Struct Vector3

A 3D vector.

Implements

System.IComparable<Vector3>

System.IEquatable<Vector3>

Inherited Members

System.Object.Equals(System.Object, System.Object)

System.Object.GetType()

System.Object.ReferenceEquals(System.Object, System.Object)

Namespace: Elements.Geometry

Assembly: Hypar.Elements.dll

Syntax

public struct Vector3 : IComparable<Vector3>, IEquatable<Vector3>

Constructors

Vector3(Vector3)

Create a Vector3 by copying the components of another Vector3.

Declaration

public Vector3(Vector3 v)

Parameters

Type	Name	Description
Vector3	v	The Vector3 to copy.

Vector3(Double, Double)

Create a vector from x, and y coordinates.

Declaration

public Vector3(double x, double y)

Parameters

Type	Name	Description
System.Double	x	The x coordinate of the vector.
System.Double	y	Thy y coordinate of the vector.

Vector3(Double, Double, Double)

Create a vector.

Declaration

[JsonConstructor]
public Vector3(double x, double y, double z)

Parameters

Type	Name	Description
System.Double	x	The x component.
System.Double	y	The y component.
System.Double	z	The z component.

Fields

COS_ANGLE_EPSILON

A tolerance for angle comparison operation of cos of 0.001 degrees.

Declaration

public const double COS_ANGLE_EPSILON = 0.99999999984769128

Field Value

Type	Description
System.Double

EPSILON

A tolerance for comparison operations of 1e-5.

Declaration

public const double EPSILON = 1E-05

Field Value

Type	Description
System.Double

Properties

Max

The largest possible value of a Vector3.

Declaration

public static readonly Vector3 Max { get; }

Property Value

Type	Description
Vector3

Min

The smallest possible value of a Vector3.

Declaration

public static readonly Vector3 Min { get; }

Property Value

Type	Description
Vector3

Origin

Create a vector at the origin.

Declaration

public static readonly Vector3 Origin { get; }

Property Value

Type	Description
Vector3

X

The X component of the vector.

Declaration

[JsonProperty("X", Required = Required.Always)]
public double X { get; set; }

Property Value

Type	Description
System.Double

XAxis

Create a vector along the X axis.

Declaration

public static readonly Vector3 XAxis { get; }

Property Value

Type	Description
Vector3

Y

The Y component of the vector.

Declaration

[JsonProperty("Y", Required = Required.Always)]
public double Y { get; set; }

Property Value

Type	Description
System.Double

YAxis

Create a vector along the Y axis.

Declaration

public static readonly Vector3 YAxis { get; }

Property Value

Type	Description
Vector3

Z

The Z component of the vector.

Declaration

[JsonProperty("Z", Required = Required.Always)]
public double Z { get; set; }

Property Value

Type	Description
System.Double

ZAxis

Create a vector along the Z axis.

Declaration

public static readonly Vector3 ZAxis { get; }

Property Value

Type	Description
Vector3

Methods

AngleTo(Vector3)

The angle in degrees from this vector to the provided vector. Note that for angles in the plane that can be greater than 180 degrees, you should use Vector3.PlaneAngleTo.

Declaration

public double AngleTo(Vector3 v)

Parameters

Type	Name	Description
Vector3	v	The vector with which to measure the angle.

Returns

Type	Description
System.Double	The angle in degrees between 0 and 180.

AreCollinear(Vector3, Vector3, Vector3)

Check whether three points are on the same line.

Declaration

[Obsolete("Use AreCollinearByDistance or AreCollinearByAngle instead")]
public static bool AreCollinear(Vector3 a, Vector3 b, Vector3 c)

Parameters

Type	Name	Description
Vector3	a	The first point.
Vector3	b	The second point.
Vector3	c	The third point.

Returns

Type	Description
System.Boolean	True if the points are on the same line, false otherwise.

