AutoOpenUnitVec (Euclid)

AutoOpenUnitVec Module

Namespace: Euclid
Assembly: Euclid.dll

When Euclid is opened this module will be auto-opened. It only contains extension members for type UnitVec.

Type extensions

Type extension	Description
`this.AngleDiamondInXYTo` Full Usage: `this.AngleDiamondInXYTo` Parameters: b : `UnitVec` Returns: `float` Modifiers: inline	Returns positive angle for rotating Counter-Clockwise from this vector to vector '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 vector. Extended Type: `UnitVec` b : `UnitVec` Returns: `float`
`this.AsPnt` Full Usage: `this.AsPnt` Parameters: () : `unit` Returns: `Pnt` Modifiers: inline	Convert 3D unit-vector to 3D point. Extended Type: `UnitVec` () : `unit` Returns: `Pnt`
`this.AsPnt` Full Usage: `this.AsPnt` Returns: `Pnt` Modifiers: inline	Convert 3D unit-vector to 3D point. Extended Type: `UnitVec` Returns: `Pnt`
`this.AsVc` Full Usage: `this.AsVc` Parameters: () : `unit` Returns: `Vc` Modifiers: inline	Convert 3D unit-vector to 2D vector, discarding the Z value. Extended Type: `UnitVec` () : `unit` Returns: `Vc`
`this.AsVc` Full Usage: `this.AsVc` Returns: `Vc` Modifiers: inline	Convert 3D unit-vector to 2D vector, discarding the Z value. Extended Type: `UnitVec` Returns: `Vc`
`this.AsVec` Full Usage: `this.AsVec` Parameters: () : `unit` Returns: `Vec` Modifiers: inline	Convert 3D unit-vector to 3D vector. Extended Type: `UnitVec` () : `unit` Returns: `Vec`
`this.AsVec` Full Usage: `this.AsVec` Returns: `Vec` Modifiers: inline	Convert 3D unit-vector to 3D vector. Extended Type: `UnitVec` Returns: `Vec`
`this.Cross` Full Usage: `this.Cross` Parameters: b : `UnitVec` Returns: `Vec` Modifiers: inline	Cross product, of two 3D unit-vectors. The resulting vector is perpendicular to both input vectors. The length of this resulting vector is the squared area of the parallelogram spanned by the input vectors. Or the sine of the angle between the two unit-vectors. Its direction follows the right-hand rule. A x B = \|A\| * \|B\| * sin(angle) Extended Type: `UnitVec` b : `UnitVec` Returns: `Vec`
`this.Cross` Full Usage: `this.Cross` Parameters: b : `Vec` Returns: `Vec` Modifiers: inline	Cross product, of a 3D unit-vectors an a 3D vector. The resulting vector is perpendicular to both input vectors. The length of this resulting vector is the squared 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: `UnitVec` b : `Vec` Returns: `Vec`
`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 vector. Extended Type: `UnitVec` () : `unit` Returns: `float`
`this.Direction180InXY` Full Usage: `this.Direction180InXY` 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 vector. Extended Type: `UnitVec` 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 vector. Fails if vector is vertical. Extended Type: `UnitVec` () : `unit` Returns: `float`
`this.Direction2PiInXY` Full Usage: `this.Direction2PiInXY` 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 vector. Fails if vector is vertical. Extended Type: `UnitVec` Returns: `float`
`this.Direction360InXY` Full Usage: `this.Direction360InXY` Parameters: () : `unit` Returns: `float` Modifiers: inline	Returns the angle in Degrees from X-axis in World X-Y plane. Going Counter-Clockwise till 360. For World X-Y plane. Considers only the X and Y components of the vector. Extended Type: `UnitVec` () : `unit` Returns: `float`
`this.Direction360InXY` Full Usage: `this.Direction360InXY` Returns: `float` Modifiers: inline	Returns the angle in Degrees from X-axis in World X-Y plane. Going Counter-Clockwise till 360. For World X-Y plane. Considers only the X and Y components of the vector. Extended Type: `UnitVec` Returns: `float`
`this.DirectionDiamondInXY` Full Usage: `this.DirectionDiamondInXY` Parameters: () : `unit` Returns: `float` Modifiers: inline	The diamond angle is always positive and in the range of 0.0 to 4.0 (for 360 Degrees) 0.0 = Xaxis, going Counter-Clockwise. Ignoring Z component. This is the fastest angle computation since it does not use Math.Cos or Math.Sin. It is useful for radial sorting. For X-Y plane. Considers only the X and Y components of the vector. Extended Type: `UnitVec` () : `unit` Returns: `float`
`this.DirectionDiamondInXY` Full Usage: `this.DirectionDiamondInXY` Returns: `float` Modifiers: inline	The diamond angle is always positive and in the range of 0.0 to 4.0 (for 360 Degrees) 0.0 = Xaxis, going Counter-Clockwise. Ignoring Z component. This is the fastest angle computation since it does not use Math.Cos or Math.Sin. It is useful for radial sorting. For X-Y plane. Considers only the X and Y components of the vector. Extended Type: `UnitVec` Returns: `float`
`this.DirectionPiInXY` Full Usage: `this.DirectionPiInXY` Parameters: () : `unit` Returns: `float` Modifiers: inline	Returns the angle in Radians from X-axis in World X-Y plane, Ignores orientation. Range 0.0 to Pi. For World X-Y plane. Considers only the X and Y components of the vector. Fails if vector is vertical. Extended Type: `UnitVec` () : `unit` Returns: `float`
`this.DirectionPiInXY` Full Usage: `this.DirectionPiInXY` Returns: `float` Modifiers: inline	Returns the angle in Radians from X-axis in World X-Y plane, Ignores orientation. Range 0.0 to Pi. For World X-Y plane. Considers only the X and Y components of the vector. Fails if vector is vertical. Extended Type: `UnitVec` Returns: `float`
`this.Dot` Full Usage: `this.Dot` Parameters: b : `UnitVec` Returns: `float` Modifiers: inline	Dot product, or scalar product of two 3D unit-vectors. Returns a float. This float of unit-vectors is the Cosine of the angle between the two vectors. Extended Type: `UnitVec` b : `UnitVec` Returns: `float`
`this.Dot` Full Usage: `this.Dot` Parameters: b : `Vec` Returns: `float` Modifiers: inline	Dot product, or scalar product of a 3D unit-vector with a 3D vector. Returns a float. This float is the projected length of the 3D vector on the direction of the unit-vector. Extended Type: `UnitVec` b : `Vec` Returns: `float`
`this.DotCosine` Full Usage: `this.DotCosine` Parameters: b : `UnitVec` Returns: `float<MeasureProduct<cosine, MeasureOne>>` Modifiers: inline	Dot product, or scalar product of two 3D unit-vector. This float of unit-vectors is the Cosine of the angle between the two vectors. Returns a float with a unit of Measure Euclid.Cosine.cosine. This is useful for comparing the angle to precomputed values in the Euclid.Cosine module. Extended Type: `UnitVec` b : `UnitVec` Returns: `float<MeasureProduct<cosine, MeasureOne>>`
