AutoOpenVector3d (Rhino.Scripting.Fsharp)

AutoOpenVector3d Module

Namespace: Rhino.Scripting.FSharp
Assembly: Rhino.Scripting.FSharp.dll

When Rhino.Scripting.FSharp is opened this module will be auto-opened. It only contains extension members for type Vector3d.

Type extensions

Type extension	Description
`this.AngleDiamondInXYTo` Full Usage: `this.AngleDiamondInXYTo` Parameters: b : `Vector3d` Returns: `float` Modifiers: inline	Returns positive angle for rotating Counter-Clockwise from this Vector3d to Vector3d 'b' . In Diamond Angle. Using only proportion of X to Y components. Range of 0.0 to 4.0 (for 360 Degrees) It is the fastest angle calculation since it does not involve Cosine or ArcTangent functions. For World X-Y plane. Considers only the X and Y components of the Vector3d. Extended Type: `Vector3d` b : `Vector3d` Returns: `float`
`this.AsString` Full Usage: `this.AsString` Parameters: () : `unit` Returns: `string`	Extended Type: `Vector3d` () : `unit` Returns: `string`
`this.Direction180InXY` Full Usage: `this.Direction180InXY` Parameters: () : `unit` Returns: `float` Modifiers: inline	Returns the angle in Degrees from X-axis, Ignores orientation. Range 0.0 to 180. For World X-Y plane. Considers only the X and Y components of the Vector3d. Extended Type: `Vector3d` () : `unit` Returns: `float`
`this.Direction2PiInXY` Full Usage: `this.Direction2PiInXY` Parameters: () : `unit` Returns: `float` Modifiers: inline	Returns the angle in Radians from X-axis, Going Counter-Clockwise till two Pi. For World X-Y plane. Considers only the X and Y components of the Vector3d. Extended Type: `Vector3d` () : `unit` Returns: `float`
`this.Direction360InXY` Full Usage: `this.Direction360InXY` Parameters: () : `unit` Returns: `float` Modifiers: inline	Returns the angle in Degrees from X-axis. Going Counter-Clockwise till 360. For World X-Y plane. Considers only the X and Y components of the Vector3d. Extended Type: `Vector3d` () : `unit` Returns: `float`
`this.DirectionDiamondInXY` Full Usage: `this.DirectionDiamondInXY` Parameters: () : `unit` Returns: `float` Modifiers: inline	The diamond angle. Calculates the proportion of X to Y component. It is always positive and in the range of 0.0 to 4.0 (for 360 Degrees) 0.0 = Xaxis, going Counter-Clockwise. It is the fastest angle calculation since it does not involve Cosine or ArcTangent functions. For World X-Y plane. Considers only the X and Y components of the Vector3d. Extended Type: `Vector3d` () : `unit` Returns: `float`
`this.DirectionPiInXY` Full Usage: `this.DirectionPiInXY` Parameters: () : `unit` Returns: `float` Modifiers: inline	Returns the angle in Radians from X-axis, Ignores orientation. Range 0.0 to Pi. For World X-Y plane. Considers only the X and Y components of the Vector3d. Extended Type: `Vector3d` () : `unit` Returns: `float`
`this.Half` Full Usage: `this.Half` Parameters: () : `unit` Returns: `Vector3d` Modifiers: inline	Returns a new 3D Vector3d with half the length. Extended Type: `Vector3d` () : `unit` Returns: `Vector3d`
`this.IsHorizontal` Full Usage: `this.IsHorizontal` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Checks if 3D Vector3d is horizontal (Z component is almost zero). The absolute deviation tolerance along Z axis is 1e-9. Fails on Vector3d shorter than 1e-6. Extended Type: `Vector3d` () : `unit` Returns: `bool`
`this.IsNotZero` Full Usage: `this.IsNotZero` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Returns a boolean indicating if any of X, Y and Z is not exactly 0.0. Extended Type: `Vector3d` () : `unit` Returns: `bool`
`this.IsOppositeOrientation` Full Usage: `this.IsOppositeOrientation` Parameters: other : `Vector3d` Returns: `bool` Modifiers: inline	Checks if the angle between the two 3D Vector3d is more than 180 degrees. Calculates the dot product of two 3D Vector3d. Then checks if it is smaller than minus 1e-12. Fails if any of the two Vector3d is shorter than zeroLengthTolerance (1e-12). Extended Type: `Vector3d` other : `Vector3d` Returns: `bool`
`this.IsParallelAndOrientedTo` Full Usage: `this.IsParallelAndOrientedTo` Parameters: other : `Vector3d` minCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool` Modifiers: inline	Checks if two 3D Vector3d are parallel. Takes the line orientation into account too. The default angle tolerance is 0.25 degrees. This tolerance can be customized by an optional minium cosine value. See Rhino.Scripting.FSharp.Cosine module. Fails on Vector3d shorter than zeroLengthTolerance (1e-12). Extended Type: `Vector3d` other : `Vector3d` minCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool`
`this.IsParallelTo` Full Usage: `this.IsParallelTo` Parameters: other : `Vector3d` minCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool` Modifiers: inline	Checks if two 3D Vector3d are parallel. Ignores the line orientation. The default angle tolerance is 0.25 degrees. This tolerance can be customized by an optional minium cosine value. See Rhino.Scripting.FSharp.Cosine module. Fails on Vector3d shorter than zeroLengthTolerance (1e-12). Extended Type: `Vector3d` other : `Vector3d` minCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool`
