ElmoMC Multi-Axis Motion Controller-Maestro Motion Control - Manual (Page 69)

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