The surface of an object is an unknown implicit function f(x)=0. Continuation methods provide an elegant way to traverse this problem by building an atlas made out of charts like a travelling map.
In the figure there is an example. The blue charts are the explored region, hence a one-to-one correspondence to the object surface exist. The red charts are the boundaries of the explored region. The choice of the direction can be selected based on the curvatures at the chart center point, and depending on the exploration task. That is, for friction coefficient recovery, flat surfaces are desirable, and for shape recovery, high curvatures are richer in information.
The surface of an object is an unknown implicit function f(x)=0. Continuation methods provide an elegant way to traverse this problem by building an atlas made out of charts like a travelling map.
In the figure there is an example. The blue charts are the explored region, hence a one-to-one correspondence to the object surface exist. The red charts are the boundaries of the explored region. The choice of the direction can be selected based on the curvatures at the chart center point, and depending on the exploration task. That is, for friction coefficient recovery, flat surfaces are desirable, and for shape recovery, high curvatures are richer in information.