/// <summary>
///
/// </summary>
/// <param name="point"></param>
/// <returns></returns>
public bool ContainsIncl(Vec3d point)
{
return(X.ContainsIncl(point.X) && Y.ContainsIncl(point.Y) && Z.ContainsIncl(point.Z));
}
/// <summary>
/// Returns the area gradient of the given triangle with respect to each vertex
/// https://www.cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf p 64
/// </summary>
/// <param name="p0"></param>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <param name="g0"></param>
/// <param name="g1"></param>
/// <param name="g2"></param>
/// <returns></returns>
public static void GetTriAreaGradients(Vec3d p0, Vec3d p1, Vec3d p2, out Vec3d g0, out Vec3d g1, out Vec3d g2)
{
var d0 = p1 - p0;
var d1 = p2 - p1;
var d2 = p0 - p2;
var n = Vec3d.Cross(d0, d1);
n.Unitize();
g0 = Vec3d.Cross(n, d1) * 0.5;
g1 = Vec3d.Cross(n, d2) * 0.5;
g2 = g0 + g1;
}
/// <summary>
/// Returns the shortest vector from line a to line b.
/// http://geomalgorithms.com/a07-_distance.html
/// </summary>
/// <param name="startA"></param>
/// <param name="endA"></param>
/// <param name="startB"></param>
/// <param name="endB"></param>
/// <returns></returns>
public static Vec3d LineLineShortestVector(Vec3d startA, Vec3d endA, Vec3d startB, Vec3d endB)
{
Vec3d u = endA - startA;
Vec3d v = endB - startB;
Vec3d w = startA - startB;
LineLineClosestPoints(u, v, w, out double tu, out double tv);
return(v * tv - u * tu - w);
}
/// <summary>
/// Assumes the given axes are orthonormal.
/// </summary>
/// <param name="vector"></param>
/// <param name="xAxis"></param>
/// <param name="yAxis"></param>
/// <returns></returns>
public static double GetAngleInPlane(Vec3d vector, Vec3d xAxis, Vec3d yAxis)
{
double t = Math.Atan2(Vec3d.Dot(vector, xAxis), Vec3d.Dot(vector, yAxis));
return((t < 0.0) ? t + SlurMath.TwoPI : t); // shift discontinuity to 0
}
/// <summary>
///
/// </summary>
/// <param name="point"></param>
/// <param name="a"></param>
/// <param name="b"></param>
/// <param name="c"></param>
/// <returns></returns>
public static Vec3d GetBarycentric(Vec3d point, Vec3d a, Vec3d b, Vec3d c)
{
// TODO
throw new NotImplementedException();
}
/// <summary>
/// Projects a point to the given plane along the given direction.
/// </summary>
/// <param name="point"></param>
/// <param name="direction"></param>
/// <param name="origin"></param>
/// <param name="normal"></param>
/// <returns></returns>
public static Vec3d ProjectToPlaneAlong(Vec3d point, Vec3d origin, Vec3d normal, Vec3d direction)
{
return(point + Vec3d.MatchProjection(direction, origin - point, normal));
}
/// <summary>
/// http://www.block.arch.ethz.ch/brg/files/2013-ijss-vanmele-shaping-tension-structures-with-actively-bent-linear-elements_1386929572.pdf
/// </summary>
/// <param name="v0"></param>
/// <param name="v1"></param>
/// <returns></returns>
public static Vec3d GetCurvatureVector(Vec3d v0, Vec3d v1)
{
Vec3d v2 = Vec3d.Cross(v0, v1);
return(Vec3d.Cross((v0.SquareLength * v1 - v1.SquareLength * v0), v2) / (2.0 * v2.SquareLength));
}
/// <summary>
/// Assumes the given vectors are orthonormal.
/// </summary>
/// <param name="y"></param>
/// <param name="z"></param>
private void SetYZ(Vec3d y, Vec3d z)
{
_x = Vec3d.Cross(y, z);
_y = y;
_z = z;
}
/// <summary>
/// Assumes the given vectors are orthonormal.
/// </summary>
/// <param name="z"></param>
/// <param name="x"></param>
private void SetZX(Vec3d z, Vec3d x)
{
_x = x;
_y = Vec3d.Cross(z, x);
_z = z;
}
/// <summary>
///
/// </summary>
public OrthoBasis3d(Vec3d x, Vec3d y)
: this()
{
Set(x, y);
}
/// <summary>
/// Assumes the given vectors are orthonormal.
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
private void SetXY(Vec3d x, Vec3d y)
{
_x = x;
_y = y;
_z = Vec3d.Cross(x, y);
}
/// <summary>
///
/// </summary>
/// <param name="point"></param>
public void Include(Vec3d point)
{
X.Include(point.X);
Y.Include(point.Y);
Z.Include(point.Z);
}
/// <summary>
///
/// </summary>
/// <param name="delta"></param>
public void Expand(Vec3d delta)
{
X.Expand(delta.X);
Y.Expand(delta.Y);
Z.Expand(delta.Z);
}
/// <summary>
///
/// </summary>
/// <param name="delta"></param>
public void Translate(Vec3d delta)
{
X.Translate(delta.X);
Y.Translate(delta.Y);
Z.Translate(delta.Z);
}
/// <summary>
///
/// </summary>
/// <param name="point"></param>
/// <param name="origin"></param>
/// <param name="normal"></param>
/// <returns></returns>
public static Vec3d ProjectToPlane(Vec3d point, Vec3d origin, Vec3d normal)
{
return(point + Vec3d.Project(origin - point, normal));
}
/// <summary>
/// Applies this rotation to the given vector.
