/// <summary>
/// Normalizes the specified Plane3D.NormalVector.
/// </summary>
/// <param name="src">Plane</param>
public static void Normalize(this Plane3D src)
{
var v = src.NormalVector;
v.Normalize();
src.NormalVector = v;
}
public static List <Line3D> GetIntersection(this Polygon3D polygon, Plane3D plane)
{
var points = new List <WM.Point3D>(2);
var count = polygon.Count;
for (var i = 1; i < count; ++i)
{
var l0 = polygon[i - 1];
var l = polygon[i] - l0;
var d = WM.Vector3D.DotProduct(l, plane.NormalVector);
if (!d.IsZero(1e-12))
{
d = GetIntersecionDistance(l0, l, plane);
if (d.IsGreaterOrEqual(0) && d.IsLesserOrEqual(1)) // d >= 0 && d <= 1
{
var intersection = d * l + l0;
points.Add(intersection);
}
}
}
RemoveDuplicates(points);
count = points.Count;
// System.Diagnostics.Debug.Assert(!(count > 2 && count % 2 != 0));
var lines = new List <Line3D>(count / 2);
for (var i = 1; i < count; i += 2)
{
var line = new Line3D(points[i - 1], points[i]);
lines.Add(line);
}
return(lines);
}
/// <summary>
/// Gets intersection of two planes
/// </summary>
/// <param name="plane1">The first plane</param>
/// <param name="plane2">The second plane</param>
/// <param name="pointOnLine">Point on line where <paramref name="plane1"/> and <paramref name="plane1"/> are intersecting</param>
/// <param name="dirVect">Direction vector of the intersection</param>
/// <returns>True if intersection exists</returns>
public static bool GetIntersection(Plane3D plane1, Plane3D plane2, out WM.Point3D pointOnLine, out WM.Vector3D dirVect)
{
#if DEBUG
// Normal vectors should be normalized
WM.Vector3D testVect1 = plane1.NormalVector;
testVect1.Normalize();
WM.Vector3D testVect2 = plane2.NormalVector;
testVect2.Normalize();
Debug.Assert(WM.Vector3D.DotProduct(plane1.NormalVector, plane2.NormalVector).IsEqual(WM.Vector3D.DotProduct(testVect1, testVect2)));
#endif
double normalDot = WM.Vector3D.DotProduct(plane1.NormalVector, plane2.NormalVector);
double D = (1 - normalDot * normalDot);
if (D.IsZero())
{
pointOnLine = new WM.Point3D(double.NaN, double.NaN, double.NaN);
dirVect = new WM.Vector3D(double.NaN, double.NaN, double.NaN);
return(false);
}
double h1 = -1 * plane1.GetD();
double h2 = -1 * plane2.GetD();
double c1 = (h1 - h2 * normalDot) / D;
double c2 = (h2 - h1 * normalDot) / D;
dirVect = WM.Vector3D.CrossProduct(plane1.NormalVector, plane2.NormalVector);
dirVect.Normalize();
pointOnLine = (WM.Point3D)(c1 * plane1.NormalVector + c2 * plane2.NormalVector);
return(true);
}
/// <summary>
/// Gets distance of the <paramref name="point"/> from <paramref name="line"/>
/// </summary>
/// <param name="line">Line</param>
/// <param name="point">Point</param>
/// <returns>Distance</returns>
public static double Distance(ref StraightLine line, ref WM.Point3D point)
{
Plane3D tempPln = new Plane3D(point, line.Direction);
var temPlnIntersection = tempPln.GetIntersection(ref line);
return((temPlnIntersection - point).Length);
}
/// <summary>
/// Returns the ordered tuple. Point in Item1 is closer to the plane
/// </summary>
/// <param name="src">Plane</param>
/// <param name="pt1">Tested point1</param>
/// <param name="pt2">Tested point2</param>
/// <returns>The ordered tuple</returns>
public static Tuple <IPoint3D, IPoint3D> OrderPointsByDistance(this Plane3D src, IPoint3D pt1, IPoint3D pt2)
{
double distPt1 = Math.Abs(src.GetPointDistance(pt1));
double distPt2 = Math.Abs(src.GetPointDistance(pt2));
if (distPt1 > distPt2)
{
return(new Tuple <IPoint3D, IPoint3D>(pt2, pt1));
}
return(new Tuple <IPoint3D, IPoint3D>(pt1, pt2));
}
/// <summary>
/// Calculates intersection of the plane and line which is defined by direction vector <paramref name="l"/> and point <paramref name="l0"/>
/// </summary>
/// <param name="src">Plane</param>
/// <param name="ray">Straight line</param>
/// <returns>Found intersection. If intersection doesn't NaN is set</returns>
public static WM.Point3D GetIntersection(this Plane3D src, ref StraightLine ray)
{
double d = WM.Vector3D.DotProduct(src.NormalVector, ray.Direction);
if (d.IsZero())
{
return(new WM.Point3D(double.NaN, double.NaN, double.NaN));
}
double dd = WM.Vector3D.DotProduct((src.PointOnPlane - ray.Point), src.NormalVector) / d;
return(ray.Point + dd * ray.Direction);
}
/// <summary>
/// Calculates intersection of the plane and line which is defined by direction vector <paramref name="l"/> and point <paramref name="l0"/>
/// </summary>
/// <param name="src">Plane</param>
/// <param name="l0">Point on line</param>
/// <param name="l">Direction vector of line</param>
/// <returns>Found intersection. If intersection doesn't NaN is set</returns>
public static WM.Point3D GetIntersection(this Plane3D src, WM.Point3D l0, WM.Vector3D l)
{
double d = WM.Vector3D.DotProduct(src.NormalVector, l);
if (d.IsZero())
{
return(new WM.Point3D(double.NaN, double.NaN, double.NaN));
}
double dd = WM.Vector3D.DotProduct((src.PointOnPlane - l0), src.NormalVector) / d;
return(l0 + dd * l);
}
/// <summary>
/// Return the new instance of the paralel plane
/// </summary>
/// <param name="src">Source plane</param>
/// <param name="offset">Distance between planes.
