Given the figure below, find the shortest network of straight line segments (like a Steiner tree, or like parts of a Delaunay triangulation) that connects the four circled points while staying in the purple region. No line in the network can cross or enter an area that isn't purple, but point contact is allowed.
Note, the coordinates of the outer points of the green pentagram are [(29, 7), (2, 29), (-27, 11), (-19, -22), (15, -25)] (CCW from right), and the coordinates of the vertices of the purple figure are [(0, 100), (30, 30), (100, 0), (30, -30), (0, -100), (-30, -30), (-100, 0), (-30, 30)] (CW from top). Each square in the background grid is 10 x 10 units. Solution attempts can be given as drawings, but node coordinates are needed for objective comparisons of path length.
As an example, the figure below shows (in blue) a valid network of length 405.4 that is not minimal.