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The fast Fourier transform (FFT) is an algorithm to compute the discrete Fourier coefficients with a substantial time saving over conventional methods. The finite word length used in the computer causes an error in computing the Fourier coefficients. This paper derives explicit expressions for the mean square error in the FFT when floating-point arithmetics are used. Upper and lower bounds for the total relative mean square error are given. The theoretical results are in good agreement with the actual error observed by taking the FFT of data sequences.

There has been a rapid technical progress in three‐dimensional (3D) computer graphics. But gathering surface and texture data is yet a laborious task. This paper addresses the problem of mapping photographic images on the surface of a 3D object whose geometric data are already known. We propose an efficient and handy method for acquiring textures and mapping them precisely on the surface, employing a digital camera alone. We describe an algorithm for selecting a minimal number of camera positions that can cover the entire surface of a given object and also an algorithm to determine camera’s position and direction for each photograph taken so as to paste it to the corresponding surfaces precisely. We obtained a matching accuracy within a pixel on a surface through three experimental examples, by which the practicability of our method is demonstrated.

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