Elmomc Multi-Axis Motion Controller-Maestro Motion Contro Manual do Utilizador descarregar pdf (Página 70)

Appendix C: Intersection point of two lines

defined by the end points

Line L

is defined by its end points P

) and P

). Line L

is defined by end

points

) and P

Note: ∆X

= X

– X

, ∆Y

= Y

– Y

, ∆X

= X

– X

, ∆Y

= Y

– Y

= ∆Y

/∆X

, q

= ∆X

/∆Y

, k

= ∆Y

/∆X

, q

= ∆X

/∆Y

Calculation of the two lines intersection point (X,Y) depends on the each line position

relative to coordinate axes. The following cases are possible.

a) X

≠ X

, Y

≠ Y

, X

≠ X

, Y

≠ Y

To define intersection point, use

(X – X

)∆Y

= (Y – Y

)∆X

(a3.1)

(X – X

)∆Y

= (Y – Y

)∆X

(a3.2)

X∆Y

– X

∆Y

= Y∆X

– Y

∆X

(a3.3)

X∆Y

– X

∆Y

= Y∆X

– Y

∆X

(a3.4)

From (a3.3) the results are

X = X

+ Yq

– Y

(a3.5)

and substituting into (a3.4) the results are

+ Yq

– Y

)∆Y

– X

∆Y

= Y∆X

– Y

∆X

(a3.6)

that produces

Y = [(q

+ X

– X

)∆Y

–Y

∆X

]/(q

∆Y

– ∆X

) (a3.7)

and X can be calculated by (a3.5).

b) X

≠ X

, Y

≠ Y

, X

= X

, Y

≠ Y

To find an intersection point use

(X – X

)/∆X

= (Y – Y

)/∆Y

(a3.8)

X = X

(a3.9)

Maestro Software Manual

MAN-MLT (Ver. 2.0)

C-1

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