This paper describes an implementation of the Cubic Rational Polynomial Camera model developed as part of the FOCUS project. FOCUS ([1]) is on ongoing “shared vision” IR&D project jointly sponsored by Lockheed Martin Missiles and Space (LMMSS/Sunnyvale) and General Electric CR&D. A cubic camera has the advantage that all cameras, such as projective, affine and the linear pushbroom, which map th...

For a general nonsingular cubic fourfold X ⊂ P5 and e ≥ 5 an odd integer, we show that the space Me parametrizing rational curves of degree e on X is non-uniruled. For e ≥ 6 an even integer, we prove that the generic fiber dimension of the maximally rationally connected fibration of Me is at most one, i.e. passing through a very general point of Me there is at most one rational curve. For e < 5...

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In this study, we investigate some new analytical solutions to the (1 + 1)-dimensional nonlinear Dispersive Modified Benjamin–Bona–Mahony equation and the (2 + 1)-dimensional cubic Klein–Gordon equation by using the generalized Kudryashov method. After we submitted the general properties of the generalized Kudryashov method in Section 2, we applied this method to these problems to obtain some n...

The unit sphere, centered at the origin in R, has a dense set of points with rational coordinates. We give an elementary proof of this fact that includes explicit bounds on the complexity of the coordinates: for every point v on the unit sphere in R, and every > 0, there is a point r = (r1, r2, . . . , rn) such that: • ||r− v||∞ < . • r is also a point on the unit sphere; P r i = 1. • r has rat...

A piecewise rational cubic spline has been introduced to visualize the positive data in its natural form. It is attempted that the spline method preserves the shape of the data when it is positive. The spline representation is interpolatory and applicable to the scalar valued data. The shape parameters, in the description of the rational cubic, have been constrained in such a way that they cont...

We obtain the distribution of inflection points and singularities on a parametric rational cubic curve segment with aid of Mathematica (A System of for Doing Mathematics by Computer). The reciprocal numbers of the magnitudes of the end slopes determine the occurrence of inflection points and singularities on the segment. Its use enables us to check whether the segment has inflection points or a...

A construction is given for a planar rational Pythagorean hodograph spiral which interpolates any two-point G Hermite data that a spiral can match. When the curvature at one of the points is zero, the construction gives the unique interpolant that is the involute of a rational Pythagorean hodograph curve of the form cubic over linear. Otherwise, the spiral comprises an involute of a Tschirnhaus...

The study of singular cubic surfaces is quite an old subject, since their classification (over C) goes back to Schlafli [39] and Cay ley [8]. However, a recent account by Bruce and Wall [6] has shown that modern singularity theory can give much insight into this classification. One of the main themes of the present paper is that this approach is also useful over an arbitrary perfect field k for...