Find closest point in triangle to point?

Questions & Answers
1

Is there an easy way to find the closest point in triangle to triangle?

Step 1: Get the triangle index and add a plane to the three vertices.

Step 2: Use Vector3.ProjectOnPlane to put a point on the plane.

Step 3: Use cross products with the three vertices and the point.

Step 4: If the point is on a side inside the triangle then bool is true.

This seems to work, but I don’t know how to get true if the point is in one triangle or false if none.

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

public class PointOnPlaneInTriangle : MonoBehaviour
{
    public bool PointIn;

    private Vector3 Point;

    private Vector3 CamPos;

    public List<Plane> Planes = new List<Plane>();

    // Start is called before the first frame update
    void Start()
    {
        
    }

    // Update is called once per frame
    void Update()
    {
        CamPos = Camera.main.transform.position;

        Mesh mesh = GetComponent<MeshFilter>().sharedMesh;

        var triangles = mesh.triangles;
        var vertices = mesh.vertices;

        for (int i = 0; i < triangles.Length; i += 3)
        {
            Vector3 p1 = vertices[triangles[i + 0]];
            Vector3 p2 = vertices[triangles[i + 1]];
            Vector3 p3 = vertices[triangles[i + 2]];

            Vector3 tp1 = transform.TransformPoint(p1);
            Vector3 tp2 = transform.TransformPoint(p2);
            Vector3 tp3 = transform.TransformPoint(p3);

            Planes.Add(new Plane(tp1, tp2, tp3));

            for (int e = 0; e < Planes.Count; ++e)
            {
                Point = Vector3.ProjectOnPlane(CamPos, Planes[e].normal);
            }

            Vector3 Side1P1 = Vector3.Cross(tp1 - tp2, Point - tp1).normalized;
            Vector3 Side1P2 = Vector3.Cross(tp1 - tp2, tp3 - tp1).normalized;

            Vector3 Side2P1 = Vector3.Cross(tp2 - tp3, Point - tp2).normalized;
            Vector3 Side2P2 = Vector3.Cross(tp2 - tp3, tp1 - tp2).normalized;

            Vector3 Side3P1 = Vector3.Cross(tp3 - tp1, Point - tp3).normalized;
            Vector3 Side3P2 = Vector3.Cross(tp3 - tp1, tp2 - tp3).normalized;

            if (Vector3.Dot(Side1P1, Side1P2) >= 0 && Vector3.Dot(Side2P1, Side2P2) >= 0 && Vector3.Dot(Side3P1, Side3P2) >= 0)
            {
                PointIn = true;
            }
            else
            {
                PointIn = false;
            }

            Debug.Log(PointIn);
        }
    }
}
2

Found this.

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

public class PointOnPlaneInTriangle : MonoBehaviour
{
    public bool PointIn;

    private Vector3 Point;

    private Vector3 CamPos;

    public List<Plane> Planes = new List<Plane>();

    // Start is called before the first frame update
    void Start()
    {
        
    }

    // Update is called once per frame
    void Update()
    {
        CamPos = Camera.main.transform.position;

        Mesh mesh = GetComponent<MeshFilter>().sharedMesh;

        int[] triangles = mesh.triangles;
        Vector3[] vertices = mesh.vertices;

        for (int i = 0; i < triangles.Length; i += 3)
        {
            Vector3 p1 = vertices[triangles[i + 0]];
            Vector3 p2 = vertices[triangles[i + 1]];
            Vector3 p3 = vertices[triangles[i + 2]];

            Vector3 tp1 = transform.TransformPoint(p1);
            Vector3 tp2 = transform.TransformPoint(p2);
            Vector3 tp3 = transform.TransformPoint(p3);

            Planes.Add(new Plane(tp1, tp2, tp3));

            for (int e = 0; e < Planes.Count; ++e)
            {
                Point = Vector3.ProjectOnPlane(CamPos, Planes[e].normal);
            }

            //Point in triangle test: blackpawn.com/texts/pointinpoly

            // Compute vectors
            Vector3 v0 = tp3 - tp1;
            Vector3 v1 = tp2 - tp1;
            Vector3 v2 = Point - tp1;

            // Compute dot products
            float dot00 = Vector3.Dot(v0, v0);
            float dot01 = Vector3.Dot(v0, v1);
            float dot02 = Vector3.Dot(v0, v2);
            float dot11 = Vector3.Dot(v1, v1);
            float dot12 = Vector3.Dot(v1, v2);

            // Compute barycentric coordinates
            float invDenom = 1 / (dot00 * dot11 - dot01 * dot01);
            float u = (dot11 * dot02 - dot01 * dot12) * invDenom;
            float v = (dot00 * dot12 - dot01 * dot02) * invDenom;
	    
	        // Check if point is in triangle
            if (u >= 0 && v >= 0 && u + v < 1)
            {
                PointIn = true;
            }
            else
            {
                PointIn = false;
            }

            Debug.Log(PointIn);
        }
    }
}