/// <summary>
///
/// </summary>
/// <param name="y"></param>
/// <param name="yz"></param>
/// <returns></returns>
public static OrthoBasis3d CreateFromYZ(Vector3d y, Vector3d yz)
{
OrthoBasis3d result = default;
result.SetYZ(y, yz);
return(result);
}
/// <summary>
///
/// </summary>
/// <param name="direction"></param>
/// <param name="up"></param>
/// <returns></returns>
public static Quaterniond CreateLookAt(Vector3d direction, Vector3d up)
{
// impl ref
// http://www.opengl-tutorial.org/intermediate-tutorials/tutorial-17-quaternions/
return(new Quaterniond(OrthoBasis3d.CreateLookAt(direction, up)));
}
/// <summary>
///
/// </summary>
/// <param name="x"></param>
/// <param name="xz"></param>
/// <returns></returns>
public static OrthoBasis3d CreateFromXZ(Vector3d x, Vector3d xz)
{
OrthoBasis3d result = default;
result.SetXY(x, xz);
return(result);
}
/// <summary>
///
/// </summary>
/// <param name="z"></param>
/// <param name="xz"></param>
/// <returns></returns>
public static OrthoBasis3d CreateFromZX(Vector3d z, Vector3d xz)
{
OrthoBasis3d result = default;
result.SetZX(z, xz);
return(result);
}
/// <summary>
///
/// </summary>
/// <param name="y"></param>
/// <param name="xy"></param>
/// <returns></returns>
public static OrthoBasis3d CreateFromYX(Vector3d y, Vector3d xy)
{
OrthoBasis3d result = default;
result.SetYX(y, xy);
return(result);
}
/// <summary>
/// Applies the inverse of this rotation to the given rotation in place.
/// </summary>
/// <param name="other"></param>
/// <returns></returns>
public OrthoBasis3d ApplyInverse(ref OrthoBasis3d other)
{
var x = ApplyInverse(other._x);
var y = ApplyInverse(other._y);
return(new OrthoBasis3d
{
_x = x,
_y = y,
_z = Vector3d.Cross(x, y)
});
}
/// <summary>
///
/// </summary>
/// <param name="rotation"></param>
public void Set(ref OrthoBasis3d rotation)
{
// impl ref
// http://www.cs.ucr.edu/~vbz/resources/quatut.pdf
(var x, var y, var z) = rotation;
double trace = x.X + y.Y + z.Z;
if (trace > 0.0)
{
double s = Math.Sqrt(trace + 1.0);
W = 0.5 * s;
s = 0.5 / s;
X = (y.Z - z.Y) * s;
Y = (z.X - x.Z) * s;
Z = (x.Y - y.X) * s;
}
else if (Math.Abs(x.X) > Math.Abs(y.Y) && Math.Abs(x.X) > Math.Abs(z.Z))
{
double s = Math.Sqrt(1.0 + x.X - y.Y - z.Z);
X = 0.5 * s;
s = 0.5 / s;
Y = (x.Y + y.X) * s;
Z = (z.X + x.Z) * s;
W = (y.Z - z.Y) * s;
}
else if (Math.Abs(y.Y) > Math.Abs(z.Z))
{
double s = Math.Sqrt(1.0 - x.X + y.Y - z.Z);
Y = 0.5 * s;
s = 0.5 / s;
X = (x.Y + y.X) * s;
Z = (y.Z + z.Y) * s;
W = (z.X - x.Z) * s;
}
else
{
double s = Math.Sqrt(1.0 - x.X - y.Y + z.Z);
Z = 0.5 * s;
s = 0.5 / s;
X = (z.X + x.Z) * s;
Y = (y.Z + z.Y) * s;
W = (x.Y - y.X) * s;
}
}
/// <summary>
///
/// </summary>
/// <param name="rotation"></param>
public Quaterniond(OrthoBasis3d rotation)
: this()
{
Set(ref rotation);
}
/// <summary>
///
/// </summary>
/// <param name="eye"></param>
/// <param name="target"></param>
/// <param name="up"></param>
/// <returns></returns>
public static Orient3d CreateLookAt(Vector3d eye, Vector3d target, Vector3d up)
{
return(new Orient3d(OrthoBasis3d.CreateLookAt(target - eye, up), eye));
}
/// <summary>
/// Creates a relative rotation from r0 to r1.
