I'm facing some trouble with finding the area of a region which is described by x-y coordinates (or line equations) and a curved line represented by logspiral. I tried my best in coming up with the following illustration below to show what I mean:
- 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
I understand that I could find the intersection of the 2 half-spaces using 2 equations describing the 2 straight line portions (say using
RegionIntersection), but I'm not too sure how I could incorporate the logspiral equation to get the bounding area using
I'm inclined to convert the logspiral equation to parametric form for this purpose, but I have no idea how to move on from there.
I would really appreciate any help or advice regarding this problem, I have been losing some sleep thinking about this question.