`this.IsHorizontal` Full Usage: `this.IsHorizontal` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Checks if 3D unit-vector is horizontal (Z component is almost zero). The absolute deviation tolerance along Z axis is 1e-9. Fails on vectors shorter than 1e-6. Extended Type: `UnitVec` () : `unit` Returns: `bool`
`this.IsHorizontal` Full Usage: `this.IsHorizontal` Returns: `bool` Modifiers: inline	Checks if 3D unit-vector is horizontal (Z component is almost zero). The absolute deviation tolerance along Z axis is 1e-9. Fails on vectors shorter than 1e-6. Extended Type: `UnitVec` Returns: `bool`
`this.IsOppositeOrientation` Full Usage: `this.IsOppositeOrientation` Parameters: other : `UnitVec` Returns: `bool` Modifiers: inline	Checks if the angle between the two 3D unit-vectors is more than 180 degrees. Calculates the dot product of two 3D unit-vectors. Then checks if it is smaller than minus 1e-12. Extended Type: `UnitVec` other : `UnitVec` Returns: `bool`
`this.IsOppositeOrientation` Full Usage: `this.IsOppositeOrientation` Parameters: other : `Vec` Returns: `bool` Modifiers: inline	Checks if the angle between the this 23D unit-vectors and a 2D vector is more than 180 degrees. Calculates the dot product of a 3D vector and a unit-vectors. Then checks if it is smaller than minus 1e-12. Extended Type: `UnitVec` other : `Vec` Returns: `bool`
`this.IsParallelAndOrientedTo` Full Usage: `this.IsParallelAndOrientedTo` Parameters: other : `UnitVec` minCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool` Modifiers: inline	Checks if two 3D unit-vectors 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 Euclid.Cosine module. Extended Type: `UnitVec` other : `UnitVec` minCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool`
`this.IsParallelAndOrientedTo` Full Usage: `this.IsParallelAndOrientedTo` Parameters: other : `Vec` minCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool` Modifiers: inline	Checks if this 3D unit-vectors and a 3D vector 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 Euclid.Cosine module. Extended Type: `UnitVec` other : `Vec` minCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool`
`this.IsParallelTo` Full Usage: `this.IsParallelTo` Parameters: other : `UnitVec` minCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool` Modifiers: inline	Checks if two 3D unit-vectors 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 Euclid.Cosine module. Extended Type: `UnitVec` other : `UnitVec` minCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool`
`this.IsParallelTo` Full Usage: `this.IsParallelTo` Parameters: other : `Vec` minCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool` Modifiers: inline	Checks if this 3D unit-vectors and a 3D vector 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 Euclid.Cosine module. Extended Type: `UnitVec` other : `Vec` minCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool`
`this.IsPerpendicularTo` Full Usage: `this.IsPerpendicularTo` Parameters: other : `UnitVec` maxCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool` Modifiers: inline	Checks if two 3D unit-vectors 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 Euclid.Cosine module. Extended Type: `UnitVec` other : `UnitVec` maxCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool`
`this.IsPerpendicularTo` Full Usage: `this.IsPerpendicularTo` Parameters: other : `Vec` maxCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool` Modifiers: inline	Checks if this 3D unit-vectors and a 3D vector 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 Euclid.Cosine module. Extended Type: `UnitVec` other : `Vec` maxCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool`
`this.IsVertical` Full Usage: `this.IsVertical` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Checks if 3D unit-vector is parallel to the world Z axis. Ignoring orientation. The absolute deviation tolerance along X and Y axis is 1e-9. Same as v.IsZAligned Extended Type: `UnitVec` () : `unit` Returns: `bool`
`this.IsVertical` Full Usage: `this.IsVertical` Returns: `bool` Modifiers: inline	Checks if 3D unit-vector is parallel to the world Z axis. Ignoring orientation. The absolute deviation tolerance along X and Y axis is 1e-9. Same as v.IsZAligned Extended Type: `UnitVec` Returns: `bool`
`this.IsXAligned` Full Usage: `this.IsXAligned` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Checks if 3D unit-vector is parallel to the world X axis. Ignoring orientation. The absolute deviation tolerance along Y and Z axis is 1e-9. Extended Type: `UnitVec` () : `unit` Returns: `bool`
`this.IsXAligned` Full Usage: `this.IsXAligned` Returns: `bool` Modifiers: inline	Checks if 3D unit-vector is parallel to the world X axis. Ignoring orientation. The absolute deviation tolerance along Y and Z axis is 1e-9. Extended Type: `UnitVec` Returns: `bool`
`this.IsYAligned` Full Usage: `this.IsYAligned` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Checks if 3D unit-vector is parallel to the world Y axis. Ignoring orientation. The absolute deviation tolerance along X and Z axis is 1e-9. Extended Type: `UnitVec` () : `unit` Returns: `bool`
`this.IsYAligned` Full Usage: `this.IsYAligned` Returns: `bool` Modifiers: inline	Checks if 3D unit-vector is parallel to the world Y axis. Ignoring orientation. The absolute deviation tolerance along X and Z axis is 1e-9. Extended Type: `UnitVec` Returns: `bool`
`this.IsZAligned` Full Usage: `this.IsZAligned` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Checks if 3D unit-vector is parallel to the world Z axis. Ignoring orientation. The absolute deviation tolerance along X and Y axis is 1e-9. Same as v.IsVertical Extended Type: `UnitVec` () : `unit` Returns: `bool`
`this.IsZAligned` Full Usage: `this.IsZAligned` Returns: `bool` Modifiers: inline	Checks if 3D unit-vector is parallel to the world Z axis. Ignoring orientation. The absolute deviation tolerance along X and Y axis is 1e-9. Same as v.IsVertical Extended Type: `UnitVec` Returns: `bool`
`this.LengthInXY` Full Usage: `this.LengthInXY` Parameters: () : `unit` Returns: `float` Modifiers: inline	Returns the length of the 3D vector projected into World X-Y plane. Extended Type: `UnitVec` () : `unit` Returns: `float`
