AutoOpenVec (Euclid)

AutoOpenVec Module

Namespace: Euclid
Assembly: Euclid.dll

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

Type extensions

Type extension	Description
`this.AngleDiamondInXYTo` Full Usage: `this.AngleDiamondInXYTo` Parameters: b : `Vec` 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: `Vec` b : `Vec` Returns: `float`
`this.AsPnt` Full Usage: `this.AsPnt` Parameters: () : `unit` Returns: `Pnt` Modifiers: inline	Convert 3D vector to 3D point. Extended Type: `Vec` () : `unit` Returns: `Pnt`
`this.AsVc` Full Usage: `this.AsVc` Parameters: () : `unit` Returns: `Vc` Modifiers: inline	Convert 3D vector to 2D vector, discarding the Z value. Extended Type: `Vec` () : `unit` Returns: `Vc`
`this.Cross` Full Usage: `this.Cross` Parameters: b : `UnitVec` Returns: `Vec` Modifiers: inline	Cross product, of a 3D vector and a 3D unit-vectors. The resulting vector is perpendicular to both input vectors. The length of this resulting vector 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: `Vec` b : `UnitVec` Returns: `Vec`
`this.Cross` Full Usage: `this.Cross` Parameters: b : `Vec` Returns: `Vec` Modifiers: inline	Cross product, of a 3D unit-vector and a 3D vectors. The resulting vector is perpendicular to both input vectors. The length of this resulting vector 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: `Vec` 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: `Vec` () : `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 vector. Extended Type: `Vec` () : `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 vector. Extended Type: `Vec` () : `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 vector. Extended Type: `Vec` () : `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 vector. Extended Type: `Vec` () : `unit` Returns: `float`
`this.Dot` Full Usage: `this.Dot` Parameters: b : `Vec` Returns: `float` Modifiers: inline	Dot product, or scalar product of two 3D vectors. Returns a float. Extended Type: `Vec` b : `Vec` Returns: `float`
`this.Dot` Full Usage: `this.Dot` Parameters: 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: `Vec` b : `UnitVec` Returns: `float`
`this.Half` Full Usage: `this.Half` Parameters: () : `unit` Returns: `Vec` Modifiers: inline	Returns a new 3D vector with half the length. Extended Type: `Vec` () : `unit` Returns: `Vec`
`this.IsHorizontal` Full Usage: `this.IsHorizontal` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Checks if 3D vector is horizontal (Z component is almost zero). The absolute deviation tolerance along Z axis is 1e-9 (axisAlignmentTolerance). Fails on vectors shorter than 1e-6. Extended Type: `Vec` () : `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: `Vec` () : `unit` Returns: `bool`
`this.IsOppositeOrientation` Full Usage: `this.IsOppositeOrientation` Parameters: other : `Vec` Returns: `bool` Modifiers: inline	Checks if the angle between the two 3D vectors is more than 90 degrees. Calculates the dot product of two 3D vectors. Then checks if it is smaller than minus 1e-12. Fails if any of the two vectors is shorter than zeroLengthTolerance (1e-12). Extended Type: `Vec` other : `Vec` Returns: `bool`
`this.IsOppositeOrientation` Full Usage: `this.IsOppositeOrientation` Parameters: other : `UnitVec` Returns: `bool` Modifiers: inline	Checks if the angle between this 3D vectors and a 3D unit-vector is more than 90 degrees. Calculates the dot product of a 3D vector and a unit-vectors. Then checks if it is smaller than -1e-12. Fails if the vector is shorter than zeroLengthTolerance (1e-12). Extended Type: `Vec` other : `UnitVec` Returns: `bool`
`this.IsParallelAndOrientedTo` Full Usage: `this.IsParallelAndOrientedTo` Parameters: other : `Vec` minCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool` Modifiers: inline	Checks if two 3D 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 minimum cosine value. See Euclid.Cosine module. Fails on vectors shorter than UtilEuclid.zeroLengthTolerance (1e-12). Extended Type: `Vec` other : `Vec` minCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool`
