Question

Oh god this must be so simple. I have a heading in range (0, 2π) and two points from which I get the heading in between. I must compare them to see if one is within a range of the other. What I’ve got so far is.

//get the angle
float angle = atan(here.x - there.x, here.y - there.y);

//atan2 uses (-pi, pi) range, convert to (0, 2pi)
if(angle < 0) angle += 2*pi;

//subtract them pesky headings
float diff = angle - givenAngle;

//a difference of 350 degrees really is a difference of 10 degrees
if(diff > pi) diff = 2*pi - diff;

//a difference of -10 degrees really is a difference of 10 degrees
if(diff < 0) diff *= -1;

//check if the point is in range of givenAngle
if(diff > fov) do_magic(diff - fov);

However, I get all sorts of issues when both angles wrap around to zero and I’ve been wasting way too much brainpower in solving this solved problem.

Where am I doing it wrong? How can I find the difference between two headings correctly?

Answer 1

One of the main problems was in this line:

float angle = atan(here.x - there.x, here.y - there.y);

It was kind of tricky to notice, but that’s not the right argument order for atan – even the mathematical definition on wikipedia takes the y component (sine) before the x component (cosine).

float angle = atan(here.y - there.y, here.x - there.x);

A second problem is that, as it turns out, angle was off by 180 degrees. In other words, instead of calculating here - there, I should be calculating there - here.

float angle = atan(there.y - here.y, there.x - here.x);

Add in sverre’s observation about the incorrect order of operations, and we have something that works much better:

float angle = atan(there.y - here.y, there.x - here.x);
if(angle < 0) angle += pi * 2; //use (0, 2pi) range, the same as angle
float diff = abs(angle - givenAngle);
if(diff > pi) diff = 2*pi - diff;
if(diff > fov) do_magic(diff - fov);