Elmomc Multi-Axis Motion Controller-Maestro Motion Contro Manual do Utilizador descarregar pdf (Página 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

) and (X

) we can calculate the

coefficients

A,B,C for the three possible cases:

a) X

≠ X

and Y

≠ Y

The line equation can be written in a form

(X – X

)/(X

– X

) = (Y – Y

)/(Y

– Y

) (a2.1)

(X – X

)/ ∆X = (Y – Y

)/∆Y (a2.2)

that can be transformed into

X∆Y – X

∆Y –Y∆X + Y

∆X = X∆Y –Y∆X +(Y

∆X - X

∆Y) = 0 (a2.3)

From (a2.3) we get

A = ∆Y, B = –∆X, C = Y

∆X – X

∆Y (a2.4)

b) X

≠ X

and Y

= Y

The line equation is

Y = Y

or Y – Y

= 0 (a2.5)

So for

A, B and C we have

A = 0, B = 1, C = –Y

(a2.6)

c) X

= X

and Y

≠ Y

The line equation is

X = X

or X – X

= 0 (a2.7)

So for

A, B, C we have

A = 1, B = 0, C = – X

(a2.8)

Maestro Software Manual

MAN-MLT (Ver. 2.0)

B-1

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