| | |
| | | return 0f; |
| | | } |
| | | |
| | | public static float GetQuatLength(Quaternion q) |
| | | { |
| | | return Mathf.Sqrt(q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w); |
| | | } |
| | | |
| | | public static Quaternion GetQuatConjugate(Quaternion q) |
| | | { |
| | | return new Quaternion(-q.x, -q.y, -q.z, q.w); |
| | | } |
| | | |
| | | /// <summary> |
| | | /// Logarithm of a unit quaternion. The result is not necessary a unit quaternion. |
| | | /// </summary> |
| | | public static Quaternion GetQuatLog(Quaternion q) |
| | | { |
| | | Quaternion res = q; |
| | | res.w = 0; |
| | | |
| | | if (Mathf.Abs(q.w) < 1.0f) |
| | | { |
| | | float theta = Mathf.Acos(q.w); |
| | | float sin_theta = Mathf.Sin(theta); |
| | | |
| | | if (Mathf.Abs(sin_theta) > 0.0001) |
| | | { |
| | | float coef = theta / sin_theta; |
| | | res.x = q.x * coef; |
| | | res.y = q.y * coef; |
| | | res.z = q.z * coef; |
| | | } |
| | | } |
| | | |
| | | return res; |
| | | } |
| | | |
| | | public static Quaternion GetQuatExp(Quaternion q) |
| | | { |
| | | Quaternion res = q; |
| | | |
| | | float fAngle = Mathf.Sqrt(q.x * q.x + q.y * q.y + q.z * q.z); |
| | | float fSin = Mathf.Sin(fAngle); |
| | | |
| | | res.w = Mathf.Cos(fAngle); |
| | | |
| | | if (Mathf.Abs(fSin) > 0.0001) |
| | | { |
| | | float coef = fSin / fAngle; |
| | | res.x = coef * q.x; |
| | | res.y = coef * q.y; |
| | | res.z = coef * q.z; |
| | | } |
| | | |
| | | return res; |
| | | } |
| | | |
| | | /// <summary> |
| | | /// SQUAD Spherical Quadrangle interpolation [Shoe87] |
| | | /// </summary> |
| | | public static Quaternion GetQuatSquad(float t, Quaternion q0, Quaternion q1, Quaternion a0, Quaternion a1) |
| | | { |
| | | float slerpT = 2.0f * t * (1.0f - t); |
| | | |
| | | Quaternion slerpP = Slerp(q0, q1, t); |
| | | Quaternion slerpQ = Slerp(a0, a1, t); |
| | | |
| | | return Slerp(slerpP, slerpQ, slerpT); |
| | | } |
| | | |
| | | public static Quaternion GetSquadIntermediate(Quaternion q0, Quaternion q1, Quaternion q2) |
| | | { |
| | | Quaternion q1Inv = GetQuatConjugate(q1); |
| | | Quaternion p0 = GetQuatLog(q1Inv * q0); |
| | | Quaternion p2 = GetQuatLog(q1Inv * q2); |
| | | Quaternion sum = new Quaternion(-0.25f * (p0.x + p2.x), -0.25f * (p0.y + p2.y), -0.25f * (p0.z + p2.z), -0.25f * (p0.w + p2.w)); |
| | | |
| | | return q1 * GetQuatExp(sum); |
| | | } |
| | | |
| | | /// <summary> |
| | | /// Smooths the input parameter t. |
| | | /// If less than k1 ir greater than k2, it uses a sin. |
| | | /// Between k1 and k2 it uses linear interp. |
| | | /// </summary> |
| | | public static float Ease(float t, float k1, float k2) |
| | | { |
| | | float f; float s; |
| | | |
| | | f = k1 * 2 / Mathf.PI + k2 - k1 + (1.0f - k2) * 2 / Mathf.PI; |
| | | |
| | | if (t < k1) |
| | | { |
| | | s = k1 * (2 / Mathf.PI) * (Mathf.Sin((t / k1) * Mathf.PI / 2 - Mathf.PI / 2) + 1); |
| | | } |
| | | else |
| | | if (t < k2) |
| | | { |
| | | s = (2 * k1 / Mathf.PI + t - k1); |
| | | } |
| | | else |
| | | { |
| | | s = 2 * k1 / Mathf.PI + k2 - k1 + ((1 - k2) * (2 / Mathf.PI)) * Mathf.Sin(((t - k2) / (1.0f - k2)) * Mathf.PI / 2); |
| | | } |
| | | |
| | | return (s / f); |
| | | } |
| | | |
| | | /// <summary> |
| | | /// We need this because Quaternion.Slerp always uses the shortest arc. |
