How do I calculate a point on a circle s circumference

Question

How can the following function be implemented in various languages   Calculate the  x y  point on the circumference of a circle  given input values of    Radius Angle Origin  optional parameter  if supported by the language

User · Answer

Who needs trig when you have complex numbers    include  lt complex h gt   include  lt math h gt    define PI      3 14159265358979323846  typedef complex double Point   Point point on circle   double radius  double angle in degrees  Point centre         return centre   radius   cexp   PI   I     angle in degrees    180 0

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Calculating point around circumference of circle given distance travelled  For comparison    This may be useful in Game AI when moving around a solid object in a direct path   public static Point DestinationCoordinatesArc Int32 startingPointX  Int32 startingPointY      Int32 circleOriginX  Int32 circleOriginY  float distanceToMove      ClockDirection clockDirection  float radius           Note  distanceToMove and radius parameters are float type to avoid integer division        which will discard remainder      var theta    distanceToMove   radius     clockDirection    ClockDirection Clockwise   1   -1       var destinationX   circleOriginX    startingPointX - circleOriginX    Math Cos theta  -  startingPointY - circleOriginY    Math Sin theta       var destinationY   circleOriginY    startingPointX - circleOriginX    Math Sin theta     startingPointY - circleOriginY    Math Cos theta           Round to avoid integer conversion truncation     return new Point  Int32 Math Round destinationX    Int32 Math Round destinationY            lt summary gt      Possible clock directions       lt  summary gt  public enum ClockDirection        Description  quot Time moving forwards  quot        Clockwise       Description  quot Time moving moving backwards  quot        CounterClockwise    private void ButtonArcDemo Click object sender  EventArgs e        Brush aBrush    Brush Brushes Black      Graphics g   this CreateGraphics         var startingPointX   125      var startingPointY   75      for  var count   0  count  lt  62  count                  var point   DestinationCoordinatesArc              startingPointX  startingPointX  startingPointY  startingPointY              circleOriginX  75  circleOriginY  75              distanceToMove  5              clockDirection  ClockDirection Clockwise  radius  50           g FillRectangle aBrush  point X  point Y  1  1            startingPointX   point X          startingPointY   point Y              Pause to visually observe confirm clock direction         System Threading Thread Sleep 35            Debug WriteLine   quot DestinationCoordinatesArc  point X    point Y  quot

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Implemented in JavaScript  ES6             Calculate x and y in circle s circumference        param  Object  input - The input parameters        param  number  input radius - The circle s radius        param  number  input angle - The angle in degrees        param  number  input cx - The circle s origin x        param  number  input cy - The circle s origin y        returns  Array number number   The calculated x and y    function pointsOnCircle   radius  angle  cx  cy          angle   angle     Math PI   180       Convert from Degrees to Radians     const x   cx   radius   Math sin angle       const y   cy   radius   Math cos angle       return   x  y         Usage  const   x  y     pointsOnCircle   radius  100  angle  180  cx  150  cy  150     console log  x  y     Codepen  x000D   x000D         Calculate x and y in circle s circumference     param  Object  input - The input parameters     param  number  input radius - The circle s radius     param  number  input angle - The angle in degrees     param  number  input cx - The circle s origin x     param  number  input cy - The circle s origin y     returns  Array number number   The calculated x and y     function pointsOnCircle   radius  angle  cx  cy       angle   angle     Math PI   180       Convert from Degrees to Radians   const x   cx   radius   Math sin angle     const y   cy   radius   Math cos angle     return   x  y       const canvas   document querySelector  canvas    const ctx   canvas getContext  2d     function draw  x  y       ctx clearRect  0  0  canvas width  canvas height      ctx beginPath      ctx strokeStyle    orange     ctx arc  100  100  80  0  2   Math PI     ctx lineWidth   3    ctx stroke      ctx closePath       ctx beginPath      ctx fillStyle    indigo     ctx arc  x  y  6  0  2   Math PI     ctx fill      ctx closePath          let angle   0      In degrees setInterval function       const   x  y     pointsOnCircle   radius  80  angle  angle    cx  100  cy  100       console log  x  y      draw  x  y      document querySelector   degrees   innerHTML   angle     amp deg      document querySelector   points   textContent   x toFixed           y toFixed        100    x000D   lt p gt Degrees   lt span id  degrees  gt 0 lt  span gt  lt  p gt   lt p gt Points on Circle  x y    lt span id  points  gt 0 0 lt  span gt  lt  p gt   lt canvas width  200  height  200  style  border  1px solid  gt  lt  canvas gt  x000D   x000D   x000D

User · Answer

The parametric equation for a circle is  x   cx   r   cos a  y   cy   r   sin a    Where r is the radius  cx cy the origin  and a the angle   That s pretty easy to adapt into any language with basic trig functions  Note that most languages will use radians for the angle in trig functions  so rather than cycling through 0  360 degrees  you re cycling through 0  2PI radians

User · Answer

Here is my implementation in C        public static PointF PointOnCircle float radius  float angleInDegrees  PointF origin                   Convert from degrees to radians via multiplication by PI 180                 float x    float  radius   Math Cos angleInDegrees   Math PI   180F     origin X          float y    float  radius   Math Sin angleInDegrees   Math PI   180F     origin Y           return new PointF x  y

[algorithm] How do I calculate a point on a circle’s circumference?

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