/// <summary>
/// Returns the position of the first non-zero digit, after the
/// decimal point. Note that the maximum return value is 10,
/// which is a design decision in the implementation.
/// </summary>
/// <param name="step">The input value.</param>
/// <returns>The position of the first non-zero digit.</returns>
public static int StepDecimals(double step)
{
double[] sd = new double[] {
0.9999,
0.09999,
0.009999,
0.0009999,
0.00009999,
0.000009999,
0.0000009999,
0.00000009999,
0.000000009999,
0.0000000009999,
0.00000000009999,
0.000000000009999,
0.0000000000009999,
0.00000000000009999,
0.000000000000009999,
};
double abs = Mathd.Abs(step);
double decs = abs - (int)abs; // Strip away integer part
for (int i = 0; i < sd.Length; i++)
{
if (decs >= sd[i])
{
return(i);
}
}
return(0);
}
public Vector3d Intersect3(Planed b, Planed c)
{
double denom = _normal.Cross(b._normal).Dot(c._normal);
if (Mathd.Abs(denom) <= Mathd.Epsilon)
{
return(new Vector3d());
}
Vector3d result = b._normal.Cross(c._normal) * D +
c._normal.Cross(_normal) * b.D +
_normal.Cross(b._normal) * c.D;
return(result / denom);
}
public Vector3d IntersectSegment(Vector3d begin, Vector3d end)
{
Vector3d segment = begin - end;
double den = _normal.Dot(segment);
if (Mathd.Abs(den) <= Mathd.Epsilon)
{
return(new Vector3d());
}
double dist = (_normal.Dot(begin) - D) / den;
if (dist < -Mathd.Epsilon || dist > 1.0f + Mathd.Epsilon)
{
return(new Vector3d());
}
return(begin + segment * -dist);
}
public Vector3d IntersectRay(Vector3d from, Vector3d dir)
{
double den = _normal.Dot(dir);
if (Mathd.Abs(den) <= Mathd.Epsilon)
{
return(new Vector3d());
}
double dist = (_normal.Dot(from) - D) / den;
// This is a ray, before the emitting pos (from) does not exist
if (dist > Mathd.Epsilon)
{
return(new Vector3d());
}
return(from + dir * -dist);
}
/// <summary>
/// Returns the result of the spherical linear interpolation between
/// this quaternion and `to` by amount `weight`, but without
/// checking if the rotation path is not bigger than 90 degrees.
/// </summary>
/// <param name="to">The destination quaternion for interpolation. Must be normalized.</param>
/// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
/// <returns>The resulting quaternion of the interpolation.</returns>
public Quatd Slerpni(Quatd to, double weight)
{
double dot = Dot(to);
if (Mathd.Abs(dot) > 0.9999f)
{
return(this);
}
double theta = Mathd.Acos(dot);
double sinT = 1.0f / Mathd.Sin(theta);
double newFactor = Mathd.Sin(weight * theta) * sinT;
double invFactor = Mathd.Sin((1.0f - weight) * theta) * sinT;
return(new Quatd
(
invFactor * x + newFactor * to.x,
invFactor * y + newFactor * to.y,
invFactor * z + newFactor * to.z,
invFactor * w + newFactor * to.w
));
}
public Quatd Slerpni(Quatd b, double t)
{
double dot = Dot(b);
if (Mathd.Abs(dot) > 0.9999f)
{
return(this);
}
double theta = Mathd.Acos(dot);
double sinT = 1.0f / Mathd.Sin(theta);
double newFactor = Mathd.Sin(t * theta) * sinT;
double invFactor = Mathd.Sin((1.0f - t) * theta) * sinT;
return(new Quatd
(
invFactor * x + newFactor * b.x,
invFactor * y + newFactor * b.y,
invFactor * z + newFactor * b.z,
invFactor * w + newFactor * b.w
));
}
public bool IsNormalized()
{
return(Mathd.Abs(LengthSquared() - 1.0f) < Mathd.Epsilon);
}
public Vector4d Abs()
{
return(new Vector4d(Mathd.Abs(x), Mathd.Abs(y), Mathd.Abs(z), Mathd.Abs(w)));
}
/// <summary>
/// Returns a new vector with all components in absolute values (i.e. positive).
/// </summary>
/// <returns>A vector with <see cref="Mathd.Abs(double)"/> called on each component.</returns>
public Vector2d Abs()
{
return(new Vector2d(Mathd.Abs(x), Mathd.Abs(y)));
}
/// <summary>
/// Returns whether the quaternion is normalized or not.
/// </summary>
/// <returns>A bool for whether the quaternion is normalized or not.</returns>
public bool IsNormalized()
{
return(Mathd.Abs(LengthSquared - 1) <= Mathd.Epsilon);
}
public bool HasPoint(Vector3d point, double epsilon = Mathd.Epsilon)
{
double dist = _normal.Dot(point) - D;
return(Mathd.Abs(dist) <= epsilon);
}
/// <summary>
/// Returns a new vector with all components in absolute values (i.e. positive).
/// </summary>
/// <returns>A vector with <see cref="Mathd.Abs(double)"/> called on each component.</returns>
public Vector3d Abs()
{
return(new Vector3d(Mathd.Abs(x), Mathd.Abs(y), Mathd.Abs(z)));
}