loess predict with new x values

Question

I am attempting to understand how the predict.loess function is able to compute new predicted values (y_hat) at points x that do not exist

Answer 1

Found the answer on page 42 of the manual:

In this algorithm a set of points typically small in number is selected for direct    
computation using the loess fitting method and a surface is evaluated using an interpolation
method that is based on blending functions. The space of the factors is divided into
rectangular cells using an algorithm based on k-d trees. The loess fit is evaluated at
the cell vertices and then blending functions do the interpolation. The output data
structure stores the k-d trees and the fits at the vertices. This information
is used by predict() to carry out the interpolation.