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Diffstat (limited to 'docs/physics.md')
| -rw-r--r-- | docs/physics.md | 10 |
1 files changed, 3 insertions, 7 deletions
diff --git a/docs/physics.md b/docs/physics.md index 4877f64..d484cb0 100644 --- a/docs/physics.md +++ b/docs/physics.md @@ -73,7 +73,7 @@ R_ISCO = 3.0 * SagA_rs // ISCO (6M) The scene editor uses a friendlier grid. The constant `SCENE_UNITS_PER_RS = 3.0` (in [`src/scene/scene_types.h`](../src/scene/scene_types.h)) sets three grid units to one Schwarzschild radius. When the renderer hands a placed object to the shader -it scales the position by $\text{SagA\_rs}/3$ to get metres, so the editor and the +it scales the position by $r_s/3$ (the code's `SagA_rs / 3`) to get metres, so the editor and the simulation always agree on where things sit. ## The Schwarzschild metric @@ -188,14 +188,10 @@ far from the hole and lose the trajectory near it, so the step scales with dista from the photon sphere: $$ -\Delta\lambda = \operatorname{clamp}\!\left(0.02\,\max(r - r_\text{photon},\,0),\; \Delta_\text{min},\; \Delta_\text{max}\right), -\qquad -\begin{aligned} -\Delta_\text{min} &= 10^6\\ -\Delta_\text{max} &= 2\times10^{10} -\end{aligned} +\Delta\lambda = \mathrm{clamp}\!\left(0.02\,\max(r - r_\text{photon},\,0),\; \Delta_\text{min},\; \Delta_\text{max}\right), $$ +with $\Delta_\text{min} = 10^6$ and $\Delta_\text{max} = 2\times10^{10}$ metres. Far out, the ray is in near-flat space and crosses it in a handful of long strides. Near the photon sphere, where the path bends hardest and mistakes show the most, the step shrinks to follow the curve. A second clamp forces the step |