Signed Distance Fields

The mathematical foundation of Soyuz.

What Is An SDF?

A Signed Distance Field is a function that takes a point in 3D space and returns the distance to the nearest surface:

• Positive values are outside the shape.
• Negative values are inside the shape.
• Zero is exactly on the surface.

Why SDFs?

• Boolean operations become compact math.
• Smooth blending is natural.
• The model is resolution independent until mesh export.
• GPU raymarching can preview the field efficiently.

From SDF To Mesh

SDFs are useful for modeling and previewing. Games and 3D software usually need triangle meshes, so Soyuz uses Marching Cubes to convert SDFs to exportable meshes.