尝试使用 Equirectangular Projection 将 2D 坐标转换为 3D 坐标。但是失败了。我究竟做错了什么？

Question

目前，我正在Unity中制作一个360视频应用。我使用等距柱状投影的 Unity Skybox Panoramic shader that does equirectangular projection. Now I am trying to set some buttons on the video by some 2D points given. The 2D point system is a bit tricky and is different from the Cartesian one (my boss requested it...). The range of x-axis is from -90 (top) to 90 (bottom), and is used as vertical axis. The range of y-axis is from -180 to 180, and is used as horizontal axis. Now on the topic of calculating the 3D coordinates, I read the wiki page 成功制作了要渲染的视频，并看到了方程式。我假设 φ1 和 λ0 为零，因为没有旋转？所以计算中的λ（经度）和φ（纬度）就是y（横坐标）和-x（纵坐标）。由于经度和纬度也只是球坐标中的 θ 和 φ，我使用这个 C# 程序计算坐标：

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

public class CreateButtons : MonoBehaviour {

    public GameObject testObject;
    public Vector2 generatePositionStart;
    public Vector2 generatePositionEnd;
    public float radius = 50f;
    const float LONPERPIXEL = 3840f / 360f;

    // Use this for initialization
    void Start () {
        Vector3 pointS = GetPoint (radius, generatePositionStart.y * LONPERPIXEL, -generatePositionStart.x * LONPERPIXEL);
        GameObject start = Instantiate (testObject, pointS, Quaternion.identity) as GameObject;
        start.name = "Start";
        Vector3 pointE = GetPoint (radius, generatePositionEnd.y * LONPERPIXEL, -generatePositionEnd.x * LONPERPIXEL);
        GameObject end = Instantiate (testObject, pointE, Quaternion.identity) as GameObject;
        end.name = "End";
    }

    Vector3 GetPoint (float rho, float theta, float phi) {
        float x = rho * Mathf.Sin (theta) * Mathf.Cos (phi);
        float y = rho * Mathf.Sin (theta) * Mathf.Sin (phi);
        float z = rho * Mathf.Cos (theta);
        return new Vector3 (x, y, z);
    }
}

程序会计算按钮的两个二维坐标（左上角和右下角）。然后在 3D 位置上生成两个球体。但是，计算出的 3D 坐标不在正确的位置上。我是不是做错了什么？

P.S.: 我发现了另一个方程，它说它是一个逆映射方程。我试过了，但还是错了位置。等式如下所示：

float x = rho * Mathf.Cos (theta) * Mathf.Cos (phi);
float y = rho * Mathf.Sin (theta) * Mathf.Cos (phi);
float z = rho * Mathf.Sin (theta);

Answer 1

现在，我要回答自己了。这段代码有几个问题：

转换不需要LONPERPIXEL。
Unity Cos 和 Sin 函数使用弧度，所以 theta 和 phi 必须相乘 Mathf.Deg2Rad.
GetPoint()中的方程完全错误。

所以这里是正确的代码：

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

public class CreateButtons : MonoBehaviour {

    public GameObject testObject;
    public Vector2 generatePositionStart;
    public Vector2 generatePositionEnd;
    public float radius = 50f;

    // Use this for initialization
    void Start () {
        Vector3 pointS = GetPoint (radius, generatePositionStart.y * Mathf.Deg2Rad, -generatePositionStart.x * Mathf.Deg2Rad);
        GameObject start = Instantiate (testObject, pointS, Quaternion.identity) as GameObject;
        start.name = "Start";
        Vector3 pointE = GetPoint (radius, generatePositionEnd.y * Mathf.Deg2Rad, -generatePositionEnd.x * Mathf.Deg2Rad);
        GameObject end = Instantiate (testObject, pointE, Quaternion.identity) as GameObject;
        end.name = "End";
    }

    // Update is called once per frame
    void Update () {

    }

    Vector3 GetPoint (float rho, float theta, float phi) {
        float x = rho * Mathf.Sin (theta) * Mathf.Cos (phi);
        float y = rho * Mathf.Sin (phi);
        float z = rho * Mathf.Cos (theta) * Mathf.Cos (phi);
        return new Vector3 (x, y, z);
    }
}

尝试使用 Equirectangular Projection 将 2D 坐标转换为 3D 坐标。但是失败了。我究竟做错了什么？

Try using Equirectangular Projection to convert 2D coordinates to 3D coordinates. But failed. What am I doing wrong?

c#

projection

unity3d

360-degrees

360-panorama