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Pijush Ghosh, Pradeep K. Jain, "An Algebra of Geometric Shapes," IEEE Computer Graphics and Applications, vol. 13, no. 5, pp. 5059, September/October, 1993.  
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@article{ 10.1109/38.232114, author = {Pijush Ghosh and Pradeep K. Jain}, title = {An Algebra of Geometric Shapes}, journal ={IEEE Computer Graphics and Applications}, volume = {13}, number = {5}, issn = {02721716}, year = {1993}, pages = {5059}, doi = {http://doi.ieeecomputersociety.org/10.1109/38.232114}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  MGZN JO  IEEE Computer Graphics and Applications TI  An Algebra of Geometric Shapes IS  5 SN  02721716 SP50 EP59 EPD  5059 A1  Pijush Ghosh, A1  Pradeep K. Jain, PY  1993 VL  13 JA  IEEE Computer Graphics and Applications ER   
A simple algebra of shapes with 2D planar regions is developed. The fact that a 2D region can be completely described by a onedimensional, closedboundary curve if it is homogeneous is used in the presented approach, which first converts the spatial description of the closed curve into an equivalent Fourier series description and then uses the Fourierdescription to define binary composition operations that combine two planar shapes to form another planar shape. It is shown how the geometric system comprising the set of all planar shapes and the composition operations can be mapped onto the algebraic system of linear/vector space.
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