Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
Computer-Aided Design in Manufacturing
Computer-Aided Design in Manufacturing
Computer-Aided Graphics and Design
Computer-Aided Graphics and Design
Computer-Aided Design and Manufacture
Computer-Aided Design and Manufacture
CAD: Principles and Applications
CAD: Principles and Applications
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In many real-life situations (including computer-aided design and radiotelescope network design), it is necessary to estimate the derivative of a function from approximate measurement results. Usually, there exist several (approximate) models that describe measurement errors; these models may have different numbers of parameters. If we use different models, we may get estimates of different accuracy. In the design stage, we often have little information about these models, so, it is necessary to choose a model based only on the number of parameters n and on the number of measurements N.In mathematical terms, we want to estimate how having N equations Σj cijaj = yi with n (n ) unknowns aj influences the accuracy of the result (cij are known coefficients, and yi are known with a standard deviation σ[y]). For that, we assume that the coefficients cij are independent random variables with 0 average and standard deviation 1 (this assumption is in good accordance with real-life situations). Then, we can use computer simulations to find the standard deviation σ' of the resulting error distribution for ai. For large n, this distribution is close to Gaussian (see, e.g., [21], pp. 2.17, 6.5, 9.8, and reference therein), so, we can safely assume that the actual errors are within the 3σ' limit.