`this.IsParallelAndOrientedTo` Full Usage: `this.IsParallelAndOrientedTo` Parameters: other : `UnitVec` minCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool` Modifiers: inline	Checks if this 3D vectors and a 3D unit-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 minimum cosine value. See Euclid.Cosine module. Fails on vectors shorter than UtilEuclid.zeroLengthTolerance (1e-12). Extended Type: `Vec` 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 two 3D vectors are parallel. Ignores the line orientation. The default angle tolerance is 0.25 degrees. This tolerance can be customized by an optional minimum cosine value. See Euclid.Cosine module. Fails on vectors shorter than UtilEuclid.zeroLengthTolerance (1e-12). Extended Type: `Vec` 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 this 3D vectors and a 3D unit-vector are parallel. Ignores the line orientation. The default angle tolerance is 0.25 degrees. This tolerance can be customized by an optional minimum cosine value. See Euclid.Cosine module. Fails on vectors shorter than UtilEuclid.zeroLengthTolerance (1e-12). Extended Type: `Vec` other : `UnitVec` minCosine : `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 two 3D 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 minimum cosine value. The default cosine is 0.0043633 ( = 89.75 deg) See Euclid.Cosine module. Fails on vectors shorter than UtilEuclid.zeroLengthTolerance (1e-12). Extended Type: `Vec` other : `Vec` maxCosine : `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 this 3D vectors and a 3D unit-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 minimum cosine value. The default cosine is 0.0043633 ( = 89.75 deg) See Euclid.Cosine module. Fails on vectors shorter than UtilEuclid.zeroLengthTolerance (1e-12). Extended Type: `Vec` other : `UnitVec` maxCosine : `float<MeasureProduct<cosine, MeasureOne>>` Returns: `bool`
`this.IsTiny` Full Usage: `this.IsTiny` Parameters: tol : `float` Returns: `bool` Modifiers: inline	Check if the 3D vector is shorter than the tolerance. Also checks if any component is a NaN. Extended Type: `Vec` tol : `float` Returns: `bool`
`this.IsTinySq` Full Usage: `this.IsTinySq` Parameters: tol : `float` Returns: `bool` Modifiers: inline	Check if the 3D vectors square length is shorter than the squared tolerance. Also checks if any component is a NaN. Extended Type: `Vec` tol : `float` Returns: `bool`
`this.IsUnit` Full Usage: `this.IsUnit` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Test if the 3D vector is a unit-vector. Test if the vectors square length is within 6 float steps of 1.0 So between 0.99999964 and 1.000000715. Extended Type: `Vec` () : `unit` Returns: `bool`
`this.IsVertical` Full Usage: `this.IsVertical` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Checks if 3D vector is parallel to the world Z axis. Ignoring orientation. The absolute deviation tolerance along X and Y axis is 1e-9 (axisAlignmentTolerance). Fails on vectors shorter than 1e-6. Same as v.IsZAligned Extended Type: `Vec` () : `unit` Returns: `bool`
`this.IsXAligned` Full Usage: `this.IsXAligned` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Checks if 3D vector is parallel to the world X axis. Ignoring orientation. The absolute deviation tolerance along Y and Z axis is 1e-9 (axisAlignmentTolerance). Fails on vectors shorter than 1e-6. Extended Type: `Vec` () : `unit` Returns: `bool`
`this.IsYAligned` Full Usage: `this.IsYAligned` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Checks if 3D vector is parallel to the world Y axis. Ignoring orientation. The absolute deviation tolerance along X and Z axis is 1e-9 (axisAlignmentTolerance). Fails on vectors shorter than 1e-6. Extended Type: `Vec` () : `unit` Returns: `bool`
`this.IsZAligned` Full Usage: `this.IsZAligned` Parameters: () : `unit` Returns: `bool` Modifiers: inline	Checks if 3D vector is parallel to the world Z axis. Ignoring orientation. The absolute deviation tolerance along X and Y axis is 1e-9 (axisAlignmentTolerance). Fails on vectors shorter than 1e-6. Same as v.IsVertical Extended Type: `Vec` () : `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: `Vec` () : `unit` 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: `Vec` () : `unit` 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: `Vec` () : `unit` Returns: `float`
