Vector3.OrthoNormalize

描述

使向量归一化并相互正交。

归一化 normal。归一化 tangent 并确保它与 normal 正交（即它们之间的夹角为 90 度）。

其他资源: Normalize 函数。

描述

使向量归一化并相互正交。

归一化 normal。归一化 tangent 并确保它与 normal 正交。归一化 binormal 并确保它与 normal 和 tangent 都正交。

空间中的点通常用标准 XYZ 轴系统中的坐标来指定。但是，如果您将三个向量解释为“轴”，那么它们就可以被解释为“轴”，只要它们是归一化的（即，大小为 1）且正交（即，相互垂直）。

创建自己的坐标轴很有用，例如，如果您想沿任意方向缩放网格而不是仅仅沿着 XYZ 轴缩放 - 您可以在自己的坐标系中转换顶点，缩放它们，然后转换回来。通常，这种变换只沿一个轴进行，而另外两个轴要么保持不变，要么被平等对待。例如，可以通过沿一个轴向上缩放，而沿另外两个轴按比例向下缩放来对网格应用拉伸效果。这意味着，一旦第一个轴向量被指定，另外两个轴向量是什么并不重要，只要它们是归一化的且正交即可。OrthoNormalize 可用于确保第一个向量是法向量，然后为另外两个轴生成两个归一化的正交向量。

// Mesh "stretch" effect along a chosen axis.

using UnityEngine;
using System.Collections;

public class ExampleClass : MonoBehaviour
{
    // The axis and amount of scaling.
    public Vector3 stretchAxis;
    public float stretchFactor = 1.0F;

    // MeshFilter component and arrays for the original and transformed vertices.
    private MeshFilter mf;
    private Vector3[] origVerts;
    private Vector3[] newVerts;

    // Our new basis vectors.
    private Vector3 basisA;
    private Vector3 basisB;
    private Vector3 basisC;

    void Start()
    {
        // Get the Mesh Filter, then make a copy of the original vertices
        // and a new array to calculate the transformed vertices.
        mf = GetComponent<MeshFilter>();
        origVerts = mf.mesh.vertices;
        newVerts = new Vector3[origVerts.Length];
    }

    void Update()
    {
        // BasisA is just the specified axis for stretching - the
        // other two are just arbitrary axes generated by OrthoNormalize.
        basisA = stretchAxis;
        Vector3.OrthoNormalize(ref basisA, ref basisB, ref basisC);

        // Copy the three new basis vectors into the rows of a matrix
        // (since it is actually a 4x4 matrix, the bottom right corner
        // should also be set to 1).
        Matrix4x4 toNewSpace = new Matrix4x4();
        toNewSpace.SetRow(0, basisA);
        toNewSpace.SetRow(1, basisB);
        toNewSpace.SetRow(2, basisC);
        toNewSpace[3, 3] = 1.0F;

        // The scale values are just the diagonal entries of the scale
        // matrix. The vertices should be stretched along the first axis
        // and squashed proportionally along the other two.
        Matrix4x4 scale = new Matrix4x4();
        scale[0, 0] = stretchFactor;
        scale[1, 1] = 1.0F / stretchFactor;
        scale[2, 2] = 1.0F / stretchFactor;
        scale[3, 3] = 1.0F;

        // The inverse of the first matrix transforms the vertices back to
        // the original XYZ coordinate space(transpose is the same as inverse
        // for an orthogonal matrix, which this is).
        Matrix4x4 fromNewSpace = toNewSpace.transpose;

        // The three matrices can now be combined into a single symmetric matrix.
        Matrix4x4 trans = toNewSpace * scale * fromNewSpace;

        // Transform each of the mesh's vertices by the symmetric matrix.
        int i = 0;
        while (i < origVerts.Length)
        {
            newVerts[i] = trans.MultiplyPoint3x4(origVerts[i]);
            i++;
        }

        // ...and finally, update the mesh with the new vertex array.
        mf.mesh.vertices = newVerts;
    }
}

其他资源: Normalize 函数。