在Unity中计算点一个给定的距离垂直于一条线在一个圆上的角度

Question

I crafted a model to illustrate what I am trying to calculate. Given a line (vector) between two anchor points, I want to place one or more game objects a certain distance tangential to the midpoint of that vector and at designated angles (radians?) along a circle that is perpendicular to the vector.

In this illustration, an imaginary circle is placed at midpoint and perpendicular to the line between Anchor 1 and Anchor 2. I want to calculate the Vector3 positions of three points (P1, P2, and P3). The intent is to place objects at each of those points. The entire assembly will a gameobject that can rotate in space. (There will be a single game object with each object a child.)

I have scoured StackOverflow and the Unity communities and cannot find examples that help me make those three placements.

Any ideas?

Answer 1

Instead of trig, consider vector math and quaternions. Use cross products to find the 0 angle offset and quaternions to rotate it according to the angle. See comments for explanation.

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

For those interested, here's my Component adaptation of @Ruzihm's solution. The PlaceObjectsOnCirclePerpendicularToVectorLine component is placed on an empty game object.

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;
        }
    }
}

Here's what it looks like in the Scene view:

And here's what the component looks like in the inspector:

Again, brilliant, @Ruzihm! Exactly what I wanted!