/// <summary>
/// Spherically interpolates between a and b by a factor.
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <param name="factor"></param>
/// <returns></returns>
public static Quaternion Slerp(Quaternion a, Quaternion b, float factor)
{
float x, y, z, w;
float opposite, inverse;
var dot = Dot(a, b);
if (Maths.Abs(dot) > (1.0 - Mathf.Epsilon))
{
inverse = 1.0f - factor;
opposite = factor * Maths.Sign(dot);
}
else
{
var acos = (float)Maths.Acos(Maths.Abs(dot));
var inverseSin = (float)(1.0 / Maths.Sin(acos));
inverse = (float)(Maths.Sin((1.0f - factor) * acos) * inverseSin);
opposite = (float)(Maths.Sin(factor * acos) * inverseSin * Maths.Sign(dot));
}
x = (inverse * a.X) + (opposite * b.X);
y = (inverse * a.Y) + (opposite * b.Y);
z = (inverse * a.Z) + (opposite * b.Z);
w = (inverse * a.W) + (opposite * b.W);
return(new Quaternion(x, y, z, w));
}
/// <summary>
/// 判断两数是否符号相同
/// </summary>
/// <param name="value"></param>
/// <param name="other"></param>
/// <returns>同号时返回true;异号返回false</returns>
public static bool IsSameSign(this double value, double other)
{
if (value.IsZero())
{
return(other.IsZero());
}
else if (other.IsZero())
{
return(false);
}
else//两数皆不为0
{
return(Math.Sign(value) * Math.Sign(other) >= 0);
}
}
public void Sign()
{
//Sign(int)
const int ip1 = 1;
const int in1 = -1;
Cmpr(Fast.Sign(ip1), Def.Sign(ip1), "Sign(1)");
Cmpr(Fast.Sign(in1), Def.Sign(in1), "Sign(-1)");
Cmpr(Fast.Sign(int.MaxValue), Def.Sign(int.MaxValue), "Sign(int.max)");
Cmpr(Fast.Sign(int.MaxValue - 1), Def.Sign(int.MaxValue - 1), "Sign(int.max-1)");
Cmpr(Fast.Sign(int.MinValue), Def.Sign(int.MinValue), "Sign(int.min)");
Cmpr(Fast.Sign(int.MinValue + 1), Def.Sign(int.MinValue + 1), "Sign(int.min+1)");
//Sign(long)
const long lp1 = 1;
const long ln1 = -1;
Cmpr(Fast.Sign(lp1), Def.Sign(lp1), "Sign(1L)");
Cmpr(Fast.Sign(ln1), Def.Sign(ln1), "Sign(-1L)");
Cmpr(Fast.Sign(long.MaxValue), Def.Sign(long.MaxValue), "Sign(long.max)");
Cmpr(Fast.Sign(long.MaxValue - 1L), Def.Sign(long.MaxValue - 1L), "Sign(long.max-1)");
Cmpr(Fast.Sign(long.MinValue), Def.Sign(long.MinValue), "Sign(long.min)");
Cmpr(Fast.Sign(long.MinValue + 1L), Def.Sign(long.MinValue + 1L), "Sign(long.min+1)");
//Sign(short)
const short sp1 = 1;
const short sn1 = -1;
Cmpr(Fast.Sign(sp1), Def.Sign(sp1), "Sign(1s)");
Cmpr(Fast.Sign(sn1), Def.Sign(sn1), "Sign(-1s)");
Cmpr(Fast.Sign(short.MaxValue), Def.Sign(short.MaxValue), "Sign(short.max)");
Cmpr(Fast.Sign((short)(short.MaxValue - 1)), Def.Sign((short)(short.MaxValue - 1)), "Sign(short.max-1)");
Cmpr(Fast.Sign(short.MinValue), Def.Sign(short.MinValue), "Sign(short.min)");
Cmpr(Fast.Sign((short)(short.MinValue + 1)), Def.Sign((short)(short.MinValue + 1)), "Sign(short.min+1)");
//Sign(sbyte)
const sbyte bp1 = 1;
const sbyte bn1 = -1;
Cmpr(Fast.Sign(bp1), Def.Sign(bp1), "Sign(1b)");
Cmpr(Fast.Sign(bn1), Def.Sign(bn1), "Sign(-1b)");
Cmpr(Fast.Sign(sbyte.MaxValue), Def.Sign(sbyte.MaxValue), "Sign(sbyte.max)");
Cmpr(Fast.Sign((sbyte)(sbyte.MaxValue - 1)), Def.Sign((sbyte)(sbyte.MaxValue - 1)), "Sign(sbyte.max-1)");
