public void ACosTest()
{
float actual = MathHelper.Round(MathHelper.Acos(0f), 6);
float expected = 1.570796f;
Assert.AreEqual(expected, actual);
}
public void Acos(double expected, double input)
{
// Act
var actual = MathHelper.Acos(input);
// Assert
Assert.Equal(expected, actual);
}
public static Props FromCommonProps(CameraFrame frame)
{
var forward = frame.Forward;
var yaw = MathHelper.Atan2(forward.Xz.X, -forward.Xz.Y);
var pitch = MathHelper.Acos(Vector3.Dot(new Vector3(forward.X, 0, forward.Z).Normalize(), forward));
return(new Props
{
Eye = frame.Eye,
Yaw = yaw,
Pitch = pitch
});
}
public static Quaternion Slerp(float t, Quaternion q1, Quaternion q2)
{
float cosTheta = Dot(q1, q2);
if (cosTheta > 0.9995f)
{
return(Normalize((1.0f - t) * q1 + t * q2));
}
else
{
float theta = MathHelper.Acos(MathHelper.Clamp(cosTheta, -1.0f, 1.0f));
float thetap = theta * t;
Quaternion qperp = Normalize(q2 - q1 * cosTheta);
return(q1 * MathHelper.Cos(thetap) + qperp * MathHelper.Sin(thetap));
}
}
public static Quaternion Slerp(Quaternion left, Quaternion right, float amount)
{
var cosTheta = MathHelper.Clamp(Dot(left, right), -1f, 1f);
var theta = MathHelper.Acos(cosTheta);
var sinTheta = MathHelper.Sin(theta);
var invSinTheta = 1.0f / sinTheta;
var wLeft = MathHelper.Sin((1.0f - amount) * theta) * invSinTheta;
var wRight = MathHelper.Sin(amount * theta) * invSinTheta;
if (cosTheta < 0f)
{
wRight = -wRight;
}
return(new Quaternion(
wLeft * left.X + wRight * right.X,
wLeft * left.Y + wRight * right.Y,
wLeft * left.Z + wRight * right.Z,
wLeft * left.W + wRight * right.W));
}
public static bool FrustumCheckChunk(Vector3i pos_to_check)
{
return(MathHelper.RadiansToDegrees(MathHelper.Acos(Vector3.Dot(Camera.Front.Normalized(),
(Camera.Position - ConvertChunkToWorldCoordinates(pos_to_check)).Normalized()))) >
Camera.Frustrum / 2f);
}
/// <summary>
/// Calculates the angles and sides.
/// </summary>
/// <param name="data">The data.</param>
/// <remarks>
/// http://cossincalc.com/
/// </remarks>
private static TriangleData CalculateAnglesAndSides(TriangleData data)
{
// A
if (MathHelper.IsEqualToZero(data.A))
{
if (!MathHelper.IsEqualToZero(data.B) && !MathHelper.IsEqualToZero(data.C))
{
data.A = 180 - data.B - data.C;
}
else if (!MathHelper.IsEqualToZero(data.B) && !MathHelper.IsEqualToZero(data.a) && !MathHelper.IsEqualToZero(data.b))
{
data.A = MathHelper.Asin(MathHelper.Sin(data.B) * data.a / data.b);
}
else if (!MathHelper.IsEqualToZero(data.B) && !MathHelper.IsEqualToZero(data.b) && !MathHelper.IsEqualToZero(data.c))
{
if (MathHelper.IsEqualToZero(data.C))
{
data.C = MathHelper.Asin(MathHelper.Sin(data.B) * data.c / data.b);
}
data.A = 180 - data.B - data.C;
}
else if (!MathHelper.IsEqualToZero(data.B) && !MathHelper.IsEqualToZero(data.a) && !MathHelper.IsEqualToZero(data.c))
{
double a2 = data.a * data.a;
double c2 = data.c * data.c;
if (MathHelper.IsEqualToZero(data.b))
{
data.b = System.Math.Sqrt(a2 + c2 - (2 * data.a * data.c * MathHelper.Cos(data.B)));
}
double b2 = data.b * data.b;
data.A = MathHelper.Acos((b2 + c2 - a2) / (2 * data.b * data.c));
}
else if (!MathHelper.IsEqualToZero(data.C) && !MathHelper.IsEqualToZero(data.a) && !MathHelper.IsEqualToZero(data.b))
{
double a2 = data.a * data.a;
double b2 = data.b * data.b;
if (MathHelper.IsEqualToZero(data.c))
{
data.c = System.Math.Sqrt(a2 + b2 - (2 * data.a * data.b * MathHelper.Cos(data.C)));
