宇宙公式:
Xn=n/π*cost (t=0,1/2π,π,3/2π,2π)
Yn=n/π*t*sint (t=0,1/2π,π,3/2π,2π)
Zn=n/π*t (t=0,1/2π,π,3/2π,2π)
un=u_n-1+sin(t+m)
(t=0,1/2π,π,3/2π,2π,
m值
0.125概率是0,
0.125概率是1/2π,
0.125概率是π,
0.125概率是3/2π,
0.5的概率是没有叠加波,sin(t+m)是0,un=u_n-1就是保持上一轮波形以下是一个使用Unity3D和C#实现的程序,用于根据给定的公式创建一个螺旋形状:
unity3D程序:
```csharp
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
public class SpiralGenerator : MonoBehaviour
{
public int numberOfPoints = 100;
public float scale = 1f;
public GameObject pointPrefab;
private void Start()
{
GenerateSpiral();
}
private void GenerateSpiral()
{
float t;
float m;
float probability;
float un = 0;
for (int n = 0; n < numberOfPoints; n++)
{
t = 2 * Mathf.PI * n / (numberOfPoints - 1);
probability = Random.value;
if (probability < 0.125f)
{
m = 0;
}
else if (probability < 0.25f)
{
m = 1 / (2 * Mathf.PI);
}
else if (probability < 0.375f)
{
m = Mathf.PI;
}
else if (probability < 0.5f)
{
m = 3 / (2 * Mathf.PI);
}
else
{
m = 0;
un = un - Mathf.Sin(t + m);
}
float Xn = n / Mathf.PI * Mathf.Cos(t);
float Yn = n / Mathf.PI * t * Mathf.Sin(t);
float Zn = n / Mathf.PI * t;
Vector3 position = new Vector3(Xn, Yn, Zn) * scale;
Instantiate(pointPrefab, position, Quaternion.identity, transform);
}
}
}
```
将此脚本添加到Unity场景中的空游戏对象上,并将一个表示螺旋点的预制件(例如一个小球体)分配给`pointPrefab`变量。脚本将在场景中生成螺旋形状。你可以通过调整`numberOfPoints`和`scale`变量来控制螺旋的精细程度和大小。