heading in a cartesian coordinate system question

Hello,

I have 2 points in a cartesian coordinate system, where the first point is always (0,0). Given the second point and a heading in degrees, how would I write an algorithm to determine if the 2nd point is traveling in the general direction of (0,0) ?

For example:

Point a (0,0)
Point b (10,0)
Point b heading = 270 degrees

This would be true this 270 degrees points right and point b is 10 units right of point a. I would probably also want this is be fuzzy somewhat, in that anything from say + or - 30 degrees would also be true, or something like this.

Does there exist any known algorithms, implemented in C++, to help me with this problem?

Thanks!
Alex

Quote:

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Originally Posted by aseminov

For example:

Point a (0,0)
Point b (10,0)
Point b heading = 270 degrees

This would be true this 270 degrees points right and point b is 10 units right of point a.

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I don't quite get your definition of heading. With a heading of 270 degrees point b is headed straight south isn't it? It means it must be somewhere on the positive y-axis to be going towards a, like at (0,10) or something.

The problem itself is basic trigonometry: Determine the heading of the vector starting at b ending at a. That's the heading b must have to end up at a (travelling along a straight line).

Quote:

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I don't quite get your definition of heading. With a heading of 270 degrees point b is headed straight south isn't it? It means it must be somewhere on the positive y-axis to be going towards a, like at (0,10) or something.

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If xX is horizontal and Y is vertical, then 10, 0 is 10 units to the right of 0,0 alnong the X axis. A 270 degree heading would be due West. And point straight to 0,0.

Quote:

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The problem itself is basic trigonometry: Determine the heading of the vector starting at b ending at a. That's the heading b must have to end up at a (travelling along a straight line).

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Absoulely!

Quote:

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Originally Posted by mlgoff

If xX is horizontal and Y is vertical, then 10, 0 is 10 units to the right of 0,0 alnong the X axis. A 270 degree heading would be due West. And point straight to 0,0.

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No, 270 degrees would not be due west, 180 would.

Making a 180 degree turn means going in the opposite direction. If you're starting at origo travelling eastward and then make a 180 degree turn you will be going westward back toward origo. 270 degrees would mean going south (as does also -90 degrees).

Understand that you are using a compass-style definition of headings, which differs from standard angular measurements used by most trig functions by direction (clockwise vs. counterclockwise) and by 90 degrees (or, pi/2 radians, since most trig functions use radians, not degrees).

With that understanding, look at the atan2() function. To get the compass heading in degrees from point b to point a, use the following:

Code:

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double compass_heading = 90.0 - 57.29578 * atan2( by-ay, bx-ax );
if (compass_heading >= 360.0)
  compass_heading -= 360.;
if (compass_heading < 0.0)
  compass_heading += 360.;

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In your case, where point a is at the origin, ay=ax=0, which simplifies the equation a bit.

To determine if the actual heading is "close enough" to the compass heading, just test against limits:

Code:

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double limit = 30.0;  /* in degrees */
double actual_heading = /* whatever */;
if ( fabs( actual_heading - compass_heading ) < limit
{
  /* it's close enough
}
else
{
  /* it's not close enough */
}

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fabs() is the floating point absolute value function.

Mike

Quote:

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Originally Posted by MikeAThon

Understand that you are using a compass-style definition of headings,

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The OP has started several threads on this topic and this best describes the actual problem I think,

http://forums.codeguru.com/showthread.php?t=523000

Thanks, nuzzle, you're right! That thread is much more complete than this one.