/// <summary>
/// 两个向量的球形插值
/// </summary>
/// <param name="a">向量a</param>
/// <param name="b">向量b</param>
/// <param name="t">t的值在[0..1]</param>
/// <returns></returns>
public static Vector3RightHand Slerp(Vector3RightHand a, Vector3RightHand b, float t)
{
// Quaternion fromQua = Quaternion.LookRotation(from, Vector3.up);
// Quaternion toQua = Quaternion.LookRotation(to, Vector3.up);
// Quaternion endQua = Quaternion.Slerp(fromQua, toQua, t);
//
// Vector3 endDir = endQua * Vector3.forward;
// endDir.Normalize();
//
// float length = Mathf3d.Lerp(from.magnitude, to.magnitude, t);
// return endDir.normalized * length;
if (t <= 0)
{
return(a);
}
else if (t >= 1)
{
return(b);
}
Vector3RightHand v = RotateTo(a, b, Vector3RightHand.Angle(a, b) * t);
//向量的长度，跟线性插值一样计算
float length = b.magnitude * t + a.magnitude * (1 - t);
return(v.normalized * length);
}
//static Quaternion FromToRotation(Vector3 fromDiection, Vector3 toDirection)
//根据两个向量计算出旋转量，计算出来的旋转量为从fromDiection,旋转到toDirection的旋转量。
//这句话意思很明显了。就是计算旋转量。
//那么LookRotation(Vector3 forward)计算的是，Z轴旋转到forward的旋转量。
//推出：Quaternion.LookRotation(new Vector3(1,0,0)) == Quaternion.FromToRotation(Vector3.forward, new Vector3(1,0,0));
//因为前者就是计算向前向量到当前向量（1,0,0）的旋转量的，其实现过程就是后者喽。
public static QuaternionRightHand FromToRotation(Vector3RightHand v1, Vector3RightHand v2)
{
// fromDirection.Normalize();
// toDirection.Normalize();
// Quaternion fromQua = LookRotation(fromDirection);
// Quaternion toQua = LookRotation(toDirection);
// fromQua = Normalize(fromQua);
// toQua = Normalize(toQua);
//Vector3 fromDir = fromQua * Vector3.forward;
//Vector3 toDir = toQua * Vector3.forward;
//Quaternion ret = RotateTowards(fromQua, toQua, float.MaxValue);
//return ret;
return(QuaternionRightHand.AngleAxis(Vector3RightHand.Angle(v1, v2), Vector3RightHand.Cross(v1, v2)));
}
/// <summary>
/// 将向量from向向量to旋转角度angle
/// </summary>
/// <param name="from"></param>
/// <param name="to"></param>
/// <param name="angle"></param>
/// <returns></returns>
static Vector3RightHand RotateTo(Vector3RightHand from, Vector3RightHand to, float angle)
{
//如果两向量角度为0
if (Vector3RightHand.Angle(from, to) == 0)
{
return(from);
}
//旋转轴
Vector3RightHand n = Vector3RightHand.Cross(from, to);
//旋转轴规范化
n.Normalize();
//旋转矩阵
Matrix4x4RightHand rotateMatrix = new Matrix4x4RightHand();
//旋转的弧度
double radian = angle * Mathf.PI / 180;
float cosAngle = (float)Mathf.Cos((float)radian);
float sinAngle = (float)Mathf.Sin((float)radian);
//矩阵的数据
//这里看不懂的自行科普矩阵知识
rotateMatrix.SetRow(0, new Vector4(n.x * n.x * (1 - cosAngle) + cosAngle, n.x * n.y * (1 - cosAngle) + n.z * sinAngle, n.x * n.z * (1 - cosAngle) - n.y * sinAngle, 0));
rotateMatrix.SetRow(1, new Vector4(n.x * n.y * (1 - cosAngle) - n.z * sinAngle, n.y * n.y * (1 - cosAngle) + cosAngle, n.y * n.z * (1 - cosAngle) + n.x * sinAngle, 0));
rotateMatrix.SetRow(2, new Vector4(n.x * n.z * (1 - cosAngle) + n.y * sinAngle, n.y * n.z * (1 - cosAngle) - n.x * sinAngle, n.z * n.z * (1 - cosAngle) + cosAngle, 0));
rotateMatrix.SetRow(3, new Vector4(0, 0, 0, 1));
Vector4 v = Vector3RightHand.ToVector4(from);
Vector3RightHand vector = new Vector3RightHand();
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 3; j++)
{
vector[i] += v[j] * rotateMatrix[j, i];
}
}
return(vector);
}