AreCollinearByAngle(Vector3, Vector3, Vector3, Double)

Check whether three points are on the same line within certain angle. Order is important since unsigned abc angle is checked. This function is much faster than AreCollinearByDistance but angle deviation scales with the distance of points being compared. If points are far away from each other they might appear collinear even if there are large distance offsets between them.

Declaration

public static bool AreCollinearByAngle(Vector3 a, Vector3 b, Vector3 c, double cosAngleTolerance = 0.99999999984769128)

Parameters

Type	Name	Description
Vector3	a	The first point.
Vector3	b	The second point.
Vector3	c	The third point.
System.Double	cosAngleTolerance	Angle tolerance as cos.

Returns

Type	Description
System.Boolean

AreCollinearByDistance(Vector3, Vector3, Vector3, Double)

Check whether three points are on the same line within certain distance. This function is slower than AreCollinearByAngle and less suitable for high complexity code.

Declaration

public static bool AreCollinearByDistance(Vector3 a, Vector3 b, Vector3 c, double tolerance = 1E-05)

Parameters

Type	Name	Description
Vector3	a	The first point.
Vector3	b	The second point.
Vector3	c	The third point.
System.Double	tolerance	Distance tolerance.

Returns

Type	Description
System.Boolean	True if the points are on the same line, false otherwise.

AreCoplanar(Vector3, Vector3, Vector3, Vector3)

Are four provided points on the same plane?

Declaration

public static bool AreCoplanar(Vector3 a, Vector3 b, Vector3 c, Vector3 d)

Parameters

Type	Name	Description
Vector3	a
Vector3	b
Vector3	c
Vector3	d

Returns

Type	Description
System.Boolean

AtNEqualSpacesAlongLine(Line, Int32, Boolean)

Create vectors at n equal spaces along the provided line.

Declaration

public static IList<Vector3> AtNEqualSpacesAlongLine(Line line, int n, bool includeEnds = false)

Parameters

Type	Name	Description
Line	line	The line.
System.Int32	n	The number of samples along the line.
System.Boolean	includeEnds	A flag indicating whether or not to include points for the start and end of the line.

Returns

Type	Description
System.Collections.Generic.IList<Vector3>

Average(Vector3)

Compute the average of this Vector3 and v.

Declaration

public Vector3 Average(Vector3 v)

Parameters

Type	Name	Description
Vector3	v	The vector with which to compute the average.

Returns

Type	Description
Vector3	A vector which is the average of this and v.

CCW(Vector3, Vector3, Vector3)

Check whether three points are wound CCW in two dimensions.

Declaration

public static double CCW(Vector3 a, Vector3 b, Vector3 c)

Parameters

Type	Name	Description
Vector3	a	The first point.
Vector3	b	The second point.
Vector3	c	The third point.

Returns

Type	Description
System.Double	Greater than 0 if the points are CCW, less than 0 if they are CW, and 0 if they are collinear.

ClosestPointOn(Line, Boolean)

Get the closest point on the line from this point.

Declaration

public Vector3 ClosestPointOn(Line line, bool infinite = false)

Parameters

Type	Name	Description
Line	line	The line on which to find the closest point.
System.Boolean	infinite	If true, line will be treated as infinite. (False by default)

Returns

Type	Description
Vector3	The closest point on the line from this point.

CompareTo(Vector3)

Implement IComparable interface.

Declaration

public int CompareTo(Vector3 v)

Parameters

Type	Name	Description
Vector3	v

Returns

Type	Description
System.Int32

ComputeDefaultBasisVectors()

Compute basis vectors for this vector. By default, the cross product of the world Z axis and this vector are used to compute the U direction. If this vector is parallel the world Z axis, then the world Y axis is used instead.

Declaration

public (Vector3 U, Vector3 V) ComputeDefaultBasisVectors()

Returns

Type	Description
System.ValueTuple<Vector3, Vector3>

Cross(Vector3)

Compute the cross product of this vector and v.

