Intersection of two lines defined in (rho/theta ) parameterization

by

Looking at the Wikipedia page, I see that the equation of a straight line corresponding to a given given r, θ pair is

r = x cosθ + y sinθ

Thus, if I understand, given two pairs r1, θ1 and r2, θ2, to find the intersection you must solve for the unknowns x,y the following linear 2×2 system:

x cos θ1 + y sin θ1 = r1
x cos θ2 + y sin θ2 = r2

that is AX = b, where

A = [cos θ1  sin θ1]   b = |r1|   X = |x|
    [cos θ2  sin θ2]       |r2|       |y|

More Related Contents:

  1. Not able to calculate in C.How do you calculate in C?
  2. What is the behavior of integer division?
  3. The most efficient way to implement an integer based power function pow(int, int)
  4. Undefined reference to `sin` [duplicate]
  5. How do I determine the number of digits of an integer in C?
  6. Increasing accuracy of solution of transcendental equation
  7. Divide a number by 3 without using *, /, +, -, % operators
  8. Make a sphere with equidistant vertices
  9. Explain this snippet which finds the maximum of two integers without using if-else or any other comparison operator?
  10. How to use nan and inf in C?
  11. Using M_PI with C89 standard
  12. How do you print the EXACT value of a floating point number?
  13. Representing integers in doubles
  14. get closest point to a line
  15. How to find largest triangle in convex hull aside from brute force search
  16. Compute fast log base 2 ceiling
  17. How to concatenate two integers in C
  18. C – How to implement Set data structure?
  19. Algorithm to rotate an image 90 degrees in place? (No extra memory)
  20. find if 4 points on a plane form a rectangle?
  21. C: how to break apart a multi digit number into separate variables?
  22. log2 not found in my math.h?
  23. Why is the behavior of the modulo operator (%) different between C and Ruby for negative integers?
  24. Fitting largest circle in free area in image with distributed particle
  25. Extend a line segment a specific distance
  26. The algorithm to find the point of intersection of two 3D line segment
  27. Evaluate Mathematical Function from String [closed]
  28. Conditional tests in primality by trial division
  29. A possible algorithm for determining whether two strings are anagrams of one another? [closed]
  30. How sqrt() of GCC works after compiled? Which method of root is used? Newton-Raphson?

Leave a Comment