/// <summary>
/// Scale the given quaternion to unit length
/// </summary>
/// <param name="q">The quaternion to normalize</param>
/// <returns>The normalized quaternion</returns>
static QuaternionRightHand Normalize(QuaternionRightHand q)
{
float scale = 1.0f / q.Length;
QuaternionRightHand result = new QuaternionRightHand(q.xyz * scale, q.w * scale);
return(result);
}
/// <summary>
/// 可以用来计算ojbtoworld矩阵
/// </summary>
/// <param name="pos"></param>
/// <param name="q"></param>
/// <param name="s"></param>
/// <returns></returns>
public static Matrix4x4RightHand TRS(Vector3RightHand pos, QuaternionRightHand q, Vector3RightHand s)
{
Matrix4x4RightHand posMatrix = Matrix4x4RightHand.identity;
posMatrix.m03 = pos.x;
posMatrix.m13 = pos.y;
posMatrix.m23 = pos.z;
Matrix4x4RightHand rotateMatrix = Matrix4x4RightHand.identity;
rotateMatrix.m00 = 1 - 2 * q.y * q.y - 2 * q.z * q.z;
rotateMatrix.m10 = 2 * q.x * q.y + 2 * q.w * q.z;
rotateMatrix.m20 = 2 * q.x * q.z - 2 * q.w * q.y;
rotateMatrix.m01 = 2 * q.x * q.y - 2 * q.w * q.z;
rotateMatrix.m11 = 1 - 2 * q.x * q.x - 2 * q.z * q.z;
rotateMatrix.m21 = 2 * q.y * q.z + 2 * q.w * q.x;
rotateMatrix.m02 = 2 * q.x * q.z + 2 * q.w * q.y;
rotateMatrix.m12 = 2 * q.y * q.z - 2 * q.w * q.x;
rotateMatrix.m22 = 1 - 2 * q.x * q.x - 2 * q.y * q.y;
Matrix4x4RightHand scaleMatrix = Scale(s);
Matrix4x4RightHand ret = posMatrix * rotateMatrix * scaleMatrix;
return(ret);
}
public static QuaternionRightHand LookRotation(Vector3RightHand forward, Vector3RightHand up)
{
forward = Vector3RightHand.Normalize(forward);
Vector3RightHand right = Vector3RightHand.Normalize(Vector3RightHand.Cross(up, forward));
up = Vector3RightHand.Cross(forward, right);
var m00 = right.x;
var m01 = right.y;
var m02 = right.z;
var m10 = up.x;
var m11 = up.y;
var m12 = up.z;
var m20 = forward.x;
var m21 = forward.y;
var m22 = forward.z;
float num8 = (m00 + m11) + m22;
var quaternion = new QuaternionRightHand();
if (num8 > 0f)
{
var num = (float)Mathf.Sqrt(num8 + 1f);
quaternion.w = num * 0.5f;
num = 0.5f / num;
quaternion.x = (m12 - m21) * num;
quaternion.y = (m20 - m02) * num;
quaternion.z = (m01 - m10) * num;
return(quaternion);
}
if ((m00 >= m11) && (m00 >= m22))
{
var num7 = (float)Mathf.Sqrt(((1f + m00) - m11) - m22);
var num4 = 0.5f / num7;
quaternion.x = 0.5f * num7;
quaternion.y = (m01 + m10) * num4;
quaternion.z = (m02 + m20) * num4;
quaternion.w = (m12 - m21) * num4;
return(quaternion);
}
if (m11 > m22)
{
var num6 = (float)Mathf.Sqrt(((1f + m11) - m00) - m22);
var num3 = 0.5f / num6;
quaternion.x = (m10 + m01) * num3;
quaternion.y = 0.5f * num6;
quaternion.z = (m21 + m12) * num3;
quaternion.w = (m20 - m02) * num3;
return(quaternion);
}
var num5 = (float)Mathf.Sqrt(((1f + m22) - m00) - m11);
var num2 = 0.5f / num5;
quaternion.x = (m20 + m02) * num2;
quaternion.y = (m21 + m12) * num2;
quaternion.z = 0.5f * num5;
quaternion.w = (m01 - m10) * num2;
return(quaternion);
}
public override bool Equals(object other)
{
if (!(other is QuaternionRightHand))
{
return(false);
}
QuaternionRightHand quaternion = (QuaternionRightHand)other;
return(this.x.Equals(quaternion.x) && this.y.Equals(quaternion.y) && this.z.Equals(quaternion.z) && this.w.Equals(quaternion.w));
}
public static QuaternionRightHand Inverse(QuaternionRightHand rotation)
{
float lengthSq = rotation.LengthSquared;
if (lengthSq != 0.0)
{
float i = 1.0f / lengthSq;
