- #1
Alibeg
- 12
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Hi. I'd like to know whether is it possible to do the following, and if so, how...(and also, whether is it possible to solve similar problems)
I have parametric equation of a curve and I need to find its intersection with a ray that starts at the origin of the coordinate system and makes known angle with the positive x-axis.
Curve:
x = ( R-r )( cos([tex]\varphi[/tex]) - cos([tex]\theta[/tex]) ) + D cos([tex]\varphi[/tex] (R-r)/r - [tex]\theta[/tex] (R-r)/r )
y = ( R-r )( sin([tex]\varphi[/tex]) - sin([tex]\theta[/tex]) ) + D sin([tex]\varphi[/tex] (R-r)/r - [tex]\theta[/tex] (R-r)/r )
R, r and D are known constants.
Ray:
y = tan([tex]\beta[/tex]) x
[tex]\beta[/tex], [tex]\theta[/tex] and [tex]\varphi[/tex] are angles, [tex]\varphi[/tex] is my parameter, [tex]\theta[/tex] and [tex]\beta[/tex] are some variable angles.
I need to find the coordinates of the intersection of curve and the ray as a function of [tex]\theta[/tex] and [tex]\beta[/tex].
In short I want to know coordinates of intersection but without the parameter [tex]\varphi[/tex] in them.
I have parametric equation of a curve and I need to find its intersection with a ray that starts at the origin of the coordinate system and makes known angle with the positive x-axis.
Curve:
x = ( R-r )( cos([tex]\varphi[/tex]) - cos([tex]\theta[/tex]) ) + D cos([tex]\varphi[/tex] (R-r)/r - [tex]\theta[/tex] (R-r)/r )
y = ( R-r )( sin([tex]\varphi[/tex]) - sin([tex]\theta[/tex]) ) + D sin([tex]\varphi[/tex] (R-r)/r - [tex]\theta[/tex] (R-r)/r )
R, r and D are known constants.
Ray:
y = tan([tex]\beta[/tex]) x
[tex]\beta[/tex], [tex]\theta[/tex] and [tex]\varphi[/tex] are angles, [tex]\varphi[/tex] is my parameter, [tex]\theta[/tex] and [tex]\beta[/tex] are some variable angles.
I need to find the coordinates of the intersection of curve and the ray as a function of [tex]\theta[/tex] and [tex]\beta[/tex].
In short I want to know coordinates of intersection but without the parameter [tex]\varphi[/tex] in them.