8 research outputs found
Evaluating the cylindricity of a nominally cylindrical point set
International audienceThe minimum zone cylinder of a set of points in three dimensions is the cylindric crown defined by a pair of coaxial cylinders with minimal radial separation (width). In the context of tolerancing metrology, the set of points is nominally cylindrical, i.e., the points are known to lie in close proximity of a known reference cylinder. Using approximations which are valid only in the neighborhood of the reference cylinder, we can get a very good approximation of the minimum zone cylinder. The process provides successive approximations, and each iteration involves the solution of a linear programming problem in six dimensions. The error between the approximation and the optimal solution converges very rapidly (typically in three iterations in practice) down to a limit error of (8 omega^2)/R ( where omega is the width and R is the external radius of the zone cylinder)
Evaluating the Cylindricity of a Nominally Cylindrical Point Set (Draft)
The minimum zone cylinder of a set of points in three dimensions is the cylindric crown defined by a pair of coaxial cylinders with minimal radial separation (width). In the context of tolerancing metrology, the set of points is nominally cylindrical, i.e., the points are known to lie in close proximity of a known reference cylinder. Using approximations which are valid only in the neighborhood of the reference cylinder, we can get a very good approximation of the minimum zone cylinder. The process provides successive approximations, and each iteration involves the solution of a linear programming problem in six dimensions. The error between the approximation and the optimal solution converges very rapidly (typically in three iterations in practice) down to a limit error of 8omega_0^2/R (where omega_0 is the width and R is the external radius of the zone cylinder)
Culling a Set of Points for Roundness or Cylindricity Evaluations
International audienceRoundness and cylindricity evaluations are among the most important problems in computational metrology, and are based on sets of surface measurements (input data points). A recent approach to such evaluations is based on a linear-programming approach yielding a rapidly converging solution. Such a solution is determined by a fixed-size subset of a large input set. With the intent to simplify the main computational task, it appears desirable to cull from the input any point that cannot provably define the solution. In this note we present an analysis and an efficient solution to the problem of culling the input set. For input data points arranged in cross-sections under mild conditions of uniformity, this algorithm runs in linear time
Evaluating the cylindricity of a nominally cylindrical point set
Abstract The minimum zone cylinder of a set of points in three dimensions is the cylindric crown defined by a pair of coaxial cylinders with minimal radial separation (width). In the context of tolerancing metrology, the set of points is nominally cylindrical, i.e., the points are known to lie in close proximity of a known reference cylinder. Using approximations which are valid only in the neighborhood of the reference cylinder, we can get a very good approximation of the minimum zone cylinder. The process provides successive approximations, and each iteration involves the solution of a linear programming problem in six dimensions. The error between the approximation and the optimal solution converges very rapidly (typically in three iterations in practice) down to a limit error of 8ω 2 0 R ( where ω 0 is the width and R is the external radius of the zone cylinder)
Evaluating the cylindricity of a nominally cylindrical point set (draft)
Theme 2 - Genie logiciel et calcul symbolique - projet PrismeSIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : 14802 E, issue : a.1999 n.3747 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc
Large bichromatic point sets admit empty monochromatic 4-gons
We consider a variation of a problem stated by ErdËťos
and Szekeres in 1935 about the existence of a number
fES(k) such that any set S of at least fES(k) points in
general position in the plane has a subset of k points
that are the vertices of a convex k-gon. In our setting
the points of S are colored, and we say that a (not necessarily
convex) spanned polygon is monochromatic if
all its vertices have the same color. Moreover, a polygon
is called empty if it does not contain any points of
S in its interior. We show that any bichromatic set of
n ≥ 5044 points in R2 in general position determines
at least one empty, monochromatic quadrilateral (and
thus linearly many).Postprint (published version