计算圆中点的位置

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最佳答案

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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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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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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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!

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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;
}

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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).

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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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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)

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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 > 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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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)

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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<=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);
}

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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