多少线经过障碍物

Question

I got a problem to solve. Look at the picture: Image .

• Red filled Ellipse is an obstacle.
• Black dots are beginning and end of "road".
• Blue line, is shortest way from one point to another.

I draw obstacles using mouse (mouse click creates ellipse), then i put in cords of start and the end, and then i use DrawLine to draw line from point to point. The question here is, how can i check or count, how many pixels of line, goes trough obstacle?

I thought of putting every pixel color in a 2D array before drawing the line, and then check it somehow on the numbers, counting shortest way from point to point, and checking how many 255's (obstacle number) would it meet in that array? As you see, i can create obstacle that way, so line will go trough the middle, just some part of it, or even next to it. I am simply lacking any idea how to do that. I need it, so i could rate every "road". More it goes trough obstacle, the less rate it gets.

Any ideas? Any algorithm?

Answer 1

1. Using the equations of the ellipse and the line , find the intersection points of the line with the outline of the ellipse (there may be 2, 1 or no intersections). You can find a worked example of this here .
2. If there are indeed 2 intersection points, use the distance formula to calculate the distance between them.