Struct Vector3

Defines a Vector in Euclidean space with coordinates X, Y, and Z. Referenced from https://github.com/mcneel/rhinocommon/blob/master/dotnet/opennurbs/opennurbs_point.cs

Inherited Members

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

System.Object.GetType()

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

Syntax

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

Constructors

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Vector3(Point3)

Initializes a new instance of a vector, copying the three components from the three coordinates of a point.

Declaration

public Vector3(Point3 point)

Parameters

Type	Name	Description
Point3	point	The point to copy from.

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Vector3(Vector3)

Initializes a new instance of a vector, copying the three components from a vector.

Declaration

public Vector3(Vector3 vector)

Parameters

Type	Name	Description
Vector3	vector	A double-precision vector.

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Vector3(Double, Double, Double)

Initializes a new instance of a vector, using its three components.

Declaration

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

Parameters

Type	Name	Description
System.Double	x	The X (first) component.
System.Double	y	The Y (second) component.
System.Double	z	The Z (third) component.

Properties

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IsUnitVector

Gets a value indicating whether or not this is a unit vector. A unit vector has length 1.

Declaration

public readonly bool IsUnitVector { get; }

Property Value

Type	Description
System.Boolean

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IsValid

Gets a value indicating whether this vector is valid. A valid vector must be formed of valid component values for x, y and z.

Declaration

public readonly bool IsValid { get; }

Property Value

Type	Description
System.Boolean

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IsZero

Gets a value indicating whether the X, Y, and Z values are all equal to 0.0.

Declaration

public readonly bool IsZero { get; }

Property Value

Type	Description
System.Boolean

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Item[Int32]

Declaration

public double this[int i] { get; set; }

Parameters

Type	Name	Description
System.Int32	i

Property Value

Type	Description
System.Double

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Length

Computes the length (or magnitude, or size) of this vector. This is an application of Pythagoras' theorem. If this vector is invalid, its length is considered 0.

Declaration

public readonly double Length { get; }

Property Value

Type	Description
System.Double

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Size

Dimension of vector.

Declaration

public readonly int Size { get; }

Property Value

Type	Description
System.Int32

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SquareLength

Computes the squared length (or magnitude, or size) of this vector. This is an application of Pythagoras' theorem. While the Length property checks for input validity, this property does not. You should check validity in advance, if this vector can be invalid.

Declaration

public readonly double SquareLength { get; }

Property Value

Type	Description
System.Double

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Unset

Gets the value of the vector with each component set to GeoSharkMath.UNSET_VALUE.

Declaration

public static readonly Vector3 Unset { get; }

Property Value

Type	Description
Vector3

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X

Gets or sets the X (first) component of the vector.

Declaration

public double X { readonly get; set; }

Property Value

Type	Description
System.Double

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XAxis

Gets the value of the vector with components 1,0,0.

Declaration

public static readonly Vector3 XAxis { get; }

Property Value

Type	Description
Vector3

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Y

Gets or sets the Y (second) component of the vector.

Declaration

public double Y { readonly get; set; }

Property Value

Type	Description
System.Double

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YAxis

Gets the value of the vector with components 0,1,0.

Declaration

public static readonly Vector3 YAxis { get; }

Property Value

Type	Description
Vector3

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Z

Gets or sets the Z (third) component of the vector.

Declaration

public double Z { readonly get; set; }

Property Value

Type	Description
System.Double

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ZAxis

Gets the value of the vector with components 0,0,1.

Declaration

public static readonly Vector3 ZAxis { get; }

Property Value

Type	Description
Vector3

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Zero

Gets the value of the vector with components 0,0,0.

Declaration

public static readonly Vector3 Zero { get; }

Property Value

Type	Description
Vector3

Methods

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Amplify(Double)

Gets a new amplified vector by unitizing and uniformly scaling this vector by the amplitude value.

Declaration

public Vector3 Amplify(double amplitude)

Parameters

Type	Name	Description
System.Double	amplitude	The scalar value to amplify the vector.

Returns

Type	Description
Vector3	The amplified vector.

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CompareTo(Vector3)

Compares this Vector3 with another Vector3.

Component evaluation priority is first X, then Y, then Z.

