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Compute turning distance between polyshape objects


td = turningdist(poly1,poly2) returns an array of turning distances between the corresponding element pairs of two polyshape arrays with compatible sizes. The turning distance between two polyshape objects is a measure of how closely their shapes match, regardless of rotation or scaling. A turning distance close to 0 indicates a near match. The larger the value, the more the two shapes differ.

TD(i,j) is the turning distance between the ith polyshape in poly1 and the jth polyshape in poly2.


td = turningdist(polyvec) returns a matrix of turning distances between element pairs of a vector of polyshape objects.


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Create and plot two squares of different sizes and locations, represented as polyshape objects poly1 and poly2.

poly1 = nsidedpoly(4,'SideLength',1);
poly2 = nsidedpoly(4,'SideLength',3,'Center',[3 3]);
hold on 
axis equal
hold off

Because the two squares have the same shape despite their scaling, their turning distance is 0.

td = turningdist(poly1,poly2)
td = 0

Create and plot a third polyshape, and compare its turning distance to poly1. Since their shapes have more differences than poly1 and poly2, the turning distance is larger.

poly3 = nsidedpoly(20,'Center',[3 3]);
hold on
axis equal
hold off

td = turningdist(poly1,poly3)
td = 0.4443

Input Arguments

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First input polyshape, specified as a scalar, vector, matrix, or multidimensional array.

Second input polyshape, specified as a scalar, vector, matrix, or multidimensional array.

polyshape vector.

Output Arguments

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Turning distance, returned as a scalar, vector, matrix, or multidimensional array whose elements are greater than or equal to 0.

  • If you input two polyshape arguments, then they must have compatible sizes. For example, if two input polyshape vectors have different lengths M and N, then they must have different orientations (one must be a row vector and one must be a column vector). td is then M-by-N or N-by-M depending on the orientation of each input vector. For more information on compatible array sizes, see Compatible Array Sizes for Basic Operations.

  • If you input a single polyshape vector with length N, then td is N-by-N.

Data Types: double


[1] Arkin, E.M., Chew, L.P., Huttenlocher, D.P., Kedem, K., and Mitchell, J.S.B. "An efficiently computable metric for comparing polygonal shapes." IEEE Transactions on Pattern Analysis and Machine Intelligence. Vol. 13, Number 3, 1991, pp. 209-16. doi:10.1109/34.75509.

Extended Capabilities

Version History

Introduced in R2018a

See Also