🔦 RayTracerCPU

A CPU-based ray tracer built from scratch in modern C++, with zero external dependencies.
This is a personal learning project focused on understanding the mathematics and physics behind computer graphics rendering.

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About

Ray tracing is one of the most elegant algorithms in computer graphics — it simulates how light travels by casting rays from a virtual camera into a 3D scene and computing the color of each pixel based on what those rays hit.

This project implements a ray tracer step by step, starting from first principles:

• 🧮 Linear algebra — 3D vectors, dot/cross products, normalization
• 📐 Geometric intersections — ray–sphere, ray–plane equations
• 💡 Phong lighting model — ambient, diffuse, and specular components
• 🌑 Shadows — shadow ray casting with epsilon bias
• 🪞 Reflections — recursive ray tracing with depth limiting
• 🖼️ PPM image output — zero-dependency image format, readable by any viewer

The goal is to deeply understand the rendering pipeline by writing every piece of it by hand, in C++, without relying on graphics libraries.

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Features

Feature	Status
Vec3 class — operators, dot, cross, length, normalize	✅ Done
Ray class — P(t) = origin + t·direction	✅ Done
Image — PPM output (P3 format)	✅ Done
Gradient sky render	✅ Done
Interactive Vec3 test menu	✅ Done
Camera — viewport and ray generation per pixel	🚧 In progress
Sphere — ray–sphere intersection	🚧 In progress
Hittable / HittableList — polymorphic scene objects	🚧 In progress
Phong shading (Light, Material)	📋 Planned
Shadow rays	📋 Planned
Recursive reflections	📋 Planned
Multi-object scene composition	📋 Planned

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Build & Run

Requirements: g++ with C++17 support (no other dependencies needed).

# Clone the repository
git clone https://github.com/semedooo/RayTracerCPU.git
cd RayTracerCPU

# Build
make

# Run
make run
# or
./raytracer

Clean build artifacts:

make clean

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Usage

The program starts an interactive menu for testing vector operations and rendering:

=== Ray Tracer CPU - Tests ===
1. Sum (+)
2. Subtraction (-)
3. Multiplication (*)
4. Division (/)
5. Dot Product (dot)
6. Cross Product (cross)
7. Length (length)
8. Normalize (normalized)
9. Generate test PPM image
0. Exit

Selecting option 9 generates a gradient test image at output/test.ppm.

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Project Structure

RayTracerCPU/
├── Makefile              # Build rules (g++, C++17)
├── README.md
├── PLANO.md              # Development roadmap (Portuguese)
├── include/
│   ├── Vec3.h            # ✅ 3D vector math
│   ├── Point.h           # ✅ 3D point (P3)
│   ├── Ray.h             # ✅ Ray: origin + t·direction
│   ├── Image.h           # ✅ PPM image output
│   ├── Camera.h          # 🚧 Viewport & ray generation
│   ├── Hittable.h        # 🚧 Abstract hittable interface
│   ├── Sphere.h          # 🚧 Sphere geometry
│   ├── Light.h           # 📋 Point light source
│   └── Material.h        # 📋 Phong material properties
├── src/
│   └── main.cpp          # Entry point & interactive test menu
└── output/
    └── *.ppm             # Rendered images (generated at runtime)

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Core Concepts

Vec3 — 3D Vector Math

All geometry lives in Vec3, a zero-overhead class implementing the full set of operations needed for ray tracing:

• Component-wise +, -, *, /
• Dot product: a·b = ax·bx + ay·by + az·bz (used in lighting and intersection tests)
• Cross product: a×b (used for constructing coordinate frames)
• Normalization: v̂ = v / ‖v‖ (directions must always be unit vectors)

Ray — Parametric Line

A ray is defined as P(t) = origin + t × direction, where t ≥ 0.
For every pixel on screen, a ray is cast from the camera's origin through that pixel's viewport position.

Ray–Sphere Intersection

Substituting the ray equation into the sphere equation yields a quadratic in t.
The discriminant Δ = b² − 4ac tells us:

• Δ < 0 → no intersection
• Δ = 0 → tangent (one point)
• Δ > 0 → two intersections (entry and exit)

Phong Lighting Model

Each visible surface point is shaded using three components:

• Ambient — constant base light (Ia)
• Diffuse — Id = kd · I · max(0, n̂ · l̂) — brighter surfaces face the light (kd = diffuse reflectance, I = light intensity)
• Specular — (r̂ · v̂)^α — mirror-like highlight based on shininess

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Technologies

• Language: C++17
• Build: GNU Make + g++
• Image format: PPM (P3 text format — zero dependencies)
• Dependencies: none (standard library only)

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Roadmap

See PLANO.md for the full step-by-step development plan, including theory notes for each stage.

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Author

Manuel Semedo — Computer Science student
Built as a hands-on study of computer graphics, from scratch.