find the proportional area of some squares confined betwnn a ring in C#

Question

Hi
Could any one help me solve this problem- the related picture has been uploaded, please look at that first.
I have a regular cartesian grid with known dimensions. then I will superimpose an annular ring ( two concentric circles with known radius). I want to find out the AREAL proportion of ALL squares(grid) which fall inside the annulus, separately.FOR EXAMPLE, If you open the file, I want to obtain the area of each coloured part of squares and print them to a TEXT file.
Thanks

Vladimir Nani · Answer

Firstly you need to define bounding rectangle around your figure (blue box) that has dimensions multiple of grid step. Then find which grid vertices are inside your figure. In my example i look if distance from center of my circle is less or equal to the radius. With ring you also need to check if it is greater or equal to the smaller radius. These vertices are colored with red. After that you need to loop throw all little squares in your bounding rectangle and find out how many red vertices are part of these little squares. Then for each square find it`s intersection points with your circle(or ring). Just set your circle(ring) equation equal to line equation (your square side). You`ll get two points or one when side of bounding region is tangent to circle. You need to consider each quarter of circle because circle intersecting with line gives two points but you need only one for your current square the second intersection point you will need after some iterations. There are four situations of finding area : area = ( ARectangle + ASegment, ASquare, ATrapezioid + ASegment, ATriangle +ASegment) I hope i helped you. If you`ll have some questions about function implementations ask.