`this.LengthInXY` Full Usage: `this.LengthInXY` Returns: `float` Modifiers: inline	Returns the length of the 3D vector projected into World X-Y plane. Extended Type: `UnitVec` Returns: `float`
`this.LengthSqInXY` Full Usage: `this.LengthSqInXY` Parameters: () : `unit` Returns: `float` Modifiers: inline	Returns the squared length of the 3D vector projected into World X-Y plane. The square length is faster to calculate and often good enough for use cases such as sorting vectors by length. Extended Type: `UnitVec` () : `unit` Returns: `float`
`this.LengthSqInXY` Full Usage: `this.LengthSqInXY` Returns: `float` Modifiers: inline	Returns the squared length of the 3D vector projected into World X-Y plane. The square length is faster to calculate and often good enough for use cases such as sorting vectors by length. Extended Type: `UnitVec` Returns: `float`
`this.MatchesOrientation` Full Usage: `this.MatchesOrientation` Parameters: other : `UnitVec` Returns: `bool` Modifiers: inline	Checks if the angle between the two 3D unit-vectors is less than 180 degrees. Calculates the dot product of two 3D unit-vectors. Then checks if it is bigger than 1e-12. Extended Type: `UnitVec` other : `UnitVec` Returns: `bool`
`this.MatchesOrientation` Full Usage: `this.MatchesOrientation` Parameters: other : `Vec` Returns: `bool` Modifiers: inline	Checks if the angle between the this 3D unit-vectors and a 3D vector is less than 180 degrees. Calculates the dot product of a 3D vector and a unit-vectors. Then checks if it is bigger than 1e-12. Extended Type: `UnitVec` other : `Vec` Returns: `bool`
`this.PerpendicularInXY` Full Usage: `this.PerpendicularInXY` Parameters: () : `unit` Returns: `Vec` Modifiers: inline	Returns a perpendicular horizontal vector. Rotated counterclockwise. Or Vec.Zero if input is vertical. Just does Vec(-v.Y, v.X, 0.0) Extended Type: `UnitVec` () : `unit` Returns: `Vec`
`this.PerpendicularInXY` Full Usage: `this.PerpendicularInXY` Returns: `Vec` Modifiers: inline	Returns a perpendicular horizontal vector. Rotated counterclockwise. Or Vec.Zero if input is vertical. Just does Vec(-v.Y, v.X, 0.0) Extended Type: `UnitVec` Returns: `Vec`
`this.RotateOnZ90CCW` Full Usage: `this.RotateOnZ90CCW` Parameters: () : `unit` Returns: `UnitVec` Modifiers: inline	90 Degree rotation Counter-Clockwise around Z-axis. Extended Type: `UnitVec` () : `unit` Returns: `UnitVec`
`this.RotateOnZ90CCW` Full Usage: `this.RotateOnZ90CCW` Returns: `UnitVec` Modifiers: inline	90 Degree rotation Counter-Clockwise around Z-axis. Extended Type: `UnitVec` Returns: `UnitVec`
`this.RotateOnZ90CW` Full Usage: `this.RotateOnZ90CW` Parameters: () : `unit` Returns: `UnitVec` Modifiers: inline	90 Degree rotation clockwise around Z-axis. Extended Type: `UnitVec` () : `unit` Returns: `UnitVec`
`this.RotateOnZ90CW` Full Usage: `this.RotateOnZ90CW` Returns: `UnitVec` Modifiers: inline	90 Degree rotation clockwise around Z-axis. Extended Type: `UnitVec` Returns: `UnitVec`
`this.Transform` Full Usage: `this.Transform` Parameters: m : `Matrix` Returns: `Vec` Modifiers: inline	Multiplies a Matrix with a 3D vector. Since a 3D vector represents a direction or an offset in space, but not a location, the implicit the 4th dimension is 0.0 so that all translations are ignored. (Homogeneous Vector) The resulting vector is not unitized. Extended Type: `UnitVec` m : `Matrix` Returns: `Vec`
`this.TransformRigid` Full Usage: `this.TransformRigid` Parameters: m : `RigidMatrix` Returns: `UnitVec` Modifiers: inline	Multiplies (or applies) a RigidMatrix to a 3D unit-vector. Since a 3D vector represents a direction or an offset in space, but not a location, all translations are ignored. (Homogeneous Vector) Extended Type: `UnitVec` m : `RigidMatrix` Returns: `UnitVec`
`this.WithX` Full Usage: `this.WithX` Parameters: x : `float` Returns: `Vec` Modifiers: inline	Returns a new 3D vector with new X coordinate, Y and Z stay the same. Extended Type: `UnitVec` x : `float` Returns: `Vec`
`this.WithY` Full Usage: `this.WithY` Parameters: y : `float` Returns: `Vec` Modifiers: inline	Returns a new 3D vector with new y coordinate, X and Z stay the same. Extended Type: `UnitVec` y : `float` Returns: `Vec`
`this.WithZ` Full Usage: `this.WithZ` Parameters: z : `float` Returns: `Vec` Modifiers: inline	Returns a new 3D vector with new z coordinate, X and Y stay the same. Extended Type: `UnitVec` z : `float` Returns: `Vec`
`UnitVec.Xaxis()` Full Usage: `UnitVec.Xaxis()` Parameters: () : `unit` Returns: `UnitVec` Modifiers: inline	Returns the World X-axis with length one: UnitVec(1, 0, 0) Extended Type: `UnitVec` () : `unit` Returns: `UnitVec`
`UnitVec.Xaxis` Full Usage: `UnitVec.Xaxis` Returns: `UnitVec` Modifiers: inline	Returns the World X-axis with length one: UnitVec(1, 0, 0) Extended Type: `UnitVec` Returns: `UnitVec`
`UnitVec.Yaxis()` Full Usage: `UnitVec.Yaxis()` Parameters: () : `unit` Returns: `UnitVec` Modifiers: inline	Returns the World Y-axis with length one: UnitVec(0.1, 0) Extended Type: `UnitVec` () : `unit` Returns: `UnitVec`
`UnitVec.Yaxis` Full Usage: `UnitVec.Yaxis` Returns: `UnitVec` Modifiers: inline	Returns the World Y-axis with length one: UnitVec(0.1, 0) Extended Type: `UnitVec` Returns: `UnitVec`
`UnitVec.Zaxis()` Full Usage: `UnitVec.Zaxis()` Parameters: () : `unit` Returns: `UnitVec` Modifiers: inline	Returns the World Z-axis with length one: UnitVec(0, 0, 1) Extended Type: `UnitVec` () : `unit` Returns: `UnitVec`
`UnitVec.Zaxis` Full Usage: `UnitVec.Zaxis` Returns: `UnitVec` Modifiers: inline	Returns the World Z-axis with length one: UnitVec(0, 0, 1) Extended Type: `UnitVec` Returns: `UnitVec`
`UnitVec.add a b` Full Usage: `UnitVec.add a b` Parameters: a : `UnitVec` b : `UnitVec` Returns: `Vec` Modifiers: inline	Add two 3D unit-vectors together. Returns a new (non-unitized) 3D vector. Extended Type: `UnitVec` a : `UnitVec` b : `UnitVec` Returns: `Vec`
`UnitVec.angle180 a b` Full Usage: `UnitVec.angle180 a b` Parameters: a : `UnitVec` b : `UnitVec` Returns: `float` Modifiers: inline	Returns positive angle between two 3D unit-vectors in Degrees. Takes vector orientation into account. Range 0 to 180 Degrees. Extended Type: `UnitVec` a : `UnitVec` b : `UnitVec` Returns: `float`
