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Modelling a 2D region based on equation and coordinates

Posted 10 years ago

Greetings to my fellow Mathematica users!

I'm an amateur user of Mathematica and I'm currently facing some trouble with modelling of a planar region which is described by 3 x-y coordinates and a curved line represented by an equation. I tried my best in coming up with the illustration below to show what I mean:

enter image description here <-- Description of Planar region

  • B = Angle between Horizontal (at x2,y2) and the line described by r
  • r = Equation of the curve region, described by: r = a*exp(B)
  • a = Value of r when B = 0
  • (x,y) = Coordinates of the vertices

Is Mathematica able to model such a region defined by 3 coordinates and an equation? I'm bordering on the edge of frustration in trying to look for the way to create this region in Mathematica. I would really be grateful if someone could point me in the right direction of defining such a region.

Thank you in advance and have a great day!

Regards Corse

POSTED BY: Ben Corse
2 Replies
Posted 10 years ago

Hi David!

Thanks for your reply!

What I mean by 'model' is just to generate the shape as described above. Actually the primary objective for me doing this is to be able to obtain the area of its interior for various values of coordinates and angle (B).

Would you happen to know of more efficient ways to do this?

POSTED BY: Ben Corse

It's not clear what you mean by "model". Do you mean to shade the region? Or calculate points on the periphery? Or what?

You could think of moving the point {x2, y2} to the origin. (See the Mathematica GeometricTransformation and Translate routines). Then you could always translate your resulting expressions back.

There is a problem in that there is nothing to guarantee that {x1, y1} and {x3, y3} lie on the curve. At best they can be used to give the direction of the two straight lines and thus determine an angle for B. I think there is a VectorAngle routine or you could use a trigonometric expression.

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