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# The first step of the algorithm is the minimization

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Unformatted text preview: the measurement data through an opportune homogeneous transformation matrix in order to minimize the distance between the cloud of measured points and the reference element of the class of revolution surfaces from which the sampling comes. The best transformation parameters are searched minimizing the distance between the cloud of measured points and a geometric element (datum) having the same geometric nature of the reference element of the class of the revolution surface. If the datum is composed by two or three geometrical element we can find the best fit as result of two fitting operations. When we consider a complex feature, like a cone or a paraboloid, the datum is composed by two reference elements. As you can verify the two reference feature must have different dimensions, i.e. there must be no homeomorphism which carries an element of the datum in the other. This characteristic gives us the possibility to find an order between the reference elements of the datum, by means of an adequate criterion based on the number of dimensions of the reference elements. This order can be used f...
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## This note was uploaded on 08/03/2010 for the course DD 1234 taught by Professor Zczxc during the Spring '10 term at Magnolia Bible.

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