DynamicCreateMesh.cs

using UnityEngine;
using System.Collections.Generic;

[RequireComponent(typeof(MeshRenderer))]
[RequireComponent(typeof(MeshFilter))]
public class DynamicCreateMesh : MonoBehaviour
{
    // 変更箇所 : Materialを保持するようにする
    [SerializeField]
    private Material _mat;
    private Mesh _mesh;
    private MeshFilter _filter;

    private List<GameObject> _points = new List<GameObject>();

    //
    private void Start()
    {
        //頂点の設定
        _mesh = new Mesh();
        _mesh.vertices = new Vector3[] {
            new Vector3 (0, 1f),
            new Vector3 (1f, -1f),
            new Vector3 (-1f, -1f),
        };
        _mesh.triangles = new int[] {
            0, 1, 2
        };

        //
        foreach (var pos in _mesh.vertices)
        {
            Debug.Log(pos);

            GameObject obj = new GameObject("point");
            obj.transform.SetParent(transform);
            obj.transform.localPosition = pos;
            _points.Add(obj);
        }

        // 修正箇所 : 各頂点に対してUV座標を設定しています
        _mesh.uv = new Vector2[] {
            new Vector2 (0.5f, 1f),
            new Vector2 (1f, 0),
            new Vector2 (0, 0),
        };

        _filter = GetComponent<MeshFilter>();
        _filter.sharedMesh = _mesh;
        
        // 変更箇所 : MeshRendererからMaterialにアクセスし、Materialをセットするようにする
        var renderer = GetComponent<MeshRenderer>();
        renderer.material = _mat;
    }

    //
    void Update()
    {
        int len = _filter.sharedMesh.vertices.Length;
        Vector3[] vec3 = new Vector3[len];
        for (int i = 0 ; i < len; i++)
        {
            vec3[i] = _points[i].transform.localPosition;
        }

        _mesh.vertices = vec3;
        
        _mesh.RecalculateNormals();
        _mesh.RecalculateBounds();
        _filter.sharedMesh = _mesh;
    }
}