当你有复数的时候谁还需要三角函数

#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 ) );
}

当你有复数的时候谁还需要三角函数

#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 ) );
}

在给定的距离下计算圆周上的点。 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。

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}");
    }
}

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

圆的参数方程是

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

r是半径，cx cy是原点，a是角度。

这很容易适应任何带有基本三角函数的语言。请注意，大多数语言会在三角函数中使用弧度作为角度，因此，而不是在0..360度，你在0。2π弧度。

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);
}