/// <summary>
/// Calculates the unit length edge normal.
/// </summary>
public static Vec3d GetEdgeNormal <V, E, F>(this IHalfedge <V, E, F> hedge)
where V : IHeVertex <V, E, F>, IVertex3d
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
return(GetEdgeNormal(hedge, IVertex3dStatic <V> .GetPosition));
}
/// <summary>
/// Returns the area of the quadrilateral formed between this halfedge, its previous, and the given face center.
/// See W in http://www.cs.columbia.edu/~keenan/Projects/Other/TriangleAreasCheatSheet.pdf.
/// </summary>
public static double GetArea <V, E, F>(this IHalfedge <V, E, F> hedge, Vec3d faceCenter)
where V : IHeVertex <V, E, F>, IVertex3d
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
return(GetArea(hedge, IVertex3dStatic <V> .GetPosition, faceCenter));
}
/// <summary>
/// Returns the area of the quadrilateral formed between this halfedge, its previous, and the center of their adjacent face.
/// See W in http://www.cs.columbia.edu/~keenan/Projects/Other/TriangleAreasCheatSheet.pdf.
/// </summary>
public static double GetArea <V, E, F>(this IHalfedge <V, E, F> hedge, Func <V, Vec3d> getPosition, Func <F, Vec3d> getCenter)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
return(hedge.GetArea(getPosition, getCenter(hedge.Face)));
}
/// <summary>
/// Calcuated as the exterior between adjacent faces.
/// Result is in range [0 - 2Pi].
/// Assumes the given face normals are unitized.
/// </summary>>
public static double GetDihedralAngle <V, E, F>(this IHalfedge <V, E, F> hedge, Func <F, Vec3d> getNormal)
where V : IHeVertex <V, E, F>, IVertex3d
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
return(GetDihedralAngle(hedge, IVertex3dStatic <V> .GetPosition, getNormal));
}
/// <summary>
/// Calculates the cotangent of the angle opposite this halfedge.
/// Assumes the halfedge is in a triangular face.
/// http://www.cs.columbia.edu/~keenan/Projects/Other/TriangleAreasCheatSheet.pdf
/// </summary>
public static double GetCotangent <V, E, F>(this IHalfedge <V, E, F> hedge)
where V : IHeVertex <V, E, F>, IVertex3d
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
return(GetCotangent(hedge, IVertex3dStatic <V> .GetPosition));
}
/// <summary>
///
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <param name="hedge"></param>
/// <param name="getPosition"></param>
/// <returns></returns>
public static Line ToLine <V, E>(this IHalfedge <V, E> hedge, Func <V, Vec3d> getPosition)
where V : IHeVertex <V, E>
where E : IHalfedge <V, E>
{
Vec3d p0 = getPosition(hedge.Start);
Vec3d p1 = getPosition(hedge.End);
return(new Line(p0.X, p0.Y, p0.Z, p1.X, p1.Y, p1.Z));
}
/// <summary>
/// Returns the angle between this halfedge and its previous at its start vertex.
/// Result is between 0 and Pi.
/// </summary>
/// <returns></returns>
public static double GetAngle <V, E>(this IHalfedge <V, E> hedge, Func <V, Vec3d> getPosition)
where V : IHeVertex <V, E>
where E : IHalfedge <V, E>
{
var p = getPosition(hedge.Start);
return(Vec3d.Angle(
getPosition(hedge.PreviousAtStart.End) - p,
getPosition(hedge.End) - p));
}
/// <summary>
/// Calculates the halfedge normal as the cross product of the previous halfedge and this one.
/// </summary>
public static Vec3d GetNormal <V, E, F>(this IHalfedge <V, E, F> hedge, Func <V, Vec3d> getPosition)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
Vec3d p = getPosition(hedge.Start);
return(Vec3d.Cross(
p - getPosition(hedge.PreviousInFace.Start),
getPosition(hedge.End) - p
));
}
/// <summary>
/// Returns the angle between this halfedge and its previous at its start vertex.
/// Result is between 0 and Pi.
/// </summary>
/// <returns></returns>
public static double GetAngle <V, E, F>(this IHalfedge <V, E, F> hedge, Func <V, Vec3d> getPosition)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
var p = getPosition(hedge.Start);
return(Vec3d.Angle(
getPosition(hedge.PreviousInFace.Start) - p,
getPosition(hedge.NextInFace.Start) - p
));
}
/// <summary>
/// Calculates the cotangent of the angle opposite this halfedge.
/// Assumes the halfedge is in a triangular face.
/// http://www.cs.columbia.edu/~keenan/Projects/Other/TriangleAreasCheatSheet.pdf
/// </summary>
public static double GetCotangent <V, E, F>(this IHalfedge <V, E, F> hedge, Func <V, Vec3d> getPosition)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
Vec3d p = getPosition(hedge.PreviousInFace.Start);
return(Vec3d.Cotangent(
getPosition(hedge.Start) - p,
getPosition(hedge.End) - p
));
}
/// <summary>
/// Returns the area of the quadrilateral formed between this halfedge, its previous, and the given face center.
/// See W in http://www.cs.columbia.edu/~keenan/Projects/Other/TriangleAreasCheatSheet.pdf.
/// </summary>
public static double GetArea <V, E, F>(this IHalfedge <V, E, F> hedge, Func <V, Vec3d> getPosition, Vec3d faceCenter)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
Vec3d p0 = getPosition(hedge.PreviousInFace.Start);
Vec3d p1 = getPosition(hedge.Start);
Vec3d p2 = getPosition(hedge.End);
Vec3d v0 = (p2 - p1 + p1 - p0) * 0.5;
return(Vec3d.Cross(v0, faceCenter - p1).Length * 0.5); // area of projected planar quad
}
/// <summary>
/// Calculates the unit length edge normal.
