BarycentricCoordinates.cs

BarycentricCoordinates.cs

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

// https://rhetty.github.io/2018/03/20/三角形线性插值——重心坐标/
// https://zh.wikipedia.org/wiki/笛卡尔坐标系
// https://en.wikipedia.org/wiki/Barycentric_coordinate_system

public struct BarycentricCoordinates
{
    private Vector2 _a, _b, _c; // 三角形
    private float _s; // 三角形面积

    public bool IsTriangle { get; private set; }

	public void SetTriangle(Vector2 a, Vector2 b, Vector2 c)
    {
        _a = a;
        _b = b;
        _c = c;

        IsTriangle = a != b && a != c && b != c;
        if (IsTriangle)
            _s = CalcS(a, b, c);
    }

    // 计算P点的重心坐标
    public Vector3 CalcBarycentricPos(Vector2 p)
    {
        var sa = CalcS(p, _b, _c);
        var sb = CalcS(p, _c, _a);
        var sc = CalcS(p, _a, _b);
        return new Vector3(sa / _s, sb / _s, sc / _s);
    }

    // 计算P点的笛卡尔坐标
    public Vector2 CalcCartesianPos(Vector3 v)
    {
        return v.x * _a + v.y * _b + v.z * _c;
    }

    public static bool InTriangle(Vector3 v)
    {
        return v.x >= 0 && v.x <= 1
            && v.y >= 0 && v.y <= 1
            && v.z >= 0 && v.z <= 1;
    }

    private static float CalcS(Vector2 a, Vector2 b, Vector3 c)
    {
        // 1  ax  ay
        // 1  bx  by
        // 1  cx  cy
        var s = b.x * c.y + a.x * b.y + c.x * a.y - c.x * b.y - b.x * a.y - a.x * c.y;
        return s * 0.5f;
    }

}