`this.IsPerpendicularTo` Full Usage: `this.IsPerpendicularTo` Parameters: other : `Vector3d` maxCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool` Modifiers: inline	Checks if two 3D Vector3d are perpendicular to each other. The default angle tolerance is 89.75 to 90.25 degrees. This tolerance can be customized by an optional minium cosine value. The default cosine is 0.0043633 ( = 89.75 deg) See Rhino.Scripting.FSharp.Cosine module. Fails on Vector3d shorter than zeroLengthTolerance (1e-12). Extended Type: `Vector3d` other : `Vector3d` maxCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool`
`this.IsTiny` Full Usage: `this.IsTiny` Parameters: tol : `float` Returns: `bool` Modifiers: inline	Check if the 3D Vector3d is shorter than the tolerance. Also checks if any component is a NaN. Extended Type: `Vector3d` tol : `float` Returns: `bool`
`this.IsTinySq` Full Usage: `this.IsTinySq` Parameters: tol : `float` Returns: `bool` Modifiers: inline	Check if the 3D Vector3d square length is shorter than the squared tolerance. Also checks if any component is a NaN. Extended Type: `Vector3d` tol : `float` Returns: `bool`
`this.IsUnit` Full Usage: `this.IsUnit` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Test if the 3D Vector3d is a unit-Vector3d. Test if the Vector3d square length is within 6 float steps of 1.0 So between 0.99999964 and 1.000000715. Extended Type: `Vector3d` () : `unit` Returns: `bool`
`this.IsVertical` Full Usage: `this.IsVertical` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Checks if 3D Vector3d is parallel to the world Z axis. Ignoring orientation. The absolute deviation tolerance along X and Y axis is 1e-9. Fails on Vector3d shorter than 1e-6. Same as v.IsZAligned Extended Type: `Vector3d` () : `unit` Returns: `bool`
`this.IsXAligned` Full Usage: `this.IsXAligned` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Checks if 3D Vector3d is parallel to the world X axis. Ignoring orientation. The absolute deviation tolerance along Y and Z axis is 1e-9. Fails on Vector3d shorter than 1e-6. Extended Type: `Vector3d` () : `unit` Returns: `bool`
`this.IsYAligned` Full Usage: `this.IsYAligned` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Checks if 3D Vector3d is parallel to the world Y axis. Ignoring orientation. The absolute deviation tolerance along X and Z axis is 1e-9. Fails on Vector3d shorter than 1e-6. Extended Type: `Vector3d` () : `unit` Returns: `bool`
`this.IsZAligned` Full Usage: `this.IsZAligned` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Checks if 3D Vector3d is parallel to the world Z axis. Ignoring orientation. The absolute deviation tolerance along X and Y axis is 1e-9. Fails on Vector3d shorter than 1e-6. Same as v.IsVertical Extended Type: `Vector3d` () : `unit` Returns: `bool`
`this.IsZero` Full Usage: `this.IsZero` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Returns a boolean indicating whether X, Y and Z are all exactly 0.0. Extended Type: `Vector3d` () : `unit` Returns: `bool`
`this.LengthInXY` Full Usage: `this.LengthInXY` Parameters: () : `unit` Returns: `float` Modifiers: inline	Returns the length of the 3D Vector3d projected into World X-Y plane. Extended Type: `Vector3d` () : `unit` Returns: `float`
`this.LengthSq` Full Usage: `this.LengthSq` Parameters: () : `unit` Returns: `float` Modifiers: inline	Returns the squared length of the 3D vector. The square length is faster to calculate and often good enough for use cases such as sorting vectors by length. Extended Type: `Vector3d` () : `unit` Returns: `float`
`this.LengthSqInXY` Full Usage: `this.LengthSqInXY` Parameters: () : `unit` Returns: `float` Modifiers: inline	Returns the squared length of the 3D Vector3d projected into World X-Y plane. The square length is faster to calculate and often good enough for use cases such as sorting Vector3d by length. Extended Type: `Vector3d` () : `unit` Returns: `float`
`this.MatchesOrientation` Full Usage: `this.MatchesOrientation` Parameters: other : `Vector3d` Returns: `bool` Modifiers: inline	Checks if the angle between the two 3D Vector3d is less than 180 degrees. Calculates the dot product of two 3D Vector3d. Then checks if it is bigger than 1e-12. Fails if any of the two Vector3d is shorter than zeroLengthTolerance (1e-12). Extended Type: `Vector3d` other : `Vector3d` Returns: `bool`
`this.PerpendicularInXY` Full Usage: `this.PerpendicularInXY` Parameters: () : `unit` Returns: `Vector3d` Modifiers: inline	Returns a perpendicular horizontal Vector3d. Rotated counterclockwise. Or Vector3d.Zero if input is vertical. Just does Vector3d(-v.Y, v.X, 0.0) Extended Type: `Vector3d` () : `unit` Returns: `Vector3d`
`this.RotateOnZ90CCW` Full Usage: `this.RotateOnZ90CCW` Parameters: () : `unit` Returns: `Vector3d` Modifiers: inline	90 Degree rotation Counter-Clockwise around Z-axis. Extended Type: `Vector3d` () : `unit` Returns: `Vector3d`
`this.RotateOnZ90CW` Full Usage: `this.RotateOnZ90CW` Parameters: () : `unit` Returns: `Vector3d` Modifiers: inline	90 Degree rotation clockwise around Z-axis. Extended Type: `Vector3d` () : `unit` Returns: `Vector3d`
`this.ToVector3d` Full Usage: `this.ToVector3d` Parameters: () : `unit` Returns: `Vector3d`	To convert a Vector3f (as it is used in Mesh normals) to a Vector3d (as it is used in most other Rhino Geometries) Extended Type: `Vector3f` () : `unit` Returns: `Vector3d`
