Unity Mesh(七) Mesh給球貼圖

之前在  

Unity Mesh(三) Mesh畫球

   中已經說明了如何畫球，現在我們在這個球的基礎上貼圖。

          這裏我們有個極座標和直角座標的轉換，具體我也不是很明白，反正就是拿來用吧，據某位大神講解，極座標（球座標）由球半徑，水平角和垂直角決定，我們完全可以理解爲三維座標轉換成uv座標的方程，也就是三維座標映射到uv座標上，f(u,v)=[x,y,z]這樣的一個映射關係，映射關係取決於函數具體怎麼定義的或者這個球是怎麼畫的，不同的模型有不同的方法，典型的克萊因瓶一個uv完整的模型，它有自己的函數。

好了，樓主還是參考的Jasper Flick的方法，這個大神一直很崇拜。

f(u,v)=[x,y,z]

u=asin(y) / π + ½.

v=atan2(x, z) / -2π

unity自帶的球貼圖會在兩個極點出現扭曲Twisting的現象：

包括我們之前建立的球也沒有考慮到這一個點，原因是計算極點的座標時，極點只有一個座標，但是極點每個四分之一圓實際上是我們極點四個三角形公用了一個uv座標，這樣就會造成扭曲現象，解決方法是我們把極點的點拆分成四個相同的點，一個面一個。

這樣的話，我們之前畫球的點稍稍有改動，上下兩個極點分別加三個點。

這樣這個問題就解決了！

下面我們直接上圖：

這個最後的完整代碼如下：

using UnityEngine;
using System.Collections;

[RequireComponent(typeof(MeshFilter), typeof(MeshRenderer))]
public class DrawOctahedronSphere : MonoBehaviour
{
    public Material mat;

    public int subdivisions;
    public int radius;

    private static Vector3[] directions = {
        Vector3.left,
        Vector3.back,
        Vector3.right,
        Vector3.forward
    };

    void Start()
    {
        DrawSphere(subdivisions, radius);
    }

    public void DrawSphere(int subdivisions = 0, float radius = 1)
    {
        if (subdivisions > 4)
        {
            subdivisions = 4;
        }

        gameObject.GetComponent<MeshRenderer>().material = mat;

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

        int resolution = 1 << subdivisions;
        Vector3[] vertices = new Vector3[(resolution + 1) * (resolution + 1) * 4 - 3 * (resolution * 2 - 1)];
        int[] triangles = new int[(1 << (subdivisions * 2 + 3)) * 3];
        CreateOctahedron(vertices, triangles, resolution);

        if (radius != 1f)
        {
            for (int i = 0; i < vertices.Length; i++)
            {
                vertices[i] *= radius;
            }
        }

        Vector3[] normals = new Vector3[vertices.Length];
        Normalize(vertices, normals);

        Vector2[] uv = new Vector2[vertices.Length];
        CreateUV(vertices, uv);

        
        mesh.vertices = vertices;
        mesh.triangles = triangles;
        mesh.normals = normals;
        mesh.uv = uv;
    }

    private static void CreateOctahedron(Vector3[] vertices, int[] triangles, int resolution)
    {
        int v = 0, vBottom = 0, t = 0;

        for (int i = 0; i < 4; i++)
        {
            vertices[v++] = Vector3.down;
        }

        for (int i = 1; i <= resolution; i++)
        {
            float progress = (float)i / resolution;
            Vector3 from, to;
            vertices[v++] = to = Vector3.Lerp(Vector3.down, Vector3.forward, progress);
            for (int d = 0; d < 4; d++)
            {
                from = to;
                to = Vector3.Lerp(Vector3.down, directions[d], progress);
                t = CreateLowerStrip(i, v, vBottom, t, triangles);
                v = CreateVertexLine(from, to, i, v, vertices);
                vBottom += i > 1 ? (i - 1) : 1;
            }
            vBottom = v - 1 - i * 4;
        }

        for (int i = resolution - 1; i >= 1; i--)
        {
            float progress = (float)i / resolution;
            Vector3 from, to;
            vertices[v++] = to = Vector3.Lerp(Vector3.up, Vector3.forward, progress);
            for (int d = 0; d < 4; d++)
            {
                from = to;
                to = Vector3.Lerp(Vector3.up, directions[d], progress);
                t = CreateUpperStrip(i, v, vBottom, t, triangles);
                v = CreateVertexLine(from, to, i, v, vertices);
                vBottom += i + 1;
            }
            vBottom = v - 1 - i * 4;
        }

        for (int i = 0; i < 4; i++)
        {
            triangles[t++] = vBottom;
            triangles[t++] = v;
            triangles[t++] = ++vBottom;
            vertices[v++] = Vector3.up;
        }
    }

    private static int CreateVertexLine(Vector3 from, Vector3 to, int steps, int v, Vector3[] vertices)
    {
        for (int i = 1; i <= steps; i++)
        {
            vertices[v++] = Vector3.Lerp(from, to, (float)i / steps);
        }
        return v;
    }

    private static int CreateLowerStrip(int steps, int vTop, int vBottom, int t, int[] triangles)
    {
        for (int i = 1; i < steps; i++)
        {
            triangles[t++] = vBottom;
            triangles[t++] = vTop - 1;
            triangles[t++] = vTop;

            triangles[t++] = vBottom++;
            triangles[t++] = vTop++;
            triangles[t++] = vBottom;
        }
        triangles[t++] = vBottom;
        triangles[t++] = vTop - 1;
        triangles[t++] = vTop;
        return t;
    }

    private static int CreateUpperStrip(int steps, int vTop, int vBottom, int t, int[] triangles)
    {
        triangles[t++] = vBottom;
        triangles[t++] = vTop - 1;
        triangles[t++] = ++vBottom;
        for (int i = 1; i <= steps; i++)
        {
            triangles[t++] = vTop - 1;
            triangles[t++] = vTop;
            triangles[t++] = vBottom;

            triangles[t++] = vBottom;
            triangles[t++] = vTop++;
            triangles[t++] = ++vBottom;
        }
        return t;
    }


    private static void Normalize(Vector3[] vertices, Vector3[] normals)
    {
        for (int i = 0; i < vertices.Length; i++)
        {
            normals[i] = vertices[i] = vertices[i].normalized;
        }
    }

    private static void CreateUV(Vector3[] vertices, Vector2[] uv)
    {
        float previousX = 1f;
        for (int i = 0; i < vertices.Length; i++)
        {
            Vector3 v = vertices[i];
            if (v.x == previousX)
            {
                uv[i - 1].x = 1f;
            }
            previousX = v.x;
            Vector2 textureCoordinates;
            textureCoordinates.x = Mathf.Atan2(v.x, v.z) / (-2f * Mathf.PI);
            if (textureCoordinates.x < 0f)
            {
                textureCoordinates.x += 1f;
            }
            textureCoordinates.y = Mathf.Asin(v.y) / Mathf.PI + 0.5f;
            uv[i] = textureCoordinates;
        }
        uv[vertices.Length - 4].x = uv[0].x = 0.125f;
        uv[vertices.Length - 3].x = uv[1].x = 0.375f;
        uv[vertices.Length - 2].x = uv[2].x = 0.625f;
        uv[vertices.Length - 1].x = uv[3].x = 0.875f;
    }
}