Fitting data points with some model function such that the sum of squared o
rthogonal distances is minimized is well-known as TLS, i.e. as total least
squares, see Van Huffel (1997). We consider situations where the model is s
uch that there might be no perpendiculars from certain data points onto the
model function and where one has to replace certain orthogonal distances b
y shortest ones, e.g. to corner or border line points. We introduce this co
nsidering the (now incomplete) TLS fit by a finite piece of a straight line
. Then we study general model functions with linear parameters and modify a
well-known descent algorithm (see Seufer (1996), Seufer/Spath (1997), Spat
h (1996), Spath (1997a) and Spath (1997b)) for fitting with them. As applic
ations (to be used in computational metrology) we discuss incomplete TLS fi
tting with a segment of a circle, the area of a circle in space, with a cyl
inder, and with a rectangle (see also Gander/Hrebicek (1993)). Numerical ex
amples are given for each case. Mathematics Subject Classification (1991):
65D10.