Algorithm 2 Strategy 2: Hand position with threshold.

Input: Hand position $P_h\in {\mathbb{R}}^3$, threshold distance ${\lambda }_d$.

Output: Best point $P\ast$ in the set of $P_i$, $i=1\dots 16$.

1: Build a k-d tree for all points $P_i$ in the scene.

2: function ST2($P_h$, $P_{prev}$)

3:     $P_{next}$← best from k-d tree.

4:     if $\left|\right|(P_{next},P_h)\left|\right|<{\lambda }_d$ then

5:         $P\ast \leftarrow P_{next}$

6:     else

7:         $P\ast \leftarrow P_{prev}$

8:     end if

9:     $P_{prev}\leftarrow P\ast$

10:    return P

11: end function