/// Positive value is in the direction of normal vector of this plane</param>
/// <returns>The new instance of the plane</returns>
public static Plane3D Offset(this Plane3D src, double offset)
{
if (offset.IsZero())
{
return(new Plane3D(src));
}
var v = WM.Vector3D.Multiply(src.NormalVector, offset);
var n = v;
n.Normalize();
return(new Plane3D(src.PointOnPlane + v, n));
}
public Plane3D GetPlane()
{
if (this.Count < 3)
{
return(null);
}
var v1 = this[0] - this[1];
var v2 = this[2] - this[1];
var n = WM.Vector3D.CrossProduct(v1, v2);
n.Normalize();
var p = new Plane3D(this[0], n);
return(p);
}
/// <summary>
/// Returns the distance of <paramref name="line1"/> and <paramref name="line2"/>
/// </summary>
/// <param name="line1">The first line</param>
/// <param name="line2">The second line</param>
/// <returns>Distance</returns>
public static double Distance(ref StraightLine line1, ref StraightLine line2)
{
var dot = Math.Abs(WM.Vector3D.DotProduct(line1.Direction, line2.Direction));
if (dot.IsEqual(1, 1e-8))
{
// lines are parallel
var pln = new Plane3D(line1.Point, line1.Direction);
var line2Intersection = pln.GetIntersection(ref line2);
return((line1.Point - line2Intersection).Length);
}
var cross = WM.Vector3D.CrossProduct(line1.Direction, line2.Direction);
var pln2 = new Plane3D(line1.Point, cross);
var dist = pln2.GetPointDistance(ref line2.Point);
return(Math.Abs(dist));
}
/// <summary>
/// Calculates intersection of the plane and line <paramref name="lineSeg"/>
/// </summary>
/// <param name="src">Plane</param>
/// <param name="lineSeg">Line segment</param>
/// <returns></returns>
public static WM.Point3D GetIntersection(this Plane3D src, ILineSegment3D lineSeg)
{
var l = new WM.Vector3D(lineSeg.EndPoint.X - lineSeg.StartPoint.X,
lineSeg.EndPoint.Y - lineSeg.StartPoint.Y,
lineSeg.EndPoint.Z - lineSeg.StartPoint.Z);
l.Normalize();
double d = WM.Vector3D.DotProduct(src.NormalVector, l);
if (d.IsZero())
{
return(new WM.Point3D(double.NaN, double.NaN, double.NaN));
}
WM.Point3D l0 = lineSeg.StartPoint.ToMediaPoint();
double dd = WM.Vector3D.DotProduct((src.PointOnPlane - l0), src.NormalVector) / d;
return(l0 + dd * l);
}
/// <summary>
/// Transforms a Plane3D from GCS to LCS
/// </summary>
/// <param name="pln">Plane to be tranformed [In GCS].</param>
/// <returns>Plane in LCS</returns>
public Plane3D TransformToLCS(Plane3D pln)
{
return(new Plane3D(TransformToLCS(pln.PointOnPlane), TransformToLCS(pln.NormalVector)));
}
private static double GetIntersecionDistance(WM.Point3D linePoint, WM.Vector3D lineDir, Plane3D plane)
{
var d = WM.Vector3D.DotProduct(plane.PointOnPlane - linePoint, plane.NormalVector) / WM.Vector3D.DotProduct(lineDir, plane.NormalVector);
return(d);
}
/// <summary>
/// Copy constructor
/// </summary>
/// <param name="src">Source</param>
public Plane3D(Plane3D src)
{
this.point = src.point;
this.normal = src.normal;
}
/// <summary>
/// Caluclates distance from a point to a plane
/// </summary>
/// <param name="src">Plane</param>
/// <param name="p">Point</param>
/// <returns>Distance from a point to a plane (positive value is in the direction of the normal vector)</returns>
public static double GetPointDistance(this Plane3D src, IPoint3D p)
{
return((WM.Vector3D.DotProduct(src.NormalVector, new WM.Vector3D(p.X, p.Y, p.Z)) + src.GetD()) / src.NormalVector.Length);
}
/// <summary>
/// Caluclates distance from a point to a plane
/// </summary>
/// <param name="src">Plane</param>
/// <param name="p">Point</param>
/// <returns>Distance from a point to a plane (positive value is in the direction of the normal vector)</returns>
public static double GetPointDistance(this Plane3D src, ref WM.Point3D p)
{
return((WM.Vector3D.DotProduct(src.NormalVector, (WM.Vector3D)p) + src.GetD()) / src.NormalVector.Length);
}
/// <summary>
/// Gets parameter d in plane equation ax + by + cz + d = 0
/// </summary>
/// <param name="src">Source plane</param>
/// <returns>Returns d parameter</returns>
public static double GetD(this Plane3D src)
{
return(-1 * WM.Vector3D.DotProduct(src.NormalVector, (WM.Vector3D)src.PointOnPlane));
}