Update README and change lambda characters in identifiers for MSVC.

2D_lensing.cpp

@@ -17,7 +17,7 @@ double c = 299792458.0;
 double G = 6.67430e-11;
 
 struct Ray;
-void rk4Step(Ray& ray, double dλ, double rs);
+void rk4Step(Ray& ray, double d_lambda, double rs);
 
 // --- Structs --- //
 struct Engine {
@@ -109,8 +109,8 @@ struct Ray{
         // step 3) store conserved quantities
         L = r*r * dphi;
         double f = 1.0 - SagA.r_s/r;  
-        double dt_dλ = sqrt( (dr*dr)/(f*f) + (r*r*dphi*dphi)/f );
-        E = f * dt_dλ;
+        double dt_d_lambda = sqrt( (dr*dr)/(f*f) + (r*r*dphi*dphi)/f );
+        E = f * dt_d_lambda;
         // step 4) start trail :
         trail.push_back({x, y});
     }
@@ -146,10 +146,10 @@ struct Ray{
 
         glDisable(GL_BLEND);
     }
-    void step(double dλ, double rs) {
+    void step(double d_lambda, double rs) {
         // 1) integrate (r,φ,dr,dφ)
         if(r <= rs) return; // stop if inside the event horizon
-        rk4Step(*this, dλ, rs);
+        rk4Step(*this, d_lambda, rs);
 
         // 2) convert back to cartesian x,y
         x = r * cos(phi);
@@ -169,46 +169,46 @@ void geodesicRHS(const Ray& ray, double rhs[4], double rs) {
 
     double f = 1.0 - rs/r;
 
-    // dr/dλ = dr
+    // dr/d_lambda = dr
     rhs[0] = dr;
-    // dφ/dλ = dphi
+    // dφ/d_lambda = dphi
     rhs[1] = dphi;
 
-    // d²r/dλ² from Schwarzschild null geodesic:
-    double dt_dλ = E / f;
+    // d²r/d_lambda² from Schwarzschild null geodesic:
+    double dt_d_lambda = E / f;
     rhs[2] = 
-        - (rs/(2*r*r)) * f * (dt_dλ*dt_dλ)
+        - (rs/(2*r*r)) * f * (dt_d_lambda*dt_d_lambda)
         + (rs/(2*r*r*f)) * (dr*dr)
         + (r - rs) * (dphi*dphi);
 
-    // d²φ/dλ² = -2*(dr * dphi) / r
+    // d²φ/d_lambda² = -2*(dr * dphi) / r
     rhs[3] = -2.0 * dr * dphi / r;
 }
 void addState(const double a[4], const double b[4], double factor, double out[4]) {
     for (int i = 0; i < 4; i++)
         out[i] = a[i] + b[i] * factor;
 }
-void rk4Step(Ray& ray, double dλ, double rs) {
+void rk4Step(Ray& ray, double d_lambda, double rs) {
     double y0[4] = { ray.r, ray.phi, ray.dr, ray.dphi };
     double k1[4], k2[4], k3[4], k4[4], temp[4];
 
     geodesicRHS(ray, k1, rs);
-    addState(y0, k1, dλ/2.0, temp);
+    addState(y0, k1, d_lambda/2.0, temp);
     Ray r2 = ray; r2.r=temp[0]; r2.phi=temp[1]; r2.dr=temp[2]; r2.dphi=temp[3];
     geodesicRHS(r2, k2, rs);
 
-    addState(y0, k2, dλ/2.0, temp);
+    addState(y0, k2, d_lambda/2.0, temp);
     Ray r3 = ray; r3.r=temp[0]; r3.phi=temp[1]; r3.dr=temp[2]; r3.dphi=temp[3];
     geodesicRHS(r3, k3, rs);
 
-    addState(y0, k3, dλ, temp);
+    addState(y0, k3, d_lambda, temp);
     Ray r4 = ray; r4.r=temp[0]; r4.phi=temp[1]; r4.dr=temp[2]; r4.dphi=temp[3];
     geodesicRHS(r4, k4, rs);
 