`UnitVec.angle2PiInXY (a, b)` Full Usage: `UnitVec.angle2PiInXY (a, b)` Parameters: a : `UnitVec` b : `UnitVec` Returns: `float` Modifiers: inline	Returns positive angle from vector 'a' to vector 'b' projected in X-Y plane. In Radians. Considering Counter-Clockwise rotation round the World Z-axis. Range: 0.0 to 2 Pi ( = 0 to 360 Degrees) Extended Type: `UnitVec` a : `UnitVec` b : `UnitVec` Returns: `float`
`UnitVec.angle360InXY (a, b)` Full Usage: `UnitVec.angle360InXY (a, b)` Parameters: a : `UnitVec` b : `UnitVec` Returns: `float` Modifiers: inline	Returns positive angle of two 3D unit-vector projected in X-Y plane in Degrees. Considering positive rotation round the World Z-axis. Range: 0 to 360 Degrees. Extended Type: `UnitVec` a : `UnitVec` b : `UnitVec` Returns: `float`
`UnitVec.angle90 a b` Full Usage: `UnitVec.angle90 a b` Parameters: a : `UnitVec` b : `UnitVec` Returns: `float` Modifiers: inline	Returns positive angle between two 3D unit-vectors in Degrees, Ignores vector orientation. Range: 0 to 90 Degrees. Extended Type: `UnitVec` a : `UnitVec` b : `UnitVec` Returns: `float`
`UnitVec.angleDiamondInXY (a, b)` Full Usage: `UnitVec.angleDiamondInXY (a, b)` Parameters: a : `UnitVec` b : `UnitVec` Returns: `float` Modifiers: inline	Returns positive angle for rotating Counter-Clockwise from vector 'a' to vector '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 vector. Extended Type: `UnitVec` a : `UnitVec` b : `UnitVec` Returns: `float`
`UnitVec.angleHalfPi a b` Full Usage: `UnitVec.angleHalfPi a b` Parameters: a : `UnitVec` b : `UnitVec` Returns: `float` Modifiers: inline	Returns positive angle between two 3D unit-vectors in Radians. Ignores orientation. Range 0.0 to Pi/2 ( = 0 to 90 Degree) Extended Type: `UnitVec` a : `UnitVec` b : `UnitVec` Returns: `float`
`UnitVec.anglePi a b` Full Usage: `UnitVec.anglePi a b` Parameters: a : `UnitVec` b : `UnitVec` Returns: `float` Modifiers: inline	Returns angle between two 3D unit-vectors in Radians. Takes vector orientation into account. Range 0.0 to Pi( = 0 to 180 Degree) Extended Type: `UnitVec` a : `UnitVec` b : `UnitVec` Returns: `float`
`UnitVec.areParallel other v` Full Usage: `UnitVec.areParallel other v` Parameters: other : `UnitVec` v : `UnitVec` Returns: `bool` Modifiers: inline	Checks if Angle between two vectors is Below 0.25 Degree. Ignores vector orientation. Extended Type: `UnitVec` other : `UnitVec` v : `UnitVec` Returns: `bool`
`UnitVec.areParallelAndMatchOrientation other v` Full Usage: `UnitVec.areParallelAndMatchOrientation other v` Parameters: other : `UnitVec` v : `UnitVec` Returns: `bool` Modifiers: inline	Checks if Angle between two vectors is between 98.75 and 90.25 Degree. Ignores vector orientation. Extended Type: `UnitVec` other : `UnitVec` v : `UnitVec` Returns: `bool`
`UnitVec.arePerpendicular other v` Full Usage: `UnitVec.arePerpendicular other v` Parameters: other : `UnitVec` v : `UnitVec` Returns: `bool` Modifiers: inline	Checks if Angle between two vectors is between 98.75 and 90.25 Degree. Ignores vector orientation. Extended Type: `UnitVec` other : `UnitVec` v : `UnitVec` Returns: `bool`
`UnitVec.asPnt v` Full Usage: `UnitVec.asPnt v` Parameters: v : `UnitVec` Returns: `Pnt` Modifiers: inline	Convert 3D unit-vector to 3D point. Extended Type: `UnitVec` v : `UnitVec` Returns: `Pnt`
`UnitVec.asPt v` Full Usage: `UnitVec.asPt v` Parameters: v : `UnitVec` Returns: `Pt` Modifiers: inline	Convert 3D unit-vector to 2D point by ignoring Z value. Extended Type: `UnitVec` v : `UnitVec` Returns: `Pt`
`UnitVec.asUnitVc v` Full Usage: `UnitVec.asUnitVc v` Parameters: v : `UnitVec` Returns: `UnitVc` Modifiers: inline	Convert 3D unit-vector to 2D unit-vector by ignoring Z value and unitizing again. Extended Type: `UnitVec` v : `UnitVec` Returns: `UnitVc`
`UnitVec.asVc v` Full Usage: `UnitVec.asVc v` Parameters: v : `UnitVec` Returns: `Vc` Modifiers: inline	Convert 3D unit-vector to 2D vector by ignoring Z value. Extended Type: `UnitVec` v : `UnitVec` Returns: `Vc`
`UnitVec.asVec v` Full Usage: `UnitVec.asVec v` Parameters: v : `UnitVec` Returns: `Vec` Modifiers: inline	Convert 3D unit-vector to 3D vector. Extended Type: `UnitVec` v : `UnitVec` Returns: `Vec`
`UnitVec.create (fromPt, toPt)` Full Usage: `UnitVec.create (fromPt, toPt)` Parameters: fromPt : `Pnt` toPt : `Pnt` Returns: `UnitVec` Modifiers: inline	Create 3D unit-vector from start and endpoint. Does the unitizing too. Extended Type: `UnitVec` fromPt : `Pnt` toPt : `Pnt` Returns: `UnitVec`
`UnitVec.createFromMembersXYZ vec` Full Usage: `UnitVec.createFromMembersXYZ vec` Parameters: vec : `^T` Returns: `UnitVec` 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. Does the unitizing too. Internally this is not using reflection at runtime but F# Statically Resolved Type Parameters at compile time. Extended Type: `UnitVec` vec : `^T` Returns: `UnitVec`
`UnitVec.createFromMembersxyz vec` Full Usage: `UnitVec.createFromMembersxyz vec` Parameters: vec : `^T` Returns: `UnitVec` 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. Does the unitizing too. Internally this is not using reflection at runtime but F# Statically Resolved Type Parameters at compile time. Extended Type: `UnitVec` vec : `^T` Returns: `UnitVec`
`UnitVec.createFromPnt pt` Full Usage: `UnitVec.createFromPnt pt` Parameters: pt : `Pnt` Returns: `UnitVec` Modifiers: inline	Create 3D unit-vector from 3D point. Does the unitizing too. Extended Type: `UnitVec` pt : `Pnt` Returns: `UnitVec`
`UnitVec.createFromVec v` Full Usage: `UnitVec.createFromVec v` Parameters: v : `Vec` Returns: `UnitVec` Modifiers: inline	Create 3D unit-vector from 3D vector. Does the unitizing too. Extended Type: `UnitVec` v : `Vec` Returns: `UnitVec`
`UnitVec.cross (a, b)` Full Usage: `UnitVec.cross (a, b)` Parameters: a : `UnitVec` b : `Vec` Returns: `Vec` Modifiers: inline	Cross product, of a 3D unit-vectors an a 3D vector. It is also known as the Determinant, Wedge Product or Outer Product. The resulting vector is perpendicular to both input vectors. The length of this resulting vector is the squared 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: `UnitVec` a : `UnitVec` b : `Vec` Returns: `Vec`
`UnitVec.cross (a, b)` Full Usage: `UnitVec.cross (a, b)` Parameters: a : `Vec` b : `UnitVec` Returns: `Vec` Modifiers: inline	Cross product, of a 3D vector and a 3D unit-vectors. It is also known as the Determinant, Wedge Product or Outer Product. The resulting vector is perpendicular to both input vectors. The length of this resulting vector is the squared 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: `UnitVec` a : `Vec` b : `UnitVec` Returns: `Vec`
