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### Full text of “X Collection “

Kluwer Academic Publishers, pp. We use the presented approach to interpolate a network of points and associated normals with piecewise polynomial surfaces with polynomial area element.

The result is the implicit equation of the locus. Starting with a re-formulation of metrical quantities in n-dimensional affine space using linear algebraic tools, we can then talk about visualising geometric objects in n-dimensional space. Hermite interpolation by hypocycloids and epicycloids with rational offsets. Analytical hierarchy process AHP. The aim of this paper is to show the role of geometry and mathematics in the cartography and different options for access to the distortions of the territory, such as optimization of extreme value of distortion, summing and integral criterion on area territory, in some case using criterion with the requirement of a minimum mean value of scale distortion in a given area.

References [1] Gruber, P. Application of the AHP method allowed to perform a diagnostic comparative assessment of objects business entitiesboth objects and accepted assessment criteria were compared in pairs with each other the evaluator’s preferences subjectivity of assessments are treated in the Analytic Hierarchy Process as a natural phenomenon.

We describe this function using an implicit algebraic equation and the rational Puiseux series of its branches.

The satellite picture of the same object taken from two different directions may be treated as two-image parallel projection.

## Numerical solution of the Kiessl model

An actual problem affected by the precision of positioning geodetic points using new GNSS technologies in coordinate systems dewkriptivn the precision of the map projection. Our main goal is the interpolation of Gk data at the boundaries of ruled surfaces and canal surfaces. Their mixtures with the analytic use of homogenous coordinates is applied on projective theorems.

Fundamentals of the analytic hierarchy process. We suggest certain explanations. We show that for a rational surface the Gram determinant of its tangent space is a perfect square if and only if the Gram determinant of its normal space is a perfect square.

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We propose an alternative adaptive subdivision scheme, which ensures the approximation degree 4 both for the inflection—free segments and the segments with inflections. A scaling method for priorities in hierarchical structures. As an answer it has to be stated that a proper visualisation is only one part, the other, more important, is the addressee.

Except for the most simple loci such as lines, circles or possibly conics, this topic is not contained in most geonetrie texts. Authors want to present the basic concepts of tensigrity structures which are described in the original patents and on the base of this present the realization geometrid tensigrity structures which were realized in architecture. The gauss map at the inflection point is not regular and in the neighborhood is typically not injective.

The associated equilateral spherical conics have the property that the three vertices of a regular right-angled spherical triangle can simultaneously move along. Thank to the addition, basing on the image, it will be possible to figure out geometrical features of the photographed object. Therefore, the lecture takes up the cudgels on behalf of geoemtrie solid education in Geometry, including Descriptive Geometry. Konstytucja Rzeczpospolitej Polskiej z dnia 2 kwietnia r. Each point of space has two points assigned, that come from projections of the given point in the defined directions.

The support function is thus not regular and typically multivalued. Hence, we deal with rational, elliptic or hyperelliptic curves that desskriptivn birational to plane curves in the Weierstrass form and thus they are square-root parameterizable. Journal of Mathematical Psychology, 15, pp.

The use of dynamic geometry software Cabri, GeoGebra, Sketchpad, If cones deskritpivn this type are tangent to a regular quadric then their apices are located on a sphere. A new viewpoint can give us new ideas and concepts that lead to a simplified solution of the mathematical problem. Sbornik z 19 seminmare: Together with geometric criteria, useful solutions, i.

Springer Spektrum, in preparation. The concept of choosing an infinite hyperplane is used for making deskri;tivn in an affine space to solve projective problems and vice-versa. We will pay specific attention to the three-dimensional space and the most important object in it: The degrees of deskriptovn equations admit a prediction of the number of possible solutions. Nowadays new groups of scientists are looking for the best and precisly definition for tensigrity and they are trying to defined true or false tensigrity structures.

And the history of developing this idea is interesting either. Handbook of convex geometry.

The Universe of Quadrics. Book 1, Science and technologies in geology. Multidisciplinary Aspects of Production Engineering.