Declaration

public Vector3 Cross(Vector3 v)

Parameters

Type	Name	Description
Vector3	v	The vector with which to compute the cross product.

Returns

Type	Description
Vector3

Cross(Double, Double, Double)

Compute the cross product of this vector and a vector composed of the provided components.

Declaration

public Vector3 Cross(double x, double y, double z)

Parameters

Type	Name	Description
System.Double	x	X
System.Double	y	Y
System.Double	z	Z

Returns

Type	Description
Vector3

DistanceTo(Line)

Find the distance from this point to the line.

Declaration

public double DistanceTo(Line line)

Parameters

Type	Name	Description
Line	line

Returns

Type	Description
System.Double

DistanceTo(Line, out Vector3)

Find the distance from this point to the line, and output the location of the closest point on that line. Using formula from https://diego.assencio.com/?index=ec3d5dfdfc0b6a0d147a656f0af332bd

Declaration

public double DistanceTo(Line line, out Vector3 closestPoint)

Parameters

Type	Name	Description
Line	line	The line to find the distance to.
Vector3	closestPoint	The point on the line that is closest to this point.

Returns

Type	Description
System.Double

DistanceTo(Plane)

The distance from this point to the plane. The distance will be negative when this point lies "behind" the plane.

Declaration

public double DistanceTo(Plane p)

Parameters

Type	Name	Description
Plane	p	The plane.

Returns

Type	Description
System.Double

DistanceTo(Polygon)

Find the shortest distance from this point to any point within the polygon

Declaration

public double DistanceTo(Polygon polygon)

Parameters

Type	Name	Description
Polygon	polygon	The polygon for computing the distance

Returns

Type	Description
System.Double

DistanceTo(Polygon, out Vector3)

Find the shortest distance from this point to any point within the polygon, and output the location of the closest point on that polygon.

Declaration

public double DistanceTo(Polygon polygon, out Vector3 closestPoint)

Parameters

Type	Name	Description
Polygon	polygon	The polygon for computing the distance
Vector3	closestPoint	Point within the polygon that is closest to this point

Returns

Type	Description
System.Double

DistanceTo(Polyline)

Find the shortest distance from this point to any point on the polyline, and output the location of the closest point on that polyline.

Declaration

public double DistanceTo(Polyline polyline)

Parameters

Type	Name	Description
Polyline	polyline	The polyline for computing the distance.

Returns

Type	Description
System.Double

DistanceTo(Polyline, out Vector3)

Find the shortest distance from this point to any point on the polyline, and output the location of the closest point on that polyline.

Declaration

public double DistanceTo(Polyline polyline, out Vector3 closestPoint)

Parameters

Type	Name	Description
Polyline	polyline	The polyline for computing the distance.
Vector3	closestPoint	The point on the polyline that is closest to this point.

Returns

Type	Description
System.Double

DistanceTo(Ray)

The distance from this point to the ray. The ray is treated as being infinitely long.

Declaration

public double DistanceTo(Ray ray)

Parameters

Type	Name	Description
Ray	ray	The target ray.

Returns

Type	Description
System.Double

DistanceTo(Vector3)

The distance from this point to v.

Declaration

public double DistanceTo(Vector3 v)

Parameters

Type	Name	Description
Vector3	v	The target vector.

Returns

Type	Description
System.Double	The distance between this vector and the provided vector.

DistanceTo((Vector3 from, Vector3 to), out Vector3)

Find the distance from this point to the edge, and output the location of the closest point on that line. Using formula from https://diego.assencio.com/?index=ec3d5dfdfc0b6a0d147a656f0af332bd

Declaration

public double DistanceTo((Vector3 from, Vector3 to) edge, out Vector3 closestPoint)

Parameters

Type	Name	Description
System.ValueTuple<Vector3, Vector3>	edge	The edge to find the distance to.
Vector3	closestPoint	The point on the line that is closest to this point.

