Calculating the position of points in a circle
AlgorithmMathTrigonometryGeometryAlgorithm Problem Overview
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 :)
Algorithm Solutions
Solution 1 - Algorithm
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;
Solution 2 - Algorithm
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.
Solution 3 - Algorithm
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 < 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!
Solution 4 - Algorithm
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<=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("top: ", top, ", left: ", left);
}
Solution 5 - Algorithm
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
}
Solution 6 - Algorithm
PHP Solution:
class point{
private $x = 0;
private $y = 0;
public function setX($xpos){
$this->x = $xpos;
}
public function setY($ypos){
$this->y = $ypos;
}
public function getX(){
return $this->x;
}
public function getY(){
return $this->y;
}
public function printX(){
echo $this->x;
}
public function printY(){
echo $this->y;
}
}
function drawCirclePoints($points, $radius, &$center){
$pointarray = array();
$slice = (2*pi())/$points;
for($i=0;$i<$points;$i++){
$angle = $slice*$i;
$newx = (int)($center->getX() + ($radius * cos($angle)));
$newy = (int)($center->getY() + ($radius * sin($angle)));
$point = new point();
$point->setX($newx);
$point->setY($newy);
array_push($pointarray,$point);
}
return $pointarray;
}
Solution 7 - Algorithm
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).
Solution 8 - Algorithm
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) ->
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)
Solution 9 - Algorithm
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
Solution 10 - Algorithm
Here is an R version based on the @Pirijan answer above.
points <- 8
radius <- 10
center_x <- 5
center_y <- 5
drawCirclePoints <- function(points, radius, center_x, center_y) {
slice <- 2 * pi / points
angle <- slice * seq(0, points, by = 1)
newX <- center_x + radius * cos(angle)
newY <- center_y + radius * sin(angle)
plot(newX, newY)
}
drawCirclePoints(points, radius, center_x, center_y)
Solution 11 - Algorithm
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)
Solution 12 - Algorithm
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 > 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;
}
}
Solution 13 - Algorithm
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]))