如何计算圆周上的一点？

Question

以下功能如何用各种语言实现？

给定输入值，计算圆周上的(x,y) 点：

• 半径
• 角度
• 来源（可选参数，如果语言支持）

Answer 1

parametric equation for a circle 是

x = cx + r * cos(a)
y = cy + r * sin(a)

其中r是半径，cx,cy是原点，a是角度。

这很容易适应任何具有基本三角函数的语言。 请注意，大多数语言将使用radians 作为三角函数中的角度，因此不是循环通过 0..360 度，而是循环通过 0..2PI 弧度。

Answer 2

这是我在 C# 中的实现：

    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);
    }

Answer 3

当你有complex numbers时谁需要触发：

#include <complex.h>
#include <math.h>

#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 ) );
}

Answer 4

在 JavaScript (ES6) 中实现：

/**
    * 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 ];

}

---

用法：

const [ x, y ] = pointsOnCircle({ radius: 100, angle: 180, cx: 150, cy: 150 });
console.log( x, y );

Codepen

/**
 * 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 + "°";
  document.querySelector("#points").textContent = x.toFixed() + "," + y.toFixed();

}, 100 );

<p>Degrees: <span id="degrees">0</span></p>
<p>Points on Circle (x,y): <span id="points">0,0</span></p>
<canvas width="200" height="200" style="border: 1px solid"></canvas>

Answer 5

在给定距离的圆周上计算点。
为了比较... 这在游戏 AI 中沿直接路径围绕固体对象移动时可能很有用。

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));
}

/// <summary>
/// Possible clock directions.
/// </summary>
public enum ClockDirection
{
    [Description("Time moving forwards.")]
    Clockwise,
    [Description("Time moving moving backwards.")]
    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 < 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($"DestinationCoordinatesArc({point.X}, {point.Y}");
    }
}

Answer 6

int x = (int)(radius * Math.Cos(degree * Math.PI / 180F)) + cCenterX;
int y = (int)(radius * Math.Sin(degree * Math.PI / 180F)) + cCenterY;

cCenterX 和 cCenterY 是圆的中心点