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Scene graphs, as found in many visualization systems are a well-established concept for modeling virtual scenes in computer graphics. State-of-the-art approaches typically issue appropriate draw commands while traversing the graph. Equipped with a functional programming mindset we take a different approach and utilize attribute grammars as a central concept for modeling the problem domain declaratively. Instead of issuing draw commands imperatively, we synthesize first class objects describing appropriate draw commands. In order to make this approach practical in the face of dynamic changes to the scene graph, we utilize incremental evaluation, and thereby avoid repeated evaluation of unchanged parts. Our application prototypically demonstrates how complex systems benefit from domain-specific languages, declarative problem solving and the implications thereof. Besides from being concise and expressive, our solution demonstrates a real-world use case of self-adjusting computation which elegantly extends scene graphs with well-defined reactive semantics and efficient, incremental execution.

We introduce an incremental rendering layer on top of standard graphics APIs such as OpenGL or DirectX in the form a virtual machine (VM), which efficiently maintains an optimized, compiled representation of arbitrary high-level scene representations at all times. This includes incremental processing of structural changes such as additions and removals of scene parts, as well as in-place updates of scene data. Our approach achieves a significant framerate increase for typical workloads and reasonable performance for high-frequency changes. Processing is performed in running time O(Δ), where Δ is proportional to the size of the change and the optimized representation has no runtime overhead with respect to the underlying graphics API. This is achieved by tracking and applying all changes as incremental updates to appropriate data structures and by adaptively synthesizing a program of abstract machine code. In a final step this abstract program is incrementally mapped to executable machine code --- comparable to what just-in-time compilers do. Our main contributions are (i) an abstract interface for rendering and visualization systems enabling incremental evaluation, (ii) adaptively optimized abstract machine code in the context of stateless graphics commands, and (iii) subsequent adaptive compilation to executable machine code including on-the-fly defragmentation.

In order to simplify shader programming we propose a system to specify composable shaders in a functional way directly in typical implementation languages of modern rendering frameworks. In constrast to existing pipeline shader frameworks, our system exposes a radically simplified pipeline, which we purposefully aligned with our basic intuition of shaders as compositions of per-primitive and per-pixel operations. By programming the shaders in the host language, we additionally remove the complexity of handling different programming languages for shaders and the rest of the framework.