Angulation Utility (2D) |
This page contains a 2D positioning routine (by angulation).
Refer to the following diagram for the explanation that follows:
Assume this web page is a physical piece of paper and that an object's motion is confined to two dimensions--in the plane of this page.
Parameters are defined as follows:
1) two sensors are separated by a constant, known, distance, K1, along the x axis;
2) the two sensors look in the direction of positive y (they look up, and cannot "see" behind them);
3) the object's position, P, is defined by its (x,y) coordinates of a coordinate system with origin located at the left sensor (see the diagram above);
4) each sensor can detect the angle between the x axis and the object's location, but not the distance to the object;
5) the left sensor detects angle, A1, between the x axis and the object's position; the right sensor detects angle, A2, between the x axis and the object's position. NEITHER OF THESE ANGLES CAN BE LESS THAN OR EQUAL TO ZERO, OR GREATER THAN OR EQUAL TO 180 DEGREES.
The utility posted on this page accepts three inputs, the values of K1, A1, and A2, and outputs the (x, y) coordinates of the object.
Keep in mind that units will be consistent. For example, if the value you enter for K1 represents meters, the values output for x and y will also represent meters.
IMPORTANT: The values you enter for A1 and A2 must be degrees, NOT radians.