I'm looking for someone to aid me in understanding the undefined vectors of this paper I'm hoping that the answer will seem intuitive to someone with a strong understanding of computational geometry. I will also preface that I have already tried to contact the authors of the paper to no avail, hence why I am asking here.
In the paper it explains that the options for the next point on the path are weighted with a function that acts on 3 parameters ($\alpha$, $\beta$ and $d$), the paper goes on to say
Ideally, the three geometrical parameters should as small as possible. Thus, an evaluation criterion has been applied to optimize these parameters. Assuming that the green path vector in Fig. 4 is $v_{pl}$, and the angle $\alpha$ between the vpn (the next yellow vector) and $v_{pl}$ is calculated in Eq. (2). The angle $\beta$ between stress vector (vstress) and v_{pn} is calculated by Eq. (3). And the distance d between two nearby points on the path is also calculated.
However the paper never explains what the "yellow vector" and "green vector" actually are besides the figure shown below
From the image you could assume that the green and yellow arrows are tangents to the curve at two points along the medial axis however the paper states that
The algorithm is executed until there are no more medial axis points left or the search area is empty.
implying that the points are polled from the medial axis which is a discretised curve, not the continuous curve depicted, which muddies the waters as to what either of the two vectors represent. Along with this if the yellow arrow was a tangent curve it would be on the outside of the curve and not the inside. annoyingly there is no reference of green or yellow arrows anywhere else in the paper, so I have no idea how to impliment the algorithm.
thank for any help.