Is there a special function to compute the length between one vertex and an interior point of a polygon ?

I am looking for a built-in Matlab function to compute one vertex and an interior point on a Polygon ?

[Walter Roberson]

"straight through" (euclidean distance), or by traveling around the perimeter ?

[Susan Arnold]

I think striaght through. For example I have a triangle with three vertices A,B,C and a point inside q. I need a function which is capable of find the length between the point q and A for example to find at the end the area of the triangles generated because the point q.

[Jan]

I do not understand the question. The distance between q and A seems to be trivial. But what does "find the area of triangles generated because the point q" mean?

[Matt J]

For example I have a triangle with three vertices A,B,C and a point inside q. I need a function which is capable of find the length between the point q and A for example

You should modify the title of your post since the distance between q and A is not a "length between specific vertices". It is the distance between one vertex and an interior point.

Answer 1

[Walter Roberson]

http://www.mathopenref.com/coordtrianglearea.html

Answer 2

[Matt J]

You can use delaunayTriangulation to partition the polygon+q into triangles. Use the ConnectivityList property to find the vertices of the sub-triangles and then their area.

[Susan Arnold]

I think it is a good idea, as shown in the following link. But how can I insert a query point q inside the Delaunay triangles. http://stackoverflow.com/questions/21965041/finding-area-of-resultant-triangles-of-delaunay-trianglulation?rq=1

[Matt J]

When you create a DT object

DT = delaunayTriangulation(P)

include the query point in P together with the polygon vertices.

[Susan Arnold]

I meant, how can I recognize this point or how can I extract this point from the DT ?!!

[Matt J]

The link I gave you explains the book-keeping of points in the triangulation. In particular, if you enter the query point as row P(j,:) when you build the DT object, then this point will be given a vertex ID of j, as explained here. The other methods and properties of DT use this ID to identify points in the triangulation.