Cubic surfaces containing one rational line 40
Local parametrization of cubic surfaces
... are rational numbers then the coefficients of the computed local parametrization are real algebraic ...applications one prefers to work with floating point numbers, taking into account the existence of ...
19
On rational surfaces I.
... 1 is a line if and only if dim L -1 1 = d im L -2 . Assume that 1 is a component of the image of a point on the S ; such a point must be one of the P i , say P . L et P„ be the ordinary point of S of which ...
20
Rational points on smooth cubic hypersurfaces
... curves One of the most interesting types of varieties in Number Theory are elliptic ...genus one and O ∈ ...a cubic equation with only one point, the base point O, on the line at ...
100
Cubic Differentials in the Differential Geometry of Surfaces
... Then ˜ φ is a convex 3-dimensional solution to the Monge-Amp`ere equation. This construction allows the point singularities of the parabolic affine sphere structures above to be extended to singularities along ...
37
Cubic surfaces over finite fields
... In Chapter 5, for a cubic surface S defined over a finite field K and containing a K-line `, we introduce the c-invariants of S with respect to `. The c-invariants are integers that give information ...
104
Spectral involutions on rational elliptic surfaces
... of rational elliptic ...all rational elliptic surfaces we focus attention on a five dimensional family of rational elliptic surfaces admitting a particular involution τ , and then we ...
C1 Positivity Constrained Interpolation By Weighted Rational Cubic Triangles
... Bézier surfaces are commonly used to represent any arbitrary 3D shape with certain level of continuity ...shapes one can imagine and have great continuity ...a rational Bézier ...the rational ...
34
Constrained interpolation using rational cubic spline with three parameters
... 1 rational cubic spline function (cubic/quadratic) with three parameters is used to construct a constrained interpolating curve that lies below or above an arbitrary straight line or between ...
11
Data Visualization for Constrained Data using C2 Rational Cubic Spline
... 2 Rational Cubic Spline Mohd Nain Hj Awang, Muhammad Abbas, Ahmad Abd Majid and Jamaludin Md Ali Abstract—In this paper a rational cubic function in the form of cubic/quadratic, with ...
6
Visualization Of Curve And Surface Data Using Rational Cubic Ball Functions
... and surfaces deals with two types of data which are regularly spaced data and scattered data ...data. One of the approach is the shape preserving ...
38
2 Rational Cubic Functions
... piecewise rational cubic spline [5] has been used to visualize the positive data in its natural ...a rational cubic have been constrained in such a way that they preserve the shape of the ...
7
Rational Parametrization of Surfaces
... the one in Schicho (1995); it is based on an algorithm for the resolution of singularities by Hironaka ...Second, one can do other things than parametrization using ...
29
Curves & Surfaces. One Line Bison, Tyler Foust,
... • Smooth curve defined by some control points. • Moving the control points changes the curve[r] ...
30
Periodic minimal surfaces of cubic symmetry
... minimal surfaces turn out to be unstable when ‘evolved’ by Surface Evolver; as the area per unit volume decreases, a critical configuration arises, indicat- ing that the surface collapses catastrophically to ...
18
Parameterization of rational translational surfaces
... translational surfaces but starting from the implicit point of ...a rational space curve, which plays the role C P 1 , and we compute a parameterization, P 1 (t 1 ), of C P 1 ...
23
Explicit decomposition of a rational prime in a cubic field
... In this paper we treat the case when K is a cubic field and p is a prime dividing ind(θ). When p is a common index divisor of K (the only possibility is p = 2), we quote the results in [2]. When p is not a common ...
11
Constrained Interpolation By Parametric Rational Cubic Splines
... Extension from this paper, we will derive an alternative constrained interpolation scheme using rational cubic curve whereas the weights associated with the inner Bezier [r] ...
33
Double Cubic Singular Blend Bézier Surfaces
... and surfaces and expand their descriptive ...and surfaces, and therefore do not cause progressive ...the cubic singular mixed Bézier surface in parameter splicing and geometric ...
24
Hilbert-Kunz Functions of Cubic Curves and Surfaces
... Here we exhibit the Hilbert-Kunz functions of plane elliptic curves in odd characteristic and of plane nodal cubics. Combining this work with results in [7] and [8] completes the explicit determination of Hilbert-Kunz ...
20
Rational two-parameter families of spheres and rational offset surfaces
... offset surfaces admit rational param- eterizations if and only if Φ is a rational sub-variety of a ratio- nal isotropic hyper-surface in R 4 ...envelope surfaces Ψ and rational offset ...
18