how to define the location of points within a shape that is invariant to shape transformation?

How can we define the location of points within a shape such that when the shape goes through horizontal or vertical transform, the definition of its location remains almost unchanged? For example, while triangle A transforms to triangle B, the location of P remains similar with respect to the triangle. Obviously, Cartesian coordinates will not work here as they would change a lot after the transformation.

The solution better be general for all type of shapes, such as quadrangle, hexagon or even circle. Thanks a lot!

Answer 1

[Image Analyst]

There are lots of points inside the triangle that are still inside it after you transform the triangle's shape and location.

If you convert it to a digital image, (say with poly2mask), you can simply AND the two digital images.

Otherwise to do it analytically for an original triangle, and a new triangle that's overlapped, and thus having a common/overlap region that may have anywhere from 3 to 6 sides will be very tricky.

[Howard NS]

Thanks, but what I am asking is to find a way to respsent the relative position of points inside the triangle such as after horizontal or vertical transformation the representation of points position remain unchanged.

simply speaking, the Ps from triangle A and B are topoloically equavalent. But how to respresent this?