Declaration

public int CompareTo(Vector3 other)

Parameters

Type	Name	Description
Vector3	other	The other Vector3 to use in comparison.

Returns

Type	Description
System.Int32	0: if this is identical to other -1: if this.X < other.X -1: if this.X == other.X and this.Y < other.Y -1: if this.X == other.X and this.Y == other.Y and this.Z < other.Z +1: otherwise.

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CrossProduct(Vector3, Vector3)

Computes the cross product (or vector product, or exterior product) of two vectors.

This operation is not commutative.

Declaration

public static Vector3 CrossProduct(Vector3 a, Vector3 b)

Parameters

Type	Name	Description
Vector3	a	First vector.
Vector3	b	Second vector.

Returns

Type	Description
Vector3	A new vector that is perpendicular to both a and b, has Length == a.Length * b.Length and with a result that is oriented following the right hand rule.

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DotProduct(Vector3, Vector3)

Computes the dot product between two vectors.

Declaration

public static double DotProduct(Vector3 vector1, Vector3 vector2)

Parameters

Type	Name	Description
Vector3	vector1	The first vector.
Vector3	vector2	The second vector with which compute the dot product.

Returns

Type	Description
System.Double	The dot product.

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EpsilonEquals(Vector3, Double)

Declaration

public bool EpsilonEquals(Vector3 vector, double epsilon)

Parameters

Type	Name	Description
Vector3	vector
System.Double	epsilon

Returns

Type	Description
System.Boolean

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Equals(Vector3)

Determines whether the specified vector has the same value as the present vector.

Declaration

public bool Equals(Vector3 vector)

Parameters

Type	Name	Description
Vector3	vector	The specified vector.

Returns

Type	Description
System.Boolean	true if vector has the same coordinates as this; otherwise false.

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Equals(Object)

Determines whether the specified System.Object is a Vector3d and has the same values as the present vector.

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
System.Object	obj	The specified object.

Returns

Type	Description
System.Boolean	true if obj is a Vector3d and has the same coordinates as this; otherwise false.

Overrides

System.ValueType.Equals(System.Object)

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GetHashCode()

Computes the hash code for the current vector.

Declaration

public override int GetHashCode()

Returns

Type	Description
System.Int32	A non-unique number that represents the components of this vector.

Overrides

System.ValueType.GetHashCode()

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IsParallelTo(Vector3, Double)

Determines whether this vector is parallel to another vector, within a provided tolerance.

Declaration

public int IsParallelTo(Vector3 other, double angleTolerance = 0.0174532925199433)

Parameters

Type	Name	Description
Vector3	other	Vector to use for comparison.
System.Double	angleTolerance	Angle tolerance (in radians).

Returns

Type	Description
System.Int32	Parallel indicator: +1 = both vectors are parallel. 0 = vectors are not parallel or at least one of the vectors is zero. -1 = vectors are anti-parallel.

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IsPerpendicularTo(Vector3, Double)

Determines whether this vector is perpendicular to another vector, within a provided angle tolerance.

Declaration

public bool IsPerpendicularTo(Vector3 other, double angleTolerance = 0.0174532925199433)

Parameters

Type	Name	Description
Vector3	other	Vector to use for comparison.
System.Double	angleTolerance	Angle tolerance (in radians).

Returns

Type	Description
System.Boolean	true if vectors form Pi-radians (90-degree) angles with each other; otherwise false.

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PerpendicularTo(Point3, Point3, Point3)

Computes the perpendicular of a vector given three points.
Result is not unitized.

Declaration

public Vector3 PerpendicularTo(Point3 pt1, Point3 pt2, Point3 pt3)

Parameters

Type	Name	Description
Point3	pt1	First point.
Point3	pt2	Second point.
Point3	pt3	Third point.

Returns

Type	Description
Vector3	The perpendicular vector.

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PerpendicularTo(Vector3)

Computes the perpendicular to another vector.
https://stackoverflow.com/questions/11132681/what-is-a-formula-to-get-a-vector-perpendicular-to-another-vector
Result is not unitized.

Declaration

public static Vector3 PerpendicularTo(Vector3 vector)

Parameters

Type	Name	Description
Vector3	vector	The other vector.

Returns

Type	Description
Vector3	The perpendicular vector.

