# Instrumentation & Measurement Magazine 25-5 - 18

```Section Line Scan Measurement Principle
The laser scanning measurement method based on the section
line is a common measurement method in reverse engineering.
The section line is the intersection line obtained by a
group of parallel two-dimensional planes and the surface
or the equidistant surface of the surface, and the intersection
line is used as the measurement curve of the workpiece
to be measured [8]. First, a reference plane is set, and the center
of the workpiece is calculated by the preset target point. At
the same time, the center of the workpiece is vertically projected
to the reference plane and recorded as the origin of the
reference plane. The data acquisition device always moves
in the reference plane. Each measurement track in the reference
plane intersects with the vertical projection of the surface
of the workpiece to be measured, forming the measurement
curve on the current projection plane. The overall surface
data of the workpiece can be measured by designing a reasonable
two-dimensional data acquisition trajectory. At the same
time, the planning measurement points in the design curve
correspond to the surface measurement points on the corresponding
workpiece section one by one. For a point A(x0
,y0
,y1,z1). According to the projection relation, x0
=x1
, y0
,z0
)
on the design curve, the measuring point on the workpiece is
A'(x1
and the reading zL of the sensor. The principle of section
line method is shown in Fig. 1.
Curve Fitting and
B-spline Wavelet
Decomposition
The method of uniform
select the minimum sampling
interval on the
planned cross-section
line to obtain the initial
sampling point. The purpose
of this is to make the
sampling points contain
all the information of the
curve. Then, the method
in this section is used for
resampling. The initial m
sampling points on a section
line are recorded as
point sets
QQj
  . The
m
point set Q is used as the
initial control vertex of the
Non-Uniform Rational BSpline
NURBS curve [9] for
surface fitting. The chord
length parameter method
is used to calculate the parameters
j0
t
j
18
m
of
control
points. The calculation formula
is as follows:
j0
Fig. 1. The principle of section line method.
IEEE Instrumentation & Measurement Magazine
August 2022
The z-axis coordinate of the measuring point can be obtained
by z0
QQ

tt 1ii m
 

i0
In order to approximate the initial point as a quadratic
curve, a NURBS curve of k degree is introduced, which is defined
as:
rt ()  wB t Q() i
 0,i ik
m
i
 wB t
m
i
0,i ik
()
t t t 
01
 mk
(2)
where wi is the weight factor of the control points of the curve,
and Bi,k is the B-spline basis function of k degrees.
In this paper, B-spline wavelet transform [10] is used to
decompose the fitting curve. B-spline wavelet transform is a
mathematical tool which decomposes B-spline functions belonging
to Vd
space through the projection of Vd−1
and Wd−1
.
The space Wi is defined as a wavelet space, and the functions
in Wi are called wavelets. B-spline wavelet is a wavelet
function with minimum support [10]. According to the naming
habits commonly used by wavelet, the ψi
the B-spline wavelet basis function. The B-spline basis function
vector of space Vi
defined by φi(Bk,1,...,Bk,n,)T
=y1 nn 1
 
i 11
.  ( ,, ii )
expressed as:
(t) represents
, and the vector
of B-spline wavelet basis function of space Wi is defined as
T . Then, a NURBS curve in space Vi
can be
r u uC ii
i () ()T
(3)
QQ


ii1
ii 1
(1)
```

# Instrumentation & Measurement Magazine 25-5

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