VISUALIZATION OF THE POLYPOINT TRANSFORMATIONS’ OBJECTS USING THE INTERPOLATION GAUSSIAN FUNCTION

Abstract

The study covers curves modelling to display objects based on interpolation Gauss function after using polypoint transformations, namely, after the transformation of the geometric object shape influenced by deformation changes.

Objects’ simulation using non-linear geometric transformations (e.g., polypoint transformations) allows getting a real time results, reduces the time for processing the received data.

Polypoint transformations method lies in the fact that the deformation object’s changes occur because of changing the space in which the object is located. Transformation space is given using points and named a basis. Transformation object is also a certain set of points. The polypoint coordinate concept is introduced in the study, it equals the number of basis points. Transformation is carried out when user changes the basis of points. Points of the object immersed in a basis are also being transformed influenced by basis of points changes. Thus, the output is a particular object as a set of points. For point interpolation the interpolation Gaussian function is used.

The study covers the different types of interpolation Gaussian function: normal, parametric, and total. The interpolation Gaussian function is n-times differentiable, and resistant to small deviations of the original data. The method of the interpolation Gaussian function, in contrast to most other interpolation methods can be extended to n-dimensional space that leads to a greater variability of the solutions and reduction of the calculation errors in the simulation.

The modelling system was created based on mathematical apparatus of the interpolation Gaussian function simulation, which allows curves building according the given frame, including closed curves. It is often necessary to visualize the closed objects when we use the polypoint transformations. This system is needed to get a computer analysis of the polypoint transformations results.

Keywords: deformation modelling, polypoint representations, approximation, interpolation Gaussian function.