`this.ToVector3f` Full Usage: `this.ToVector3f` Parameters: () : `unit` Returns: `Vector3f`	To convert Vector3d (as it is used in most other Rhino Geometries) to a Vector3f (as it is used in Mesh normals) Extended Type: `Vector3d` () : `unit` Returns: `Vector3f`
`this.Unitized` Full Usage: `this.Unitized` Parameters: () : `unit` Returns: `Vector3d` Modifiers: inline	Returns a new 3D Vector3d unitized. Fails with RhinoScriptingFSharpException if the length of the Vector3d is too small (1e-16) to unitize. Extended Type: `Vector3d` () : `unit` Returns: `Vector3d`
`this.WithLength` Full Usage: `this.WithLength` Parameters: desiredLength : `float` Returns: `Vector3d` Modifiers: inline	Returns a new 3D Vector3d scaled to the desired length. Same as Vector3d.withLength. Extended Type: `Vector3d` desiredLength : `float` Returns: `Vector3d`
`this.WithX` Full Usage: `this.WithX` Parameters: x : `float` Returns: `Vector3d` Modifiers: inline	Returns a new 3D Vector3d with new X coordinate, Y and Z stay the same. Extended Type: `Vector3d` x : `float` Returns: `Vector3d`
`this.WithY` Full Usage: `this.WithY` Parameters: y : `float` Returns: `Vector3d` Modifiers: inline	Returns a new 3D Vector3d with new y coordinate, X and Z stay the same. Extended Type: `Vector3d` y : `float` Returns: `Vector3d`
`this.WithZ` Full Usage: `this.WithZ` Parameters: z : `float` Returns: `Vector3d` Modifiers: inline	Returns a new 3D Vector3d with new z coordinate, X and Y stay the same. Extended Type: `Vector3d` z : `float` Returns: `Vector3d`
`Vector3d.Xaxis()` Full Usage: `Vector3d.Xaxis()` Parameters: () : `unit` Returns: `Vector3d` Modifiers: inline	Returns the World X-axis with length one: Vector3d(1, 0, 0) Extended Type: `Vector3d` () : `unit` Returns: `Vector3d`
`Vector3d.Yaxis()` Full Usage: `Vector3d.Yaxis()` Parameters: () : `unit` Returns: `Vector3d` Modifiers: inline	Returns the World Y-axis with length one: Vector3d(0, 1, 0) Extended Type: `Vector3d` () : `unit` Returns: `Vector3d`
`Vector3d.Zaxis()` Full Usage: `Vector3d.Zaxis()` Parameters: () : `unit` Returns: `Vector3d` Modifiers: inline	Returns the World Z-axis with length one: Vector3d(0, 0, 1) Extended Type: `Vector3d` () : `unit` Returns: `Vector3d`
`Vector3d.add a b` Full Usage: `Vector3d.add a b` Parameters: a : `Vector3d` b : `Vector3d` Returns: `Vector3d` Modifiers: inline	Add two 3D Vector3d together. Returns a new 3D Vector3d. Extended Type: `Vector3d` a : `Vector3d` b : `Vector3d` Returns: `Vector3d`
`Vector3d.angle180 a b` Full Usage: `Vector3d.angle180 a b` Parameters: a : `Vector3d` b : `Vector3d` Returns: `float`	Returns positive angle between two 3D Vector3d in Degrees. Takes Vector3d orientation into account, Range 0 to 180 Degrees. Extended Type: `Vector3d` a : `Vector3d` b : `Vector3d` Returns: `float`
`Vector3d.angle2PiInXY (a, b)` Full Usage: `Vector3d.angle2PiInXY (a, b)` Parameters: a : `Vector3d` b : `Vector3d` Returns: `float` Modifiers: inline	Returns positive angle from Vector3d 'a' to Vector3d 'b' projected in X-Y plane. In Radians. Considering Counter-Clockwise rotation round the World Zaxis. Range: 0.0 to 2 Pi ( = 0 to 360 Degrees) Extended Type: `Vector3d` a : `Vector3d` b : `Vector3d` Returns: `float`
`Vector3d.angle360InXY (a, b)` Full Usage: `Vector3d.angle360InXY (a, b)` Parameters: a : `Vector3d` b : `Vector3d` Returns: `float` Modifiers: inline	Returns positive angle of two 3D Vector3d projected in X-Y plane. In Degrees. Considering positive rotation round the World Z-axis. Range: 0 to 360 Degrees. Extended Type: `Vector3d` a : `Vector3d` b : `Vector3d` Returns: `float`
`Vector3d.angle90 a b` Full Usage: `Vector3d.angle90 a b` Parameters: a : `Vector3d` b : `Vector3d` Returns: `float`	Returns positive angle between two 3D Vector3d in Degrees. Ignores Vector3d orientation, Range: 0 to 90 Degrees. Extended Type: `Vector3d` a : `Vector3d` b : `Vector3d` Returns: `float`
`Vector3d.angleDiamondInXY (a, b)` Full Usage: `Vector3d.angleDiamondInXY (a, b)` Parameters: a : `Vector3d` b : `Vector3d` Returns: `float` Modifiers: inline	Returns positive angle for rotating Counter-Clockwise from Vector3d 'a' to Vector3d 'b' . In Diamond Angle. Using only proportion of X to Y components. Range of 0.0 to 4.0 (for 360 Degrees) It is the fastest angle calculation since it does not involve Cosine or ArcTangent functions. For World X-Y plane. Considers only the X and Y components of the Vector3d. Extended Type: `Vector3d` a : `Vector3d` b : `Vector3d` Returns: `float`
`Vector3d.angleHalfPi a b` Full Usage: `Vector3d.angleHalfPi a b` Parameters: a : `Vector3d` b : `Vector3d` Returns: `float`	Returns positive angle between two 3D Vector3d in Radians. Ignores Vector3d orientation, Range: 0.0 to Pi/2 ( = 0 to 90 Degrees) Extended Type: `Vector3d` a : `Vector3d` b : `Vector3d` Returns: `float`
`Vector3d.anglePi a b` Full Usage: `Vector3d.anglePi a b` Parameters: a : `Vector3d` b : `Vector3d` Returns: `float`	Returns positive angle between two 3D Vector3d in Radians. Takes Vector3d orientation into account, Range 0.0 to Pi( = 0 to 180 Degree). Extended Type: `Vector3d` a : `Vector3d` b : `Vector3d` Returns: `float`
`Vector3d.areParallel other v` Full Usage: `Vector3d.areParallel other v` Parameters: other : `Vector3d` v : `Vector3d` Returns: `int` Modifiers: inline	Checks if Angle between two Vector3d is Below 0.25 Degree. Ignores Vector3d orientation. Fails on zero length Vector3d, tolerance 1e-12. Extended Type: `Vector3d` other : `Vector3d` v : `Vector3d` Returns: `int`