}
double c2 = data.c * data.c;
data.A = MathHelper.Acos((b2 + c2 - a2) / (2 * data.b * data.c));
}
else if (!MathHelper.IsEqualToZero(data.C) && !MathHelper.IsEqualToZero(data.a) && !MathHelper.IsEqualToZero(data.c))
{
if (MathHelper.IsEqualToZero(data.A))
{
data.A = MathHelper.Asin(MathHelper.Sin(data.C) * data.a / data.c);
}
data.B = 180 - data.A - data.C;
}
else if (!MathHelper.IsEqualToZero(data.C) && !MathHelper.IsEqualToZero(data.b) && !MathHelper.IsEqualToZero(data.c))
{
if (MathHelper.IsEqualToZero(data.B))
{
data.B = MathHelper.Asin(MathHelper.Sin(data.C) * data.b / data.c);
}
data.A = 180 - data.B - data.C;
}
else
{
throw new ArithmeticException("This scenario is not implemented yet.");
}
}
// B
if (MathHelper.IsEqualToZero(data.B))
{
if (!MathHelper.IsEqualToZero(data.A) && !MathHelper.IsEqualToZero(data.C))
{
data.B = 180 - data.A - data.C;
}
else if (!MathHelper.IsEqualToZero(data.A) && !MathHelper.IsEqualToZero(data.a) && !MathHelper.IsEqualToZero(data.b))
{
data.B = MathHelper.Asin(MathHelper.Sin(data.A) * data.b / data.a);
}
else if (!MathHelper.IsEqualToZero(data.A) && !MathHelper.IsEqualToZero(data.b) && !MathHelper.IsEqualToZero(data.c))
{
double b2 = data.b * data.b;
double c2 = data.c * data.c;
if (MathHelper.IsEqualToZero(data.a))
{
data.a = System.Math.Sqrt(b2 + c2 - (2 * data.b * data.c * MathHelper.Cos(data.A)));
}
double a2 = data.a * data.a;
data.B = MathHelper.Acos((a2 + c2 - b2) / (2 * data.a * data.c));
}
else if (!MathHelper.IsEqualToZero(data.A) && !MathHelper.IsEqualToZero(data.a) && !MathHelper.IsEqualToZero(data.c))
{
if (MathHelper.IsEqualToZero(data.C))
{
data.C = MathHelper.Asin(MathHelper.Sin(data.A) * data.c / data.a);
}
data.B = 180 - data.A - data.C;
}
else
{
throw new ArithmeticException("This scenario is not implemented yet.");
}
}
// C
if (MathHelper.IsEqualToZero(data.C))
{
if (!MathHelper.IsEqualToZero(data.A) && !MathHelper.IsEqualToZero(data.B))
{
data.C = 180 - data.A - data.B;
}
else
{
throw new ArithmeticException("This scenario is not implemented yet.");
}
}
// a
if (MathHelper.IsEqualToZero(data.a))
{
if (!MathHelper.IsEqualToZero(data.A) && !MathHelper.IsEqualToZero(data.B) && !MathHelper.IsEqualToZero(data.b))
{
data.a = MathHelper.Sin(data.A) * data.b / MathHelper.Sin(data.B);
}
else if (!MathHelper.IsEqualToZero(data.A) && !MathHelper.IsEqualToZero(data.C) && !MathHelper.IsEqualToZero(data.c))
{
data.a = MathHelper.Sin(data.A) * data.c / MathHelper.Sin(data.C);
}
else
{
throw new ArithmeticException("This scenario is not implemented yet.");
}
}
// b
if (MathHelper.IsEqualToZero(data.b))
{
if (!MathHelper.IsEqualToZero(data.A) && !MathHelper.IsEqualToZero(data.B) && !MathHelper.IsEqualToZero(data.a))
{
data.b = MathHelper.Sin(data.B) * data.a / MathHelper.Sin(data.A);
}
else
{
throw new ArithmeticException("This scenario is not implemented yet.");
}
}
// c
if (MathHelper.IsEqualToZero(data.c))
{
if (!MathHelper.IsEqualToZero(data.A) && !MathHelper.IsEqualToZero(data.C) && !MathHelper.IsEqualToZero(data.a))
{
data.c = MathHelper.Sin(data.C) * data.a / MathHelper.Sin(data.A);
}
else
{
throw new ArithmeticException("This scenario is not implemented yet.");
}
}
return(IsAngleAndSidesCalculated(data)
? data
: CalculateAnglesAndSides(data));
}
public static float Acos(float radians) => (float)MathHelper.Acos(radians);