Returns

Type	Description
System.Double

Dot(Vector3)

Compute the dot product of this vector and v.

Declaration

public double Dot(Vector3 v)

Parameters

Type	Name	Description
Vector3	v	The vector with which to compute the dot product.

Returns

Type	Description
System.Double	A value between 1 and -1.

Dot(Double, Double, Double)

Compute the dot product of this vector and a vector composed of the provided components.

Declaration

public double Dot(double x, double y, double z)

Parameters

Type	Name	Description
System.Double	x	X
System.Double	y	Y
System.Double	z	Z

Returns

Type	Description
System.Double	A value between 1 and -1.

Equals(Vector3)

Is this vector equal to the provided vector?

Declaration

public bool Equals(Vector3 other)

Parameters

Type	Name	Description
Vector3	other	The vector to test.

Returns

Type	Description
System.Boolean	Returns true if all components of the two vectors are within Epsilon, otherwise false.

Equals(Object)

Is this vector equal to the provided vector?

Declaration

public override bool Equals(object other)

Parameters

Type	Name	Description
System.Object	other	The vector to test.

Returns

Type	Description
System.Boolean	Returns true if all components of the two vectors are within Epsilon, otherwise false.

Overrides

System.ValueType.Equals(System.Object)

GetHashCode()

Get the hash code for the vector.

Declaration

public override int GetHashCode()

Returns

Type	Description
System.Int32

Overrides

System.ValueType.GetHashCode()

IsAlmostEqualTo(Vector3, Double)

Determine whether this vector's components are equal to those of v, within tolerance.

Declaration

public bool IsAlmostEqualTo(Vector3 v, double tolerance = 1E-05)

Parameters

Type	Name	Description
Vector3	v	The vector to compare.
System.Double	tolerance	Optional custom tolerance value.

Returns

Type	Description
System.Boolean	True if the difference of this vector and the supplied vector's components are all within Tolerance, otherwise false.

IsAlmostEqualTo(Double, Double, Double)

Determine whether this vector's components are equal to the provided components, within tolerance.

Declaration

public bool IsAlmostEqualTo(double x, double y, double z = 0)

Parameters

Type	Name	Description
System.Double	x	The x component to compare.
System.Double	y	The y component to compare.
System.Double	z	The z component to compare.

Returns

Type	Description
System.Boolean	True if the difference of this vector and the supplied vector's components are all within Tolerance, otherwise false.

IsNaN()

Are any components of this vector NaN?

Declaration

public bool IsNaN()

Returns

Type	Description
System.Boolean	True if any components are NaN otherwise false.

IsParallelTo(Vector3, Double)

Determine whether this vector is parallel to v.

Declaration

public bool IsParallelTo(Vector3 v, double tolerance = 1E-05)

Parameters

Type	Name	Description
Vector3	v	The vector to compare to this vector.
System.Double	tolerance	The amount of tolerance in the parallel comparison.

Returns

Type	Description
System.Boolean	True if the vectors are parallel, otherwise false.

IsUnitized()

Is this vector of unit length?

Declaration

public bool IsUnitized()

Returns

Type	Description
System.Boolean	True if the vector is of unit length, otherwise false.

IsZero()

Is this vector zero length?

Declaration

public bool IsZero()

Returns

Type	Description
System.Boolean	True if this vector's components are all less than Epsilon.

Length()

Get the length of this vector.

Declaration

public double Length()

Returns

Type	Description
System.Double

LengthSquared()

Get the squared length of this vector.

Declaration

public double LengthSquared()

Returns

Type	Description
System.Double

Negate()

Construct a new vector which is the inverse of this vector.

Declaration

public Vector3 Negate()

Returns

Type	Description
Vector3	A new vector which is the inverse of this vector.

PlaneAngleTo(Vector3)

Calculate a counter-clockwise plane angle between this vector and the provided vector in the XY plane.

