A set union contains every point belonging to at least one shape. For signed distance functions (SDFs), a point is inside the union when at least one input function is negative, so the union is computed with the minimum function. section 10.2.2
The representation determines both the implementation and its practical trade-offs:
- SDFs reduce union to a one-line minimum operation, making shape composition inexpensive and convenient. section 10.2.2
- Voxel models apply union like Boolean masks: retain pixels filled in either input model, with generally simple and robust implementations. section 12.3.4
- CAD curves and surfaces require finding intersections, splitting geometry, classifying pieces, and preserving orientation, making union comparatively complex and potentially slow. section 11.1.2
Union of two circles
Represent two radius-6 circles centered at (-2, 0) and (2, 0) with SDFs Z1 and Z2. Compute Z = minimum(Z1, Z2); the result is negative wherever either circle contains the point. section 10.2.2