/// </summary>
public static Vec3d GetEdgeNormal <V, E, F>(this IHalfedge <V, E, F> hedge, Func <V, Vec3d> getPosition)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
Vec3d p0 = getPosition(hedge.Start);
Vec3d d1 = (getPosition(hedge.PreviousInFace.Start) + getPosition(hedge.NextInFace.End)) * 0.5 - p0;
hedge = hedge.Twin;
Vec3d d2 = getPosition(hedge.Start) - p0;
Vec3d d3 = (getPosition(hedge.PreviousInFace.Start) + getPosition(hedge.NextInFace.End)) * 0.5 - p0;
return((Vec3d.Cross(d1, d2) + Vec3d.Cross(d2, d3)).Direction);
}
/// <summary>
/// Calcuated as the exterior between adjacent faces.
/// Result is in range [0 - 2Pi].
/// Assumes the given face normals are unitized.
/// </summary>>
public static double GetDihedralAngle <V, E, F>(this IHalfedge <V, E, F> hedge, Func <V, Vec3d> getPosition, Func <F, Vec3d> getNormal)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
Vec3d tangent = getPosition(hedge.End) - getPosition(hedge.Start);
tangent.Unitize();
Vec3d x = getNormal(hedge.Face);
Vec3d y = Vec3d.Cross(x, tangent);
Vec3d d = getNormal(hedge.Twin.Face);
double t = Math.Atan2(Vec3d.Dot(d, y), Vec3d.Dot(d, x));
t = (t < 0.0) ? t + SlurMath.TwoPI : t; // shift discontinuity to 0
return(SlurMath.Mod(t + Math.PI, SlurMath.TwoPI)); // add angle bw normals and faces
}
/// <summary>
/// Calcuated as the exterior between adjacent faces.
/// Result is in range [0 - 2Pi].
/// Assumes the given face normals are unitized.
/// </summary>>
public static double GetDihedralAngle <V, E, F>(this IHalfedge <V, E, F> hedge, Func <V, Vec3d> getPosition, Func <F, Vec3d> getNormal)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
// TODO
// refactor as per http://brickisland.net/DDGFall2017/2017/10/12/assignment-1-coding-investigating-curvature/
Vec3d tangent = getPosition(hedge.End) - getPosition(hedge.Start);
tangent.Unitize();
Vec3d x = getNormal(hedge.Face);
Vec3d y = Vec3d.Cross(x, tangent);
Vec3d d = getNormal(hedge.Twin.Face);
double t = Math.Atan2(Vec3d.Dot(d, y), Vec3d.Dot(d, x));
t = (t < 0.0) ? t + SlurMath.TwoPI : t; // shift discontinuity to 0
return(SlurMath.Mod(t + Math.PI, SlurMath.TwoPI)); // add angle bw normals and faces
}
/// <summary>
/// Returns the angle between this halfedge and its previous at its start vertex.
/// Result is between 0 and Pi.
/// </summary>
/// <returns></returns>
public static double GetAngle <V, E>(this IHalfedge <V, E> hedge, Func <V, Vec3d> getPosition)
where V : IHeVertex <V, E>
where E : IHalfedge <V, E>
{
return(Vec3d.Angle(hedge.GetDelta(getPosition), hedge.PrevAtStart.GetDelta(getPosition)));
}
/// <summary>
/// Returns the difference between the end vertex and the start vertex.
/// </summary>
public static Vec3d GetDelta <V, E>(this IHalfedge <V, E> hedge, Func <V, Vec3d> getValue)
where V : IHeVertex <V, E>
where E : IHalfedge <V, E>
{
return(getValue(hedge.End) - getValue(hedge.Start));
}
/// <summary>
/// Returns a linearly interpolated value at the given parameter along the halfedge.
/// </summary>
public static double Lerp <V, E>(this IHalfedge <V, E> hedge, Func <V, double> getValue, double t)
where V : IHeVertex <V, E>
where E : IHalfedge <V, E>
{
return(SlurMath.Lerp(getValue(hedge.Start), getValue(hedge.End), t));
}
/// <summary>
/// Returns the Euclidean length of the halfedge.
/// </summary>
public static double GetLength <V, E>(this IHalfedge <V, E> hedge)
where V : IHeVertex <V, E>, IVertex3d
where E : IHalfedge <V, E>
{
return(hedge.Start.Position.DistanceTo(hedge.End.Position));
}
/// <summary>
/// Returns the angle between this halfedge and the previous at its start vertex.
/// Result is between 0 and Pi.
/// </summary>
/// <returns></returns>
public static double GetAngle <V, E>(this IHalfedge <V, E> hedge)
where V : IHeVertex <V, E>, IVertex3d
where E : IHalfedge <V, E>
{
return(GetAngle(hedge, IVertex3dStatic <V> .GetPosition));
}
/// <summary>
/// Returns the Euclidean length of the halfedge.
/// </summary>
/// <returns></returns>
public static double GetLength <V, E>(this IHalfedge <V, E> hedge, Func <V, Vec3d> getPosition)
where V : IHeVertex <V, E>
where E : IHalfedge <V, E>
{
return(getPosition(hedge.Start).DistanceTo(getPosition(hedge.End)));
}
/// <summary>
/// Returns a linearly interpolated value at the given parameter along the halfedge.
/// </summary>
public static Vec3d Lerp <V, E>(this IHalfedge <V, E> hedge, Func <V, Vec3d> getValue, double t)
where V : IHeVertex <V, E>
where E : IHalfedge <V, E>
{
return(getValue(hedge.Start).LerpTo(getValue(hedge.End), t));
}
