Plane

References
[StructLayout(LayoutKind.Sequential, Pack = 8, Size = 128)] [Serializable] public struct Plane : IEquatable<Plane>, IEpsilonComparable<Plane>, ICloneable, IFormattable
Represents the value of a center point and two axes in a plane in three dimensions.

Constructors

Plane

#Since v5.0
public Plane(double a, double b, double c, double d)
Constructs a plane from an equation Ax+By+Cz+D=0.
Parameters:
a (double)
b (double)
c (double)
d (double)

Plane

#Since v5.0
public Plane(Plane other)
Copy constructor.
Parameters:
other (Plane)The source plane value.

Plane

#ExampleSince v5.0
public Plane(Point3d origin, Point3d xPoint, Point3d yPoint)
Initializes a plane from three non-collinear points.
Parameters:
origin (Point3d)Origin point of the plane.
xPoint (Point3d)Second point in the plane. The x-axis will be parallel to x_point-origin.
yPoint (Point3d)Third point on the plane that is not collinear with the first two points. taxis*(y_point-origin) will be > 0.

Plane

#ExampleSince v5.0
public Plane(Point3d origin, Vector3d normal)
Constructs a plane from a point and a normal vector.
Parameters:
origin (Point3d)Origin point of the plane.
normal (Vector3d)Non-zero normal to the plane.

Plane

#Since v5.0
public Plane(Point3d origin, Vector3d xDirection, Vector3d yDirection)
Constructs a plane from a point and two vectors in the plane.
Parameters:
origin (Point3d)Origin point of the plane.
xDirection (Vector3d)Non-zero vector in the plane that determines the x-axis direction.
yDirection (Vector3d)Non-zero vector not parallel to x_dir that is used to determine the y-axis direction. y_dir does not need to be perpendicular to x_dir.

Properties

IsValid

#Since v5.0
public bool IsValid { get; }
Gets a value indicating whether or not this is a valid plane. A plane is considered to be valid when all fields contain reasonable information and the equation jibes with point and z-axis.

Normal

#Since v5.0
public Vector3d Normal { get; }
Gets the normal of this plane. This is essentially the ZAxis of the plane.

Origin

#Since v5.0
public Point3d Origin { get; set; }
Gets or sets the origin point of this plane.

OriginX

#Since v5.0
public double OriginX { get; set; }
Gets or sets the X coordinate of the origin of this plane.

OriginY

#Since v5.0
public double OriginY { get; set; }
Gets or sets the Y coordinate of the origin of this plane.

OriginZ

#Since v5.0
public double OriginZ { get; set; }
Gets or sets the Z coordinate of the origin of this plane.

Unset

#Since v5.0
public static Plane Unset { get; }
Gets a plane that contains Unset origin and axis vectors.

WorldXY

#Since v5.0
public static Plane WorldXY { get; }
plane coincident with the World XY plane.

WorldYZ

#Since v5.0
public static Plane WorldYZ { get; }
plane coincident with the World YZ plane.

WorldZX

#Since v5.0
public static Plane WorldZX { get; }
plane coincident with the World ZX plane.

XAxis

#Since v5.0
public Vector3d XAxis { get; set; }
Gets or sets the X axis vector of this plane.

YAxis

#Since v5.0
public Vector3d YAxis { get; set; }
Gets or sets the Y axis vector of this plane.

ZAxis

#Since v5.0
public Vector3d ZAxis { get; set; }
Gets or sets the Z axis vector of this plane.

Methods

Clone

#Since v6.0
public Plane Clone()
Returns a deep copy of this instance.
Returns: A plane with the same values as this item.

ClosestParameter

#ExampleSince v5.0
[ConstOperation] public bool ClosestParameter(Point3d testPoint, out double s, out double t)
Gets the parameters of the point on the plane closest to a test point.
Parameters:
testPoint (Point3d)Point to get close to.
s (out double)Parameter along plane X-direction.
t (out double)Parameter along plane Y-direction.
Returns: true if a parameter could be found, false if the point could not be projected successfully.

ClosestPoint

#Since v5.0
[ConstOperation] public Point3d ClosestPoint(Point3d testPoint)
Gets the point on the plane closest to a test point.
Parameters:
testPoint (Point3d)Point to get close to.
Returns: The point on the plane that is closest to testPoint, or Point3d.Unset on failure.

CreateFromFrame

#Since v8.0
public static Plane CreateFromFrame(Point3d origin, Vector3d xDirection, Vector3d yDirection)
Constructs a plane from a point, and two vectors in the plane.
Parameters:
origin (Point3d)Point on the plane.
xDirection (Vector3d)Non-zero vector in the plane that determines the XAxis direction.
yDirection (Vector3d)Non-zero vector not parallel to xDirection that is used to determine the YAxis direction. Note, yDirection does not have to be perpendicular to xDirection.
Returns: A valid plane if successful, or Plane.Unset on failure.

