Fitting plane curves to three-dimensional points

Antonopoulos, A

dc.contributor.author	Antonopoulos, A	en
dc.date.accessioned	2014-03-01T01:20:32Z
dc.date.available	2014-03-01T01:20:32Z
dc.date.issued	2004	en
dc.identifier.issn	0733-9453	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15949
dc.subject	Curvature	en
dc.subject	Least square method	en
dc.subject	Surveys	en
dc.subject.classification	Engineering, Civil	en
dc.subject.other	Curve fitting	en
dc.subject.other	Least squares approximations	en
dc.subject.other	Mathematical transformations	en
dc.subject.other	Parameter estimation	en
dc.subject.other	Conformal transformations	en
dc.subject.other	Fitting plane curves	en
dc.subject.other	High-precision deformations	en
dc.subject.other	Theodolite intersections sytem	en
dc.subject.other	Industrial engineering	en
dc.subject.other	coordinate	en
dc.subject.other	least squares method	en
dc.subject.other	surveying	en
dc.title	Fitting plane curves to three-dimensional points	en
heal.type	journalArticle	en
heal.identifier.primary	10.1061/(ASCE)0733-9453(2004)130:2(73)	en
heal.identifier.secondary	http://dx.doi.org/10.1061/(ASCE)0733-9453(2004)130:2(73)	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	Fitting plane curves to the three-dimensional (M) points defining those curves can be performed by ordinary general least squares adjustment. To this, a conformal transformation of the initial 3D system to a two-dimensional system in the best-estimated plane of the curve is used. The kind and the number of the unknown transformation parameters are selected according to one's needs. In this adjustment, the coordinates of the defining points are considered observed parameters while the parameters of the aforementioned transformation and the ones defining the curve unobserved parameters. Finally, the curve-with respect to the initial system-is fully determined. Coordinate determination, together with least squares fitting of certain curves to these coordinates, is usually performed by advanced theodolite intersection systems. The straight line is a special case of curve lying in infinite number of planes, therefore, the suitable selection of the plane in which the adjustment is held is indicated, each time, by current convenience. Fitting a straight line to 3D points, a process hardly noticed in least squares textbooks, is extremely useful in high-precision deformation check and a lot of industrial survey applications. © ASCE.	en
heal.publisher	ASCE-AMER SOC CIVIL ENGINEERS	en
heal.journalName	Journal of Surveying Engineering	en
dc.identifier.doi	10.1061/(ASCE)0733-9453(2004)130:2(73)	en
dc.identifier.isi	ISI:000220960100004	en
dc.identifier.volume	130	en
dc.identifier.issue	2	en
dc.identifier.spage	73	en
dc.identifier.epage	78	en