Question

我试图创建一个圆圈，ala：

圆圈的半径为circleRadius。环的最大半径为maxRingRadius。圆圈的数量可以是任意整数，circles，需要计算，以及环的实际半径ringRadius。当圆圈从圆环中心放置ringRadius单位时，圆圈应该完全接触，如图所示。

给定circleRadius和maxRingRadius，如何找到最接近（或次最小）ringRadius的{{1}}整数，然后circles定位那些圈子？

    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：maxRingRadius也可以minRingRadius或approximateRingRadius用于我的目的。但是ringRadius应该定义下一个最近的＆＃39;这可以容纳一大堆圈子。

解决： A visual confirmation of the solution 视觉确认解决方案

Answer 1

如果我理解你的问题，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），您可以比较舍入而不是舍入的numberOfcircles，并确保差异在给定的容差范围内。请记住，使用double，您无法检查是否存在相等性，因为始终存在表示错误。

更新糟糕，我没有看到你也在询问有关定位圈子的问题。一旦你知道了环半径和中心角，它就非常简单。

如何定位具有最大环半径的圆环

1 个答案: