nurbs_dde

A C++23 / Vulkan graphics project for rendering parametric curves in R³.

Current milestone: draw a parabola in a full-screen Vulkan window.
Long-term goals: NURBS curves, delay-differential equation trajectories in R³.

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Dependencies

All fetched automatically by CMake FetchContent except the system packages below.

System packages (Ubuntu)

sudo apt update
sudo apt install -y \
    clang-17 \
    cmake \
    ninja-build \
    libvulkan-dev \
    vulkan-tools \
    vulkan-validationlayers \
    libglfw3-dev \
    glslang-tools \
    pkg-config

Set Clang 17 as default if needed:

sudo update-alternatives --install /usr/bin/clang++ clang++ /usr/bin/clang++-17 100
sudo update-alternatives --install /usr/bin/clang   clang   /usr/bin/clang-17   100

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Build

The Linux CI path uses the checked-in Clang container:

docker build -t lra-nurbs-linux -f docker/linux-clang.Dockerfile .
docker run --rm -v "$PWD:/workspace" -w /workspace lra-nurbs-linux bash -lc \
  'cmake -S . -B build -G Ninja \
     -DCMAKE_BUILD_TYPE=Release \
     -DCMAKE_C_COMPILER=clang-18 \
     -DCMAKE_CXX_COMPILER=clang++-18 \
     -DCMAKE_CXX_FLAGS="-stdlib=libc++ -fexperimental-library" \
     -DCMAKE_EXE_LINKER_FLAGS="-stdlib=libc++ -fexperimental-library" \
     -DENABLE_SANITIZERS=OFF \
     -DNDDE_ENABLE_CLANG_TIDY=OFF &&
   cmake --build build --parallel &&
   ctest --test-dir build --output-on-failure --parallel 4'

Native Linux builds use the same CMake shape:

# Configure (Debug — includes ASan + UBSan)
cmake -B build -G Ninja \
      -DCMAKE_CXX_COMPILER=clang++ \
      -DCMAKE_BUILD_TYPE=Debug

# Build
cmake --build build -j$(nproc)

For a release build:

cmake -B build-rel -G Ninja \
      -DCMAKE_CXX_COMPILER=clang++ \
      -DCMAKE_BUILD_TYPE=Release
cmake --build build-rel -j$(nproc)

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Run

./build/src/nurbs_dde
# ESC to quit

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Tests

ctest --test-dir build --output-on-failure
# or directly:
./build/tests/nurbs_dde_tests

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Project structure

nurbs_dde/
├── CMakeLists.txt
├── cmake/
│   └── CompileShaders.cmake       Shader GLSL → SPIR-V helper
├── shaders/
│   ├── curve.vert                 Line-strip vertex shader (push-constant MVP)
│   └── curve.frag                 Colour passthrough fragment shader
├── src/
│   ├── math/
│   │   └── Vec3.hpp               R³ types (thin glm wrapper)
│   ├── geometry/
│   │   ├── Curve.hpp/.cpp         Abstract parametric curve p:[t0,t1]→R³
│   │   └── Parabola.hpp/.cpp      y = at²+bt+c on XY plane
│   ├── renderer/
│   │   ├── VulkanContext.hpp/.cpp Instance / device / queues (vk-bootstrap)
│   │   ├── Swapchain.hpp/.cpp     Swapchain management
│   │   ├── Pipeline.hpp/.cpp      Line-strip graphics pipeline
│   │   └── Renderer.hpp/.cpp      Frame loop, vertex buffer, sync
│   └── app/
│       ├── Application.hpp/.cpp   Top-level orchestrator
│       └── main.cpp
└── tests/
    ├── CMakeLists.txt
    ├── test_vec3.cpp
    ├── test_parabola.cpp
    └── test_curve.cpp

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Roadmap

Milestone	Status
Full-screen Vulkan window	✅
Draw parabola (line-strip)	✅
GTest suite (geometry + math)	✅
NURBS curve (de Boor algorithm)	⏳
DDE trajectory integration (RK4 / history buffer)	⏳
Camera / orbit control in R³	⏳
Depth buffer (3-D curves)	⏳

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Design notes

• Curve abstract base — tessellate(n) gives uniform parameter samples; vertex_buffer(n) gives vec4 data ready for a Vulkan vertex buffer. NURBS will override with knot-adaptive sampling.
• Homogeneous coordinates (w = 1) in vertex buffers are intentional — rational NURBS weights will live in w.
• Push-constant MVP (64 bytes) — sufficient for 2-D curves today; a UBO will be added when camera + multiple objects are needed.
• Dynamic rendering (VK 1.3) — no VkRenderPass objects; cleaner for a geometry-exploration tool that changes frame structure frequently.
• No staging buffer yet — vertex data is uploaded via host-visible memory. A proper staging pipeline will be introduced before adding large DDE history meshes.