Calculating the position of points in a circle

Question

I m having a bit of a mind blank on this at the moment  I ve got a problem where I need to calculate the position of points around a central point  assuming they re all equidistant from the center and from each other   The number of points is variable so it s DrawCirclePoints int x  I m sure there s a simple solution  but for the life of me  I just can t see it

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Working Solution in Java   import java awt event    import java awt Robot   public class CircleMouse       circle stuff    final static int RADIUS   100  final static int XSTART   500  final static int YSTART   500  final static int DELAYMS   1  final static int ROUNDS   5   public static void main String args           long startT   System currentTimeMillis        Robot bot   null       try           bot   new Robot          catch  Exception failed            System err println  Failed instantiating Robot      failed             int mask   InputEvent BUTTON1 DOWN MASK       int howMany   360   ROUNDS      while  howMany  gt  0            int x   getX howMany           int y   getY howMany           bot mouseMove x  y           bot delay DELAYMS           System out println  x     x     y     y           howMany--             long endT   System currentTimeMillis        System out println  Duration       endT - startT                    param angle               in degree     return     private static int getX int angle        double radians   Math toRadians angle       Double x   RADIUS   Math cos radians    XSTART      int result   x intValue         return result                 param angle               in degree     return     private static int getY int angle        double radians   Math toRadians angle       Double y   RADIUS   Math sin radians    YSTART      int result   y intValue         return result

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A point at angle theta on the circle whose centre is  x0 y0  and whose radius is r is  x0   r cos theta  y0   r sin theta   Now choose theta values evenly spaced between 0 and 2pi

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PHP Solution     class point      private  x   0      private  y   0      public function setX  xpos            this- gt x    xpos            public function setY  ypos            this- gt y    ypos            public function getX            return  this- gt x            public function getY            return  this- gt y            public function printX            echo  this- gt x            public function printY            echo  this- gt y              function drawCirclePoints  points   radius   amp  center        pointarray   array         slice    2 pi     points      for  i 0  i lt  points  i              angle    slice  i           newx    int   center- gt getX       radius   cos  angle              newy    int   center- gt getY       radius   sin  angle              point   new point             point- gt setX  newx            point- gt setY  newy           array push  pointarray  point             return  pointarray

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Given a radius length r and an angle t in radians and a circle s center  h k   you can calculate the coordinates of a point on the circumference as follows  this is pseudo-code  you ll have to adapt it to your language    float x   r cos t    h  float y   r sin t    k

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Based on the answer above from Daniel  here s my take using Python3   import numpy   def circlepoints points radius center       shape          slice   2   3 14   points     for i in range points           angle   slice   i         new x   center 0    radius numpy cos angle          new y   center 1    radius numpy sin angle           p    new x new y          shape append p       return shape  print circlepoints 100 20  0 0

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Placing a number in a circular path    variable  let number   12     how many number to be placed let size   260     size of circle i e  w   h   260 let cx  size 2     center of x in a circle  let cy   size 2     center of y in a circle  let r   size 2     radius of a circle  for let i 1  i lt  number  i        let ang   i  Math PI  number 2      let left   cx    r Math cos ang      let top   cy    r Math sin ang      console log  quot top   quot   top   quot   left   quot   left

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The angle between each of your points is going to be 2Pi x so you can say that for points n  0 to x-1 the angle from a defined 0 point is 2nPi x   Assuming your first point is at  r 0   where r is the distance from the centre point  then the positions relative to the central point will be   rCos 2nPi x  rSin 2nPi x

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Here is how I found out a point on a circle with javascript  calculating the angle  degree  from the top of the circle     const centreX   50     centre x of circle   const centreY   50     centre y of circle   const r   20     radius   const angleDeg   45     degree in angle from top   const radians   angleDeg    Math PI 180     const pointY   centreY -  Math cos radians    r      specific point y on the circle for the angle   const pointX   centreX    Math sin radians    r      specific point x on the circle for the angle

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Using one of the above answers as a base  here s the Java Android example   protected void onDraw Canvas canvas        super onDraw canvas        RectF bounds   new RectF canvas getClipBounds         float centerX   bounds centerX        float centerY   bounds centerY         float angleDeg   90f      float radius   20f      float xPos   radius    float Math cos Math toRadians angleDeg     centerX      float yPos   radius    float Math sin Math toRadians angleDeg     centerY         draw my point at xPos yPos

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Here is an R version based on the  Pirijan answer above   points  lt - 8 radius  lt - 10 center x  lt - 5 center y  lt - 5  drawCirclePoints  lt - function points  radius  center x  center y      slice  lt - 2   pi   points   angle  lt - slice   seq 0  points  by   1     newX  lt - center x   radius   cos angle    newY  lt - center y   radius   sin angle     plot newX  newY     drawCirclePoints points  radius  center x  center y

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Here s a solution using C    void DrawCirclePoints int points  double radius  Point center        double slice   2   Math PI   points      for  int i   0  i  lt  points  i                  double angle   slice   i          int newX    int  center X   radius   Math Cos angle            int newY    int  center Y   radius   Math Sin angle            Point p   new Point newX  newY           Console WriteLine p             Sample output from DrawCirclePoints 8  10  new Point 0 0       X 10 Y 0   X 7 Y 7   X 0 Y 10   X -7 Y 7   X -10 Y 0   X -7 Y -7   X 0 Y -10   X 7 Y -7    Good luck

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I had to do this on the web  so here s a coffeescript version of  scottyab s answer above   points   8 radius   10 center    x  0  y  0   drawCirclePoints    points  radius  center  - gt    slice   2   Math PI   points   for i in  0   points      angle   slice   i     newX   center x   radius   Math cos angle      newY   center y   radius   Math sin angle      point    x  newX  y  newY      console log point  drawCirclePoints points  radius  center

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For the sake of completion  what you describe as  position of points around a central point assuming they re all equidistant from the center   is nothing but  Polar Coordinates   And you are asking for way to Convert between polar and Cartesian coordinates which is given as x   r cos t   y   r sin t

[algorithm] Calculating the position of points in a circle

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