return(new QuaternionRightHand(rotation.xyz * -i, rotation.w * i));
}
return(rotation);
}
public static QuaternionRightHand Slerp(QuaternionRightHand a, QuaternionRightHand b, float t)
{
if (t > 1)
{
t = 1;
}
if (t < 0)
{
t = 0;
}
return(SlerpUnclamped(a, b, t));
}
public static QuaternionRightHand RotateTowards(QuaternionRightHand from, QuaternionRightHand to, float maxDegreesDelta)
{
float num = QuaternionRightHand.Angle(from, to);
if (num == 0f)
{
return(to);
}
float t = Mathf.Min(1f, maxDegreesDelta / num);
return(QuaternionRightHand.SlerpUnclamped(from, to, t));
}
public static QuaternionRightHand Lerp(QuaternionRightHand from, QuaternionRightHand to, float t)
{
if (t > 1)
{
t = 1;
}
if (t < 0)
{
t = 0;
}
return(Slerp(from, to, t));
}
//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)));
}
static void ToAxisAngleRad(QuaternionRightHand q, out Vector3RightHand axis, out float angle)
{
if (Mathf.Abs(q.w) > 1.0f)
{
q.Normalize();
}
angle = 2.0f * (float)Mathf.Acos(q.w); // angle
float den = (float)Mathf.Sqrt(1.0f - q.w * q.w);
if (den > 0.0001f)
{
axis = q.xyz / den;
}
else
{
// This occurs when the angle is zero.
// Not a problem: just set an arbitrary normalized axis.
axis = new Vector3RightHand(1, 0, 0);
}
}
public static QuaternionRightHand AngleAxis(float degress, Vector3RightHand axis)
{
if (axis.sqrMagnitude == 0.0f)
{
return(identity);
}
QuaternionRightHand result = identity;
var radians = degress * Mathf.Deg2Rad;
radians *= 0.5f;
axis.Normalize();
axis = axis * (float)Mathf.Sin(radians);
result.x = axis.x;
result.y = axis.y;
result.z = axis.z;
result.w = (float)Mathf.Cos(radians);
return(Normalize(result));
}
public static void Test()
{
Vector3RightHand pos = new Vector3RightHand(100, 200, 300);
QuaternionRightHand rotate = QuaternionRightHand.identity;
rotate.eulerAngles = new Vector3RightHand(40, 50, 60);
//Console.WriteLine("测试Quaternion " + rotate);
Vector3RightHand scale = new Vector3RightHand(7, 8, 9);
Matrix4x4RightHand trs = TRS(pos, rotate, scale);
Console.WriteLine("测试trs\n" + trs.ToString());
Matrix4x4RightHand transpose = Transpose(trs);
Console.WriteLine("测试转置矩阵\n" + transpose.ToString());
Matrix4x4RightHand inverse = Inverse(trs);
Console.WriteLine("测试逆矩阵\n" + inverse.ToString());
Matrix4x4RightHand posMatrix = Matrix4x4RightHand.identity;
posMatrix.m03 = pos.x;
posMatrix.m13 = pos.y;
posMatrix.m23 = pos.z;
Vector4 point = new Vector4(0, 0, 0, 1);
Vector4 newPoint = posMatrix * point;
float fov = 60;
float aspect = (float)16 / 9;
float zNear = 1;
float zFar = 1000;
Matrix4x4RightHand perspectiveMat = Matrix4x4RightHand.Perspective(fov, aspect, zNear, zFar);
Console.WriteLine("测试透视矩阵\n" + perspectiveMat.ToString());
//Console.ReadLine();
}
public static bool operator !=(QuaternionRightHand lhs, QuaternionRightHand rhs)
{
return(QuaternionRightHand.Dot(lhs, rhs) <= 0.999999f);
}
public void ToAngleAxis(out float angle, out Vector3RightHand axis)
{
QuaternionRightHand.ToAxisAngleRad(this, out axis, out angle);
angle *= Mathf.Rad2Deg;
}
public static float Angle(QuaternionRightHand a, QuaternionRightHand b)
{
float f = QuaternionRightHand.Dot(a, b);
return((float)Mathf.Acos(Mathf.Min(Mathf.Abs(f), 1f)) * 2f * 57.29578f);
}
private static QuaternionRightHand SlerpUnclamped(QuaternionRightHand a, QuaternionRightHand b, float t)
{
// if either input is zero, return the other.