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Reverse()

Reverses (inverts) this vector in place.

If this vector is Invalid, no changes will occur and false will be returned.

Declaration

public Vector3 Reverse()

Returns

Type	Description
Vector3	Returns a reversed vector on success or Vector3d.Unset if the vector is invalid.

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Rotate(Vector3, Double)

Rotates this vector around a given axis.
The rotation is computed using Rodrigues Rotation formula.
https://handwiki.org/wiki/Rodrigues%27_rotation_formula

Declaration

public Vector3 Rotate(Vector3 axis, double radiansAngle)

Parameters

Type	Name	Description
Vector3	axis	Axis of rotation.
System.Double	radiansAngle	Angle of rotation (in radians).

Returns

Type	Description
Vector3	Rotated vector.

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ToString()

Returns the string representation of the current vector, in the form X,Y,Z.

Declaration

public override string ToString()

Returns

Type	Description
System.String	A string with the current location of the point.

Overrides

System.ValueType.ToString()

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TripleProduct(Vector3, Vector3)

The triple product of this vector and the two specified vectors.

Declaration

public double TripleProduct(Vector3 middle, Vector3 right)

Parameters

Type	Name	Description
Vector3	middle	The second vector.
Vector3	right	The third vector.

Returns

Type	Description
System.Double	The real number equal to the triple product.

Remarks

The scalar triple product is defined as the dot product of one of the vectors with the cross product of the other two. Geometrically, this product is the (signed) volume of the parallelepiped formed by the three vectors given.

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Unitize()

Unitizes the vector. A unit vector has length 1 unit.

Declaration

public Vector3 Unitize()

Returns

Type	Description
Vector3	A new vector unitized.

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VectorAngle(Vector3, Vector3)

Compute the angle in radians between two vectors.
This operation is commutative.

Declaration

public static double VectorAngle(Vector3 a, Vector3 b)

Parameters

Type	Name	Description
Vector3	a	First vector for angle.
Vector3	b	Second vector for angle.

Returns

Type	Description
System.Double	If the input is valid, the angle in radians between a and b; GeoSharkMath.UNSET_VALUE otherwise.

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VectorAngleOnPlane(Vector3, Vector3, Plane, out Double)

Computes the angle in radians on a plane between two vectors.

Declaration

public static double VectorAngleOnPlane(Vector3 a, Vector3 b, Plane plane, out double reflexAngle)

Parameters

Type	Name	Description
Vector3	a	First vector.
Vector3	b	Second vector.
Plane	plane	Two-dimensional plane on which to perform the angle measurement.
System.Double	reflexAngle

Returns

Type	Description
System.Double	On success, the angle (in radians) between a and b as projected onto the plane; GeoSharkMath.UNSET_VALUE on failure.

Operators

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Addition(Vector3, Vector3)

Sums up two vectors.

Declaration

public static Vector3 operator +(Vector3 vector1, Vector3 vector2)

Parameters

Type	Name	Description
Vector3	vector1	A vector.
Vector3	vector2	A second vector.

Returns

Type	Description
Vector3	A new vector that results from the componentwise addition of the two vectors.

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Division(Vector3, Double)

Divides a Vector3 by a number, having the effect of shrinking it.

Declaration

public static Vector3 operator /(Vector3 vector, double t)

Parameters

Type	Name	Description
Vector3	vector	A vector.
System.Double	t	A number.

Returns

Type	Description
Vector3	A new vector that is componentwise divided by t.

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Equality(Vector3, Vector3)

Determines whether two vectors have the same value.

Declaration

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

Parameters

Type	Name	Description
Vector3	a	A vector.
Vector3	b	Another vector.

Returns

Type	Description
System.Boolean	true if all coordinates are pairwise equal; false otherwise.

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GreaterThan(Vector3, Vector3)

Determines whether the first specified vector comes after (has superior sorting value than) the second vector.

Components evaluation priority is first X, then Y, then Z.

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 a.X is larger than b.X, or a.X == b.X and a.Y is larger than b.Y, or a.X == b.X and a.Y == b.Y and a.Z is larger than b.Z; otherwise, false.

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GreaterThanOrEqual(Vector3, Vector3)

Determines whether the first specified vector comes after (has superior sorting value than) the second vector, or it is equal to it.

