R-functions and chevron surfaces in mechanical engineering

Optimized smoothing of discrete models of the implicitly defined geometrical objects' surfaces

“…Consider the results of applying the local algorithm for improving the positions of nodes, based on minimizing the distance-length functional, in order to improve the surface mesh defined by the function (2). The original model is shown in Fig.…”

“…Implicit functions can be constructed step-by-step using set-theoretic operations (negation, disjunction, conjunction). Such operations are implemented in the form of systems of R-functions [1,2]. In most cases, a system of R-functions is used in practice to construct F [2] 1 1 2 2 1 2 1 2 1 2 2 2 1 2 1 2…”

“…The simplest form of such a predicate is the restriction to the sign of some real function in the form of the inequality F(P)≥0. For example, the function sphere(x, y, z)=r 2 -x 2 -y 2 -z 2 is greater than zero at the points of the domain limited by a sphere of radius r centered…”

Construction of the Functional Voxel Model for a Spline Curve

“…The curve passes through the boundary points of the segment 2. First derivatives of the neighbor segments of the spline should be equal in the boundary points These conditions can be described by the system of four equations (2).…”

“…The necessity to construct the maximally accurate computer geometrical models for the contemporary design problems remains to be the primary. Nowadays the Set-theoretic operations for the analytical modelling of a space of the complex function (Rvachev function [1,2]) are one of the most curious approaches to constructing the analytically set objects of complex geometrical shape.…”