A,b,c, A) x, X – x – ElmoMC Multi-Axis Motion Controller-Maestro Motion Control User Manual
Page 69: Y – y, X = (y – y, X∆y – x, Y –y∆x + y, X∆y –y∆x +(y, X - x, Y) = 0
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Appendix B: Coefficients of the line
standard equation for the line defined
by the end points
If the line L is defined by its end points
(X
1
,Y
1
)
and
(X
2
,Y
2
)
we can calculate the
coefficients
A,B,C
for the three possible cases:
a) X
1
≠ X
2
and
Y
1
≠ Y
2
.
The line equation can be written in a form
(X – X
1
)/(X
2
– X
1
) = (Y – Y
1
)/(Y
2
– Y
1
)
(a2.1)
or
(X – X
1
)/ ∆X = (Y – Y
1
)/∆Y
(a2.2)
that can be transformed into
X∆Y – X
1
∆
Y –Y∆X + Y
1
∆
X
=
X∆Y –Y∆X +(Y
1
∆
X - X
1
∆
Y) = 0
(a2.3)
From (a2.3) we get
A =
∆
Y, B = –∆X, C = Y
1
∆
X – X
1
∆
Y
(a2.4)
b) X
1
≠ X
2
and
Y
1
= Y
2
.
The line equation is
Y = Y
1
or
Y – Y
1
= 0
(a2.5)
So for
A, B
and
C
we have
A = 0, B = 1, C = –Y
1
(a2.6)
c) X
1
= X
2
and
Y
1
≠ Y
2
.
The line equation is
X = X
1
or
X – X
1
= 0
(a2.7)
So for
A, B, C
we have
A = 1, B = 0, C = – X
1
(a2.8)
Maestro
Software Manual
MAN-MLT (Ver. 2.0)
B-1