examples/polargrapher.html

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<!DOCTYPE html>
<script src="../wwwbasic.js"></script>
<script type="text/basic">
  DECLARE FUNCTION TRANSFORMX(x,y,theta,xorg)
  DECLARE FUNCTION TRANSFORMY(x,y,theta,yorg)
  DECLARE FUNCTION POLARFUNCTION(theta)
  DECLARE FUNCTION RANDOM1TO(num)

  SCREEN 8
  scaler = 2000 'number of rays to project(higher=better resolution)
  tau = 6.28318530718
  increment = tau/scaler 'subdivisions of angles
  screenheight = 200
  screenwidth = 640
  initxorigin = screenwidth/2 'origin definition
  inityorigin = screenheight/2 'origin definition
  distortionfixer = (screenwidth/screenheight)/2 'distorts x-axis to make even plane
  revolutions = 2 'number of revolutions around origin
  graphcolor = RANDOM1TO(15) 'random color of graph (1 to 15)

  FOR i = 1 to revolutions * scaler
      angle = increment*i
      x = TRANSFORMX(POLARFUNCTION(angle),0,angle,initxorigin)
      y = TRANSFORMY(-POLARFUNCTION(angle),0,angle,inityorigin) ' function negated due
      LINE (x, y)-(x, y), graphcolor                            ' to coordinate system
  NEXT i

  'Here is the linear algebra that gives these functions:

  'Rotation Matrix (https://en.wikipedia.org/wiki/Rotation_matrix)
  '      vvv
  '[ cos Θ   -sin Θ] [ x ]   [ x origin on screen ]   [ x ]
  '[               ] [   ] + [                    ] = [   ] rotated Θ radians
  '[ sin Θ    cos Θ] [ y ]   [ y origin on screen ]   [ y ] around the given origin

  FUNCTION TRANSFORMX(x,y,theta,xorg)
  TRANSFORMX = (x * COS(theta) - y * SIN(theta))*distortionfixer + xorg
  END FUNCTION

  FUNCTION TRANSFORMY(x,y,theta,yorg)
  TRANSFORMY = (x*SIN(theta) + y*COS(theta))/distortionfixer + yorg
  END FUNCTION

  FUNCTION POLARFUNCTION(theta)
    'Try uncommenting these one at a time for more cool graphs
    'POLARFUNCTION = 20*(2*theta/tau)
    'POLARFUNCTION = 80 * SIN(2.5*theta)
    'POLARFUNCTION = 80*SQR(SIN(2*theta))
    'POLARFUNCTION = 80*(SIN(theta) + (SIN(2.5*theta))^3)
    POLARFUNCTION = 80*((COS(5*theta))^2 + SIN(3*theta) + 0.3)
  END FUNCTION

  FUNCTION RANDOM1TO(num) 'returns a random number between 1 to num, inclusive
      RANDOM1TO = INT(RND()*num) + 1
  END FUNCTION
</script>