From 2b4b36963da25c1146d7855415ea3172699fb388 Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Fri, 28 Nov 2025 21:37:41 -0500
Subject: [PATCH] update: add help function

---
 src/render.c | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/src/render.c b/src/render.c
index 1dc2c09..18690f3 100644
--- a/src/render.c
+++ b/src/render.c
@@ -3,12 +3,20 @@
 #include "common.h"
 #include "init.h"
 
+inline double xy_to_b(double x, double y) {
+  double tanpsi2 = x*x+y*y;
+  double cotpsi2 = 1/tanpsi2;
+  double b = R0/sqrt(f(R0)*(1+cotpsi2));
+  return b;
+}
+
 int MC_pixel_render(const System *system, int i, int j, const gsl_spline *spline, double *rgb, int pixel_render_max, double pixel_render_err){
   double dw = (system->w)/(system->W); // width and hight of one pixel
   double x_lu = i*dw - (system->w)/2;
   double y_lu = -j*dw + (system->H)*dw/2;
 
   //TODO: fill the MC intergral
+  // linear rgb = ∫ rgb(χ, ϕ) sin^2(χ) χ'(ψ) dx dy
 
   return 0;
 }