`UnitVec.determinant (u, v, w)` Full Usage: `UnitVec.determinant (u, v, w)` Parameters: u : `UnitVec` v : `UnitVec` w : `UnitVec` Returns: `float` Modifiers: inline	Returns three vectors Determinant. This is also the signed volume of the Parallelepipeds define by these three vectors. Also called scalar triple product, mixed product, box product, or in german: Spatprodukt. It is defined as the dot product of one of the vectors with the Cross Product of the other two. Extended Type: `UnitVec` u : `UnitVec` v : `UnitVec` w : `UnitVec` Returns: `float`
`UnitVec.difference a b` Full Usage: `UnitVec.difference a b` Parameters: a : `UnitVec` b : `UnitVec` Returns: `float` Modifiers: inline	Returns the distance between the tips of two 3D unit-vectors. Extended Type: `UnitVec` a : `UnitVec` b : `UnitVec` Returns: `float`
`UnitVec.differenceSq a b` Full Usage: `UnitVec.differenceSq a b` Parameters: a : `UnitVec` b : `UnitVec` Returns: `float` Modifiers: inline	Returns the squared distance between the tips of two 3D unit-vectors. This operation is slightly faster than Vec.difference and sufficient for many algorithms like finding closest points. Extended Type: `UnitVec` a : `UnitVec` b : `UnitVec` Returns: `float`
`UnitVec.direction2PiInXY v` Full Usage: `UnitVec.direction2PiInXY v` Parameters: v : `UnitVec` Returns: `float` Modifiers: inline	Returns positive angle of 3D unit-vector 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 vector. Extended Type: `UnitVec` v : `UnitVec` Returns: `float`
`UnitVec.direction360InXY v` Full Usage: `UnitVec.direction360InXY v` Parameters: v : `UnitVec` Returns: `float` Modifiers: inline	Returns positive angle of 3D unit-vector 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 vector. Extended Type: `UnitVec` v : `UnitVec` Returns: `float`
`UnitVec.directionDiamondInXY v` Full Usage: `UnitVec.directionDiamondInXY v` Parameters: v : `UnitVec` Returns: `float` Modifiers: inline	The diamond angle. Returns positive angle of 3D unit-vector 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 vector. Extended Type: `UnitVec` v : `UnitVec` Returns: `float`
`UnitVec.dot (a, b)` Full Usage: `UnitVec.dot (a, b)` Parameters: a : `UnitVec` b : `Vec` Returns: `float` Modifiers: inline	Dot product, or scalar product of a 3D unit-vector with a 3D vector. Returns a float. This float is the projected length of the 3D vector on the direction of the unit-vector. Extended Type: `UnitVec` a : `UnitVec` b : `Vec` Returns: `float`
`UnitVec.dot (a, b)` Full Usage: `UnitVec.dot (a, b)` Parameters: a : `Vec` b : `UnitVec` Returns: `float` Modifiers: inline	Dot product, or scalar product of a 3D vector with a 3D unit-vector. Returns a float. This float is the projected length of the 3D vector on the direction of the unit-vector. Extended Type: `UnitVec` a : `Vec` b : `UnitVec` Returns: `float`
`UnitVec.dotCosine a b` Full Usage: `UnitVec.dotCosine a b` Parameters: a : `UnitVec` b : `UnitVec` Returns: `float<MeasureProduct<cosine, MeasureOne>>` Modifiers: inline	Dot product, or scalar product of two 3D unit-vector. This float of unit-vectors is the Cosine of the angle between the two vectors. Returns a float with a unit of Measure Euclid.Cosine.cosine. This is useful for comparing the angle to precomputed values in the Euclid.Cosine module. Extended Type: `UnitVec` a : `UnitVec` b : `UnitVec` Returns: `float<MeasureProduct<cosine, MeasureOne>>`
`UnitVec.equals tol a b` Full Usage: `UnitVec.equals tol a b` Parameters: tol : `float` a : `UnitVec` b : `UnitVec` Returns: `bool` Modifiers: inline	Checks if two 3D unit-vectors are equal within tolerance. Identical unit-vectors in opposite directions are not considered equal. Use a tolerance of 0.0 to check for an exact match. Extended Type: `UnitVec` tol : `float` a : `UnitVec` b : `UnitVec` Returns: `bool`
`UnitVec.flip v` Full Usage: `UnitVec.flip v` Parameters: v : `UnitVec` Returns: `UnitVec` Modifiers: inline	Negate or inverse a 3D unit-vectors. Returns a new 3D unit-vector. Same as UnitVec.reverse. Extended Type: `UnitVec` v : `UnitVec` Returns: `UnitVec`
`UnitVec.flipToPointUp v` Full Usage: `UnitVec.flipToPointUp v` Parameters: v : `UnitVec` Returns: `UnitVec` Modifiers: inline	Flips the vector if Z part is smaller than 0.0 Extended Type: `UnitVec` v : `UnitVec` Returns: `UnitVec`
`UnitVec.getX v` Full Usage: `UnitVec.getX v` Parameters: v : `UnitVec` Returns: `float` Modifiers: inline	Gets the X part of this 3D unit-vector. Extended Type: `UnitVec` v : `UnitVec` Returns: `float`
`UnitVec.getY v` Full Usage: `UnitVec.getY v` Parameters: v : `UnitVec` Returns: `float` Modifiers: inline	Gets the Y part of this 3D unit-vector. Extended Type: `UnitVec` v : `UnitVec` Returns: `float`
`UnitVec.getZ v` Full Usage: `UnitVec.getZ v` Parameters: v : `UnitVec` Returns: `float` Modifiers: inline	Gets the Z part of this 3D unit-vector. Extended Type: `UnitVec` v : `UnitVec` Returns: `float`
`UnitVec.intersection (ptA, ptB, vA, vB, relAngleDiscriminant)` Full Usage: `UnitVec.intersection (ptA, ptB, vA, vB, relAngleDiscriminant)` Parameters: ptA : `Pnt` - The start point of the first line. ptB : `Pnt` - The start point of the second line. vA : `UnitVec` - The unit-vector of the first line. vB : `UnitVec` - The unit-vector of the second line. 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 vectors are considered parallel. Use the module Euclid.UtilEuclid.RelAngleDiscriminant to set another tolerance here. Returns: `ValueOption<float * float>` For (almost) zero length or (almost) parallel vectors: 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. Modifiers: inline	Intersects two infinite 3D lines. The lines are defined by a start point and a vector. 'ValueNone' is returned, if the angle between the vectors 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: `UnitVec` ptA : `Pnt` The start point of the first line. ptB : `Pnt` The start point of the second line. vA : `UnitVec` The unit-vector of the first line. vB : `UnitVec` The unit-vector of the second line. 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 vectors are considered parallel. Use the module Euclid.UtilEuclid.RelAngleDiscriminant to set another tolerance here. Returns: `ValueOption<float * float>` For (almost) zero length or (almost) parallel vectors: 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.
