Ray Marching is a method for visualizing 3D scenes used in rendering without explicitly representing geometry as polygons. This approach is particularly popular in procedural graphics and shaders, such as those in ShaderToy, where scenes are created using mathematical functions.
Core Principle
Unlike classical Ray Tracing, which seeks the exact intersection of a ray with geometry, Ray Marching works iteratively. The ray moves through space in small steps until it reaches an object or exceeds the maximum number of iterations.
The process can be described with the following algorithm:
- Ray Generation: A ray is created from the viewpoint (camera), with its direction computed based on the pixel coordinates on the screen.
- Iterative Progression: The ray moves along its direction with a step size determined by the Signed Distance Function (SDF). This function returns the minimum distance to the nearest surface.
- Hit Detection: If the SDF value becomes smaller than a given threshold (e.g., 0.001), the ray is considered to have reached the surface of an object.
- Iteration Limit: If the number of steps exceeds a defined limit, the process stops, and the pixel is treated as background.
- Lighting and Shading: If the ray reaches a surface, lighting calculations are applied (e.g., normals can be computed through numerical differentiation of the SDF), followed by effects such as shadows and reflections.
Signed Distance Function (SDF)
The key concept in Ray Marching is the Signed Distance Function. It determines the distance from a given point in space to the nearest surface of an object. Examples include:
- Sphere: distance = length(p) - r
- Cube: distance = max(abs(p.x) - s, abs(p.y) - s, abs(p.z) - s)
- Shape Union: min(distance1, distance2)
SDF allows for describing complex objects without explicitly storing their geometry, making this method a powerful tool in procedural graphics.
Advantages and Disadvantages
Pros:
- Flexibility – Enables the creation of complex scenes without meshes.
- Compactness – Scenes are encoded using formulas.
- Realism – Global illumination, soft shadows, and reflections can be easily integrated.
Cons:
- High Computational Complexity – Requires many iterations.
- Artifacts – Insufficient precision can lead to "holes" or incorrect intersections.
Conclusion
Ray Marching is a powerful technique used in procedural graphics and the demoscene. While it demands significant computational resources, its flexibility allows for the creation of impressive visual effects and mathematically defined scenes.
This method is especially interesting for rendering researchers and those who want to gain a deeper understanding of modern shader techniques.
