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Dual representation of spatial rational Pythagorean-hodograph curvesKozak, Jernej ; Knez, Marjetka, 1978- ; Vitrih, Vito, 1981-In this paper, the dual representation of spatial parametric curves and its properties are studied. In particular, rational curves have a polynomial dual representation, which turns out to be both ... theoretically and computationally appropriate to tackle the main goal of the paper: spatial rational Pythagorean-hodograph curves (PH curves). The dual representation of a rational PH curve is generated here by a quaternion polynomial which defines the Euler-Rodrigues frame of a curve. Conditions which imply low degree dual form representation are considered in detail. In particular, a linear quaternion polynomial leads to cubic or reparameterized cubic polynomial PH curves. A quadratic quaternion polynomial generates a wider class of rational PH curves, and perhaps the most useful is the ten-parameter family of cubic rational PH curves, determined here in the closed form.Source: Computer Aided Geometric Design. - ISSN 0167-8396 (Vol. 31, no. 1, 2014, str. 43-56)Type of material - article, component partPublish date - 2014Language - englishCOBISS.SI-ID - 1536233156
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Kozak, Jernej | 03425 |
Knez, Marjetka, 1978- | 23467 |
Vitrih, Vito, 1981- | 27559 |
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