`Vector3d.areParallelAndMatchOrientation other v` Full Usage: `Vector3d.areParallelAndMatchOrientation other v` Parameters: other : `Vector3d` v : `Vector3d` Returns: `bool` Modifiers: inline	Checks if Angle between two Vector3d is less than 0.25 Degree and orientation matches. Fails on zero length Vector3d, tolerance 1e-12. Extended Type: `Vector3d` other : `Vector3d` v : `Vector3d` Returns: `bool`
`Vector3d.arePerpendicular other v` Full Usage: `Vector3d.arePerpendicular other v` Parameters: other : `Vector3d` v : `Vector3d` Returns: `bool` Modifiers: inline	Checks if Angle between two Vector3d is between 98.75 and 90.25 Degree. Ignores Vector3d orientation. Fails on zero length Vector3d, tolerance 1e-12. Extended Type: `Vector3d` other : `Vector3d` v : `Vector3d` Returns: `bool`
`Vector3d.bisector a b` Full Usage: `Vector3d.bisector a b` Parameters: a : `Vector3d` b : `Vector3d` Returns: `Vector3d` Modifiers: inline	Returns a (not unitized) bisector Vector3d in the middle direction. Code : a.Unitized + b.Unitized. Extended Type: `Vector3d` a : `Vector3d` b : `Vector3d` Returns: `Vector3d`
`Vector3d.create (x, y, z)` Full Usage: `Vector3d.create (x, y, z)` Parameters: x : `float` y : `float` z : `float` Returns: `Vector3d` Modifiers: inline	Returns a new 3D Vector3d from X, Y and Z parts. Extended Type: `Vector3d` x : `float` y : `float` z : `float` Returns: `Vector3d`
`Vector3d.createFromMembersXYZ pt` Full Usage: `Vector3d.createFromMembersXYZ pt` Parameters: pt : `^T` Returns: `Vector3d` Modifiers: inline Type parameters: ^T, ^a, ^b, ^c	Accepts any type that has a X, Y and Z (UPPERCASE) member that can be converted to a float. Internally this is not using reflection at runtime but F# Statically Resolved Type Parameters at compile time. Extended Type: `Vector3d` pt : `^T` Returns: `Vector3d`
`Vector3f.createFromMembersXYZ pt` Full Usage: `Vector3f.createFromMembersXYZ pt` Parameters: pt : `^T` Returns: `Vector3f` Modifiers: inline Type parameters: ^T, ^a, ^b, ^c	Accepts any type that has a X, Y and Z (UPPERCASE) member that can be converted to a float32. Internally this is not using reflection at runtime but F# Statically Resolved Type Parameters at compile time. Extended Type: `Vector3f` pt : `^T` Returns: `Vector3f`
`Vector3d.createFromMembersxyz pt` Full Usage: `Vector3d.createFromMembersxyz pt` Parameters: pt : `^T` Returns: `Vector3d` Modifiers: inline Type parameters: ^T, ^a, ^b, ^c	Accepts any type that has a x, y and z (lowercase) member that can be converted to a float. Internally this is not using reflection at runtime but F# Statically Resolved Type Parameters at compile time. Extended Type: `Vector3d` pt : `^T` Returns: `Vector3d`
`Vector3f.createFromMembersxyz pt` Full Usage: `Vector3f.createFromMembersxyz pt` Parameters: pt : `^T` Returns: `Vector3f` Modifiers: inline Type parameters: ^T, ^a, ^b, ^c	Accepts any type that has a x, y and z (lowercase) member that can be converted to a float32. Internally this is not using reflection at runtime but F# Statically Resolved Type Parameters at compile time. Extended Type: `Vector3f` pt : `^T` Returns: `Vector3f`
`Vector3d.cross (a, b)` Full Usage: `Vector3d.cross (a, b)` Parameters: a : `Vector3d` b : `Vector3d` Returns: `Vector3d` Modifiers: inline	Cross product, of two 3D vectors. The resulting vector is perpendicular to both input vectors. Its length is the area of the parallelogram spanned by the input vectors. Its direction follows the right-hand rule. A x B = \|A\| * \|B\| * sin(angle) Extended Type: `Vector3d` a : `Vector3d` b : `Vector3d` Returns: `Vector3d`
`Vector3d.determinant (u, v, w)` Full Usage: `Vector3d.determinant (u, v, w)` Parameters: u : `Vector3d` v : `Vector3d` w : `Vector3d` Returns: `float` Modifiers: inline	Returns three Vector3d's Determinant. This is also the signed volume of the Parallelepiped defined by these three Vector3d. Also called scalar triple product, mixed product, Box product, or in German: Spatprodukt. It is defined as the dot product of one of the Vector3d with the cross product of the other two. Extended Type: `Vector3d` u : `Vector3d` v : `Vector3d` w : `Vector3d` Returns: `float`
`Vector3d.difference a b` Full Usage: `Vector3d.difference a b` Parameters: a : `Vector3d` b : `Vector3d` Returns: `float` Modifiers: inline	Returns the distance between the tips of two 3D Vector3d. Extended Type: `Vector3d` a : `Vector3d` b : `Vector3d` Returns: `float`
`Vector3d.differenceSq a b` Full Usage: `Vector3d.differenceSq a b` Parameters: a : `Vector3d` b : `Vector3d` Returns: `float` Modifiers: inline	Returns the squared distance between the tips of two 3D Vector3d. This operation is slightly faster than Vector3d.difference and sufficient for many algorithms like finding closest Vector3d. Extended Type: `Vector3d` a : `Vector3d` b : `Vector3d` Returns: `float`
`Vector3d.direction2PiInXY v` Full Usage: `Vector3d.direction2PiInXY v` Parameters: v : `Vector3d` Returns: `float` Modifiers: inline	Returns positive angle of 3D Vector3d in World X-Y plane. Counter-Clockwise from X-axis. In Radians. Range: 0.0 to 2 Pi ( = 0 to 360 Degrees) For World X-Y plane. Considers only the X and Y components of the Vector3d. Extended Type: `Vector3d` v : `Vector3d` Returns: `float`