`UnitVec.isAngle180Above cosineValue a b` Full Usage: `UnitVec.isAngle180Above cosineValue a b` Parameters: cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `UnitVec` b : `UnitVec` Returns: `bool` Modifiers: inline	Checks if Angle between two unit-vectors is more than given Cosine. Does not ignores vector orientation.The angle between two vectors can be 0 to 180 degrees. Use the Euclid.Cosine module to get some precomputed cosine values. Extended Type: `UnitVec` cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `UnitVec` b : `UnitVec` Returns: `bool`
`UnitVec.isAngle180Below cosineValue a b` Full Usage: `UnitVec.isAngle180Below cosineValue a b` Parameters: cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `UnitVec` b : `UnitVec` Returns: `bool` Modifiers: inline	Checks if Angle between two unit-vectors is less than given Cosine. Does not ignores vector orientation. The angle between two vectors can be 0 to 180 degrees. Use the Euclid.Cosine module to get some precomputed cosine values. Extended Type: `UnitVec` cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `UnitVec` b : `UnitVec` Returns: `bool`
`UnitVec.isAngle90Above cosineValue a b` Full Usage: `UnitVec.isAngle90Above cosineValue a b` Parameters: cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `UnitVec` b : `UnitVec` Returns: `bool` Modifiers: inline	Checks if Angle between two unit-vectors is more than given Cosine. Ignores vector orientation. The angle between two vectors can be 0 to 90 degrees ignoring their direction. Use the Euclid.Cosine module to get some precomputed cosine values. Extended Type: `UnitVec` cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `UnitVec` b : `UnitVec` Returns: `bool`
`UnitVec.isAngle90Below cosineValue a b` Full Usage: `UnitVec.isAngle90Below cosineValue a b` Parameters: cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `UnitVec` b : `UnitVec` Returns: `bool` Modifiers: inline	Checks if Angle between two unit-vectors is less than given Cosine. Ignores vector orientation. The angle between two vectors can be 0 to 90 degrees ignoring their direction. Use the Euclid.Cosine module to get some precomputed cosine values. Extended Type: `UnitVec` cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `UnitVec` b : `UnitVec` Returns: `bool`
`UnitVec.isHorizontal v` Full Usage: `UnitVec.isHorizontal v` Parameters: v : `UnitVec` Returns: `bool` Modifiers: inline	Checks if 3D vector is horizontal (Z component is almost zero). Tolerance is 1e-6. Extended Type: `UnitVec` v : `UnitVec` Returns: `bool`
`UnitVec.isOppositeOrientation other v` Full Usage: `UnitVec.isOppositeOrientation other v` Parameters: other : `UnitVec` v : `UnitVec` Returns: `bool` Modifiers: inline	Checks if the angle between the two 3D unit-vectors is more than 180 degrees. Calculates the dot product of two 3D unit-vectors. Then checks if it is smaller than minus 1e-12. Extended Type: `UnitVec` other : `UnitVec` v : `UnitVec` Returns: `bool`
`UnitVec.isVertical v` Full Usage: `UnitVec.isVertical v` Parameters: v : `UnitVec` Returns: `bool` Modifiers: inline	Checks if 3D unit-vector is parallel to the world Z axis. Ignoring orientation. Tolerance is 1e-6. Same as ln.IsZAligned Extended Type: `UnitVec` v : `UnitVec` Returns: `bool`
`UnitVec.isXAligned v` Full Usage: `UnitVec.isXAligned v` Parameters: v : `UnitVec` Returns: `bool` Modifiers: inline	Checks if 3D unit-vector is parallel to the world X axis. Ignoring orientation. Tolerance is 1e-6. Extended Type: `UnitVec` v : `UnitVec` Returns: `bool`
`UnitVec.isYAligned v` Full Usage: `UnitVec.isYAligned v` Parameters: v : `UnitVec` Returns: `bool` Modifiers: inline	Checks if 3D unit-vector is parallel to the world Y axis. Ignoring orientation. Tolerance is 1e-6. Extended Type: `UnitVec` v : `UnitVec` Returns: `bool`
`UnitVec.isZAligned v` Full Usage: `UnitVec.isZAligned v` Parameters: v : `UnitVec` Returns: `bool` Modifiers: inline	Checks if 3D unit-vector is parallel to the world Z axis. Ignoring orientation. Same as ln.IsVertical Extended Type: `UnitVec` v : `UnitVec` Returns: `bool`
`UnitVec.lengthInXY v` Full Usage: `UnitVec.lengthInXY v` Parameters: v : `UnitVec` Returns: `float` Modifiers: inline	Returns vector length projected into X Y Plane. sqrt(v.X * v.X + v.Y * v.Y) Extended Type: `UnitVec` v : `UnitVec` Returns: `float`
`UnitVec.lerp (start, ende, rel)` Full Usage: `UnitVec.lerp (start, ende, rel)` Parameters: start : `UnitVec` ende : `UnitVec` rel : `float` Returns: `Vec`	Linearly interpolates between two vectors. e.g. rel=0.5 will return the middle vector, rel=1.0 the end vector, rel=1.5 a vector half the distance beyond the end vector. Extended Type: `UnitVec` start : `UnitVec` ende : `UnitVec` rel : `float` Returns: `Vec`
`UnitVec.matchOrientation orientationToMatch vecToFlip` Full Usage: `UnitVec.matchOrientation orientationToMatch vecToFlip` Parameters: orientationToMatch : `UnitVec` vecToFlip : `UnitVec` Returns: `UnitVec` Modifiers: inline	Ensure that the 3D unit-vector has a positive dot product with given 3D orientation unit-vector. Extended Type: `UnitVec` orientationToMatch : `UnitVec` vecToFlip : `UnitVec` Returns: `UnitVec`
