Real-Time Surface-Pressure Buoyancy with Adaptive Curved Clipping A Unity + C++ implementation of Hirae et al. (2025)'s closed-form hydrostatic-pressure integrator, with a custom Adaptive Curved Clipping refinement for coarse meshes on Gerstner waves.
Final project for KTH DH2323 Computer Graphics and Interaction, by Felix Stenberg.
MultipleObjectsWave.mp4
Report available here: https://github.com/Crispigt/RealTime-Buoyancy-Unity/blob/main/Report-Buoyancy.pdf
- Closed-form per-triangle buoyancy, exact force and torque, no quadrature error, even on coarse meshes (Hirae et al. 2025, Eqs. 5–9).
- Wave-agnostic C++ DLL geometry-only; the wave model lives in C# so the plugin is reusable across wave systems.
- Adaptive Curved Clipping refines per-vertex water heights along the clipping chord without geometric surface intersection. This was the project's main research contribution.
- Burst-compiled wave sampler
IJobParallelFor+Unity.Mathematics, ~6–10× speedup over plain C#. - Garland–Heckbert runtime mesh simplification for buoyancy meshes (
UnityMeshSimplifier). - Bug found in the source paper. A typographical error in Hirae et al.'s printed torque equations (Eqs. 7–9) was identified, re-derived from scratch, and corrected. The derivation notes and report draft live locally under the intentionally ignored
resources/folder. Authors have been contacted.
BunnyDragonCube.mp4
cubebobbing.mp4
DampningDifferent.mp4
| Sub-triangle winding-order bug | Paper Eq. 7–9 typo |
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FirstBug-wrongorder.mp4 |
PapperEquation.mp4 |
| Linear clipping | Adaptive curved clipping |
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Mesh simplification (Garland–Heckbert, https://github.com/whinarn/unitymeshsimplifier)
| 30,000-triangle ground truth | Roughly 7k-triangle buoyancy mesh |
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| Force Sweep | Adaptive Clipping Comparison |
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| Equilibrium Tilt (Corrected) | Equilibrium Tilt (Paper formula with typo) |
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All public clips live under report-assets/. Click to download/play:
| Metric | Value |
|---|---|
| Cube force-sweep error vs analytical |
< 10⁻⁶ % (FP noise) |
| Equilibrium tilt (corrected formula) vs Igarashi & Nakamura analytical 26.565° | 26.565°, residual torque 2.4×10⁻⁵ N·m |
| Equilibrium tilt (paper formula, with typo) | 45.000°, residual torque 215.9 N·m |
| Linear path tilt error (~7k tris) vs 30k ground truth (rough waves) | ~6° (mesh/dynamics dominated) |
| Adaptive N=4 tilt error vs 30k ground truth | ~5.5° (Adaptive vs Linear gap < 0.5°) |
| Adaptive N=4 vs N=16 difference | 0° (fully converged at N=4) |
| 100-sphere stress test, Linear C++ DLL | 363 FPS average |
| 100-sphere stress test, Adaptive N=1 (managed C#) | 53 FPS avg, degrades to 3 FPS at equilibrium |
Plots live in report-assets/plots/ and are regenerated with python resources/plot_tests.py and python resources/plot_performance.py.
| Accuracy validation | Convergence study | Stress test |
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| Equilibrium tilt, corrected formula vs paper formula |
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The plugin uses GLM as a git submodule. Initialize submodules first:
git submodule update --init --recursiveThen configure and build with CMake (Windows / Visual Studio shown; any CMake-supported toolchain works):
cd NativePlugin
cmake -S . -B build
cmake --build build --config ReleaseThe resulting DLL is consumed by Unity via [DllImport] in the buoyancy controllers.
Open BaseProject/ in Unity 6.x (URP). Ensure the Read/Write property is enabled in import settings for any mesh used for buoyancy. Press Play. Test scenes contain prefabs for the cube/bunny/dragon/sphere stress scenarios used in the report.
Blog can be found at: https://crispigt.com/dh2323
- Hirae, H., Morishima, S., & Ando, R. (2025). An Analytical Integrator for Solid-Fluid Coupled Buoyancy Forces. SIGGRAPH Asia 2025 Technical Communications.
- Hori, T. (2021). Proof that the Center of Buoyancy is Equal to the Center of Pressure by means of the Surface Integral of Hydrostatic Pressure Acting on the Inclined Ship. Nagasaki Institute of Applied Science.
- Fábián, G. (2025). Approximate and exact buoyancy calculation for real-time floating simulation of meshes. Eurographics 2025 Short Paper.
- Flick, J. (2024). Waves, Catlike Coding. https://catlikecoding.com/unity/tutorials/flow/waves/ (MIT)
- Garland, M. & Heckbert, P. (1997). Surface simplification using quadric error metrics. SIGGRAPH '97.
- Igarashi, T. & Nakamura, H. (2007). The equilibrium angles of floating cubes.
- Hwang, W. & Salvendy, G. (2010). Number of people required for usability evaluation: the
10 ± 2rule. CACM 53(5), 130–133.
Christopher Peters and the DH2323 course team at KTH. Jasper Flick (Catlike Coding) for the MIT-licensed Gerstner wave implementation. Hirae et al. for the integrator that this work builds on.
Code in this repository is released under the MIT License; see LICENSE.
Original documentation, screenshots, videos, and report media by Felix Stenberg are licensed under CC BY 4.0 unless noted otherwise.
Third-party assets and dependencies (Catlike Coding wave shader, GLM, UnityMeshSimplifier, Stanford bunny/dragon meshes) retain their respective licenses.