How to determine if a point falls within a shaded area?

Question

C++ / C#

I more or less figured out the circle and ellipse, but I can’t figure out what to do with the line at all.

Answer 1

You write down the function by which the lines are built, between which it is necessary to check whether the point lies.
You substitute X points into a function, you calculate Y for this function.
Compare with Y points. If they are equal, the point lies on the line; if not, it lies above or below, respectively.
And you just set the necessary conditions for checking how the point should lie, above or below the given lines.

Answer 2

And what about C#? This is a common math problem. If X<0, then Y must lie under the line, otherwise above the line.
You can use some library, you can dream up with Rectangle.Contains.

Answer 3

Circle:
(x - x0)^2+(y-y0)^2 < R^2 - set of points inside the circle
(x - x0)^2+(y-y0)^2 > R^2 - set of points outside the circle
R - radius of the circle, x0, y0 - coordinates of the center
Ellipse:
((x - x0)/a)^2+((y-y0)/b)^2 < 1 - set of points inside the ellipse
((x - x0)/ a)^2+((y-y0)/b)^2 > 1 - set of points outside the ellipse
a, b - radii of the ellipse
Straight lines:
x < 0 - set of points to the left of the axis 0Y
x > 0 - set of points to the right of the axis 0Y
y < 0 - set of points below the 0X axis
y > 0 - set of points above the 0X axis
ax+by < c set of points below the line given by the equation ax+by = с
ax+by > c set of points above the line given by the equation ax+by = c
For your task:
1. Find the right coefficients for all lines and curves.
2. Find out for each equation the sign that is obtained when a point hits in the shaded area
3. Create a set of tests for a point.
For example, for zone B:
The point must be inside the circle, outside the ellipse and above the straight line, that is, the following inequalities must be satisfied (the coefficients a, b x0, y0 are different for each inequality):
(x - x0)^2+(y-y0) ^2 < R^2 ((x - x0)/a)^2+((y- y0
)/b)^2 > 1
ax+by > c
belongs to the shaded area.