`Vector3d.direction360InXY v` Full Usage: `Vector3d.direction360InXY v` Parameters: v : `Vector3d` Returns: `float` Modifiers: inline	Returns positive angle of 3D Vector3d in World X-Y plane. Counter-Clockwise from X-axis. In Degree. Range: 0.0 to 2 Pi ( = 0 to 360 Degrees) For World X-Y plane. Considers only the X and Y components of the Vector3d. Extended Type: `Vector3d` v : `Vector3d` Returns: `float`
`Vector3d.directionDiamondInXY v` Full Usage: `Vector3d.directionDiamondInXY v` Parameters: v : `Vector3d` Returns: `float` Modifiers: inline	The diamond angle. Returns positive angle of 3D Vector3d in World X-Y plane. Calculates the proportion of X to Y component. It is always positive and in the range of 0.0 to 4.0 (for 360 Degrees) 0.0 = Xaxis, going Counter-Clockwise. It is the fastest angle calculation since it does not involve Cosine or ArcTangent functions. For World X-Y plane. Considers only the X and Y components of the Vector3d. Extended Type: `Vector3d` v : `Vector3d` Returns: `float`
`Vector3d.dot (a, b)` Full Usage: `Vector3d.dot (a, b)` Parameters: a : `Vector3d` b : `Vector3d` Returns: `float` Modifiers: inline	Dot product, or scalar product of two 3D vectors. Returns a float. Extended Type: `Vector3d` a : `Vector3d` b : `Vector3d` Returns: `float`
`Vector3d.equals tol a b` Full Usage: `Vector3d.equals tol a b` Parameters: tol : `float` a : `Vector3d` b : `Vector3d` Returns: `bool` Modifiers: inline	Checks if two 3D Vector3d are equal within tolerance. Identical Vector3d in opposite directions are not considered equal. Use a tolerance of 0.0 to check for an exact match. Extended Type: `Vector3d` tol : `float` a : `Vector3d` b : `Vector3d` Returns: `bool`
`Vector3d.flip v` Full Usage: `Vector3d.flip v` Parameters: v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Negate or inverse a 3D Vector3d. Returns a new 3D Vector3d. Same as Vector3d.reverse. Extended Type: `Vector3d` v : `Vector3d` Returns: `Vector3d`
`Vector3d.flipToPointUp v` Full Usage: `Vector3d.flipToPointUp v` Parameters: v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Flips the Vector3d if Z part is smaller than 0.0 Extended Type: `Vector3d` v : `Vector3d` Returns: `Vector3d`
`Vector3d.getX v` Full Usage: `Vector3d.getX v` Parameters: v : `Vector3d` Returns: `float` Modifiers: inline	Gets the X part of this 3D Vector3d. Extended Type: `Vector3d` v : `Vector3d` Returns: `float`
`Vector3d.getY v` Full Usage: `Vector3d.getY v` Parameters: v : `Vector3d` Returns: `float` Modifiers: inline	Gets the Y part of this 3D Vector3d. Extended Type: `Vector3d` v : `Vector3d` Returns: `float`
`Vector3d.getZ v` Full Usage: `Vector3d.getZ v` Parameters: v : `Vector3d` Returns: `float` Modifiers: inline	Gets the Z part of this 3D Vector3d. Extended Type: `Vector3d` v : `Vector3d` Returns: `float`
`Vector3d.intersection (ptA, ptB, vA, vB, tooShortTolerance, relAngleDiscriminant)` Full Usage: `Vector3d.intersection (ptA, ptB, vA, vB, tooShortTolerance, relAngleDiscriminant)` Parameters: ptA : `Point3d` - The start point of the first line. ptB : `Point3d` - The start point of the second line. vA : `Vector3d` - The Vector3d of the first line. vB : `Vector3d` - The Vector3d of the second line. tooShortTolerance : `float` - Is an optional length tolerance. 1e-6 by default. If one or both Vector3d are shorter than this ValueNone is returned. relAngleDiscriminant : `float<MeasureProduct<relAngDiscr, MeasureOne>>` - This is an optional tolerance for the internally calculated relative Angle Discriminant. The default value corresponds to approx 0.25 degree. Below this angle Vector3d are considered parallel. Use the module Rhino.Scripting.FSharp.RelAngleDiscriminant to set another tolerance here. Returns: `ValueOption<float * float>` For (almost) zero length or (almost) parallel Vector3d: ValueNone Else ValueSome with a tuple of the parameters at which the two infinite 2D lines intersect to each other. The tuple's order corresponds to the input order.	Intersects two infinite 3D lines. The lines are defined by a start point and a Vector3d. 'ValueNone' is returned, if the angle between the Vector3d is less than 0.25 degrees or any of them is shorter than 1e-6. These tolerances can be adjusted with optional parameters. Extended Type: `Vector3d` ptA : `Point3d` The start point of the first line. ptB : `Point3d` The start point of the second line. vA : `Vector3d` The Vector3d of the first line. vB : `Vector3d` The Vector3d of the second line. tooShortTolerance : `float` Is an optional length tolerance. 1e-6 by default. If one or both Vector3d are shorter than this ValueNone is returned. relAngleDiscriminant : `float<MeasureProduct<relAngDiscr, MeasureOne>>` This is an optional tolerance for the internally calculated relative Angle Discriminant. The default value corresponds to approx 0.25 degree. Below this angle Vector3d are considered parallel. Use the module Rhino.Scripting.FSharp.RelAngleDiscriminant to set another tolerance here. Returns: `ValueOption<float * float>` For (almost) zero length or (almost) parallel Vector3d: ValueNone Else ValueSome with a tuple of the parameters at which the two infinite 2D lines intersect to each other. The tuple's order corresponds to the input order.