| | | /// </summary> |
| | | public static Quaternion Slerp(Quaternion p, Quaternion q, float t) |
| | | { |
| | | Quaternion ret; |
| | | |
| | | float fCos = Quaternion.Dot(p, q); |
| | | |
| | | if ((1.0f + fCos) > 0.00001) |
| | | { |
| | | float fCoeff0, fCoeff1; |
| | | |
| | | if ((1.0f - fCos) > 0.00001) |
| | | { |
| | | float omega = Mathf.Acos(fCos); |
| | | float invSin = 1.0f / Mathf.Sin(omega); |
| | | fCoeff0 = Mathf.Sin((1.0f - t) * omega) * invSin; |
| | | fCoeff1 = Mathf.Sin(t * omega) * invSin; |
| | | } |
| | | else |
| | | { |
| | | fCoeff0 = 1.0f - t; |
| | | fCoeff1 = t; |
| | | } |
| | | |
| | | ret.x = fCoeff0 * p.x + fCoeff1 * q.x; |
| | | ret.y = fCoeff0 * p.y + fCoeff1 * q.y; |
| | | ret.z = fCoeff0 * p.z + fCoeff1 * q.z; |
| | | ret.w = fCoeff0 * p.w + fCoeff1 * q.w; |
| | | } |
| | | else |
| | | { |
| | | float fCoeff0 = Mathf.Sin((1.0f - t) * Mathf.PI * 0.5f); |
| | | float fCoeff1 = Mathf.Sin(t * Mathf.PI * 0.5f); |
| | | |
| | | ret.x = fCoeff0 * p.x - fCoeff1 * p.y; |
| | | ret.y = fCoeff0 * p.y + fCoeff1 * p.x; |
| | | ret.z = fCoeff0 * p.z - fCoeff1 * p.w; |
| | | ret.w = p.z; |
| | | } |
| | | |
| | | return ret; |
| | | } |
| | | #region 进制转换 |
| | | private static char[] symbolsArray = { '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', '+', '/' }; |
| | | static string symbolStr = new string(symbolsArray, 0, 64); |
| | | /// <summary> |
| | | /// 讲字符串由64进制转为10进制,前缀没用的可用字符-代替 |
| | | /// </summary> |
| | | /// <param name="val"></param> |
| | | /// <returns></returns> |
| | | public static int Convert64To10(string val) |
| | | { |
| | | val=val.Trim('-'); |
| | | int result = 0; |
| | | long longResult = 0; |
| | | val = val.Trim(); |
| | | if (string.IsNullOrEmpty(val)) { |
| | | return result; |
| | | } |
| | | if (val.Equals("0")) return 0; |
| | | for (int i = 0; i < val.Length; i++) { |
| | | if(!symbolStr.Contains(val[i].ToString())) { |
| | | //DesignDebug.LogError(string.Format("64进制格式错误{0}", val)); |
| | | return 0; |
| | | } |
| | | else { |
| | | try { |
| | | int index = 0; |
| | | for (int j = 0; j < symbolsArray.Length; j++) { |
| | | if (symbolsArray[j] == val[val.Length - i - 1]) { |
| | | index = j; |
| | | } |
| | | } |
| | | longResult += (long)System.Math.Pow(64, i) * index; |
| | | if(longResult>int.MaxValue) { |
| | | Debug.LogError("超出Int最大值,尝试转换为long类型"); |
| | | return 0; |
| | | } |
| | | result = (int)longResult; |
| | | } |
| | | catch { |
| | | Debug.LogError("运算溢出"); |
| | | return 0; |
| | | } |
| | | } |
| | | } |
| | | return result; |
| | | } |
| | | static char[] outSymbol = new char[65]; |
| | | /// <summary> |
| | | /// 将10进制转为64进制的字符串 |
| | | /// </summary> |
| | | /// <param name="val"></param> |
| | | /// <returns></returns> |
| | | public static string Convert10To64(int val) |
| | | { |
| | | if (0 == val) return "0"; |
| | | int index = 0; |
| | | long longPositive = Mathf.Abs(val); |
| | | for (index = 0; index <= 64; index++) { |
| | | if (longPositive == 0) break; |
| | | outSymbol[outSymbol.Length - index - 1] = symbolsArray[longPositive % 64]; |
| | | longPositive /= 64; |
| | | } |
| | | return new string(outSymbol,outSymbol.Length-index,index); |
| | | } |
| | | #endregion |
| | | } |