Vector3.OrthoNormalize

Description

将向量标准化并使它们彼此正交。

标准化 tangent。 标准化 tangent 并确保其与 normal 正交（即它们之间的角度为 90 度）。

另请参阅：Normalize 函数。

Description

将向量标准化并使它们彼此正交。

标准化 tangent。 标准化 tangent 并确保其与 normal 正交。 标准化 binormal 并确保其与 normal 和 tangent 正交。

空间中的点通常使用标准 XYZ 轴系的坐标指定。 但是，如果有任意三个向量为标准化向量（即其大小为 1） 并且彼此正交（即相互垂直），您就可以将它们解读为“轴”。

创建自己的坐标轴很有用，例如，若要在任意方向上缩放网格 而不只是沿 XYZ 轴缩放，则您可以将顶点变换到自己的坐标系， 对其进行缩放，然后再变换回来。通常情况下，这样的变换将仅沿一个轴进行， 另外两个轴要么保持不变，要么受到平等对待。 例如，可以通过在一个轴上放大，同时在另外两个轴上按比例缩小的方式 向网格应用拉伸效果。也就是说，一旦指定了第一个轴向量， 则另两个轴向量并不重要（只要它们是标准化并且正交的即可）。 OrthoNormalize 可用于确保第一个向量为标准化向量， 然后为其他两个轴生成标准化的正交向量。

// 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;
    }
}

另请参阅：Normalize 函数。