if (a.LengthSquared == 0.0f)
{
if (b.LengthSquared == 0.0f)
{
return(identity);
}
return(b);
}
else if (b.LengthSquared == 0.0f)
{
return(a);
}
float cosHalfAngle = a.w * b.w + Vector3RightHand.Dot(a.xyz, b.xyz);
if (cosHalfAngle >= 1.0f || cosHalfAngle <= -1.0f)
{
// angle = 0.0f, so just return one input.
return(a);
}
else if (cosHalfAngle < 0.0f)
{
b.xyz = -b.xyz;
b.w = -b.w;
cosHalfAngle = -cosHalfAngle;
}
float blendA;
float blendB;
if (cosHalfAngle < 0.99f)
{
// do proper slerp for big angles
float halfAngle = (float)Mathf.Acos(cosHalfAngle);
float sinHalfAngle = (float)Mathf.Sin(halfAngle);
float oneOverSinHalfAngle = 1.0f / sinHalfAngle;
blendA = (float)Mathf.Sin(halfAngle * (1.0f - t)) * oneOverSinHalfAngle;
blendB = (float)Mathf.Sin(halfAngle * t) * oneOverSinHalfAngle;
}
else
{
// do lerp if angle is really small.
blendA = 1.0f - t;
blendB = t;
}
QuaternionRightHand result = new QuaternionRightHand(blendA * a.xyz + blendB * b.xyz, blendA * a.w + blendB * b.w);
if (result.LengthSquared > 0.0f)
{
return(Normalize(result));
}
else
{
return(identity);
}
}
public static void Test()
{
QuaternionRightHand rotate = QuaternionRightHand.identity;
rotate.eulerAngles = new Vector3RightHand(40, 50, 60);
Debug.Log("测试euler to Quaternion \n" + rotate);
Vector3RightHand euler = rotate.eulerAngles;
Debug.Log("测试quaternion to euler \n" + euler);
Vector3RightHand dir = new Vector3RightHand(0.3f, 0.4f, 0.5f);
dir.Normalize();
QuaternionRightHand lookRotation = QuaternionRightHand.LookRotation(dir, Vector3RightHand.up);
Debug.Log("测试look rotation \n" + lookRotation);
QuaternionRightHand rotate2 = QuaternionRightHand.identity;
rotate2.eulerAngles = new Vector3RightHand(70, 80, 90);
QuaternionRightHand slerp = QuaternionRightHand.Slerp(rotate, rotate2, 0.5f);
Debug.Log("测试slerp \n" + slerp);
//Console.ReadLine();
float angle = Angle(rotate, rotate2);
Debug.Log("测试angle " + angle);
QuaternionRightHand angleAxis = AngleAxis(10, dir);
Debug.Log("测试angleAxis " + angleAxis);
Vector3RightHand dir2 = new Vector3RightHand(0.6f, 0.7f, 0.8f);
dir2.Normalize();
QuaternionRightHand rotateTowards = QuaternionRightHand.RotateTowards(QuaternionRightHand.LookRotation(dir), QuaternionRightHand.LookRotation(dir2), float.MaxValue);
Debug.Log("测试RotateTowards " + rotateTowards);
Vector3RightHand dir3 = new Vector3RightHand(1, 0, 0);
Vector3RightHand dir4 = new Vector3RightHand(0, 0, 1);
QuaternionRightHand fromToRotation = FromToRotation(dir, dir2);
//Quaternion fromToRotation = FromToRotation(dir4, dir3);
Debug.Log("测试FromToRotation " + fromToRotation);
QuaternionRightHand inverstQua = QuaternionRightHand.Inverse(fromToRotation);
Debug.Log("测试inverst " + inverstQua);
