The problem of surface reconstruction from slope or curvature measurements of rectangular areas has been examined by use of the orthogonality property of Legendre polynomials. A relation is given between the integrals involving slope or curvature data and the coefficients used in the expansion of the surface with such polynomials. It is shown that those coefficients are retrieved independently of each other. The efficiency and stability of the method have been tested with numerical examples.
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Michel Grédiac (1997) studied this question.
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