public static TVec Normal3D(TVec p, TVec q, TVec r)
{
Contract.Requires(Contract.ForAll(new TVec[] { p, q, r }, x => x != null));
Contract.Requires(Contract.ForAll(new TVec[] { p, q, r }, x => x.Dimension == 3));
return(TVec.CrossProduct(q - p, r - p));
}
public static Term Coplanarity3D(params TVec[] vecs)
{
Contract.Requires(Contract.ForAll(vecs, vec => vec != null));
Contract.Requires(Contract.ForAll(vecs, vec => vec.Dimension == 3));
var a = vecs[0];
var b = vecs[1];
var c = vecs[2];
var d = vecs[3];
var dot = TVec.CrossProduct(b - a, c - a) * (d - a); // the normal to (b-a) and (c-a) is also normal of (d-a)
return(dot);
}
private IEnumerable <TVec> GetPointsOnPlane(TVec p, TVec n)
{
var vec3d = random.NextVector3D().Normalized();
var tvec = new TVec(vec3d.X, vec3d.Y, vec3d.Z);
var t = TVec.CrossProduct(n, tvec);
var u = TVec.CrossProduct(n, t);
yield return(p + t);
yield return(p + u);
yield return(p - t);
yield return(p - u);
}
private Term[] GetConcreteAnnotationTerm(CoplanarCenters coplanarCenters)
{
var constraints = new List <Term>();
if (coplanarCenters.Elements.Length >= 2)
{
foreach (var pair in coplanarCenters.Elements.SeqPairs())
{
var c1 = pair.Item1.Center;
var n1 = pair.Item1.Normal;
var c2 = pair.Item2.Center;
var n2 = pair.Item2.Normal;
var term = (c2 - c1) * TVec.CrossProduct(n1, n2);
constraints.Add(term);
}
}
return(constraints.ToArray());
}
/// <summary>
/// Measures parallelism of two 3D vectors
/// </summary>
/// <param name="left">Left vector</param>
/// <param name="right">Right vector</param>
/// <returns></returns>
public static Term VectorParallelism3D(TVec left, TVec right)
{
return(TVec.CrossProduct(left, right).NormSquared);
}