Concurrent Binary Trees for Large-Scale Game Components

Abstract: A concurrent binary tree (CBT) is a GPU-friendly data-structure suitable for the generation of bisection based terrain tessellations, i.e., adaptive triangulations over square domains. In this paper, we expand the benefits of this data-structure in two respects. First, we show how to bring bisection based tessellations to arbitrary polygon meshes rather than just squares. Our approach consists of mapping a triangular subdivision primitive, which we refer to as a bisector, to each halfedge of the input mesh. These bisectors can then be subdivided adaptively to produce conforming triangulations solely based on halfedge operators. Second, we alleviate a limitation that restricted the triangulations to low subdivision levels. We do so by using the CBT as a memory pool manager rather than an implicit encoding of the triangulation as done originally. By using a CBT in this way, we concurrently allocate and/or release bisectors during adaptive subdivision using shared GPU memory. We demonstrate the benefits of our improvements by rendering planetary scale geometry out of very coarse meshes. Performance-wise, our triangulation method evaluates in less than 0.2ms on console-level hardware.

• The paper introduces a GPU-friendly Concurrent Binary Tree for adaptive terrain tessellation that extends to arbitrary polygon meshes.
• It details a novel memory pool management approach decoupling binary tree capacity from subdivision depth, enabling fast dynamic updates.
• Benchmark tests show real-time rendering performance with centimeter-level detail on mid-range GPUs for large-scale environments.

Concurrent Binary Trees for Large-Scale Game Components

The paper presents a GPU-friendly data structure termed Concurrent Binary Tree (CBT) to handle large-scale game components with a focus on adaptive terrain tessellation. The structure is noteworthy for its capability to handle bisection-based terrain tessellation, expanding its utility beyond square domains to arbitrary polygon meshes, and enabling high-performance rendering on mid-range GPUs.

Key Contributions

The paper's notable contributions can be structured into two primary aspects:

1. Adaptive Triangulations for Arbitrary Polygon Meshes: The paper extends CBTs to work with arbitrary polygon meshes rather than being limited to square domains. This is achieved by mapping a triangular subdivision primitive, referred to as a "bisector," to each halfedge of the input mesh. These bisectors are then subdivided adaptively to produce conforming triangulations based purely on halfedge operators. The paper's approach ensures the maintenance of a valid initialization, resulting in a simple yet effective algorithm that preserves the topology of the input mesh. This makes it well suited for animated assets.
2. Memory Pool Management: CBTs are re-purposed as a memory pool manager, moving away from the original model that implicitly encoded the triangulation. By decoupling the CBT's capacity from the maximum subdivision depth, detailed and large-scale adaptive tessellations can be managed effectively. This transformation enables dynamic memory management using shared GPU memory, resulting in real-time evaluation of adaptive triangulations.

Algorithmic Details

The adaptive triangulation method is built on the principles of halfedge meshes and bi-sectional triangulation, reminiscent of the ROAM algorithm, but with enhancements that make it suitable for parallel GPU execution.

• Initialization: Root bisectors are mapped to halfedges of the input mesh, ensuring each halfedge corresponds to a unique bisector.
• Subdivision and Decimation: Through recursive refinement rules and subdivision matrices, bisectors are adaptively refined or decimated. This process ensures topologically conforming triangulations at all times.
• Neighbor Management: The algorithm updates neighbor pointers during refinement and decimation, maintaining consistency across bisectors.

GPU Implementation

The GPU implementation leverages a multi-step pipeline for incremental updates, ensuring efficient memory management through concurrent operations. The steps involve:

1. Memory Allocation: Efficiently managing memory allocations using atomic operations.
2. Command Generation: Deciding refinement or decimation commands for bisectors based on screen-space criteria.
3. Execution of Commands: Parallel execution of commands ensuring minimum overhead.
4. Neighbor Updates: Safeguarding topological coherence by updating neighbor pointers.

Performance and Results

The method has been validated using diverse large-scale game components including an Earth-sized water system, a Moon terrain using elevation data from NASA, and a complex mesh asset. The results demonstrated the method's capability to render planetary-scale geometries with centimeter-level detail on mid-range GPUs with an average update time of 0.1 ms and rendering performance fitting within real-time constraints.

Comparative Analysis

Compared to the original CBT design, the proposed approach demonstrates marked improvements in depth capabilities and memory efficiency. The decoupling of CBT depth from triangulation depth mitigates excessive memory use and computational overhead. This is crucial for planetary-scale environments requiring deep adaptive subdivisions.

Implications and Future Work

The practical implications are evident in the enhanced rendering capabilities for large-scale terrains and other game components. Theoretically, this work opens avenues for further optimization in dynamic memory management and adaptive mesh refinement on GPUs.

Future research could focus on:

• Enhanced Precision Management: Exploring quantization techniques to replace double precision without impacting the visual fidelity.
• Application to Other Domains: Adapting these principles to other large-scale scientific simulations and real-time data visualization tasks.
• Scalable Implementations: Investigating the scalability of this approach on distributed systems for even larger environments or higher precision requirements.

In conclusion, this paper presents a robust, adaptable, and efficient system for managing large-scale adaptive triangulation on GPUs, with significant practical applications in modern game development and other real-time rendering domains.