Plane A-angle Coordinate System And Its Applicatoins On Photogrammetry
Hao Xiangyang ;
Dept. of Photogrammetry & Remote Sensing
Zhengzhou Inst.
of Surveying & Mapping
Zhengzhou, Henan 450052
People's Republic of China
Abstract
In this paper,the concept of plane d-angle coordinate system is
put forward.The characteristics of plane a-angle cordinate system
and its relations to plane rectangular coordinate system are
discussed
azimuthal angle and angle of
coordinate system are given. As
Introduction
Plane rectangular coordinate system is
the most popular and convinient
coordinate system both in theoretical
studies and practical applications . But
in some cases,it is difficult to get a
standard rectangular coordinate system
because of the limits of techenology . A
typical example can be found in the
Digital Coordinate Instument (DCI) . The
DCI is a new instrument which is commonly
used in the filed of topography, cadastre
and photogrammetry in the last a few
years.Its geometrical structureare mainly
two guides , i.e. x-axis and y-àxis , are
perpendicular toeach other . The X and Y
coordinates of the point at which the
cross aims can be displayed in real time
in the procedure of moving.Because of the
limits oftechonology,the angle between x-
axis and y-axis is not 90'but a (a X90).
The angle can be made up to 9fr45' by the
current technology.In other words, the x-
axis and y-axis do not form a strict
plane rectangular coordinate system but
a plane «-angle coordinate system . The
main purposes of DCI are to measure the
coordinates of the points on maps or
images and in turn to determine the
positions of ‘the points on maps according
to their coordinates.Because DCI's x-axis
and y-axis is not rectangular , the
measured coordinates are not in plane
rectangular coordinate system but in
plane d -angle coordinate system . It is
commonly concerned how it influences on
the coordinates of a point, the distance
between two points,the area of a polygon
and the angle between two straight lines.
Therefore,it is both theoretically and
practically significant to analyze the
characteristics of plane c -angle
coordinate system.
Plane d -angle Coordinate System
1.The Concept of Plane à-angle coordinate
System
Passing a given point O,draw two axises
The expression forms of parameters as distance, area,
intersection in plane
c -angle
its application, the effects on
coordinates,distance,area,azimuthal angle and angle of intersection
‚because of Digital Coordinate Instrument's x-axis and y-axis being
not rectangular , are analyzed respectively . Also a simple and
practical method for calculating the angle of Digital Coordinate
Instrument's x-axis and y-axis is developed.
58
between which there is a angle d( 0° <a< 180°),
This two axises,which are with the same
zero point and length scale , are called
x-axis and y-axis respectively . In this
way , a plane a-angle coordinate system
XOY is established. The coordinates of an
arbitary point M in plane d -angle
coordinate system are measured by x and
y (see Fig.1).The coordinates of point M
are signed as M(x,y).Specially,if a =90°
then the plane d -angle coordinate system
is plane rectangular coordinate system.
Fig.1
Fig.2
2.The Relations Between two Plane d-angle
Coordinate System
In Fig. 2 , XOY is a plane d,-angle
coordinate system( 7XOY-e, ) and X'OY'is
a plane da -angle coordinate system
(£X'0Y' =a; ) Suppose the coordinates of
Of point. M are (x,y) in XOY and (x',y')
inX'OY' respectively , the following
formulas can be developed easily by using
the theorem of sine.
x ere Sin (a2 —a1)
a;
; S (1)
y = sina 1
sina 2
or expressed in the form of matrix as
x' sin (œ1—a2)
1 tee mi X
Sinha
= 2 (2)
; Sina 1
y re y
Sina 2
The relationship between the two plane
à -angle coordinate systems is expressed
by formula (1) or formula (2). Specially,
if a 2=90° and a 1=a ,formula (2) becomes
into
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