How to calculate from three points the "normal" at the second point

Hello !

To program an active contour, I would need from the coordinates of 3 points to determine the normal of the second point.

As in the picture, I would have to determine the normal for point "a".

Any idea?

Thank you

[Ameer Hamza]

Do you have x-y coorinates for these points?

[David Goodmanson]

Hi Dany,

how do propose to define the normal at point A? Is it halfway in between the two dotted normals that you show, or is it something else?

[Dany DA CRUZ BORGES]

I have the x and y coordinates of the 3 points. And yes I seek to establish the vector which is at the level of A thanks to the coordinates (x, y) of the point which is on the left of A, of A and the point which is on the right of A.I have the x and y coordinates of the 3 points. And yes I seek to establish the vector which is at the level of A thanks to the coordinates (x, y) of the point which is on the left of A, of A and the point which is on the right of A.

Answer 1

[Matt J]

Once you have answered David's question, the attached function should be useful. It will find the normals to all the facets of a 2D polygon. Example,

Vertices=[0 0; 1 0; 0 1]; %vertices of a triangle

normals=vert2con_special(Vertices)

gives as output,

normals =

     0    -1
     1     1
    -1     0

[Dany DA CRUZ BORGES]

I am not sure that it is because in my case the coordinates of the normal will be [-1 -1] on the point [0 0]

[Matt J]

You still haven't told us how you define the normal at the vertices. In David's comment, he asked if this is done by averaging the face normals to the right and left of the vertex. If this is what you want, then the additional step would be,

>> normals/2+circshift(normals,[-1,0])/2

ans =

    0.5000         0
         0    0.5000
   -0.5000   -0.5000

[Dany DA CRUZ BORGES]

The normal can be defined with respect to the tangent at point "a" and to the normal of the tangent at this point.

[John D'Errico]

There is no tangent at a point of slope discontinuity. Until you define how you will treat this, there is no way to answer your question.

[Dany DA CRUZ BORGES]

I would have to calculate the tangent as in the image below, then determine the normal to this tangent.

[Matt J]

You could use John's minboundcircle function in this FEX contribution,

https://www.mathworks.com/matlabcentral/fileexchange/34767-a-suite-of-minimal-bounding-objects

to find the green circle shown in your illustration. The normal will then simply be the ray A-O from the center of the circle to the point A.