How do I expand / shrink a polygon with a fixed center point in MATLAB?

I have a polygon drawn with the LINE(x,y) command in MATLAB, where x,y are the coordinate vectors of the points that forms this polygon.

I would like to expand or shrink the polygon by a factor A.

I would like also that the center of the polygon, which has the coordinates (mean(x),mean(y)), will be a stationary point in this transformation.

Answer 1

[MathWorks Support Team]

To calculate the coordinates of this transformation, use the following equations:

xt = A*x+(1-A)*mean(x(1:end-1))
yt = A*y+(1-A)*mean(y(1:end-1))

In this case, the center coordinate (mean(x),mean(y)) will be stationary.

Note that we actually do not use the last point in x,y vectors, since that last point is redundant to the first point, and we specify that last point for the LINE command to make our polygon closed. We should not take the same point twice into account when calculating the mean of the coordinates' vectors.

For other tasks similar to this, take a look at the following submission on the MATLAB File Exchange, which was awarded the 'MATLAB Central Pick of the Week'. There may be some functionality here which be of use:

- geom2d: Geometry library for matlab. Performs geometric computations on points, lines, circles, polygons...

https://www.mathworks.com/matlabcentral/fileexchange/7844-geom2d

[Michael Abboud]

Hi Faez, I would recommend that you take a look at the following submission on the MATLAB File Exchange, which was awarded the 'MATLAB Central Pick of the Week'. There may be some functionality here which can help you achieve this task.

- geom2d: Geometry library for matlab. Performs geometric computations on points, lines, circles, polygons...

https://www.mathworks.com/matlabcentral/fileexchange/7844-geom2d

I have updated the above answer to include this link as well :)

[Jan]

[MOVED from flags] Zhiyu Xiao wrote on 23 Apr 2019 at 23:06

Great question, and it's not completely answered. Other methods all use a scaling factor rather than number of pixels.

[Please use flags only to inform admins and editors about inappropriate contents like rudeness or spam. Thanks.]

It is not clear, what you mean with "nor completely answered". Did you see Jin Mia's answers?