/// <summary>
/// Calculates a mesh for a standard euclidean catenoid.
/// This will need to be transformed to the various locations later.
/// </summary>
private static Mesh StandardCatenoid(double waist, double height)
{
Mesh mesh = new Mesh();
int res = m_params.Res * 2;
Func <double, Vector3D[]> oneCircle = z =>
{
double r = waist * Math.Cosh(z / waist);
Vector3D cen = new Vector3D(0, 0, z);
Vector3D radius = new Vector3D(r, 0);
return(Shapeways.Disk(cen, new Vector3D(0, 0, 1), radius, res));
};
double inc = height / (res * 2);
for (int i = 0; i < res; i++)
{
double z1 = inc * i;
double z2 = inc * (i + 1);
mesh.AddBand(oneCircle(z1), oneCircle(z2));
mesh.AddBand(oneCircle(-z1), oneCircle(-z2));
}
return(mesh);
}
public static Half Cosh(Half x) => (Half)M.Cosh(x);
public static double Cosh(double value)
{
return(CSMath.Cosh(value));
}
public Real Cosh()
{
return(Math.Cosh(Radians));
}
/// <summary>
/// Finds the hyperbolic cosine of an angle (radians).
/// </summary>
/// <param name="angle">An angle in radians.</param>
/// <returns name="cosh">Hyperbolic cosine of the angle.</returns>
/// <search>hyperbolic cosine</search>
public static double Cosh(double angle)
{
return(CSMath.Cosh(angle));
}
/// <summary>
/// The derivative of the phi function.
/// https://www.wolframalpha.com/input/?i=derivative+of+a*(1-x*tanh(x))%2Bb*tanh(x)
/// </summary>
private static double dPhi(double s, double A, double B)
{
double sech_squared = 1 / Math.Pow(Math.Cosh(s), 2);
return(A * (-Math.Tanh(s) - s * sech_squared) + B * sech_squared);
}
/// <summary>
/// Calculates a mesh for a standard euclidean catenoid.
/// This will need to be transformed to the various locations later.
///
/// Like above, but we adjust the xy components of the mesh using one of the mappings described here:
/// https://arxiv.org/ftp/arxiv/papers/1509/1509.06344.pdf
/// I found that paper here:
/// https://stackoverflow.com/questions/13211595/how-can-i-convert-coordinates-on-a-circle-to-coordinates-on-a-square
/// This is so we can connect up to the RLD mesh later.
/// </summary>
private static Mesh CatenoidSquared(double waist, double height)
{
Mesh mesh = new Mesh();
int res = m_params.Res * 2;
double diskRad = waist * Math.Cosh(height / 2 / waist);;
// NOTE: A band is *not* a constant height slice,
// so the input z value is the height at the edge midpoints of the square.
Func <double, Vector3D[]> oneCircle = z =>
{
bool neg = z < 0;
z = Math.Abs(z);
// Radius on disk at a starting edge midpoint.
double r = waist * Math.Cosh(z / waist);
Vector3D start = new Vector3D(r, 0);
Vector3D axis = new Vector3D(0, 0, 1);
List <Vector3D> points = new List <Vector3D>();
double angleInc = 2 * Math.PI / res;
double angle = 0;
for (int i = 0; i < res; i++)
{
Vector3D point = start;
point.RotateAboutAxis(axis, angle);
point = DiskToSquare(point, diskRad);
double zi = waist * DonHatch.acosh(point.Abs() / waist);
if (double.IsNaN(zi))
{
zi = 0;
}
if (neg)
{
zi *= -1;
}
Vector3D newPoint = new Vector3D(point.X, point.Y, zi);
if (newPoint.DNE)
{
throw new System.Exception();
}
points.Add(newPoint);
angle += angleInc;
}
return(points.ToArray());
};
double inc = height / (res * 2);
for (int i = 0; i < res; i++)
{
double z1 = inc * i;
double z2 = inc * (i + 1);
mesh.AddBand(oneCircle(z1), oneCircle(z2));
mesh.AddBand(oneCircle(-z1), oneCircle(-z2));
}
return(mesh);
}
/// <inheritdoc cref="IHyperbolicFunctions{TSelf}.Cosh(TSelf)" />
public static double Cosh(double x) => Math.Cosh(x);
static double IFloatingPoint <double> .Cosh(double x) => Math.Cosh(x);
public static float Cosh(float x)
{
return((float)Math.Cosh(x));
}
public static nfloat Cosh(nfloat value)
{
return((nfloat)Math.Cosh((double)value));
}
