Heat-induced air turbulence produces complex, depth-dependent image distortions that are challenging to reproduce interactively because thermally driven flow must be coupled with refractive light transport. Existing real-time methods often rely on single-view 2D screen-space warps that break multi-view coherence and do not model a 3D refractive volume. We present a real-time, fully 3D Lagrangian framework that models the full pipeline from thermal transport to density variation to optical refraction. Our system augments compressible Smoothed Particle Hydrodynamics (SPH) with temperature transport, buoyancy, and pressure-driven motion to capture rising plumes and turbulent mixing. We render the resulting continuous refractive-index field via curved ray tracing to model light bending in 3D. To reconcile physical fidelity with interactive performance, we introduce spatially adaptive step-size integration for curved-ray tracing, refining steps near strong refractive-index gradients while relaxing them in smooth regions to preserve temporal stability and high-frequency distortion detail without uniform oversampling. The system runs at interactive rates (about 40 fps in our prototype) and matches depth-dependent, multi-view-consistent distortions observed in real video captures more closely than image-based baselines.

翻译：热致空气湍流会产生复杂且依赖于深度的图像畸变，由于需要将热驱动流与折射光传输相耦合，这类畸变的交互式再现极具挑战性。现有实时方法通常依赖单视图二维屏幕空间扭曲，这会破坏多视图一致性且未对三维折射体积进行建模。本文提出一种实时、完全三维的拉格朗日框架，该框架对从热传输到密度变化再到光学折射的完整流程进行建模。我们的系统通过引入温度传输、浮力及压力驱动运动来增强可压缩光滑粒子流体动力学（SPH）方法，从而捕捉上升羽流和湍流混合现象。我们通过弯曲光线追踪对生成的连续折射率场进行渲染，以模拟三维空间中的光线弯曲。为在物理保真度与交互性能间取得平衡，我们提出了面向弯曲光线追踪的空间自适应步长积分方法：在强折射率梯度区域细化步长，在平滑区域放宽步长，从而在避免均匀过采样的前提下保持时间稳定性与高频畸变细节。该系统能以交互速率运行（原型系统约40帧/秒），相比基于图像的基线方法，能更精确地复现真实视频采集中所观测到的、具有深度依赖性与多视图一致性的畸变现象。