WPF: Finding an element along a path

The angle between the robots is arctan(x-distance, y-distance) (most platforms provide this 2-argument arctan that does the angle adjustment for you. You then just have to check whether this angle is less than some number away from the current heading.

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Edit 2020: Here's a much more complete analysis based on the updated example code in the question and a now-deleted imageshack image.

1. Atan2: The key function you need to find an angle between two points is atan2. This takes a Y-coordinate and X-coordinate of a vector and returns the angle between that vector and the positive X axis. The value will always be wrapped to lie between -Pi and Pi.

2. Heading vs Orientation: atan2, and in general all your math functions, work in the "mathematical standard coordinate system", which means an angle of "0" corresponds to directly east, and angles increase counterclockwise. Thus, an "mathematical angle" of Pi / 2 as given by atan2(1, 0) means an orientation of "90 degrees counterclockwise from due east", which matches the point (x=0, y=1). "Heading" is a navigational idea that expresses orientation is a clockwise angle from due north.

   • Analysis: In the now-deleted imageshack image, your "heading" of 191 degrees corresponded to a south-south-west direction. This actually an trigonometric "orientation" of -101 degrees, or -1.76. The first issue in the updated code is therefore conflating "heading" and "orientation". you can get the latter from the former by orientation_degrees = 90 - heading_degrees or orientation_radians = Math.PI / 2 - heading_radians, or alternatively you could specify input orientations in the mathematical coordinate system rather than the nautical heading coordinate system.

3. Checking that an angle lies between two others: Checking that an vector lies between two other vectors is not as simple as checking that the numeric angle value is between, because of the way the angles wrap at Pi/-Pi.

   • Analysis: in your example, the orientation is 3.3, the right edge of view is orientation 2.95, the left edge of view is 3.65. The calculated azimith is 3.0141873380511295, which happens to be correct (it does lie between). However, this would fail for azimuth values like -3, which should be calculated as "hit". See Calculating if an angle is between two angles for solutions.