieve an abstract control of the chair in an ergonomic fashion. All important parameters can be directly adjusted in the 3D view for an intuitive and fast modeling process.

We 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.

We 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.