I recently completed a comprehensive ray tracing implementation from scratch, exploring the fascinating intersection of physics, mathematics, and computer science.
What is Ray Tracing?
Ray tracing stands as one of the most elegant algorithms in computer graphics, simulating the physical behavior of light to create stunningly realistic images. Unlike rasterization (the technique used in most real-time graphics), ray tracing follows light’s natural path through a scene, capturing subtle optical phenomena like reflections, refractions, and shadows with remarkable fidelity.
Key Features of My Implementation
My ray tracer includes:
- A physics-based approach following the principles of geometric optics
- Support for reflections, shadows, and complex light behaviors
- Full implementation of the Phong illumination model
- Optimization techniques for improved performance
- Object-oriented design for extensibility
The Mathematics Behind Ray Tracing
The core of ray tracing involves solving equations for ray-object intersections. For example, determining if a ray hits a sphere requires solving a quadratic equation:
double discriminant = b * b - 4 * a * c;
if (discriminant < 0) return -1; // No intersection
double t1 = (-b - sqrt(discriminant)) / (2 * a);
double t2 = (-b + sqrt(discriminant)) / (2 * a);
The rendering equation serves as the mathematical foundation:
\[L_o(x, \omega_o) = L_e(x, \omega_o) + \int_{\Omega} f_r(x, \omega_i, \omega_o) L_i(x, \omega_i) (\omega_i \cdot n) d\omega_i\]Learn More
I’ve documented the entire process in detail in my Ray Tracing Showcase, where you’ll find:
- Complete source code with extensive comments
- In-depth explanation of the physics and math concepts
- Advanced techniques for further exploration
- Optimization strategies for high-performance rendering
If you’re interested in computer graphics, physics simulation, or computational mathematics, I encourage you to check out the full project documentation!