Trigonometry in NetLogo

There are significant differences between the basis and results of the standard trigonometric functions, such as implemented in other languages, and as implemented in Netlogo.

The differences are designed to make working with these functions easier and more intuitive for students and other modelers who are not familiar with traditional trigonometry.

There are also helper reporters designed to make certain difficult trig problems easier.

• Input and output angles are always in degrees, not radians.
• Zero degrees is at north/up/top-dead-center, NOT east/left
• Angles increase clockwise, not widdershins

Given a point with coordinates x and y and the heading h from the origin to that point, some useful things to know:

• The heading is measured clockwise from north.
• The distance from the origin to (x,y) is given by (DISTANCEXY x y)
• x = ( sin h ) * distancexy x y ;; if abs x ⇐ 1.0, then x = sin h
• y = ( cos h ) * distancexy x y ;; if abs y ⇐ 1.0, then y = cos h
• atan x y = h (see note below)
• x / y = tan h
• towardsxy x y = h (see note)

• HEADING is the angle toward which the turtle's “nose” is pointing.
  • it is the direction that the turtle will move as a result of JUMP or FORWARD or FD
  • it is the direection the turtle will look when it uses PATCH-AHEAD and IN-CONE
• DX and DY reporters report the X and Y component of the unit vector with the turtle's heading.
  • In other words, they give the relative coordinates of a point that is 1 unit from the turtle's location, in the direction the turtle is facing.
  • In other words, (xcor + dx) (ycor + dy) are the new coordinates of the turtle, if it does JUMP 1.

• dx = sin heading
• dy = cos heading
• atan dx dy = heading
• dx / dy = tan heading

Note that the NetLogo atan reporter is quadrant-aware, that is, it accepts negative inputs, and reports the correct 0 to 360 degree heading. If both x and y are zero, a run-time error occurs.

With towards or towardsxy, if the target location is the same as the current location a runtime error occurs.

E.g. “ASK TURTLES [ SET HEADING TOWARDS SELF ]” will cause a runtime error (if there are any turtles)..

With FACE or FACEXY, no action or error occurs if the target location is the same as the current location.

E.g. “ASK TURTLES [ FACE SELF ]” will not cause a runtime error, and the turtles will not change heading.