/// </summary>
/// <param name="from"></param>
/// <param name="to"></param>
public static OrthoBasis3d CreateFromTo(OrthoBasis3d from, OrthoBasis3d to)
{
return(CreateFromTo(ref from, ref to));
}
/// <summary>
///
/// </summary>
/// <param name="rotation"></param>
/// <param name="translation"></param>
public void Deconstruct(out OrthoBasis3d rotation, out Vector3d translation)
{
rotation = Rotation;
translation = Translation;
}
/// <summary>
///
/// </summary>
/// <param name="p0"></param>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <returns></returns>
public static Orient3d CreateFromPoints(Vector3d p0, Vector3d p1, Vector3d p2)
{
return(new Orient3d(OrthoBasis3d.CreateFromXY(p1 - p0, p2 - p0), p0));
}
/// <summary>
/// Applies this rotation to the given rotation in place.
/// </summary>
/// <param name="other"></param>
/// <returns></returns>
public OrthoBasis3d Apply(OrthoBasis3d other)
{
return(Apply(ref other));
}
/// <summary>
///
/// </summary>
/// <param name="rotation"></param>
/// <param name="translation"></param>
public Orient3d(OrthoBasis3d rotation, Vector3d translation)
{
Rotation = rotation;
Translation = translation;
}
/// <summary>
/// Applies the given rotation to the axis of this rotation.
/// </summary>
/// <param name="rotation"></param>
public void RotateAxis(ref OrthoBasis3d rotation)
{
_axis = rotation.Apply(_axis);
}
/// <summary>
///
/// </summary>
/// <param name="scale"></param>
/// <param name="rotation"></param>
/// <param name="translation"></param>
public Transform3d(Vector3d scale, OrthoBasis3d rotation, Vector3d translation)
{
Scale = scale;
Rotation = rotation;
Translation = translation;
}
/// <summary>
/// Creates a relative rotation from r0 to r1.
/// </summary>
/// <param name="from"></param>
/// <param name="to"></param>
public static OrthoBasis3d CreateFromTo(ref OrthoBasis3d from, ref OrthoBasis3d to)
{
var inv = from.Inverse;
return(to.Apply(ref inv));
}
/// <summary>
///
/// </summary>
/// <param name="rotation"></param>
public bool Set(ref OrthoBasis3d rotation)
{
return(Set(new Quaterniond(rotation)));
}
/// <summary>
///
/// </summary>
/// <param name="rotation"></param>
public AxisAngle3d(OrthoBasis3d rotation)
: this()
{
Set(ref rotation);
}
/// <summary>
///
/// </summary>
/// <param name="other"></param>
/// <param name="epsilon"></param>
/// <returns></returns>
public bool ApproxEquals(ref OrthoBasis3d other, double epsilon = D.ZeroTolerance)
{
return
(_x.ApproxEquals(other._x, epsilon) &&
_y.ApproxEquals(other._y, epsilon));
}
/// <summary>
///
/// </summary>
/// <param name="other"></param>
/// <param name="epsilon"></param>
/// <returns></returns>
public bool ApproxEquals(OrthoBasis3d other, double epsilon = D.ZeroTolerance)
{
return(ApproxEquals(ref other, epsilon));
}
/// <summary>
///
/// </summary>
/// <param name="rotation"></param>
public void Set(OrthoBasis3d rotation)
{
Set(ref rotation);
}
/// <summary>
///
/// </summary>
/// <param name="scale"></param>
/// <param name="orientation"></param>
public Transform3d(Vector3d scale, Orient3d orientation)
{
Scale = scale;
Rotation = orientation.Rotation;
Translation = orientation.Translation;
}
/// <summary>
///
/// </summary>
/// <param name="rotation"></param>
/// <returns></returns>
public bool Set(OrthoBasis3d rotation)
{
return(Set(ref rotation));
}
/// <summary>
/// Applies the inverse of this rotation to the given rotation in place.
/// </summary>
/// <param name="other"></param>
/// <returns></returns>
public OrthoBasis3d ApplyInverse(OrthoBasis3d other)
{
return(ApplyInverse(ref other));
}