Objective-C draw a path and detect when it closes (forms a closed shape)

I'm fairly new to game programming (but not to programming) and I want to create a space ship which leaves a trail on the screen. Now my problem is to come up with a solution how to detect if the trail left from the shi开发者_开发技巧p forms a closed shape - eg. if the ship left a trail around an object, the object is caught inside its trail so to speak.

The direction I'm thinking is to draw the path of the trail on an image not visible on the screen and every now and then try to fill it with certain color and then check if fill is caught within the trail path. However it seems like a lot of overhead.

Any ideas how to do that? I'm using cocos2d if that's of any help

In game programming you often need to think more mathematically than visually.

First does your ship continuously leaves a trail on the screen? If yes, then it will be easier to know when the shape closes : you just have to remember the coordinate where your ship started to leave a trail, then wait for the trail to approach this coordinate another time (for example within a radius of 10 pixels, or else the user will need to be really accurate to hit exactly the same pixel to close the shape).

The visual representation of the trail is only here for the user, you'll never use it to compute anything. What you will do is to keep in memory the path followed by the ship's trail : a polygon, which is nothing else than the list of coordinates it followed.

Then after you know that your shape is closed, you have to determine if an object is inside your polygon or not. It's possible that objective-c or cocos2d (I don't know much about it) already contains a built-in function to know if a point is inside a polygon. In java there is the Polygon class which makes this really easy. If you don't find anything you can do it yourself, there are already great answers about this subject on SO, here is a nice one : How can I determine whether a 2D Point is within a Polygon?