We discuss the problem of interpolating C1 Hermite data on the sphere (two points with associated first derivative vectors) by spherical rational curves.
This problem can be solved by rational curves of degree 4, the so-called rational spherical quartics. In homogeneous coordinates x = (x0,x1,x2,x3), these curves ...
In the case of the sphere S2, which is a representative of the class of oval quadrics, this equation takes the form w2 = x2 + y2 + z2. All irreducible solutions ...
A three-parameter family of spherical rational quartic curves has been derived and the singularity conditions theoretically and the shape of the solutions ...
We discuss the problem of interpolating C1 Hermite data on the sphere (two points with associated first derivative vectors) by spherical rational curves.
We discuss the problem of interpolating C1 Hermite data on the sphere (two points with associated first derivative vectors) by spherical rational curves.
In the odd dimensional case, the almost contact mani- folds provide examples of polynomial structures of degree 3. More generally, a globally framed /-manifold ...
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Bibliographic details on The shape of spherical quartics.
An octant of a sphere is a spherical triangle with three right angles and three right sides. It is sometimes called a trirectangular (spherical) triangle.
Apr 18, 2023 · A quartic polynomial has three turning points determined by the behaviour at ±∞ that resembles the quadratic (both arms up or down).
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