-    ray.r    += (dλ/6.0)*(k1[0] + 2*k2[0] + 2*k3[0] + k4[0]);
-    ray.phi  += (dλ/6.0)*(k1[1] + 2*k2[1] + 2*k3[1] + k4[1]);
-    ray.dr   += (dλ/6.0)*(k1[2] + 2*k2[2] + 2*k3[2] + k4[2]);
-    ray.dphi += (dλ/6.0)*(k1[3] + 2*k2[3] + 2*k3[3] + k4[3]);
+    ray.r    += (d_lambda/6.0)*(k1[0] + 2*k2[0] + 2*k3[0] + k4[0]);
+    ray.phi  += (d_lambda/6.0)*(k1[1] + 2*k2[1] + 2*k3[1] + k4[1]);
+    ray.dr   += (d_lambda/6.0)*(k1[2] + 2*k2[2] + 2*k3[2] + k4[2]);
+    ray.dphi += (d_lambda/6.0)*(k1[3] + 2*k2[3] + 2*k3[3] + k4[3]);
 }
 
 

CPU-geodesic.cpp

@@ -102,7 +102,7 @@ struct Camera {
 Camera camera;
 
 struct Ray;
-void rk4Step(Ray& ray, double dλ, double rs);
+void rk4Step(Ray& ray, double d_lambda, double rs);
 
 struct Engine {
     // -- Quad & Texture render -- //
@@ -290,12 +290,12 @@ struct Ray{
         // Step 3: store conserved quantities
         L = r * r * sin(theta) * dphi;
         double f = 1.0 - SagA.r_s / r;
-        double dt_dλ = sqrt((dr*dr)/f + r*r*dtheta*dtheta + r*r*sin(theta)*sin(theta)*dphi*dphi);
-        E = f * dt_dλ;
+        double dt_d_lambda = sqrt((dr*dr)/f + r*r*dtheta*dtheta + r*r*sin(theta)*sin(theta)*dphi*dphi);
+        E = f * dt_d_lambda;
     }
-    void step(double dλ, double rs) {
+    void step(double d_lambda, double rs) {
         if (r <= rs) return;
-        rk4Step(*this, dλ, rs);
+        rk4Step(*this, d_lambda, rs);
         // convert back to cartesian
         this->x = r * sin(theta) * cos(phi);
         this->y = r * sin(theta) * sin(phi);
@@ -328,7 +328,7 @@ void raytrace(vector<unsigned char>& pixels, int W, int H) {
             const double D_LAMBDA = 1e7;
             const double ESCAPE_R = 1e14;
 
-            // 2) march the ray forward in λ
+            // 2) march the ray forward in _lambda
             vec3 color(0.0f);
             if (!useGeodesics) {
                 double b = 2.0 * dot(camera.pos, dir);
@@ -399,35 +399,35 @@ void addState(const double a[6], const double b[6], double factor, double out[6]
     for (int i = 0; i < 6; i++)
         out[i] = a[i] + b[i] * factor;
 }
-void rk4Step(Ray& ray, double dλ, double rs) {
+void rk4Step(Ray& ray, double d_lambda, double rs) {
     double y0[6] = { ray.r, ray.theta, ray.phi, ray.dr, ray.dtheta, ray.dphi };
     double k1[6], k2[6], k3[6], k4[6], temp[6];
 
     geodesicRHS(ray, k1, rs);
-    addState(y0, k1, dλ/2.0, temp);
+    addState(y0, k1, d_lambda/2.0, temp);
     Ray r2 = ray;
     r2.r = temp[0]; r2.theta = temp[1]; r2.phi = temp[2];
     r2.dr = temp[3]; r2.dtheta = temp[4]; r2.dphi = temp[5];
     geodesicRHS(r2, k2, rs);
 
-    addState(y0, k2, dλ/2.0, temp);
+    addState(y0, k2, d_lambda/2.0, temp);
     Ray r3 = ray;
     r3.r = temp[0]; r3.theta = temp[1]; r3.phi = temp[2];
     r3.dr = temp[3]; r3.dtheta = temp[4]; r3.dphi = temp[5];
     geodesicRHS(r3, k3, rs);
 
