Name
Abstract | ||
|---|---|---|
Rational shapes with rational offsets, especially Pythagorean hodograph (PH) curves and Pythagorean normal vector (PN) surfaces, have been thoroughly studied for many years. However compared to PH curves, Pythagorean normal vector surfaces were introduced using dual approach only in their rational version and a complete characterization of polynomial surfaces with rational offsets, i.e., a polynomial solution of the well-known surface Pythagorean condition, still remains an open and challenging problem. In this contribution, we study a remarkable family of cubic polynomial PN surfaces with birational Gauss mapping, which represent a surface counterpart to the planar Tschirnhausen cubic. A full description of these surfaces is presented and their properties are discussed. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/978-3-642-27413-8_27 | Curves and surfaces |
Keywords | Field | DocType |
special class,rational offset,well-known surface pythagorean condition,polynomial surface,pythagorean normal vector,pythagorean normal vector field,rational version,pythagorean normal vector surface,cubic polynomial pn surface,pythagorean hodograph,polynomial solution,rational shape | Pythagorean triple,Pythagorean field,Polynomial,Mathematical analysis,Pure mathematics,Cubic function,Rational surface,Tschirnhausen cubic,Pythagorean theorem,Mathematics,Pythagorean trigonometric identity | Conference |
Citations | PageRank | References |
4 | 0.44 | 14 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Miroslav LáVičKa | 1 | 158 | 11.36 |
| Jan VršEk | 2 | 26 | 7.49 |