CreateFromNormal

#Since v8.0
public static Plane CreateFromNormal(Point3d origin, Vector3d normal)
Constructs a plane from a point and normal vector.
Parameters:
origin (Point3d)Point on the plane.
normal (Vector3d)Non-zero normal to the plane.
Returns: A valid plane if successful, or Plane.Unset on failure.

CreateFromNormalYup

#Since v8.0
public static Plane CreateFromNormalYup(Point3d origin, Vector3d normal, Vector3d yDirection)
Construct a plane from a point, a normal vector, and a vector that projects to the positive YAxis.
Parameters:
origin (Point3d)Point on the plane.
normal (Vector3d)Non-zero normal to the plane.
yDirection (Vector3d)Non-zero vector, linearly independent from normal, that projects to the positive YAxis of the plane.
Returns: A valid plane if successful, or Plane.Unset on failure.

CreateFromPoints

#Since v8.0
public static Plane CreateFromPoints(Point3d origin, Point3d xPoint, Point3d yPoint)
Construct a plane from three non-collinear points.
Parameters:
origin (Point3d)Point on the plane.
xPoint (Point3d)Second point in the plane. XAxis will be parallel to xPoint-origin.
yPoint (Point3d)Third point on the plane that is not collinear with the first two points, where YAxis*(yPoint-origin) will be > 0.
Returns: A valid plane if successful, or Plane.Unset on failure.

DistanceTo

#Since v6.0
[ConstOperation] public bool DistanceTo(BoundingBox bbox, out double min, out double max)
Returns the signed minimum and maximum distances from bounding box to this plane.
Parameters:
bbox (BoundingBox)bounding box to get distances from
min (out double)minimum signed distance from plane to box
max (out double)maximum signed distance from plane to box
Returns: false if plane has zero length normal

DistanceTo

#ExampleSince v5.0
[ConstOperation] public double DistanceTo(Point3d testPoint)
Returns the signed distance from testPoint to its projection onto this plane. If the point is below the plane, a negative distance is returned.
Parameters:
testPoint (Point3d)Point to test.
Returns: Signed distance from this plane to testPoint.

EpsilonEquals

#Since v5.4
[ConstOperation] public bool EpsilonEquals(Plane other, double epsilon)
Check that all values in other are within epsilon of the values in this
Parameters:
other (Plane)
epsilon (double)
Implements: EpsilonEquals

Equals

#
public override bool Equals(object obj)
Determines if an object is a plane and has the same components as this plane.
Parameters:
obj (object)An object.
Returns: true if obj is a plane and has the same components as this plane; false otherwise.
Overrides: ValueType.Equals

Equals

#Since v5.0
public bool Equals(Plane plane)
Determines if another plane has the same components as this plane.
Parameters:
plane (Plane)A plane.
Returns: true if plane has the same components as this plane; false otherwise.

ExtendThroughBox

#Since v5.0
public bool ExtendThroughBox(BoundingBox box, out Interval s, out Interval t)
Extends this plane through a bounding box.
Parameters:
box (BoundingBox)A box to use as minimal extension boundary.
s (out Interval)If this function returns true, the s parameter returns the Interval on the plane along the X direction that will encompass the Box.
t (out Interval)If this function returns true, the t parameter returns the Interval on the plane along the Y direction that will encompass the Box.
Returns: true on success, false on failure.

ExtendThroughBox

#Since v5.0
public bool ExtendThroughBox(Box box, out Interval s, out Interval t)
Extend this plane through a Box.
Parameters:
box (Box)A box to use for extension.
s (out Interval)If this function returns true, the s parameter returns the Interval on the plane along the X direction that will encompass the Box.
t (out Interval)If this function returns true, the t parameter returns the Interval on the plane along the Y direction that will encompass the Box.
Returns: true on success, false on failure.

FitPlaneToPoints

#Since v5.0
public static PlaneFitResult FitPlaneToPoints(IEnumerable<Point3d> points, out Plane plane, out double maximumDeviation)
Fit a plane through a collection of points.
Parameters:
points (IEnumerable<Point3d>)Points to fit to.
plane (out Plane)Resulting plane.
maximumDeviation (out double)The distance from the furthest point to the plane.
Returns: A value indicating the result of the operation.

FitPlaneToPoints

#Since v5.0
public static PlaneFitResult FitPlaneToPoints(IEnumerable<Point3d> points, out Plane plane)
Fit a plane through a collection of points.
Parameters:
points (IEnumerable<Point3d>)Points to fit to.
plane (out Plane)Resulting plane.
Returns: A value indicating the result of the operation.

Flip

#Since v5.0
public void Flip()
Flip this plane by swapping out the X and Y axes and inverting the Z axis.

GetHashCode

#
public override int GetHashCode()
Gets a non-unique hashing code for this entity.
Returns: A particular number for a specific instance of plane.
Overrides: ValueType.GetHashCode

GetPlaneEquation

#Since v5.0
[ConstOperation] public double[] GetPlaneEquation()
Gets the plane equation for this plane in the format of Ax+By+Cz+D=0.
Returns: Array of four values.

