using UnityEngine;
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using System.Collections;
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using System.Collections.Generic;
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public class MathUtils
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{
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public static float GetQuatLength(Quaternion q)
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{
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return Mathf.Sqrt(q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w);
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}
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public static Quaternion GetQuatConjugate(Quaternion q)
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{
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return new Quaternion(-q.x, -q.y, -q.z, q.w);
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}
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/// <summary>
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/// Logarithm of a unit quaternion. The result is not necessary a unit quaternion.
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/// </summary>
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public static Quaternion GetQuatLog(Quaternion q)
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{
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Quaternion res = q;
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res.w = 0;
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if (Mathf.Abs(q.w) < 1.0f)
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{
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float theta = Mathf.Acos(q.w);
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float sin_theta = Mathf.Sin(theta);
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if (Mathf.Abs(sin_theta) > 0.0001)
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{
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float coef = theta / sin_theta;
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res.x = q.x * coef;
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res.y = q.y * coef;
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res.z = q.z * coef;
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}
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}
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return res;
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}
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public static Quaternion GetQuatExp(Quaternion q)
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{
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Quaternion res = q;
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float fAngle = Mathf.Sqrt(q.x * q.x + q.y * q.y + q.z * q.z);
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float fSin = Mathf.Sin(fAngle);
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res.w = Mathf.Cos(fAngle);
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if (Mathf.Abs(fSin) > 0.0001)
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{
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float coef = fSin / fAngle;
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res.x = coef * q.x;
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res.y = coef * q.y;
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res.z = coef * q.z;
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}
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return res;
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}
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/// <summary>
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/// SQUAD Spherical Quadrangle interpolation [Shoe87]
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/// </summary>
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public static Quaternion GetQuatSquad(float t, Quaternion q0, Quaternion q1, Quaternion a0, Quaternion a1)
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{
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float slerpT = 2.0f * t * (1.0f - t);
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Quaternion slerpP = Slerp(q0, q1, t);
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Quaternion slerpQ = Slerp(a0, a1, t);
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return Slerp(slerpP, slerpQ, slerpT);
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}
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public static Quaternion GetSquadIntermediate(Quaternion q0, Quaternion q1, Quaternion q2)
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{
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Quaternion q1Inv = GetQuatConjugate(q1);
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Quaternion p0 = GetQuatLog(q1Inv * q0);
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Quaternion p2 = GetQuatLog(q1Inv * q2);
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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));
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return q1 * GetQuatExp(sum);
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}
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/// <summary>
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/// Smooths the input parameter t.
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/// If less than k1 ir greater than k2, it uses a sin.
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/// Between k1 and k2 it uses linear interp.
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/// </summary>
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public static float Ease(float t, float k1, float k2)
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{
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float f; float s;
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f = k1 * 2 / Mathf.PI + k2 - k1 + (1.0f - k2) * 2 / Mathf.PI;
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if (t < k1)
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{
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s = k1 * (2 / Mathf.PI) * (Mathf.Sin((t / k1) * Mathf.PI / 2 - Mathf.PI / 2) + 1);
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}
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else
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if (t < k2)
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{
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s = (2 * k1 / Mathf.PI + t - k1);
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}
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else
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{
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s = 2 * k1 / Mathf.PI + k2 - k1 + ((1 - k2) * (2 / Mathf.PI)) * Mathf.Sin(((t - k2) / (1.0f - k2)) * Mathf.PI / 2);
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}
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return (s / f);
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}
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/// <summary>
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/// We need this because Quaternion.Slerp always uses the shortest arc.
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/// </summary>
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public static Quaternion Slerp(Quaternion p, Quaternion q, float t)
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{
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Quaternion ret;
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float fCos = Quaternion.Dot(p, q);
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if ((1.0f + fCos) > 0.00001)
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{
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float fCoeff0, fCoeff1;
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if ((1.0f - fCos) > 0.00001)
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{
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float omega = Mathf.Acos(fCos);
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float invSin = 1.0f / Mathf.Sin(omega);
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fCoeff0 = Mathf.Sin((1.0f - t) * omega) * invSin;
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fCoeff1 = Mathf.Sin(t * omega) * invSin;
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}
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else
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{
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fCoeff0 = 1.0f - t;
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fCoeff1 = t;
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}
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ret.x = fCoeff0 * p.x + fCoeff1 * q.x;
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ret.y = fCoeff0 * p.y + fCoeff1 * q.y;
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ret.z = fCoeff0 * p.z + fCoeff1 * q.z;
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ret.w = fCoeff0 * p.w + fCoeff1 * q.w;
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}
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else
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{
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float fCoeff0 = Mathf.Sin((1.0f - t) * Mathf.PI * 0.5f);
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float fCoeff1 = Mathf.Sin(t * Mathf.PI * 0.5f);
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ret.x = fCoeff0 * p.x - fCoeff1 * p.y;
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ret.y = fCoeff0 * p.y + fCoeff1 * p.x;
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ret.z = fCoeff0 * p.z - fCoeff1 * p.w;
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ret.w = p.z;
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}
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return ret;
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}
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#region 进制转换
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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', '+', '/' };
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static string symbolStr = new string(symbolsArray, 0, 64);
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/// <summary>
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/// 讲字符串由64进制转为10进制，前缀没用的可用字符-代替
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/// </summary>
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/// <param name="val"></param>
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/// <returns></returns>
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public static int Convert64To10(string val)
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{
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val=val.Trim('-');
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int result = 0;
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long longResult = 0;
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val = val.Trim();
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if (string.IsNullOrEmpty(val)) {
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return result;
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}
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if (val.Equals("0")) return 0;
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for (int i = 0; i < val.Length; i++) {
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if(!symbolStr.Contains(val[i].ToString())) {
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//DesignDebug.LogError(string.Format("64进制格式错误{0}", val));
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return 0;
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}
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else {
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try {
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int index = 0;
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for (int j = 0; j < symbolsArray.Length; j++) {
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if (symbolsArray[j] == val[val.Length - i - 1]) {
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index = j;
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}
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}
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longResult += (long)System.Math.Pow(64, i) * index;
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if(longResult>int.MaxValue) {
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Debug.LogError("超出Int最大值，尝试转换为long类型");
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return 0;
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}
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result = (int)longResult;
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}
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catch {
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Debug.LogError("运算溢出");
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return 0;
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}
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}
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}
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return result;
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}
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static char[] outSymbol = new char[65];
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/// <summary>
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/// 将10进制转为64进制的字符串
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/// </summary>
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/// <param name="val"></param>
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/// <returns></returns>
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public static string Convert10To64(int val)
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{
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if (0 == val) return "0";
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int index = 0;
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long longPositive = Mathf.Abs(val);
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for (index = 0; index <= 64; index++) {
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if (longPositive == 0) break;
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outSymbol[outSymbol.Length - index - 1] = symbolsArray[longPositive % 64];
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longPositive /= 64;
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}
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return new string(outSymbol,outSymbol.Length-index,index);
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}
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#endregion
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}
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