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Thread: Formula For Area of Object Bounded By Lines and Radii on Cartesian Plane

  1. #1
    Apr 2018
    Ebensburg, PA

    Formula For Area of Object Bounded By Lines and Radii on Cartesian Plane

    At one time, I had a formula used in a FORTRAN program that provided the area of an object comprised of lines and radii. I provided an NC input file that contained x-y coordinates along with x-y offsets for a radius and it also indicated CW or CCW circular interpolation. The areas under the lines and radii would be summed when travelling left to right and subtracted when going right to left. I know that I can calculate the areas manually. Can someone point me to where I could find that formula?
    I know I can calculate the area under a line using the trapezoidal formula.
    I can calculate:
    Area under a radius: Area inside arc & below= area of segment + area under line x increasing clockwise or x decreasing counterclockwise motion
    Area outside arc & below = area under line - area of segment x increasing clockwise or x decreasing counterclockwise.
    When in Relative Quadrants ! & II sum areas. When in Relative Quadrants III & IV subtract areas. Circular motion will be calculated by quadrant so note about theta </= 90 should be expanded to state area calculated by quadrant.

    I found the formula in the appendix of a calculus book published ~1970-1973. I only remember that it was blue and looked similar to the jpg file.
    I know it's a stretch to find the formula but I do not know how to re-create it.

    Attached Thumbnails Attached Thumbnails Formula For Area of Object Bounded By Lines and Radii on Cartesian Plane-similar-book.jpg  
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