在 Unity 中计算点在圆上以一定角度垂直于直线的给定距离

Question

我制作了一个模型来说明我要计算的内容。给定两个锚点之间的一条线（向量），我想将一个或多个游戏对象放置在与该向量的中点相切的一定距离处，并沿垂直于向量的圆以指定的角度（弧度？）放置。

在这个插图中，一个假想的圆放置在中点并垂直于 Anchor 1 和 Anchor 2 之间的线。我想计算三个点（P1、P2 和 P3）的 Vector3 位置。目的是在每个点放置对象。整个组件将是一个可以在空间中旋转的游戏对象。 （将有一个游戏对象，每个对象都有一个子对象。）

我搜索了 StackOverflow 和 Unity 社区，但找不到可以帮助我做出这三个展示位置的示例。

有什么想法吗？

Answer 1

考虑向量数学和四元数，而不是三角。使用叉积找到 0 角度偏移和四元数根据角度旋转它。解释见 cmets。

public void PlaceObjects(Transform anchor1, Transform anchor2, float r, 
        List<Transform> objs, List<float> angles)
{
    // lists must be non-null and same size
    Debug.Assert(objs != null);
    Debug.Assert(angles != null);
    Debug.Assert(objs.Count == angles.Count);
 
    // Find midpoint and axis of rotation   
    Vector3 midpoint = 0.5f * (anchor1.position + anchor2.position);
    Vector3 axis = (anchor2.position - anchor1.position).normalized;

    // What direction should the the "zero" offset be based on? 
    // Base it on the local up of the "assembly parent" this script is attached to?
    // or Vector3.up if "0 angle" should approximate world up?
    Vector3 upDirection = transform.up;

    // Of directions perpendicular to the axis find the closest to upDirection
    // See https://stackoverflow.com/a/57698547/1092820 for more information
    Vector3 axisRight = Vector3.Cross(upDirection, axis);

    if (axisRight == Vector3.zero) 
    {
        // upDirection & axis are colinear, no unique "up-ish" exists.
        // Just give up and don't move anything.
        return;
    }

    Vector3 zeroOffsetDir = Vector3.Cross(axis, axisRight);

    for (int i = 0 ; i < objs.Count ; i++)
    {
        Transform obj = objs[i];
        float angle = angles[i];
 
        // Find a rotation that describes how to rotate a "0 angle" offset into the one 
        // the current object needs
        Quaternion rot = Quaternion.AngleAxis(angle, axis); 
     
        // Find the offset by rotating the "zero" offset, then extending it by the radius
        Vector3 offset = r * (rot * zeroOffsetDir);

        // Set the object's position based on its offset and the location of the midpoint
        obj.position = midpoint + offset;

        // Optionally, set the object's rotation based on its current forward and the new up:
        // obj.rotation = Quaternion.LookRotation(obj.forward, offset);
    }
}

Answer 2

对于那些感兴趣的人，这是我对@Ruzihm 解决方案的组件改编。 PlaceObjectsOnCirclePerpendicularToVectorLine 组件被放置在一个空的游戏对象上。

using System.Collections.Generic;
using UnityEngine;

public class PlaceObjectsOnCirclePerpendicularToVectorLine : MonoBehaviour
{
    // Adapted from https://stackoverflow.com/a/63308834/13052746, by Ruzihm.

    public Transform anchor1;
    public Transform anchor2;
    public float radius;
    public List<Transform> objs;
    public List<float> angles;

    private Vector3 anchor1PriorPosition;
    private Vector3 anchor2PriorPosition;

    // Start is called before the first frame update
    void Start()
    {
        PlaceObjects(
            anchor1,
            anchor2,
            radius,
            objs,
            angles);
    }

    // Update is called once per frame
    void Update()
    {
        PlaceObjects(
            anchor1,
            anchor2,
            radius,
            objs,
            angles);
    }

    public void PlaceObjects(
        Transform anchor1, 
        Transform anchor2, 
        float radius,
        List<Transform> objs, 
        List<float> angles)
    {

        if (anchor1PriorPosition == anchor1.position &&
            anchor2PriorPosition == anchor2.position)
        {
            // The anchors haven't moved.
            return;
        } else
        {
            anchor1PriorPosition = anchor1.position;
            anchor2PriorPosition = anchor2.position;
        }

        // lists must be non-null and same size
        Debug.Assert(objs != null);
        Debug.Assert(angles != null);
        Debug.Assert(objs.Count == angles.Count);

        // Find midpoint and axis of rotation   
        Vector3 midpoint = 0.5f * (anchor1.position + anchor2.position);
        Vector3 axis = (anchor2.position - anchor1.position).normalized;

        // What direction should the the "zero" offset be based on? 
        // Base it on the local up of the "assembly parent" this script is attached to?
        // or Vector3.up if "0 angle" should approximate world up?
        Vector3 upDirection = transform.up;

        // Of directions perpendicular to the axis find the closest to upDirection
        // See https://stackoverflow.com/a/57698547/1092820 for more information
        Vector3 axisRight = Vector3.Cross(upDirection, axis);

        //if (axisRight == Vector3.zero)
        //{
        //    // upDirection & axis are colinear, no unique "up-ish" exists.
        //    // Just give up and don't move anything.
        //    return;
        //}

        Vector3 zeroOffsetDir = Vector3.Cross(axis, axisRight);

        for (int i = 0; i < objs.Count; i++)
        {
            Transform obj = objs[i];
            float angle = angles[i];

            // Find a rotation that describes how to rotate a "0 angle" offset into the one 
            // the current object needs
            Quaternion rot = Quaternion.AngleAxis(angle, axis);

            // Find the offset by rotating the "zero" offset, then extending it by the radius
            Vector3 offset = radius * (rot * zeroOffsetDir);

            // Set the object's position based on its offset and the location of the midpoint
            obj.position = midpoint + offset;
        }
    }
}

这是场景视图中的样子：

下面是组件在检查器中的样子：

再次，精彩，@Ruzihm！正是我想要的！