zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Clothoid spline transition spirals. (English) Zbl 0756.65005

A piecewise defined planar curve, consisting of straight line segments, circular arcs and clothoid segments, which is twice continuously differentiable with respect to arc length is called a clothoid spline, as circles and straight lines can be considered limiting forms of clothoids [see E. Mehlum, Non-linear splines in Computer Aided Geometric Design, Eds. R. E. Barnhill and R. F. Riesenfield, Academic Press, New York, 173-207 (1974)]. Such splines are used in the route design of the centre lines of highways and railways [see K. G. Baass, Transportation Forum 1, 47-52 (1984)].

The authors study the problem of finding a clothoid spline transition spiral which joins two given points and matches given curvature and unit tangents at the two points. Conditions are given for the existence and uniqueness of the clothoid spline transition spirals, and algorithms for finding them are outlined [cf. D. S. Meek and R. S. D. Thomas, Comput. Aided Geom. Des. 8, No. 2, 163-174 (1991)].

MSC:
65D05Interpolation (numerical methods)
65D07Splines (numerical methods)
41A15Spline approximation
65D17Computer aided design (modeling of curves and surfaces)
41A05Interpolation (approximations and expansions)