Declaration

public double PlaneAngleTo(Vector3 v)

Parameters

Type	Name	Description
Vector3	v	The vector with which to measure the angle.

Returns

Type	Description
System.Double	Angle in degrees between 0 and 360, or NaN if the projected input vectors are invalid.

PlaneAngleTo(Vector3, Vector3)

Calculate a counter-clockwise plane angle between this vector and the provided vector, projected to the plane perpendicular to the provided normal.

Declaration

public double PlaneAngleTo(Vector3 v, Vector3 normal)

Parameters

Type	Name	Description
Vector3	v	The vector with which to measure the angle.
Vector3	normal	The normal of the plane in which you wish to calculate the angle.

Returns

Type	Description
System.Double	Angle in degrees between 0 and 360, or NaN if the projected input vectors are invalid.

Project(Plane)

Project this vector onto the plane.

Declaration

public Vector3 Project(Plane p)

Parameters

Type	Name	Description
Plane	p	The plane on which to project the point.

Returns

Type	Description
Vector3

ProjectAlong(Vector3, Plane)

Project this vector onto the plane along a vector.

Declaration

public Vector3 ProjectAlong(Vector3 v, Plane p)

Parameters

Type	Name	Description
Vector3	v	The vector along which t project.
Plane	p	The plane on which to project.

Returns

Type	Description
Vector3	A point on the plane.

ProjectOnto(Vector3)

Project vector a onto this vector.

Declaration

public Vector3 ProjectOnto(Vector3 a)

Parameters

Type	Name	Description
Vector3	a	The vector to project onto this vector.

Returns

Type	Description
Vector3	A new vector which is the projection of a onto this vector.

ToArray()

Convert a vector's components to an array.

Declaration

public double[] ToArray()

Returns

Type	Description
System.Double[]	An array of comprised of the x, y, and z components of this vector.

ToString()

A string representation of the vector.

Declaration

public override string ToString()

Returns

Type	Description
System.String	The string representation of this vector.

Overrides

System.ValueType.ToString()

TripleProduct(Vector3, Vector3)

Check if two vectors are coplanar.

Declaration

public double TripleProduct(Vector3 b, Vector3 c)

Parameters

Type	Name	Description
Vector3	b	The second vector.
Vector3	c	The third vector.

Returns

Type	Description
System.Double	True is the vectors are coplanar, otherwise false.

Unitized()

Return a new vector which is the unitized version of this vector.

Declaration

public Vector3 Unitized()

Returns

Type	Description
Vector3

Operators

Addition(Vector3, Vector3)

Add two vectors.

Declaration

public static Vector3 operator +(Vector3 a, Vector3 b)

Parameters

Type	Name	Description
Vector3	a	The first vector.
Vector3	b	The second vector.

Returns

Type	Description
Vector3	A vector which is the sum of a and b.

Division(Vector3, Double)

Divide a vector by a scalar.

Declaration

public static Vector3 operator /(Vector3 v, double a)

Parameters

Type	Name	Description
Vector3	v	The vector to divide.
System.Double	a	The scalar divisor.

Returns

Type	Description
Vector3	A vector whose magnitude is multiplied by a.

Equality(Vector3, Vector3)

Are the two vectors the same within Epsilon?

Declaration

public static bool operator ==(Vector3 a, Vector3 b)

Parameters

Type	Name	Description
Vector3	a
Vector3	b

Returns

Type	Description
System.Boolean

GreaterThan(Vector3, Vector3)

Compute whether all components of vector a are greater than those of vector b.

Declaration

public static bool operator>(Vector3 a, Vector3 b)

Parameters

Type	Name	Description
Vector3	a	The first vector.
Vector3	b	The second vector.

Returns

Type	Description
System.Boolean	True if all of a's components are greater than those of b, otherwise false.

GreaterThanOrEqual(Vector3, Vector3)

Compute whether all components of vector a are greater than or equal to those of vector b.

