As the point sampling technology evolves rapidly, there has been increasing need in generating tool path from dense
point set without creating intermediate models such as triangular meshes or surfaces. In this paper, we present a new tool path
generation method from point set using Euclidean distance fields based on Algebraic Point Set Surfaces (APSS). Once an
Euclidean distance field from the target shape is obtained, it is fairly easy to generate tool paths. In order to compute the
distance from a point in the 3D space to the point set, we locally fit an algebraic sphere using moving least square method
(MLS) for accurate and simple calculation. This process is repeated until it converges. The main advantages of our approach
are : (1) tool paths are computed directly from point set without making triangular mesh or surfaces and their offsets, and
(2) we do not have to worry about no local interference at concave region compared to the other methods using triangular
mesh or surface model. Experimental results show that our approach can generate accurate enough tool paths from a point
set in a robust manner and efficiently.