public static void OrthoNormalize (ref Vector3 normal, ref Vector3 tangent);

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。


public static void OrthoNormalize (ref Vector3 normal, ref Vector3 tangent, ref Vector3 binormal);

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 normaltangent 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。