`UnitVec.matchVecOrientation orientationToMatch vecToFlip` Full Usage: `UnitVec.matchVecOrientation orientationToMatch vecToFlip` Parameters: orientationToMatch : `Vec` vecToFlip : `UnitVec` Returns: `UnitVec` Modifiers: inline	Ensure that the 3D unit-vector has a positive dot product with given 3D orientation vector. Extended Type: `UnitVec` orientationToMatch : `Vec` vecToFlip : `UnitVec` Returns: `UnitVec`
`UnitVec.matchesOrientation other v` Full Usage: `UnitVec.matchesOrientation other v` Parameters: other : `UnitVec` v : `UnitVec` Returns: `bool` Modifiers: inline	Checks if the angle between the two 3D unit-vectors is less than 180 degrees. Calculates the dot product of two 3D unit-vectors. Then checks if it is bigger than 1e-12. Extended Type: `UnitVec` other : `UnitVec` v : `UnitVec` Returns: `bool`
`UnitVec.moveX x v` Full Usage: `UnitVec.moveX x v` Parameters: x : `float` v : `UnitVec` Returns: `Vec` Modifiers: inline	Add to the X part of this 3D unit-vectors together. Returns a new (non-unitized) 3D vector. Extended Type: `UnitVec` x : `float` v : `UnitVec` Returns: `Vec`
`UnitVec.moveY y v` Full Usage: `UnitVec.moveY y v` Parameters: y : `float` v : `UnitVec` Returns: `Vec` Modifiers: inline	Add to the Y part of this 3D unit-vectors together. Returns a new (non-unitized) 3D vector. Extended Type: `UnitVec` y : `float` v : `UnitVec` Returns: `Vec`
`UnitVec.moveZ z v` Full Usage: `UnitVec.moveZ z v` Parameters: z : `float` v : `UnitVec` Returns: `Vec` Modifiers: inline	Add to the Z part of this 3D unit-vectors together. Returns a new (non-unitized) 3D vector. Extended Type: `UnitVec` z : `float` v : `UnitVec` Returns: `Vec`
`UnitVec.notEquals tol a b` Full Usage: `UnitVec.notEquals tol a b` Parameters: tol : `float` a : `UnitVec` b : `UnitVec` Returns: `bool`	Check if two 3D unit-vectors are not equal within a given tolerance. Use a tolerance of 0.0 to check if the two unit-vectors are not exactly equal. Extended Type: `UnitVec` tol : `float` a : `UnitVec` b : `UnitVec` Returns: `bool`
`UnitVec.orientDown v` Full Usage: `UnitVec.orientDown v` Parameters: v : `UnitVec` Returns: `UnitVec` Modifiers: inline	Reverse vector if Z part is bigger than 0.0 Extended Type: `UnitVec` v : `UnitVec` Returns: `UnitVec`
`UnitVec.orientUp v` Full Usage: `UnitVec.orientUp v` Parameters: v : `UnitVec` Returns: `UnitVec` Modifiers: inline	Reverse vector if Z part is smaller than 0.0 Extended Type: `UnitVec` v : `UnitVec` Returns: `UnitVec`
`UnitVec.perpendicularInVerticalPlane v` Full Usage: `UnitVec.perpendicularInVerticalPlane v` Parameters: v : `UnitVec` Returns: `Vec` Modifiers: inline	Returns a vector that is perpendicular to the given vector and in the same vertical Plane. Projected into the X-Y plane input and output vectors are parallel and of same orientation. Not of same length, not unitized. On vertical input vector resulting vector if of zero length. Extended Type: `UnitVec` v : `UnitVec` Returns: `Vec`
`UnitVec.perpendicularInXY v` Full Usage: `UnitVec.perpendicularInXY v` Parameters: v : `UnitVec` Returns: `Vec` Modifiers: inline	Returns a perpendicular horizontal vector. Rotated counterclockwise. Just does Vec(-v.Y, v.X, 0.0) On vertical input vector resulting vector if of zero length. Extended Type: `UnitVec` v : `UnitVec` Returns: `Vec`
`UnitVec.projectToXYPlane v` Full Usage: `UnitVec.projectToXYPlane v` Parameters: v : `UnitVec` Returns: `Vec` Modifiers: inline	Project vector to World X-Y plane. Use Vc.ofUnitVec to convert to 2D vector instance. Extended Type: `UnitVec` v : `UnitVec` Returns: `Vec`
`UnitVec.reverse v` Full Usage: `UnitVec.reverse v` Parameters: v : `UnitVec` Returns: `UnitVec` Modifiers: inline	Negate or inverse a 3D unit-vectors. Returns a new 3D unit-vector. Same as UnitVec.flip. Extended Type: `UnitVec` v : `UnitVec` Returns: `UnitVec`
`UnitVec.rotateByQuaternion q v` Full Usage: `UnitVec.rotateByQuaternion q v` Parameters: q : `Quaternion` v : `UnitVec` Returns: `UnitVec` Modifiers: inline	Rotate by Quaternion. Extended Type: `UnitVec` q : `Quaternion` v : `UnitVec` Returns: `UnitVec`
`UnitVec.rotateOnZ90CCW v` Full Usage: `UnitVec.rotateOnZ90CCW v` Parameters: v : `UnitVec` Returns: `UnitVec` Modifiers: inline	90 Degree rotation Counter-Clockwise around Z-axis. Extended Type: `UnitVec` v : `UnitVec` Returns: `UnitVec`
`UnitVec.rotateOnZ90CW v` Full Usage: `UnitVec.rotateOnZ90CW v` Parameters: v : `UnitVec` Returns: `UnitVec` Modifiers: inline	90 Degree rotation clockwise around Z-axis. Extended Type: `UnitVec` v : `UnitVec` Returns: `UnitVec`
`UnitVec.rotateX angDegree v` Full Usage: `UnitVec.rotateX angDegree v` Parameters: angDegree : `float` v : `UnitVec` Returns: `UnitVec` Modifiers: inline	Rotate the 3D unit-vector in Degrees around X-axis, from Y to Z-axis, Counter Clockwise looking from right. Extended Type: `UnitVec` angDegree : `float` v : `UnitVec` Returns: `UnitVec`
`UnitVec.rotateXBy r v` Full Usage: `UnitVec.rotateXBy r v` Parameters: r : `Rotation2D` v : `UnitVec` Returns: `UnitVec` Modifiers: inline	Rotate the 3D unit-vector around X-axis, from Y to Z-axis, Counter Clockwise looking from right. Extended Type: `UnitVec` r : `Rotation2D` v : `UnitVec` Returns: `UnitVec`
