点到某三角形的最短距离

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class MathPoint2Panel : MonoBehaviour
{
    public Vector3 p1 = Vector3.zero;
    public Vector3 p2 = new Vector3(50, 0, 0);
    public Vector3 p3 = new Vector3(50, 0, 50);

    public Transform point;
    public Vector3 pt = Vector3.zero;

    public float t0;
    public float t1;

    public float test1;
    public Vector3 docNormal;

    public void Update()
    {
        Debug.DrawLine(transform.position + p1, transform.position + p2);
        Debug.DrawLine(transform.position + p2, transform.position + p3);
        Debug.DrawLine(transform.position + p3, transform.position + p1);
        
        Vector3 pa = transform.position + p1;
        Vector3 pb = transform.position + p2;
        Vector3 pc = transform.position + p3;

        // [V0, V1]
        Vector3 V0 = pb - pa;
        Vector3 V1 = pc - pa;
        // Pt = pa + (V0 * t0 + V1 * t1) // 任意一点都能如此表达

        Vector3 p = point.position;


        // p - pt = p - pa - (V0 * t0 + V1 * t1) 
        // 法向量于V0基 垂直 为 0
        // Vector3.Dot(p - pt, V0) = 0  
        // Vector3.Dot(p - pt, V1) = 0
        // (p - pa) * V0 = V0 * V0 * t0 + V1 * V0 * t1 
        // (p - pa) * V1 = V0 * V1 * t0 + V1 * V1 * t1 
        // Pt = P0 + t0 * v0 + t1 * v1 

        float A = Vector3.Dot((p - pa) , V0);
        float B = Vector3.Dot((p - pa) , V1);
        float C = Vector3.Dot(V1, V0);
        float D = Vector3.Dot(V0, V1);
        float E = Vector3.Dot(V0, V0);
        float F = Vector3.Dot(V1, V1);

        // A = V0 * V0 * t0 + V1 * V0 * t1 
        // B = V0 * V1 * t0 + V1 * V1 * t1 

        // A = E * t0 + C * t1;
        // B = D * t0 + F * t1;
        // t0 = (A - C * t1) / E;

        // B = D * (A - C * t1) / E + F * t1;
        // B * E = D * (A - C * t1) + F * E * t1;
        // B * E - D * A = F * E * t1 - D * C * t1 ;

        t1 = (B * E - D * A) / (F * E - C * D);
        t0 = (A - C * t1) / E;
		
		// 判断是否在三角形内
        if (t0 >= 0 && t0 <= 1 && t1 >= 0 && t1 <= 1 && t0 + t1 < 1)
        {
            pt = pa + (t0 * V0 + t1 * V1);  // 带入公式
        }
        else
        {
            Vector3 closed1 = Vector3.zero;
            Vector3 closed2 = Vector3.zero;
            Vector3 closed3 = Vector3.zero;
			
			// 分别求出对三条边的最短距离
            float c1 = FindDistance2Segment(p, pa, pb, out closed1);
            float c2 = FindDistance2Segment(p, pa, pc, out closed2);
            float c3 = FindDistance2Segment(p, pb, pc, out closed3);

            float min = Mathf.Min(c1, c2, c3);

            if (min == c1)
            {
                pt = closed1;
            }
            else if(min == c2)
            {
                pt = closed2;
            }
            else
            {
                pt = closed3;
            }
        }

        Debug.DrawLine(pt, p);
    }

    private float FindDistance2Segment(Vector3 pt, Vector3 p1, Vector3 p2, out Vector3 closedP)
    {
        //float radio = projection / segmentLength;
        Vector3 vSegment = p2 - p1;
        float radio = Vector3.Dot(vSegment, pt - p1) / vSegment.magnitude / vSegment.magnitude;
        if (radio <= 0)
        {
            closedP = p1;
        }
        else if (radio >= 1)
        {
            closedP = p2;
        }
        else
        {
            closedP = p1 + radio * vSegment;
        }

        return (pt - closedP).magnitude;
    }
}