c# - 如何放置最大圆环半径的圆环

我正在尝试创建一个圆圈，ala：



圆具有给定的半径circleRadius。环的最大半径为maxRingRadius。圆数可以是需要计算的任何整数circles，以及圆环的实际半径ringRadius。圆环的中心距圆环中心ringRadius单位时，应如图所示精确接触。

给定一个circleRadius和maxRingRadius，如何找到最接近（或倒数第二个）的ringRadius将适合整数circles，然后定位这些圆？

    static Vector3[] RingOfCircles(float maxRingRadius, float circleRadius) {
        //int circles = ...; // calculate this?
        //float ringRadius = ...; // calculate this?

        //Edit: Solution. These three lines are adapted from InBetween's GetNextSmallerRingRadius function but Unity3d-ized and without validation
        int circles = Mathf.RoundToInt(Mathf.PI / Mathf.Asin(circleRadius / maxRingRadius));
        float centralAngle = 2 * Mathf.PI / (numberOfCircles - 1);
        float ringRadius = circleRadius / Mathf.Sin(centralAngle / 2);

        // create ring of center points
        float radsPerCircle = (Mathf.PI * 2) / circles;
        Vector3[] centerPoints = new Vector3[circles];
        for (int i=0; i < circles; i++) {
            float angle = i * radsPerCircle;
            centerPoints[i] = new Vector3(
                Mathf.Sin(angle) * ringRadius,
                Mathf.Cos(angle) * ringRadius,
                0);
        }

        return centerPoints;
    }
`

注意：出于我的目的，maxRingRadius也可以是minRingRadius或approximateRingRadius。但是ringRadius应该定义可以容纳整数个圆的下一个最近的“环”。



解决了：

视觉确认解决方案

最佳答案

如果我正确理解了您的问题，则应该这样做：

 public static double GetNextSmallerRingRadius(double startingRingRadius, double circleRadius)
 {
     Debug.Assert(startingRingRadius >= 0);
     Debug.Assert(circleRadius > 0);

     int currentNumberOfCircles = GetCurrentNumberOfCircles(startingRingRadius, circleRadius);

     //Let's get trivial cases out of the way
     if (currentNumberOfCircles == 1)
         throw new ArgumentException();
     if (currentNumberOfCircles == 2)
         return 0; //trivial solution for 1 circle.
     if (currentNumberOfCircles == 3)
         return circleRadius; //trivial solution for 2 circles.

     double centralAngle = 2 * Math.PI / (currentNumberOfCircles - 1);
     return circleRadius / Math.Sin(centralAngle / 2);
 }

 public static double GetNextLargerRingRadius(double startingRingRadius, double circleRadius)
 {
     Debug.Assert(startingRingRadius >= 0);
     Debug.Assert(circleRadius > 0);

     int currentNumberOfCircles = GetCurrentNumberOfCircles(startingRingRadius, circleRadius);

     //Let's get trivial cases out of the way
     if (currentNumberOfCircles == 1)
         return circleRadius; //trivial solution for 2 circles.

     double centralAngle = 2 * Math.PI / (currentNumberOfCircles + 1);
     return circleRadius / Math.Sin(centralAngle / 2);
 }

 private static int GetCurrentNumberOfCircles(double startingRingRadius, double circleRadius)
 {
     if (startingRingRadius == 0)
     {
         return 1;
     }
     else
     {
         return (int)Math.Round(Math.PI / Math.Asin(circleRadius / startingRingRadius), 0); //There would need to be some logic to make sure input values are correct.
     }
 }

要验证输入（定义的半径代表有效的解决方案），您可以比较舍入的和未舍入的numberOfcircles，并确保差值在给定的公差范围内。请记住，使用double不能检查是否相等，因为始终会出现表示错误。

更新糟糕，我没有看到您也在询问有关放置圆圈的问题。一旦您知道了环的半径和圆心角，就非常简单了。

关于c# - 如何放置最大圆环半径的圆环，我们在Stack Overflow上找到一个类似的问题：https://stackoverflow.com/questions/26255590/