feat(blog/physics-black-hole-shader): Separate LaTeX markup into files

4 files changed, 43 insertions, 40 deletions

diff --git a/src/blog/the-physics-behind-a-black-hole-shader/algorithm.tex b/src/blog/the-physics-behind-a-black-hole-shader/algorithm.tex
new file mode 100644
index 0000000..3e33a11
--- /dev/null
+++ b/src/blog/the-physics-behind-a-black-hole-shader/algorithm.tex
@@ -0,0 +1,25 @@
+\begin{align*}
+    & p_{cbh} = \text{position of center of black hole}\\
+    & r_s = \text{Schwarzchild distance from } p_{cbn} \\
+    & r_{ps} = \frac{2}{3}r_s \quad \text{(photon sphere)}\\
+    & r_{ISCO} = 3 r_s \\
+    \\
+    & p_l = \text{position of light "particle"}\\
+    & v_l = \text{velocity of light "particle"}\\
+    \\
+    & r_l = \| p_l-p_{cbh} \| \quad \text{(distance between black hole and light)}\\
+    & \text{If } r_l \leq r_{ISCO} : \\
+    & \quad h = \| r_l \cross v_l \|\\
+    & \quad \text{LightMovesLimit} = \infty \\
+    & \quad \text{Repeat maximum LightMovesLimit times}:\\
+    & \qquad \text{If } r_l \leq r_s : \\
+    & \qquad \quad \text{return "Light never escapes"} \\
+    & \qquad \text{If } r_l \leq r_{ps} : \\
+    & \qquad \quad \text{LightMovesLimit} = 100 \\
+    & \qquad \text{If } r_l > r_{ISCO} : \\
+    & \qquad \quad \text{return "Light escaped black hole"} \\
+    & \qquad p_l = p_l + v_l \quad \text{(move light)}\\
+    & \qquad r_l = \| p_l-p_{cbh} \| \quad \text{(update distance to $p_{cbh}$)}\\
+    & \qquad v_l = v_l + \overrightarrow{F}(r_l,h) \quad \text{(update light velocity)} \\
+    & \quad \text{return "Light stuck in photon sphere, never escapes"}
+\end{align*}
diff --git a/src/blog/the-physics-behind-a-black-hole-shader/antonelli_formula.tex b/src/blog/the-physics-behind-a-black-hole-shader/antonelli_formula.tex
new file mode 100644
index 0000000..4d24e9a
--- /dev/null
+++ b/src/blog/the-physics-behind-a-black-hole-shader/antonelli_formula.tex
@@ -0,0 +1,8 @@
+\begin{align*}
+    & \overrightarrow{F}(r_l,h) = -\frac{3}{2} \; h^2 \; \frac{\hat{r_l}}{\|r_l\|^5} \quad \text{, where}\\
+    & h = \|r_l \cross v_l\|\\
+    & \hat{r_l} = \frac{r_l}{\|r_l\|}\\
+    & \|x\| = \text{magnitude of }x\\
+    & r_l = \text{vector from black hole center to light "particle"}\\
+    & v_l = \text{velocity of light "particle"}
+\end{align*}
diff --git a/src/blog/the-physics-behind-a-black-hole-shader/antonelli_formula_simplified.tex b/src/blog/the-physics-behind-a-black-hole-shader/antonelli_formula_simplified.tex
new file mode 100644
index 0000000..4abc30e
--- /dev/null
+++ b/src/blog/the-physics-behind-a-black-hole-shader/antonelli_formula_simplified.tex
@@ -0,0 +1,7 @@
+\begin{align*}
+    & \overrightarrow{F}(r_l,h) = -\frac{3}{2} \; h^2 \; \frac{r_l}{\|r_l\|^6} \quad \text{, where}\\
+    & h = \|r_l \cross v_l\| \text{ (calculated right before being affected by black hole)}\\
+    & \|x\| = \text{magnitude of }x\\
+    & r_l = \text{vector from black hole center to light "particle"}\\
+    & v_l = \text{velocity of light "particle"}
+\end{align*}
diff --git a/src/blog/the-physics-behind-a-black-hole-shader/index.du b/src/blog/the-physics-behind-a-black-hole-shader/index.du
index cd9f779..739e546 100644
--- a/src/blog/the-physics-behind-a-black-hole-shader/index.du
+++ b/src/blog/the-physics-behind-a-black-hole-shader/index.du
@@ -388,51 +388,14 @@ The images for my custom LaTeX equations were created on [url https://latexedito
 #### Antonelli's formula - explained
 
 ```latex
-\begin{align*}
-    & \overrightarrow{F}(r_l,h) = -\frac{3}{2} \; h^2 \; \frac{\hat{r_l}}{\|r_l\|^5} \quad \text{, where}\\
-    & h = \|r_l \cross v_l\|\\
-    & \hat{r_l} = \frac{r_l}{\|r_l\|}\\
-    & \|x\| = \text{magnitude of }x\\
-    & r_l = \text{vector from black hole center to light "particle"}\\
-    & v_l = \text{velocity of light "particle"}
-\end{align*}
+'include ./antonelli_formula.tex
 
 #### Antonelli's formula - simplified
 
 ```latex
-\begin{align*}
-    & \overrightarrow{F}(r_l,h) = -\frac{3}{2} \; h^2 \; \frac{r_l}{\|r_l\|^6} \quad \text{, where}\\
-    & h = \|r_l \cross v_l\| \text{ (calculated right before being affected by black hole)}\\
-    & \|x\| = \text{magnitude of }x\\
-    & r_l = \text{vector from black hole center to light "particle"}\\
-    & v_l = \text{velocity of light "particle"}
-\end{align*}
+'include ./antonelli_formula_simplified.tex
 
 #### Algorithm
 
 ```latex
-\begin{align*}
-    & p_{cbh} = \text{position of center of black hole}\\
-    & r_s = \text{Schwarzchild distance from } p_{cbn} \\
-    & r_{ps} = \frac{2}{3}r_s \quad \text{(photon sphere)}\\
-    & r_{ISCO} = 3 r_s \\
-    \\
-    & p_l = \text{position of light "particle"}\\
-    & v_l = \text{velocity of light "particle"}\\
-    \\
-    & r_l = \| p_l-p_{cbh} \| \quad \text{(distance between black hole and light)}\\
-    & \text{If } r_l \leq r_{ISCO} : \\
-    & \quad h = \| r_l \cross v_l \|\\
-    & \quad \text{LightMovesLimit} = \infty \\
-    & \quad \text{Repeat maximum LightMovesLimit times}:\\
-    & \qquad \text{If } r_l \leq r_s : \\
-    & \qquad \quad \text{return "Light never escapes"} \\
-    & \qquad \text{If } r_l \leq r_{ps} : \\
-    & \qquad \quad \text{LightMovesLimit} = 100 \\
-    & \qquad \text{If } r_l > r_{ISCO} : \\
-    & \qquad \quad \text{return "Light escaped black hole"} \\
-    & \qquad p_l = p_l + v_l \quad \text{(move light)}\\
-    & \qquad r_l = \| p_l-p_{cbh} \| \quad \text{(update distance to $p_{cbh}$)}\\
-    & \qquad v_l = v_l + \overrightarrow{F}(r_l,h) \quad \text{(update light velocity)} \\
-    & \quad \text{return "Light stuck in photon sphere, never escapes"}
-\end{align*}
+'include ./algorithm.tex