如何计算圆周长上的一点?

如何在各种语言中实现以下函数?

给定以下输入值，计算圆周长上的(x,y)点:

  • 半径
  • 角
  • 起源(可选参数，如果语言支持)
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下面是我在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);
}
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最佳答案

圆的参数方程是

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

其中r是半径，残雪,cy是原点，一个是角度。

这很容易适应任何带有基本三角函数的语言。注意，大多数语言会使用radians作为三角函数中的角度，所以不是循环0..360度，你在0。2π弧度。

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当你有复数时，谁还需要三角函数:

#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 ) );
}
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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 );

< a href = " https://codepen.io/kostasx/pen/vYOxwLd?编辑= 1010 noreferrer“rel = > 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 + "&deg;";
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>

小开

给定行进距离的圆周长上的计算点 相比之下…… 这可能在游戏AI中很有用，当在一个直接路径上移动一个固体物体时

enter image description here

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}");
}
}
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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


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