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- W1501808086 abstract "Many aesthetically appealing curves can be generated by using epicycloid and spirographic parametric curve equations. The difficulty in obtaining an interesting and appealing curve comes from having to choose good values for the coefficients in these equations. If a poor choice of coefficients is made the curve generated will have little regularity and a high amount of confusion. Since these curve types involve up to ten real coefficients the set of aesthetic curves is a set of measure zero on the infinite coefficient space. Rather than making random searches through coefficient space another approach which proved to be far more productive in discovering curves of aesthetic appeal was investigated. In this approach we looked at the Fourier Transform of the curves and performed editing on the coefficients in Fourier space. This approach is especially suited to the epicycloid and spirographic curve types which turn out to be simply low-order harmonic functions after suitable filtering and a rotation. As a result, curves can now be defined by free-form input and then cleaned up by this method to yield the nearest epicycle or spirograph." @default.
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- W1501808086 date "1995-01-01" @default.
- W1501808086 modified "2023-09-27" @default.
- W1501808086 title "Harmonic Curve Design" @default.
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- W1501808086 doi "https://doi.org/10.1016/s0921-2647(06)80214-5" @default.
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