2D Ray Marching: Sphere Tracing & Signed Distance Field Rendering

What is Ray Marching?

Ray marching, a technique in computer graphics, involves tracing rays from the viewer through the scene to determine what objects they intersect. Each ray is marched along its path, checking for intersections with objects at regular intervals until it either hits an object or reaches a predefined distance.

In 2D, this process can be used to render shapes and scenes by calculating distances to surfaces using signed distance fields (SDFs), which represent the shortest distance from any point in space to the nearest surface of an object.

Signed Distance Fields (SDFs)

A signed distance field is a mathematical function that assigns to each point in 3D space the shortest distance to the boundary of an object, with positive values for points outside and negative values for points inside. This concept allows for precise and efficient rendering of complex shapes.

In ray marching, SDFs are used to determine how far along a ray one needs to march before hitting an object, enabling accurate visualization without needing to explicitly trace the entire path.

Sphere Tracing

Sphere tracing is a method for rendering 3D scenes by using spheres as proxies for objects. Instead of marching rays directly through the scene, sphere tracing checks if a ray intersects with a bounding sphere around an object and then calculates the exact intersection point.

This technique can be highly efficient because it only requires checking intersections with bounding spheres, which are simpler to compute than detailed 3D models.

CSG Operations in Ray Marching

Boolean operations like union, subtract, and intersect are used to combine different shapes in ray marching. These operations allow for the creation of complex scenes from simple geometric primitives.

By applying these operations on SDFs representing individual objects, the resulting SDF can be used to render the combined shape accurately.

Frequently asked questions

Try it live

Everything above runs in your browser — open 2D Ray Marching — Sphere Tracing & SDF Explainer and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.