IsCoplanar

#Since v8.0
public bool IsCoplanar(Plane plane, double tolerance)
Test if this plane is co-planar with a another plane.
Parameters:
plane (Plane)The plane to test.
tolerance (double)Testing tolerance.
Returns: True if this plane is co-planar with the test plane, false otherwise.

IsCoplanar

#Since v8.0
public bool IsCoplanar(Plane plane)
Test if this plane is co-planar with a another plane.
Parameters:
plane (Plane)The plane to test.
Returns: True if this plane is co-planar with the test plane, false otherwise.

PointAt

#Since v5.0
[ConstOperation] public Point3d PointAt(double u, double v, double w)
Evaluate a point on the plane.
Parameters:
u (double)evaluation parameter.
v (double)evaluation parameter.
w (double)evaluation parameter.
Returns: plane.origin + u*plane.xaxis + v*plane.yaxis + z*plane.zaxis.

PointAt

#Since v5.0
[ConstOperation] public Point3d PointAt(double u, double v)
Evaluate a point on the plane.
Parameters:
u (double)evaluation parameter.
v (double)evaluation parameter.
Returns: plane.origin + u*plane.xaxis + v*plane.yaxis.

RemapToPlaneSpace

#Since v5.0
[ConstOperation] public bool RemapToPlaneSpace(Point3d ptSample, out Point3d ptPlane)
Convert a point from World space coordinates into Plane space coordinates.
Remarks: D stands for distance, not disease.
Parameters:
ptSample (Point3d)World point to remap.
ptPlane (out Point3d)Point in plane (s,t,d) coordinates.
Returns: true on success, false on failure.

Rotate

#Since v5.0
public bool Rotate(double angle, Vector3d axis, Point3d centerOfRotation)
Rotate the plane about a custom anchor point.
Parameters:
angle (double)Angle in radians.
axis (Vector3d)Axis of rotation.
centerOfRotation (Point3d)Center of rotation.
Returns: true on success, false on failure.

Rotate

#Since v5.0
public bool Rotate(double angle, Vector3d axis)
Rotate the plane about its origin point.
Parameters:
angle (double)Angle in radians.
axis (Vector3d)Axis of rotation.
Returns: true on success, false on failure.

Rotate

#Since v5.0
public bool Rotate(double sinAngle, double cosAngle, Vector3d axis, Point3d centerOfRotation)
Rotate the plane about a custom anchor point.
Parameters:
sinAngle (double)Sin(angle)
cosAngle (double)Cos(angle)
axis (Vector3d)Axis of rotation.
centerOfRotation (Point3d)Center of rotation.
Returns: true on success, false on failure.

Rotate

#Since v5.0
public bool Rotate(double sinAngle, double cosAngle, Vector3d axis)
Rotate the plane about its origin point.
Parameters:
sinAngle (double)Sin(angle).
cosAngle (double)Cos(angle).
axis (Vector3d)Axis of rotation.
Returns: true on success, false on failure.
Explicit

ICloneable.Clone

#Since v6.0
object ICloneable.Clone()

ToString

#
public override string ToString()
Constructs the string representation of this plane.
Returns: Text.
Overrides: ValueType.ToString

ToString

#Since v7.0
public string ToString(string format, IFormatProvider formatProvider)
Formats the value of the current instance using the specified format.
Parameters:
format (string)The format to use. -or- A null reference (Nothing in Visual Basic) to use the default format defined for the type of the IFormattable implementation.
formatProvider (IFormatProvider)The provider to use to format the value. -or- A null reference (Nothing in Visual Basic) to obtain the numeric format information from the current locale setting of the operating system.
Returns: The value of the current instance in the specified format.

Transform

#Since v5.0
public bool Transform(Transform xform)
Transform the plane with a Transformation matrix.
Parameters:
xform (Transform)Transformation to apply to plane.
Returns: true on success, false on failure.

Translate

#Since v5.0
public bool Translate(Vector3d delta)
Translate (move) the plane along a vector.
Parameters:
delta (Vector3d)Translation (motion) vector.
Returns: true on success, false on failure.

UpdateEquation

#Since v6.0
public bool UpdateEquation()
Update Equations
Returns: bool

ValueAt

#Since v5.7
[ConstOperation] public double ValueAt(Point3d p)
Get the value of the plane equation at the point.
Parameters:
p (Point3d)evaluation point.
Returns: returns pe[0]*p.X + pe[1]*p.Y + pe[2]*p.Z + pe[3] where pe[0], pe[1], pe[2] and pe[3] are the coefficients of the plane equation.

Operators

OperationResultDescription
Plane==PlaneboolDetermines if two planes are equal.
Plane!=PlaneboolDetermines if two planes are different.