根据所提到的内容，做一份六年级的数学课程预习教学视频---Table 1: 六年级数学核心知识点概览 | 模块 | 核心知识点 | 学习目标 This is an implementation of the technique described in [1]. It follows the paper quite closely, but adds a few things and uses some slightly different notation. If you're going to be diving into this code I recommend you start by skimming through the paper first. ## Building and Running The project builds using cmake. If you have a build directory already configured, you can build using `cmake --build build/`. To run it, simply execute the compiled program from the build directory: `build/vdb_explorer`. ## Example VDB Explorer Usage The VDB Explorer is used to view VDBs and demonstrate the basic functionality. It has a simple command line interface. There are a few hardcoded VDBs that can be loaded. After loading a VDB you can interact with the volume using mouse controls: - left-click and drag: rotate - right-click and drag: pan - middle-click and drag: zoom To show the VDB as voxels (i.e. a naive 3D grid), press the `v` key. This renders the active leaf nodes and the root node. To demonstrate ray marching through the VDB, press the `m` key. Ray marching is an iterative process and the max iterations is set by the `m` key. Increasing the max iterations shows more of the volume. To demonstrate ray tracing (single scattering only) through the VDB, press the `r` key. Ray tracing also requires max iterations, which is set by the `r` key. Ray tracing produces much nicer images, but also takes longer per frame. The frame rate is shown at the top of the window. To see a list of commands, press the `h` key. ## Source Code Structure The main entry point is `src/main.cpp`. This sets up the VDB Explorer class and runs the main loop. The VDB Explorer class (`src/vdb_explorer.cpp`) handles the window, controls, and rendering. It loads and stores VDBs. It has functions for rendering a naive voxel representation (`renderVoxels`) and for ray marching/tracing (`renderRaymarch`, `renderRaytrace`). The ray marching/tracing is implemented using compute shaders. The VDB data structure is implemented in `src/vdb.hpp` and `src/vdb.cpp`. This class contains the nodes of the tree and functions for loading, writing, and traversing the tree. Nodes are stored in separate arrays for each level (Level3, Level2, Level1, Leaf). Each node stores its child pointers and a bitmask indicating which children are active. The bitmask is the core of the VDB's sparse representation. The file `src/vdb_io.hpp` contains helper functions for reading and writing VDBs. This is not a standard VDB format, just a simple format for this project. The rendering is done using OpenGL. The shader files are in `src/shaders/`. The compute shaders (`raymarch.comp`, `raytrace.comp`) implement the core ray traversal algorithms. These shaders read VDB data from shader storage buffer objects (SSBOs). The `src/camera.hpp` and `src/camera.cpp` implement a basic camera class. The `src/timer.hpp` and `src/timer.cpp` implement a simple timer for measuring performance. The `src/util.hpp` and `src/util.cpp` contain various helper functions and data structures, including the `vec3` and `mat4` classes (simple vector and matrix implementations). ## VDB Ray Traversal Algorithms The core of this project is the implementation of the VDB ray traversal algorithms in the compute shaders. The ray marching algorithm (`raymarch.comp`) is described in Section 3 of [1]. It uses a technique called "Voxel Cone Traversal" to efficiently step through the VDB. The algorithm involves traversing down the tree to find the first active voxel along the ray, taking a step, and then traversing back up and down to find the next active voxel. This is done iteratively until the ray exits the volume or reaches the maximum number of steps. The ray tracing algorithm (`raytrace.comp`) is described in Section 4 of [1]. It extends the ray marching algorithm to support lighting and more realistic rendering effects. This implementation only supports single scattering, meaning it calculates the light scattered from the first intersection point with an active voxel. More advanced effects like multiple scattering would require extending this shader or adding more passes. Both traversal algorithms use the VDB data stored in SSBOs. The node data (child pointers and bitmasks) is laid out in memory according to the structure defined in `src/vdb.cpp` and described in Section 2 of [1]. ## Future Improvements - Implement more sophisticated lighting and shading models in the ray tracer (e.g., multiple scattering). - Implement other VDB operations like sampling, filtering, and level set operations. - Support loading standard OpenVDB files. - Improve the VDB Explorer's GUI and features (e.g., interactive volume editing, different rendering modes). - Optimize the VDB data layout and traversal for better performance on GPUs. - Implement bounding volume hierarchies within VDB nodes for faster child intersection tests. ## References [1] Museth, K. (2013). VDB: High-Resolution Sparse Volumes with Dynamic Topology. ACM Transactions on Graphics (TOG), 32(3), 29.