QuaternionRightHand lerpQua = QuaternionRightHand.Lerp(rotate, rotate2, 0.5f);
Debug.Log("测试lerp " + lerpQua);
float angle2 = 0;
Vector3RightHand axis = Vector3RightHand.zero;
lerpQua.ToAngleAxis(out angle2, out axis);
Debug.Log("测试ToAngleAxis " + angle2 + " " + axis);
//Console.ReadLine();
}
// 四元数转欧拉角
static Vector3RightHand ToEulerRad(QuaternionRightHand q)
{
// float sqw = rotation.w * rotation.w;
// float sqx = rotation.x * rotation.x;
// float sqy = rotation.y * rotation.y;
// float sqz = rotation.z * rotation.z;
// float unit = sqx + sqy + sqz + sqw; // if normalised is one, otherwise is correction factor
// float test = rotation.x * rotation.w - rotation.y * rotation.z;
// Vector3 v;
//
// if (test > 0.4995f * unit)
// { // singularity at north pole
// v.y = 2f * (float)Mathf.Atan2(rotation.y, rotation.x);
// v.x = (float)Mathf.PI / 2;
// v.z = 0;
// return NormalizeAngles(v * Mathf.Rad2Deg);
// }
// if (test < -0.4995f * unit)
// { // singularity at south pole
// v.y = -2f * (float)Mathf.Atan2(rotation.y, rotation.x);
// v.x = -(float)Mathf.PI / 2;
// v.z = 0;
// return NormalizeAngles(v * Mathf.Rad2Deg);
// }
// Quaternion q = new Quaternion(rotation.w, rotation.z, rotation.x, rotation.y);
// v.y = (float)Mathf.Atan2(2f * q.x * q.w + 2f * q.y * q.z, 1 - 2f * (q.z * q.z + q.w * q.w)); // Yaw
// v.x = (float)Mathf.Asin(2f * (q.x * q.z - q.w * q.y)); // Pitch
// v.z = (float)Mathf.Atan2(2f * q.x * q.y + 2f * q.z * q.w, 1 - 2f * (q.y * q.y + q.z * q.z)); // Roll
// return NormalizeAngles(v * Mathf.Rad2Deg) * Mathf.Deg2Rad;
float sqw = q.w * q.w;
float sqx = q.x * q.x;
float sqy = q.y * q.y;
float sqz = q.z * q.z;
float unit = sqx + sqy + sqz + sqw;
float test = q.x * q.y + q.z * q.w;
float yaw = 0.0f;
float pitch = 0.0f;
float roll = 0.0f;
// North pole singularity
if (test > 0.499f * unit)
{
yaw = 2.0f * Mathf.Atan2(q.x, q.w);
pitch = Mathf.PI * 0.5f;
roll = 0.0f;
}
// South pole singularity
else if (test < -0.499f * unit)
{
yaw = -2.0f * Mathf.Atan2(q.x, q.w);
pitch = -Mathf.PI * 0.5f;
roll = 0.0f;
}
else
{
yaw = Mathf.Atan2(2.0f * q.y * q.w - 2.0f * q.x * q.z, sqx - sqy - sqz + sqw);
pitch = Mathf.Asin(2.0f * test / unit);
roll = Mathf.Atan2(2.0f * q.x * q.w - 2.0f * q.y * q.z, -sqx + sqy - sqz + sqw);
}
// Keep angles [0..360].
if (Mathf.Sign(yaw) < 0)
{
yaw = Mathf.Deg2Rad * (360) + yaw;
}
if (Mathf.Sign(pitch) < 0)
{
pitch = Mathf.Deg2Rad * (360) + pitch;
}
if (Mathf.Sign(roll) < 0)
{
roll = Mathf.Deg2Rad * (360) + roll;
}
return(new Vector3RightHand(roll, yaw, pitch));
}
public static float Dot(QuaternionRightHand a, QuaternionRightHand b)
{
return(a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w);
}
