/// <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
}