DIRECTION

LOCAL DIRECTION: A direction relative to another direction.

GLOBAL DIRECTION: A direction not related to another direction, but based on a global definition with 0 defined to the right.

Positive Rotation: An angle turning counterclockwise is considered positive. This is why the numbers start at 0 to the right and turn counterclockwise around the circle back to 360 degrees

Negative Rotation: An angle turning clockwise is considered a negative turn.

GLOBAL CARTESEAN DIRECTION

UNITS: DEGREES

The graph above shows the directions for a Cartesian plane in degrees. The full circle goes starts at 0 degrees heading towards the right from the center and spins 360 degrees for a full circle.

GLOBAL QUADRANTS

UNITS: DEGREES and RADIANS

The graph above shows that the 360 degree full circle can be broken into 4 quadrants. Note: A full circle is 360 units in degrees or 2x3.14159 Radians

CONVERSION: 180 Degrees = pi radians

EXAMPLES

Given Local Angle: 40 degrees Clockwise to 90 degree axis.

Global Angle (degrees):
Starting at 90 degree axis and rotating 40 degrees clockwise (negative)
Global Angle = 90 + (-40)
Global Angle = 50 degrees

Global Angle (Radians)
50 Degrees (pi/180) = 0.87266
Global Angle = 0.87266 radians

Global Angle between 0-90 degrees: Quadrant 1

Given Local Angle: 30 degrees Clockwise to 180 degree axis.

Global Angle (degrees):
Starting at 180 degree axis and rotating 30 degrees clockwise (negative)
Global Angle = 180 + (-30)
Global Angle = 150 degrees

Global Angle (Radians)
150 Degrees (pi/180) = 2.61799
Global Angle = 2.61799 radians

Global Angle between 90-180 degrees: Quadrant 2

Given Local Angle: 30 degrees Counterclockwise to 180 degrees.

Global Angle (degrees):
Starting at 180 degree axis and rotating 30 degrees counterclockwise
Global Angle = 180 + (30)
Global Angle = 210 degrees

Global Angle (Radians)
210 Degrees (pi/180) = 3.66519
Global Angle = 3.66519 radians

Global Angle between 180-270 degrees: Quadrant 3

Given Local Angle: 20 degrees Counterclockwise to 270 degrees.

Global Angle (degrees):
Starting at 270 degree axis and rotating 20 degrees counterclockwise
Global Angle = 270 + (20)
Global Angle = 290 degrees

Global Angle (Radians)
290 Degrees (pi/180) = 5.06145
Global Angle = 5.06145 radians

Global Angle between 270-360 degrees: Quadrant 4

NOTE: DIRECTION!

Given Local Angle: 20 degrees Counterclockwise to 90 degree axis.

Global Angle (degrees):
Starting at 90 degree axis and rotating 20 degrees counterclockwise
Global Angle = 90 + (20) = 110 degree

HOWEVER: NOTE THE DIRECTION OF THE LINE!!!!
Its pointing into Quadrant 4 , not Quadrant 2.
If it was pointing outward, the direction would be 110 degrees.
Since it is pointing inward, we need to add 180 degrees!
Global Angle = 110 degrees + 180 degrees = 290 degrees

Global Angle between 270-360 degrees: Quadrant 4

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