2D Raytracer with SDL2

A simple real-time 2D raytracer prototype built in C with SDL2.
Rays are emitted from a light source and stopped when they hit objects (circles).
This creates a hard-shadow casting effect that can be moved interactively with the mouse.

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📸 Demo

⚡ Features

• C + SDL2 hardware-accelerated rendering (SDL_Renderer).
• Light source follows your mouse.
• Rays emitted in all directions (150 configurable).
• Circle obstacle blocks rays → real-time shadow casting.
• Basic ray–circle intersection math.

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📐 Math Behind the Raytracer

Ray equation

A ray is defined by:

$$ P(t) = O + t \cdot d, \quad t \geq 0 $$

• ( O = (x_0, y_0) ) = ray origin (light source).
• ( d = (\cos\theta, \sin\theta) ) = direction vector (unit length).
• ( t ) = distance along the ray.

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Circle equation

A circle with center ( C = (c_x, c_y) ) and radius ( r ):

$$ (x - c_x)^2 + (y - c_y)^2 = r^2 $$

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Ray–circle intersection

Plugging the ray into the circle equation:

$$ (O + t d - C) \cdot (O + t d - C) = r^2 $$

Expands to a quadratic in (t):

$$ a t^2 + b t + c = 0 $$

where:

$$ a = d \cdot d, \quad b = 2 d \cdot (O - C), \quad c = (O - C)\cdot(O - C) - r^2 $$

Discriminant:

$$ \Delta = b^2 - 4ac $$

• If ( \Delta < 0 ): no intersection.
• If ( \Delta \ge 0 ):

$$ t = \frac{-b \pm \sqrt{\Delta}}{2a} $$

Choose the smallest positive ( t ) to find the first hit.

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Hit point

The ray endpoint at intersection is:

$$ P(t_{\text{hit}}) = O + t_{\text{hit}} \cdot d $$

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Shadow casting

• Emit evenly spaced rays in a circle:

$$ \Delta \theta = \frac{2 \pi}{N} $$

• Each ray endpoint =
  • Screen edge if no hit.
  • Circle boundary if hit.

Thus obstacles block rays and create real-time shadows.

🏗️ How it Works Step by Step

1. Generate rays around full (360^\circ).

   angle = i * (2 * M_PI / RAYS_NUMBER);
   dx = cos(angle);
   dy = sin(angle);

2. Test each ray against all circles in the scene (blockers).

   • Use quadratic intersection.
   • If hit → shorten to (t_{\text{hit}}).
   • Else → keep screen border endpoint.

3. Render:

   • For each ray, draw a line from ((x_0,y_0)) → endpoint.
   • Draw obstacles and light.

4. Done → interactive raytracing demo.

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🎮 Controls

• Mouse drag → moves the light source around the window.
• Rays and shadows update in real time.