# Point along Polygon´s average normal

Hi guys,
i´m fixing some stuff in the parametric library and i din´t find an elegant solution to solve this problem, until now i was estimating the solution but is not precise enough for big scale.

Basically is how to get the 2 points along the average normal of a set of points,
which result → All angles sume = 360º

Check the help patch.

FlatPolygon_Test.zip (25.1 KB)

i wish i could help, but there are several details i dot understand… what are “the 2 points along the average normal”, where exactly should they be, the start and end point of the line in your patch?

what do you understand as “the average normal of a set of points”? points do not have a normal. surfaces can have a normal and the vector between two points can be interpreted as a normal.

also “which result → All angles sume = 360º” where are the angles that should add up to 360?

i guess @lasal means the points, where the toggle “Sum=360” turns On.

without much research into it, i presume this to be an optimization problem

ah, it flashes two times… and these two points on the line should be found?

@Tonfilm, maybe the naming is not correct, but is easy to understand, first i triangulate using the set point center, then i calculate the normal of all the triangles and then the average of them, the result is this line in the center.
Along this line exist two points which satisfy the relation, the sum of all angles between this estimated center and the initial points is 360 º.
i hope is more clear now.

Here you get the visual idea,
the left one is the unfolded surface, on result i get a closed foldable surface, (no cuts inside or overlapping)

Any idea guys?

only that if you are looking for two values that are mirrored around a center then the last part of the equation will be a square root.

searched points on line = some constant ± sqrt(some expression)

since its triangles the i would not be surprised if the sqrt part comes from a^2 + b^2 = c^2. but other than that i had no time to dig deeper.

This is what i thought, thanks

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