Components evaluation priority is first X, then Y, then Z.

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 a.X is larger than b.X, or a.X == b.X and a.Y is larger than b.Y, or a.X == b.X and a.Y == b.Y and a.Z >= b.Z; otherwise, false.

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Implicit(Vector3 to Point3)

Converts a vector3d in a point3d, without needing casting.

Declaration

public static implicit operator Point3(Vector3 vector3d)

Parameters

Type	Name	Description
Vector3	vector3d	A Vector3d.

Returns

Type	Description
Point3	The resulting Point3d.

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Implicit(Vector3 to Vector)

Converts a vector3d in a vector3, without needing casting.

Declaration

public static implicit operator Vector(Vector3 vector3d)

Parameters

Type	Name	Description
Vector3	vector3d	A Vector3d.

Returns

Type	Description
Vector	The resulting Vector3.

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Inequality(Vector3, Vector3)

Determines whether two vectors have different values.

Declaration

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

Parameters

Type	Name	Description
Vector3	a	A vector.
Vector3	b	Another vector.

Returns

Type	Description
System.Boolean	true if any coordinate pair is different; false otherwise.

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LessThan(Vector3, Vector3)

Determines whether the first specified vector comes before (has inferior sorting value than) the second vector.

Components evaluation priority is first X, then Y, then Z.

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 a.X is smaller than b.X, or a.X == b.X and a.Y is smaller than b.Y, or a.X == b.X and a.Y == b.Y and a.Z is smaller than b.Z; otherwise, false.

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LessThanOrEqual(Vector3, Vector3)

Determines whether the first specified vector comes before (has inferior sorting value than) the second vector, or it is equal to it.

Components evaluation priority is first X, then Y, then Z.

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 a.X is smaller than b.X, or a.X == b.X and a.Y is smaller than b.Y, or a.X == b.X and a.Y == b.Y and a.Z <= b.Z; otherwise, false.

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Multiply(Vector3, Vector3)

Multiplies two vectors together, returning the dot product (or inner product). This differs from the cross product.

Declaration

public static double operator *(Vector3 vector1, Vector3 vector2)

Parameters

Type	Name	Description
Vector3	vector1	A vector.
Vector3	vector2	A second vector.

Returns

Type	Description
System.Double	A value that results from the evaluation of v1.Xv2.X + v1.Yv2.Y + v1.Zv2.Z. This value equals v1.Length v2.Length * cos(alpha), where alpha is the angle between vectors.

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Multiply(Vector3, Double)

Multiplies a vector by a number, having the effect of scaling it.

Declaration

public static Vector3 operator *(Vector3 vector, double t)

Parameters

Type	Name	Description
Vector3	vector	A vector.
System.Double	t	A number.

Returns

Type	Description
Vector3	A new vector that is the original vector coordinatewise multiplied by t.

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Multiply(Double, Vector3)

Multiplies a vector by a number, having the effect of scaling it.

Declaration

public static Vector3 operator *(double t, Vector3 vector)

Parameters

Type	Name	Description
System.Double	t	A number.
Vector3	vector	A vector.

Returns

Type	Description
Vector3	A new vector that is the original vector coordinatewise multiplied by t.

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Subtraction(Vector3, Vector3)

Subtracts the second vector from the first one.

Declaration

public static Vector3 operator -(Vector3 vector1, Vector3 vector2)

Parameters

Type	Name	Description
Vector3	vector1	A vector.
Vector3	vector2	A second vector.

Returns

Type	Description
Vector3	A new vector that results from the componentwise difference of vector1 - vector2.

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UnaryNegation(Vector3)

Computes the reversed vector.

Declaration

public static Vector3 operator -(Vector3 vector)

Parameters

Type	Name	Description
Vector3	vector	A vector to negate.

Returns

Type	Description
Vector3	A new vector where all components were multiplied by -1.

Explicit Interface Implementations

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IComparable.CompareTo(Object)

Declaration

int IComparable.CompareTo(object obj)

Parameters

Type	Name	Description
System.Object	obj

Returns

Type	Description
System.Int32

Implements

System.IEquatable<T>

System.IComparable<T>

System.IComparable