`Vector3d.isAngle180Above cosineValue a b` Full Usage: `Vector3d.isAngle180Above cosineValue a b` Parameters: cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vector3d` b : `Vector3d` Returns: `bool` Modifiers: inline	Checks if Angle between two Vector3d is more than given Cosine. Does not ignore Vector3d orientation. The angle between two Vector3d can be 0 to 180 degrees. Use the Rhino.Scripting.FSharp.Cosine module to get some precomputed cosine values. Fails on zero length Vector3d, tolerance 1e-12. Extended Type: `Vector3d` cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vector3d` b : `Vector3d` Returns: `bool`
`Vector3d.isAngle180Below cosineValue a b` Full Usage: `Vector3d.isAngle180Below cosineValue a b` Parameters: cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vector3d` b : `Vector3d` Returns: `bool` Modifiers: inline	Checks if Angle between two Vector3d is less than given Cosine. Does not ignore Vector3d orientation. The angle between two Vector3d can be 0 to 180 degrees. Use the Rhino.Scripting.FSharp.Cosine module to get some precomputed cosine values Fails on zero length Vector3d, tolerance 1e-12. Extended Type: `Vector3d` cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vector3d` b : `Vector3d` Returns: `bool`
`Vector3d.isAngle90Above cosineValue a b` Full Usage: `Vector3d.isAngle90Above cosineValue a b` Parameters: cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vector3d` b : `Vector3d` Returns: `bool` Modifiers: inline	Checks if Angle between two Vector3d is more than given Cosine. Ignores Vector3d orientation. The angle between two Vector3d can be 0 to 90 degrees ignoring their direction. Use the Rhino.Scripting.FSharp.Cosine module to get some precomputed cosine values. Fails on zero length Vector3d, tolerance 1e-12. Extended Type: `Vector3d` cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vector3d` b : `Vector3d` Returns: `bool`
`Vector3d.isAngle90Below cosineValue a b` Full Usage: `Vector3d.isAngle90Below cosineValue a b` Parameters: cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vector3d` b : `Vector3d` Returns: `bool` Modifiers: inline	Checks if Angle between two Vector3d is less than given Cosine. Ignores Vector3d orientation. The angle between two Vector3d can be 0 to 90 degrees ignoring their direction. Use the Rhino.Scripting.FSharp.Cosine module to get some precomputed cosine values Fails on zero length Vector3d, tolerance 1e-12. Extended Type: `Vector3d` cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vector3d` b : `Vector3d` Returns: `bool`
`Vector3d.isHorizontal v` Full Usage: `Vector3d.isHorizontal v` Parameters: v : `Vector3d` Returns: `bool` Modifiers: inline	Checks if line is horizontal (Z component is almost zero). Tolerance is 1e-6. Fails on lines shorter than 1e-6. Extended Type: `Vector3d` v : `Vector3d` Returns: `bool`
`Vector3d.isOppositeOrientation v other` Full Usage: `Vector3d.isOppositeOrientation v other` Parameters: v : `Vector3d` other : `Vector3d` Returns: `bool` Modifiers: inline	Checks if the angle between the two 3D Vector3d is more than 180 degrees. Calculates the dot product of two 3D Vector3d. Then checks if it is smaller than minus 1e-12. If any of the two Vector3d is zero length returns false. Extended Type: `Vector3d` v : `Vector3d` other : `Vector3d` Returns: `bool`
`Vector3d.isTiny tol v` Full Usage: `Vector3d.isTiny tol v` Parameters: tol : `float` v : `Vector3d` Returns: `bool` Modifiers: inline	Check if the 3D Vector3d is shorter than the tolerance. Also checks if any component is a NaN. Extended Type: `Vector3d` tol : `float` v : `Vector3d` Returns: `bool`
`Vector3d.isTinySq tol v` Full Usage: `Vector3d.isTinySq tol v` Parameters: tol : `float` v : `Vector3d` Returns: `bool` Modifiers: inline	Check if the 3D Vector3d square length is shorter than the squared tolerance. Also checks if any component is a NaN. Extended Type: `Vector3d` tol : `float` v : `Vector3d` Returns: `bool`
`Vector3d.isVertical v` Full Usage: `Vector3d.isVertical v` Parameters: v : `Vector3d` Returns: `bool` Modifiers: inline	Checks if 3D Vector3d is parallel to the world Z axis. Ignoring orientation. Tolerance is 1e-6. Fails on Vector3d shorter than 1e-6. Same as ln.IsZAligned Extended Type: `Vector3d` v : `Vector3d` Returns: `bool`
`Vector3d.isXAligned v` Full Usage: `Vector3d.isXAligned v` Parameters: v : `Vector3d` Returns: `bool` Modifiers: inline	Checks if 3D Vector3d is parallel to the world X axis. Ignoring orientation. Tolerance is 1e-6. Fails on Vector3d shorter than 1e-6. Extended Type: `Vector3d` v : `Vector3d` Returns: `bool`
`Vector3d.isYAligned v` Full Usage: `Vector3d.isYAligned v` Parameters: v : `Vector3d` Returns: `bool` Modifiers: inline	Checks if 3D Vector3d is parallel to the world Y axis. Ignoring orientation. Tolerance is 1e-6. Fails on Vector3d shorter than 1e-6. Extended Type: `Vector3d` v : `Vector3d` Returns: `bool`