`UnitVec.rotateY angDegree v` Full Usage: `UnitVec.rotateY angDegree v` Parameters: angDegree : `float` v : `UnitVec` Returns: `UnitVec` Modifiers: inline	Rotate the 3D unit-vector in Degrees around Y-axis, from Z to X-axis, Counter Clockwise looking from back. Extended Type: `UnitVec` angDegree : `float` v : `UnitVec` Returns: `UnitVec`
`UnitVec.rotateYBy r v` Full Usage: `UnitVec.rotateYBy r v` Parameters: r : `Rotation2D` v : `UnitVec` Returns: `UnitVec` Modifiers: inline	Rotate the 3D unit-vector around Y-axis, from Z to X-axis, Counter Clockwise looking from back. Extended Type: `UnitVec` r : `Rotation2D` v : `UnitVec` Returns: `UnitVec`
`UnitVec.rotateZ angDegree v` Full Usage: `UnitVec.rotateZ angDegree v` Parameters: angDegree : `float` v : `UnitVec` Returns: `UnitVec` Modifiers: inline	Rotate the 3D unit-vector in Degrees around Z-axis, from X to Y-axis, Counter Clockwise looking from top. Extended Type: `UnitVec` angDegree : `float` v : `UnitVec` Returns: `UnitVec`
`UnitVec.rotateZBy r v` Full Usage: `UnitVec.rotateZBy r v` Parameters: r : `Rotation2D` v : `UnitVec` Returns: `UnitVec` Modifiers: inline	Rotate the 3D unit-vector around Z-axis, from X to Y-axis, Counter Clockwise looking from top. Extended Type: `UnitVec` r : `Rotation2D` v : `UnitVec` Returns: `UnitVec`
`UnitVec.scale f v` Full Usage: `UnitVec.scale f v` Parameters: f : `float` v : `UnitVec` Returns: `Vec` Modifiers: inline	Multiplies a 3D unit-vector with a scalar, also called scaling a vector. Same as UnitVec.withLength. Returns a new (non-unitized) 3D vector. Extended Type: `UnitVec` f : `float` v : `UnitVec` Returns: `Vec`
`UnitVec.slerp (start, ende, rel)` Full Usage: `UnitVec.slerp (start, ende, rel)` Parameters: start : `UnitVec` ende : `UnitVec` rel : `float` Returns: `UnitVec`	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 vectors are treated as directions rather than points in space. The direction of the returned vector 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: `UnitVec` start : `UnitVec` ende : `UnitVec` rel : `float` Returns: `UnitVec`
`UnitVec.slopeDegrees v` Full Usage: `UnitVec.slopeDegrees v` Parameters: v : `UnitVec` Returns: `float` Modifiers: inline	Returns positive or negative slope of a vector in Degrees. In relation to X-Y plane. Range -90 to +90 Degrees. Extended Type: `UnitVec` v : `UnitVec` Returns: `float`
`UnitVec.slopePercent v` Full Usage: `UnitVec.slopePercent v` Parameters: v : `UnitVec` Returns: `float` Modifiers: inline	Returns positive or negative slope of a vector in Percent. In relation to X-Y plane. 100% = 45 Degrees. Returns positive (or negative) infinity if line is vertical. Extended Type: `UnitVec` v : `UnitVec` Returns: `float`
`UnitVec.slopeRadians v` Full Usage: `UnitVec.slopeRadians v` Parameters: v : `UnitVec` Returns: `float` Modifiers: inline	Returns positive or negative slope of a vector in Radians. In relation to X-Y plane. Range -1.57 to +1.57 Radians. Extended Type: `UnitVec` v : `UnitVec` Returns: `float`
`UnitVec.transform m v` Full Usage: `UnitVec.transform m v` Parameters: m : `Matrix` v : `UnitVec` Returns: `Vec` Modifiers: inline	Multiplies a Matrix with a 3D vector. Since a 3D vector represents a direction or an offset in space, but not a location, the implicit the 4th dimension is 0.0 so that all translations are ignored. (Homogeneous Vector) The resulting vector is not unitized. Extended Type: `UnitVec` m : `Matrix` v : `UnitVec` Returns: `Vec`
`UnitVec.transformRigid m v` Full Usage: `UnitVec.transformRigid m v` Parameters: m : `RigidMatrix` v : `UnitVec` Returns: `UnitVec` Modifiers: inline	Multiplies (or applies) a RigidMatrix to a 3D unit-vector. Since a 3D vector represents a direction or an offset in space, but not a location, all translations are ignored. (Homogeneous Vector) The resulting vector is unitized too. Extended Type: `UnitVec` m : `RigidMatrix` v : `UnitVec` Returns: `UnitVec`
`UnitVec.withLength f v` Full Usage: `UnitVec.withLength f v` Parameters: f : `float` v : `UnitVec` Returns: `Vec` Modifiers: inline	Multiplies a 3D unit-vector with a scalar, also called scaling a vector. Same as UnitVec.scale. Returns a new (non-unitized) 3D vector. Extended Type: `UnitVec` f : `float` v : `UnitVec` Returns: `Vec`
`UnitVec.withX x v` Full Usage: `UnitVec.withX x v` Parameters: x : `float` v : `UnitVec` Returns: `Vec` Modifiers: inline	Returns new 3D vector with new X value, Y and Z stay the same. Extended Type: `UnitVec` x : `float` v : `UnitVec` Returns: `Vec`
`UnitVec.withY y v` Full Usage: `UnitVec.withY y v` Parameters: y : `float` v : `UnitVec` Returns: `Vec` Modifiers: inline	Returns new 3D vector with new Y value, X and Z stay the same. Extended Type: `UnitVec` y : `float` v : `UnitVec` Returns: `Vec`
`UnitVec.withZ z v` Full Usage: `UnitVec.withZ z v` Parameters: z : `float` v : `UnitVec` Returns: `Vec` Modifiers: inline	Returns new 3D vector with new z value, X and Y stay the same. Extended Type: `UnitVec` z : `float` v : `UnitVec` Returns: `Vec`