public bool IsCoincident([NotNull] Plane3D other)
{
if (!IsParallel(other))
{
return(false);
}
// They are parallel. Now check the distance to the origin:
double thisDistance = GetDistanceSigned(0, 0, 0);
double otherDistance = other.GetDistanceSigned(0, 0, 0);
// get the sign of any non-zero component of the normal:
var one = new Pnt3D(1, 1, 1);
bool oppositeDirectionNormals =
other.Normal.GetFactor(one) * Normal.GetFactor(one) < 0;
if (oppositeDirectionNormals)
{
otherDistance *= -1;
}
double e = Math.Max(Epsilon, other.Epsilon);
return(MathUtils.AreEqual(thisDistance, otherDistance, e));
}
public bool Equals(Plane3D other, double tolerance = 0)
{
return(MathUtils.AreEqual(A, other.A, tolerance) &&
MathUtils.AreEqual(B, other.B, tolerance) &&
MathUtils.AreEqual(C, other.C, tolerance) &&
MathUtils.AreEqual(D, other.D, tolerance));
}
public void AssignUndefinedZs([NotNull] Plane3D fromPlane)
{
foreach (Linestring linestring in Linestrings)
{
linestring.AssignUndefinedZs(fromPlane);
}
}
public bool IsParallel(Plane3D other)
{
double e = Math.Max(Epsilon, other.Epsilon);
Vector crossProduct = GeomUtils.CrossProduct(Normal, other.Normal);
return(MathUtils.AreEqual(crossProduct.X, 0, e) &&
MathUtils.AreEqual(crossProduct.Y, 0, e) &&
MathUtils.AreEqual(crossProduct[2], 0, e));
}
public void AssignUndefinedZs(Plane3D fromPlane)
{
foreach (Pnt3D point in GetPoints())
{
if (double.IsNaN(point.Z))
{
point.Z = fromPlane.GetZ(point.X, point.Y);
}
}
// UpdateBounds() not needed because no XY values change
}
/// <summary>
/// Adjusts the given co-planarity tolerance for a plane based on a z and xy resolution.
/// </summary>
/// <param name="plane"></param>
/// <param name="coplanarityTolerance"></param>
/// <param name="zResolution"></param>
/// <param name="xyResolution"></param>
/// <returns></returns>
public static double AdjustCoplanarityTolerance([NotNull] Plane3D plane,
double coplanarityTolerance,
double zResolution,
double xyResolution)
{
if (coplanarityTolerance >= zResolution + xyResolution)
{
// value is large enough, use as is
return(coplanarityTolerance);
}
var normal = plane.GetUnitNormal();
double dx = normal.X * xyResolution;
double dy = normal.Y * xyResolution;
double dz = normal[2] * zResolution;
var minDistance = Math.Sqrt(dx * dx + dy * dy + dz * dz);
return(Math.Max(minDistance, coplanarityTolerance));
}
public static Plane3D FitPlane([NotNull] IList <Pnt3D> points, bool isRing = false)
{
int n = isRing ? points.Count - 1 : points.Count;
Assert.ArgumentCondition(n >= 3,
"At least 3 points (4 points in a ring) are required to define a plane.");
// Origin shift for better numerical accuracy:
// Rather than just subtracting the first point, use the actual centroid to keep the coordinates close to the origin
var sum = new Pnt3D();
for (var i = 0; i < n; i++)
{
Pnt3D point = points[i];
sum += point;
}
Pnt3D centroid = sum / n;
// 3x3 covariance matrix (excluding symmetries):
double xx = 0;
double xy = 0;
double xz = 0;
double yy = 0;
double yz = 0;
double zz = 0;
foreach (Pnt3D point in points)
{
Pnt3D r = point - centroid;
double x = r.X;
double y = r.Y;
double z = r.Z;
xx += x * x;
xy += x * y;
xz += x * z;
yy += y * y;
yz += y * z;
zz += z * z;
}
// Avoid wasting significant digits by letting the numbers gow too large!
// Otherwise the D-value easily grows to 10^15 if the the input points are spaced
// by a few 100m. See CanDetermineInclinedPlaneCoincidenceMirroredAt0
// Consider using Kahan summation as well.
double div = GetDivisorToImproveEpsilon(xx, yy, zz);
xx /= div;
xy /= div;
xz /= div;
yy /= div;
yz /= div;
zz /= div;
// Use the largest determinant for better numerical conditioning
double detX = yy * zz - yz * yz;
double detY = xx * zz - xz * xz;
double detZ = xx * yy - xy * xy;
double maxDet = Math.Max(detX, Math.Max(detY, detZ));
var normal = new Vector(3);
if (MathUtils.AreEqual(detZ, maxDet))
{
normal[0] = xy * yz - xz * yy;
normal[1] = xy * xz - yz * xx;
normal[2] = detZ;
}
else if (MathUtils.AreEqual(detX, maxDet))
{
normal[0] = detX;
normal[1] = xz * yz - xy * zz;
normal[2] = xy * yz - xz * yy;
}
else
{
normal[0] = xz * yz - xy * zz;
normal[1] = detY;
normal[2] = xy * xz - yz * xx;
}
normal = OrientNormal(normal, points, isRing);
var result = new Plane3D(normal, centroid);
// It is important to remember the worst-case epsilon, especially for collinear points
result.Epsilon = Math.Max(
result.Epsilon,
MathUtils.GetDoubleSignificanceEpsilon(xx, xy, xz, yy, yz, zz));
return(result);
}