`Vector3d.isZAligned v` Full Usage: `Vector3d.isZAligned v` Parameters: v : `Vector3d` Returns: `bool` Modifiers: inline	Checks if 3D Vector3d is parallel to the world Z axis. Ignoring orientation. Tolerance is 1e-6. Fails on Vector3d shorter than 1e-6. Same as ln.IsVertical Extended Type: `Vector3d` v : `Vector3d` Returns: `bool`
`Vector3d.length v` Full Usage: `Vector3d.length v` Parameters: v : `Vector3d` Returns: `float` Modifiers: inline	Returns the length of the 3D Vector3d. Extended Type: `Vector3d` v : `Vector3d` Returns: `float`
`Vector3d.lengthInXY v` Full Usage: `Vector3d.lengthInXY v` Parameters: v : `Vector3d` Returns: `float` Modifiers: inline	Returns the Vector3d length projected into X Y Plane. sqrt(v.X * v.X + v.Y * v.Y) Extended Type: `Vector3d` v : `Vector3d` Returns: `float`
`Vector3d.lengthSq v` Full Usage: `Vector3d.lengthSq v` Parameters: v : `Vector3d` Returns: `float` Modifiers: inline	Returns the squared length of the 3D Vector3d. The square length is faster to calculate and often good enough for use cases such as sorting Vector3d by length. Extended Type: `Vector3d` v : `Vector3d` Returns: `float`
`Vector3d.lerp (start, ende, rel)` Full Usage: `Vector3d.lerp (start, ende, rel)` Parameters: start : `Vector3d` ende : `Vector3d` rel : `float` Returns: `Vector3d`	Linearly interpolates between two Vector3d. e.g. rel=0.5 will return the middle Vector3d, rel=1.0 the end Vector3d, rel=1.5 a Vector3d half the distance beyond the end Vector3d. Extended Type: `Vector3d` start : `Vector3d` ende : `Vector3d` rel : `float` Returns: `Vector3d`
`Vector3d.matchOrientation orientationToMatch vec` Full Usage: `Vector3d.matchOrientation orientationToMatch vec` Parameters: orientationToMatch : `Vector3d` vec : `Vector3d` Returns: `Vector3d` Modifiers: inline	Ensure that the 3D Vector3d has a positive dot product with given 3D orientation Vector3d. Extended Type: `Vector3d` orientationToMatch : `Vector3d` vec : `Vector3d` Returns: `Vector3d`
`Vector3d.matchesOrientation v other` Full Usage: `Vector3d.matchesOrientation v other` Parameters: v : `Vector3d` other : `Vector3d` Returns: `bool` Modifiers: inline	Checks if the angle between the two 3D Vector3d is less than 180 degrees. Calculates the dot product of two 3D Vector3d. Then checks if it is bigger than 1e-12. If any of the two Vector3d is zero length returns false. Extended Type: `Vector3d` v : `Vector3d` other : `Vector3d` Returns: `bool`
`Vector3d.moveX x v` Full Usage: `Vector3d.moveX x v` Parameters: x : `float` v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Add to the X part of this 3D Vector3d together. Returns a new 3D Vector3d. Extended Type: `Vector3d` x : `float` v : `Vector3d` Returns: `Vector3d`
`Vector3d.moveY y v` Full Usage: `Vector3d.moveY y v` Parameters: y : `float` v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Add to the Y part of this 3D Vector3d together. Returns a new 3D Vector3d. Extended Type: `Vector3d` y : `float` v : `Vector3d` Returns: `Vector3d`
`Vector3d.moveZ z v` Full Usage: `Vector3d.moveZ z v` Parameters: z : `float` v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Add to the Z part of this 3D Vector3d together. Returns a new 3D Vector3d. Extended Type: `Vector3d` z : `float` v : `Vector3d` Returns: `Vector3d`
`Vector3d.orientDown v` Full Usage: `Vector3d.orientDown v` Parameters: v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Reverse Vector3d if Z part is bigger than 0.0 Extended Type: `Vector3d` v : `Vector3d` Returns: `Vector3d`
`Vector3d.orientUp v` Full Usage: `Vector3d.orientUp v` Parameters: v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Reverse Vector3d if Z part is smaller than 0.0 Extended Type: `Vector3d` v : `Vector3d` Returns: `Vector3d`
`Vector3d.perpendicularInVerticalPlane v` Full Usage: `Vector3d.perpendicularInVerticalPlane v` Parameters: v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Returns a Vector3d that is perpendicular to the given Vector3d and in the same vertical Plane. Projected into the X-Y plane input and output Vector3d are parallel and of same orientation. Not of same length, not unitized. On vertical input Vector3d resulting Vector3d if of zero length. Extended Type: `Vector3d` v : `Vector3d` Returns: `Vector3d`
`Vector3d.perpendicularInXY v` Full Usage: `Vector3d.perpendicularInXY v` Parameters: v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Returns a perpendicular horizontal Vector3d. Rotated counterclockwise. Just does Vector3d(-v.Y, v.X, 0.0) On vertical input Vector3d resulting Vector3d if of zero length. Extended Type: `Vector3d` v : `Vector3d` Returns: `Vector3d`
`Vector3d.projectToLine ln v pt` Full Usage: `Vector3d.projectToLine ln v pt` Parameters: ln : `Line` v : `Vector3d` pt : `Point3d` Returns: `Point3d`	Project point onto a finite line in direction of v Fails if line is missed by tolerance 1e-6 Extended Type: `Vector3d` ln : `Line` v : `Vector3d` pt : `Point3d` Returns: `Point3d`