-    addState(y0, k3, dλ, temp);
+    addState(y0, k3, d_lambda, temp);
     Ray r4 = ray;
     r4.r = temp[0]; r4.theta = temp[1]; r4.phi = temp[2];
     r4.dr = temp[3]; r4.dtheta = temp[4]; r4.dphi = temp[5];
     geodesicRHS(r4, k4, rs);
 
-    ray.r      += (dλ/6.0)*(k1[0] + 2*k2[0] + 2*k3[0] + k4[0]);
-    ray.theta  += (dλ/6.0)*(k1[1] + 2*k2[1] + 2*k3[1] + k4[1]);
-    ray.phi    += (dλ/6.0)*(k1[2] + 2*k2[2] + 2*k3[2] + k4[2]);
-    ray.dr     += (dλ/6.0)*(k1[3] + 2*k2[3] + 2*k3[3] + k4[3]);
-    ray.dtheta += (dλ/6.0)*(k1[4] + 2*k2[4] + 2*k3[4] + k4[4]);
-    ray.dphi   += (dλ/6.0)*(k1[5] + 2*k2[5] + 2*k3[5] + k4[5]);
+    ray.r      += (d_lambda/6.0)*(k1[0] + 2*k2[0] + 2*k3[0] + k4[0]);
+    ray.theta  += (d_lambda/6.0)*(k1[1] + 2*k2[1] + 2*k3[1] + k4[1]);
+    ray.phi    += (d_lambda/6.0)*(k1[2] + 2*k2[2] + 2*k3[2] + k4[2]);
+    ray.dr     += (d_lambda/6.0)*(k1[3] + 2*k2[3] + 2*k3[3] + k4[3]);
+    ray.dtheta += (d_lambda/6.0)*(k1[4] + 2*k2[4] + 2*k3[4] + k4[4]);
+    ray.dphi   += (d_lambda/6.0)*(k1[5] + 2*k2[5] + 2*k3[5] + k4[5]);
 }
 
 void setupCameraCallbacks(GLFWwindow* window) {

README.md

@@ -22,13 +22,34 @@ Thank you everyone for checking out the video, if you haven't it explains code i
 
 ## **Building Requirements:**
 
-1. C++ Compiler supporting C++ 17 or newer
+### Windows
 
-2. [Cmake](https://cmake.org/)
+* It is recommended that Windows users install [Microsoft Visual Studio](https://visualstudio.microsoft.com/downloads/) and choose to install the  "Desktop development with C++" as it will give you access to all necessary build requirements and allow you to follow the build instructions directly.
+
+### macOS / Linux
+
+1. C++ Compiler supporting C++17 or newer
+   - **Linux**: `g++` or `clang++` is usually available via your system package manager (`apt`, `dnf`, `pacman`, etc.)
+   - **macOS**: Install via Xcode Command Line Tools with: `xcode-select --install`
+
+2. [CMake](https://cmake.org/)
+   - **Linux**: Available through your system package manager
+   - **macOS**: Install via [Homebrew](https://brew.sh): `brew install cmake`
 
 3. [Vcpkg](https://vcpkg.io/en/)
+   - **Linux**: Not typically available via package managers — instead, **clone and bootstrap manually**:
+     ```bash
+     git clone https://github.com/microsoft/vcpkg.git
+     cd vcpkg
+     ./bootstrap-vcpkg.sh
+     ```
+   - **macOS**: You can install the `vcpkg` executable via [Homebrew](https://formulae.brew.sh/formula/vcpkg): `brew install vcpkg`
+     > ⚠️ However, this does not clone the full source tree. You **must still clone the repo and run** `./bootstrap-vcpkg.sh` to get full vcpkg functionality.
 
 4. [Git](https://git-scm.com/)
+   - **Linux**: Available via your package manager
+   - **macOS**: Pre-installed, or install via Homebrew: `brew install git`
+
 
 ## **Build Instructions:**