/// </summary>
/// <param name="vector"></param>
/// <returns></returns>
public Vec3d Apply(Vec3d vector)
{
return(vector.X * _x + vector.Y * _y + vector.Z * _z);
}
/// <summary>
/// Projects a vector to the given plane along the given direction.
/// </summary>
/// <param name="vector"></param>
/// <param name="normal"></param>
/// <param name="direction"></param>
/// <returns></returns>
public static Vec3d ProjectToPlaneAlong(Vec3d vector, Vec3d normal, Vec3d direction)
{
return(vector - Vec3d.MatchProjection(direction, vector, normal));
}
/// <summary>
/// Applies the inverse of this rotation to the given vector.
/// </summary>
/// <param name="vector"></param>
/// <returns></returns>
public Vec3d ApplyInverse(Vec3d vector)
{
return(new Vec3d(Vec3d.Dot(vector, _x), Vec3d.Dot(vector, _y), Vec3d.Dot(vector, _z)));
}
/// <summary>
/// Returns the center of the circle that passes through the 3 given points.
/// </summary>
/// <param name="p0"></param>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <returns></returns>
public static Vec3d GetCurvatureCenter(Vec3d p0, Vec3d p1, Vec3d p2)
{
return(p1 + GetCurvatureVector(p0 - p1, p2 - p1));
}
/// <summary>
///
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="z"></param>
public void Deconstruct(out Vec3d x, out Vec3d y, out Vec3d z)
{
x = X;
y = Y;
z = Z;
}
/// <summary>
///
/// </summary>
/// <param name="p0"></param>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <returns></returns>
public static Vec3d GetCircumcenter(Vec3d p0, Vec3d p1, Vec3d p2)
{
return(p0 + GetCurvatureVector(p1 - p0, p2 - p0));
}
/// <summary>
/// http://www.opengl-tutorial.org/intermediate-tutorials/tutorial-17-quaternions/
/// </summary>
/// <param name="direction"></param>
/// <param name=""></param>
/// <returns></returns>
public static Quaterniond CreateLookAt(Vec3d direction, Vec3d up)
{
throw new NotImplementedException();
}
/// <summary>
/// Returns parameters for the closest pair of points between lines a and b.
/// http://geomalgorithms.com/a07-_distance.html
/// </summary>
/// <param name="startA"></param>
/// <param name="endA"></param>
/// <param name="startB"></param>
/// <param name="endB"></param>
/// <param name="ta"></param>
/// <param name="tb"></param>
public static void LineLineClosestPoints(Vec3d startA, Vec3d endA, Vec3d startB, Vec3d endB, out double ta, out double tb)
{
LineLineClosestPoints(endA - startA, endB - startB, startA - startB, out ta, out tb);
}
/// <summary>
///
/// </summary>
/// <param name="axis"></param>
/// <param name="angle"></param>
public Quaterniond(Vec3d axis, double angle)
: this()
{
Set(axis, angle);
}
/// <summary>
///
/// </summary>
/// <param name="point"></param>
/// <param name="a"></param>
/// <param name="b"></param>
/// <param name="c"></param>
/// <returns></returns>
public static bool IsInTriangle(Vec3d point, Vec3d a, Vec3d b, Vec3d c)
{
// TODO
throw new NotImplementedException();
}
/// <summary>
/// The axis and angle of rotation are taken from the direction and length of the given vector respectively.
/// </summary>
/// <param name="rotation"></param>
public Quaterniond(Vec3d rotation)
: this()
{
Set(rotation);
}
/// <summary>
///
/// </summary>
/// <param name="startA"></param>
/// <param name="deltaA"></param>
/// <param name="startB"></param>
/// <param name="deltaB"></param>
/// <param name="ta"></param>
/// <param name="tb"></param>
public static void LineLineClosestPoints2(Vec3d startA, Vec3d deltaA, Vec3d startB, Vec3d deltaB, out double ta, out double tb)
{
LineLineClosestPoints(deltaA, deltaB, startA - startB, out ta, out tb);
}
/// <summary>
///
/// </summary>
/// <param name="point"></param>
/// <param name="origin"></param>
/// <param name="normal"></param>
/// <returns></returns>
public static Vec3d ReflectInPlane(Vec3d point, Vec3d origin, Vec3d normal)
{
return(point + Vec3d.Project(origin - point, normal) * 2.0);
}
/// <summary>
///
/// </summary>
/// <param name="startA"></param>
/// <param name="deltaA"></param>
/// <param name="startB"></param>
/// <param name="deltaB"></param>
/// <returns></returns>
public static Vec3d LineLineShortestVector2(Vec3d startA, Vec3d deltaA, Vec3d startB, Vec3d deltaB)
{
Vec3d w = startA - startB;
LineLineClosestPoints(deltaA, deltaB, w, out double tu, out double tv);
return(deltaB * tv - deltaA * tu - w);
}
/// <summary>
///
/// </summary>
/// <param name="center"></param>
/// <param name="offsetX"></param>
/// <param name="offsetY"></param>
/// <param name="offsetZ"></param>
public Domain3d(Vec3d center, double offsetX, double offsetY, double offsetZ)
{
X = new Domain1d(center.X - offsetX, center.X + offsetX);
Y = new Domain1d(center.Y - offsetY, center.Y + offsetY);
Z = new Domain1d(center.Z - offsetZ, center.Z + offsetZ);
}