Cmpr(Fast.Sign(sbyte.MinValue), Def.Sign(sbyte.MinValue), "Sign(sbyte.min)");
Cmpr(Fast.Sign((sbyte)(sbyte.MinValue + 1)), Def.Sign((sbyte)(sbyte.MinValue + 1)), "Sign(sbyte.min+1)");
}
public static Vector3d Sign(Vector3d vector)
{
return(new Vector3d(Math.Sign(vector.x), Math.Sign(vector.y), Math.Sign(vector.z)));
}
/// <summary>
/// -1: left 0:lined 1:right
/// </summary>
public static int PointBelongedSide(Vector2 point, Vector2 from, Vector2 to)
{
return(MathLib.Sign((point.X - from.X) * (to.X - from.X) + (point.Y - from.Y) * (to.Y - from.Y)));
}
// Inverse Hyperbolic Cosecant
public static double HArccosec(double x)
{
return(MathObj.Log((MathObj.Sign(x) * MathObj.Sqrt(x * x + 1) + 1) / x));
}
// Inverse Secant
public static double Arcsec(double x)
{
return(2 * MathObj.Atan(1) - MathObj.Atan(MathObj.Sign(x) / MathObj.Sqrt(x * x - 1)));
}
public static PointPair GetIntersectionOfCircles(
Point center1,
double radius1,
Point center2,
double radius2)
{
var result = Math.InfinitePointPair;
var x1 = center1.X;
var y1 = center1.Y;
var x2 = center2.X;
var y2 = center2.Y;
var r3 = center1.Distance(center2);
if (r3 == 0)
{
return(result);
}
if (y1 == y2)
{
if (radius1 + radius1 > r3 + Epsilon &&
radius1 + r3 > radius2 + Epsilon &&
radius2 + r3 > radius1 + Epsilon &&
x1 != x2)
{
var x3 = (radius1.Sqr() + r3.Sqr() - radius2.Sqr()) / (2 * r3);
var tsqr = (radius1.Sqr() - x3.Sqr()).SquareRoot();
result.P1.X = x1 + (x2 - x1) * x3 / r3;
result.P1.Y = y1 - tsqr;
result.P2.X = result.P1.X;
result.P2.Y = y1 + tsqr;
if (x2 < x1)
{
var t = result.P1.Y;
result.P1.Y = result.P2.Y;
result.P2.Y = t;
}
}
else if ((radius1 + radius2 - r3).Abs() <= Epsilon)
{
result.P1.X = x1 + M.Sign(x2 - x1) * radius1;
result.P1.Y = y1;
result.P2 = result.P1;
}
else if ((radius1 + r3 - radius2).Abs() <= Epsilon ||
(r3 + radius2 - radius1).Abs() <= Epsilon)
{
result.P1.X = x1 + M.Sign(x2 - x1) * M.Sign(radius1 - radius2) * radius1;
result.P1.Y = y1;
result.P2 = result.P1;
}
return(result);
}
if ((radius1 + radius2 - r3).Abs() <= Epsilon)
{
r3 = radius1 / r3;
result.P1.X = x1 + (x2 - x1) * r3;
result.P1.Y = y1 + (y2 - y1) * r3;
result.P2 = result.P1;
return(result);
}
if ((radius1 + r3 - radius2).Abs() <= Epsilon ||
(radius2 + r3 - radius1).Abs() <= Epsilon)
{
r3 = radius1 / r3 * M.Sign(radius1 - radius2);
result.P1.X = x1 + (x2 - x1) * r3;
result.P1.Y = y1 + (y2 - y1) * r3;
result.P2 = result.P1;
return(result);
}
var k = -(x2 - x1) / (y2 - y1);
var b = ((radius1 - radius2) * (radius1 + radius2)
+ (x2 - x1) * (x2 + x1)
+ (y2 - y1) * (y2 + y1))
/ (2 * (y2 - y1));
var ea = k * k + 1;
var eb = 2 * (k * b - x1 - k * y1);
var ec = x1.Sqr() + b.Sqr() - 2 * b * y1 + y1.Sqr() - radius1.Sqr();
var roots = SolveSquareEquation(ea, eb, ec);
if (roots == null || roots.Count != 2)
{
return(result);
}
result.P1.X = roots[0];
result.P1.Y = roots[0] * k + b;
result.P2.X = roots[1];
result.P2.Y = roots[1] * k + b;
if (y2 > y1)
{
var t = result.P1;
result.P1 = result.P2;
result.P2 = t;
}
return(result);
}
public static int Sign(this double num)
{
return(M.Sign(num));
}