Find shortest path in 3d point cloud

Matlab has built in shortestpath function based on Dijkstra algorithm:

However the algorithm only applies to graph, We need to convert 3d point cloud to graph first in order to use it.

What constitutes a graph:

• nodes (points or vertex)
• edges (connectivity)

In matlab graph, connection is expressed as adjacency matrix, 

1. create adjacent matrix

d = pdist(PointsSet);
d_adj = squareform(d);

2. create graph and add in nodes

G = graph(d_adj) ;
G.Nodes = array2table(Position,'VariableNames',{'X','Y','Z'});

1. Random graph 

% https://www.mathworks.com/matlabcentral/answers/445321-how-to-find-shortest-distance-in-3d
% for repeatability 
rng('default')
% Generate 10 random 3d points
Position = 10*rand(10,3);
%Calculate pa