`Vector3d.projectToPlane pl v` Full Usage: `Vector3d.projectToPlane pl v` Parameters: pl : `Plane` v : `Vector3d` Returns: `Vector3d`	Project vector to Plane Fails if resulting vector is of almost zero length (RhinoMath.SqrtEpsilon) Extended Type: `Vector3d` pl : `Plane` v : `Vector3d` Returns: `Vector3d`
`Vector3d.projectToXYPlane v` Full Usage: `Vector3d.projectToXYPlane v` Parameters: v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Project Vector3d to World X-Y plane. Use Vc.ofVector3d to convert to a 2D Vector3d. Extended Type: `Vector3d` v : `Vector3d` Returns: `Vector3d`
`Vector3d.reverse v` Full Usage: `Vector3d.reverse v` Parameters: v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Negate or inverse a 3D Vector3d. Returns a new 3D Vector3d. Same as Vector3d.flip. Extended Type: `Vector3d` v : `Vector3d` Returns: `Vector3d`
`Vector3d.rotateOnZ90CCW v` Full Usage: `Vector3d.rotateOnZ90CCW v` Parameters: v : `Vector3d` Returns: `Vector3d` Modifiers: inline	90 Degree rotation Counter-Clockwise around Z-axis. Extended Type: `Vector3d` v : `Vector3d` Returns: `Vector3d`
`Vector3d.rotateOnZ90CW v` Full Usage: `Vector3d.rotateOnZ90CW v` Parameters: v : `Vector3d` Returns: `Vector3d` Modifiers: inline	90 Degree rotation clockwise around Z-axis. Extended Type: `Vector3d` v : `Vector3d` Returns: `Vector3d`
`Vector3d.scale f v` Full Usage: `Vector3d.scale f v` Parameters: f : `float` v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Multiplies a 3D Vector3d with a scalar, also called scaling a Vector3d. Returns a new 3D Vector3d. Extended Type: `Vector3d` f : `float` v : `Vector3d` Returns: `Vector3d`
`Vector3d.slerp (start, ende, rel)` Full Usage: `Vector3d.slerp (start, ende, rel)` Parameters: start : `Vector3d` ende : `Vector3d` rel : `float` Returns: `Vector3d`	Spherically interpolates between start and end by amount rel (0.0 to 1.0). The difference between this and linear interpolation (aka, "lerp") is that the Vector3d are treated as directions rather than points in space. The direction of the returned Vector3d is interpolated by the angle and its magnitude is interpolated between the magnitudes of start and end. Interpolation continues before and after the range of 0.0 and 0.1 Extended Type: `Vector3d` start : `Vector3d` ende : `Vector3d` rel : `float` Returns: `Vector3d`
`Vector3d.slopeDegrees v` Full Usage: `Vector3d.slopeDegrees v` Parameters: v : `Vector3d` Returns: `float` Modifiers: inline	Returns positive or negative slope of a Vector3d in Degrees. In relation to X-Y plane. Range -90 to +90 Degrees. Extended Type: `Vector3d` v : `Vector3d` Returns: `float`
`Vector3d.slopePercent v` Full Usage: `Vector3d.slopePercent v` Parameters: v : `Vector3d` Returns: `float` Modifiers: inline	Returns positive or negative slope of a Vector3d in Percent. In relation to X-Y plane. 100% = 45 Degrees. Returns positive (or negative) Infinity if line is vertical or input has length zero. Extended Type: `Vector3d` v : `Vector3d` Returns: `float`
`Vector3d.slopeRadians v` Full Usage: `Vector3d.slopeRadians v` Parameters: v : `Vector3d` Returns: `float` Modifiers: inline	Returns positive or negative slope of a Vector3d in Radians. In relation to X-Y plane. Range -1.57 to +1.57 Radians. Extended Type: `Vector3d` v : `Vector3d` Returns: `float`
`Vector3d.unitize v` Full Usage: `Vector3d.unitize v` Parameters: v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Returns 3D Vector3d unitized, fails on zero length Vector3d. Extended Type: `Vector3d` v : `Vector3d` Returns: `Vector3d`
`Vector3d.unitizeOrDefault defaultUnitVector3dtor v` Full Usage: `Vector3d.unitizeOrDefault defaultUnitVector3dtor v` Parameters: defaultUnitVector3dtor : `Vector3d` v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Unitize 3D Vector3d, if input Vector3d is shorter than 1e-6 the default unit-Vector3d is returned. Extended Type: `Vector3d` defaultUnitVector3dtor : `Vector3d` v : `Vector3d` Returns: `Vector3d`
`Vector3d.withLength desiredLength v` Full Usage: `Vector3d.withLength desiredLength v` Parameters: desiredLength : `float` v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Returns a new 3D Vector3d scaled to the desired length. Same as Vector3d.WithLength. Returns a new 3D Vector3d. Extended Type: `Vector3d` desiredLength : `float` v : `Vector3d` Returns: `Vector3d`
`Vector3d.withX x v` Full Usage: `Vector3d.withX x v` Parameters: x : `float` v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Returns new 3D Vector3d with new X value, Y and Z stay the same. Extended Type: `Vector3d` x : `float` v : `Vector3d` Returns: `Vector3d`
`Vector3d.withY y v` Full Usage: `Vector3d.withY y v` Parameters: y : `float` v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Returns new 3D Vector3d with new Y value, X and Z stay the same. Extended Type: `Vector3d` y : `float` v : `Vector3d` Returns: `Vector3d`
`Vector3d.withZ z v` Full Usage: `Vector3d.withZ z v` Parameters: z : `float` v : `Vector3d` Returns: `Vector3d` Modifiers: inline	Returns new 3D Vector3d with new z value, X and Y stay the same. Extended Type: `Vector3d` z : `float` v : `Vector3d` Returns: `Vector3d`