Declaration

public static bool operator >=(Vector3 a, Vector3 b)

Parameters

Type	Name	Description
Vector3	a	The first vector.
Vector3	b	The second vector.

Returns

Type	Description
System.Boolean	True if all of a's components are greater than or equal to all of those of b, otherwise false.

Implicit((Double X, Double Y, Double Z) to Vector3)

Automatically convert a tuple of three doubles into a Vector3.

Declaration

public static implicit operator Vector3((double X, double Y, double Z) vector)

Parameters

Type	Name	Description
System.ValueTuple<System.Double, System.Double, System.Double>	vector	An (X,Y,Z) tuple of doubles.

Returns

Type	Description
Vector3

Implicit((Double X, Double Y) to Vector3)

Automatically convert a tuple of two doubles into a Vector3.

Declaration

public static implicit operator Vector3((double X, double Y) vector)

Parameters

Type	Name	Description
System.ValueTuple<System.Double, System.Double>	vector	An (X,Y) tuple of doubles.

Returns

Type	Description
Vector3

Implicit((Int32 X, Int32 Y, Int32 Z) to Vector3)

Automatically convert a tuple of three ints into a Vector3.

Declaration

public static implicit operator Vector3((int X, int Y, int Z) vector)

Parameters

Type	Name	Description
System.ValueTuple<System.Int32, System.Int32, System.Int32>	vector	An (X,Y,Z) tuple of ints.

Returns

Type	Description
Vector3

Implicit((Int32 X, Int32 Y) to Vector3)

Automatically convert a tuple of two ints into a Vector3.

Declaration

public static implicit operator Vector3((int X, int Y) vector)

Parameters

Type	Name	Description
System.ValueTuple<System.Int32, System.Int32>	vector	An (X,Y) tuple of ints.

Returns

Type	Description
Vector3

Inequality(Vector3, Vector3)

Are the two vectors not the same within Epsilon?

Declaration

public static bool operator !=(Vector3 a, Vector3 b)

Parameters

Type	Name	Description
Vector3	a
Vector3	b

Returns

Type	Description
System.Boolean

LessThan(Vector3, Vector3)

Compute whether all components of vector a are less than those of vector b.

Declaration

public static bool operator <(Vector3 a, Vector3 b)

Parameters

Type	Name	Description
Vector3	a	The first vector.
Vector3	b	The second vector.

Returns

Type	Description
System.Boolean	True if all of a's components are less than those of b, otherwise false.

LessThanOrEqual(Vector3, Vector3)

Compute whether all components of vector a are less than or equal to those of vector b.

Declaration

public static bool operator <=(Vector3 a, Vector3 b)

Parameters

Type	Name	Description
Vector3	a	The first vector.
Vector3	b	The second vector.

Returns

Type	Description
System.Boolean	True if all of a's components are less than or equal to all of those of b, otherwise false.

Multiply(Vector3, Double)

Multiply a vector and a scalar.

Declaration

public static Vector3 operator *(Vector3 v, double a)

Parameters

Type	Name	Description
Vector3	v	The vector to multiply.
System.Double	a	The scalar value to multiply.

Returns

Type	Description
Vector3	A vector whose magnitude is multiplied by a.

Multiply(Double, Vector3)

Multiply a scalar and a vector.

Declaration

public static Vector3 operator *(double a, Vector3 v)

Parameters

Type	Name	Description
System.Double	a	The scalar value to multiply.
Vector3	v	The vector to multiply.

Returns

Type	Description
Vector3	A vector whose magnitude is multiplied by a.

Subtraction(Vector3, Vector3)

Subtract two vectors.

Declaration

public static Vector3 operator -(Vector3 a, Vector3 b)

Parameters

Type	Name	Description
Vector3	a	The first vector.
Vector3	b	The second vector.

Returns

Type	Description
Vector3	A vector which is the difference between a and b.

Implements

System.IComparable<T>

System.IEquatable<T>