`this.MatchesOrientation` Full Usage: `this.MatchesOrientation` Parameters: other : `Vec` Returns: `bool` Modifiers: inline	Checks if the angle between the two 3D vectors is less than 90 degrees. Calculates the dot product of two 3D vectors. Then checks if it is bigger than 1e-12. Fails if any of the two vectors is shorter than zeroLengthTolerance (1e-12). Extended Type: `Vec` other : `Vec` Returns: `bool`
`this.MatchesOrientation` Full Usage: `this.MatchesOrientation` Parameters: other : `UnitVec` Returns: `bool` Modifiers: inline	Checks if the angle between this 3D vectors and a 3D unit-vector is less than 90 degrees. Calculates the dot product of two 3D vectors. Then checks if it is bigger than 1e-12. Fails if the vector is shorter than zeroLengthTolerance (1e-12). Extended Type: `Vec` other : `UnitVec` 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: `Vec` () : `unit` Returns: `Vec`
`this.RotateByQuarterCircle` Full Usage: `this.RotateByQuarterCircle` Parameters: numberOfQuarters : `int` Returns: `Vec` Modifiers: inline	Rotates the 3D vector around the Z-axis by a given number of quarter-circles (i.e. multiples of 90 degrees or Pi/2 radians). A positive number rotates counter-clockwise, a negative number rotates clockwise. The length of the vector is preserved. Extended Type: `Vec` numberOfQuarters : `int` Returns: `Vec`
`this.RotateOnZ90CCW` Full Usage: `this.RotateOnZ90CCW` Parameters: () : `unit` Returns: `Vec` Modifiers: inline	90 Degree rotation Counter-Clockwise around Z-axis. Extended Type: `Vec` () : `unit` Returns: `Vec`
`this.RotateOnZ90CW` Full Usage: `this.RotateOnZ90CW` Parameters: () : `unit` Returns: `Vec` Modifiers: inline	90 Degree rotation clockwise around Z-axis. Extended Type: `Vec` () : `unit` Returns: `Vec`
`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 translation in space, but not a location, all translations are ignored. (Homogeneous Vector) Extended Type: `Vec` m : `Matrix` Returns: `Vec`
`this.TransformRigid` Full Usage: `this.TransformRigid` Parameters: m : `RigidMatrix` Returns: `Vec` Modifiers: inline	Multiplies (or applies) a RigidMatrix to a 3D vector. Since a 3D vector represents a direction or translation in space, but not a location, all translations are ignored. (Homogeneous Vector) Extended Type: `Vec` m : `RigidMatrix` Returns: `Vec`
`this.Unitized` Full Usage: `this.Unitized` Parameters: () : `unit` Returns: `UnitVec` Modifiers: inline	Returns the 3D vector unitized. Fails with EuclidDivByZeroException if the length of the vector is too small (1e-16) to unitize. Extended Type: `Vec` () : `unit` Returns: `UnitVec`
`this.WithLength` Full Usage: `this.WithLength` Parameters: desiredLength : `float` Returns: `Vec` Modifiers: inline	Returns a new 3D vector scaled to the desired length. Same as Vec.withLength. Extended Type: `Vec` desiredLength : `float` Returns: `Vec`
`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: `Vec` 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: `Vec` 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: `Vec` z : `float` Returns: `Vec`
`Vec.Xaxis()` Full Usage: `Vec.Xaxis()` Parameters: () : `unit` Returns: `Vec` Modifiers: inline	Returns the World X-axis with length one: Vec(1, 0, 0) Extended Type: `Vec` () : `unit` Returns: `Vec`
`Vec.Yaxis()` Full Usage: `Vec.Yaxis()` Parameters: () : `unit` Returns: `Vec` Modifiers: inline	Returns the World Y-axis with length one: Vec(0, 1, 0) Extended Type: `Vec` () : `unit` Returns: `Vec`
`Vec.Zaxis()` Full Usage: `Vec.Zaxis()` Parameters: () : `unit` Returns: `Vec` Modifiers: inline	Returns the World Z-axis with length one: Vec(0, 0, 1) Extended Type: `Vec` () : `unit` Returns: `Vec`
`Vec.add a b` Full Usage: `Vec.add a b` Parameters: a : `Vec` b : `Vec` Returns: `Vec` Modifiers: inline	Add two 3D vectors together. Returns a new 3D vector. Extended Type: `Vec` a : `Vec` b : `Vec` Returns: `Vec`
`Vec.angle180 a b` Full Usage: `Vec.angle180 a b` Parameters: a : `Vec` b : `Vec` Returns: `float` Modifiers: inline	Returns positive angle between two 3D vectors in Degrees. Takes vector orientation into account, Range 0 to 180 Degrees. Extended Type: `Vec` a : `Vec` b : `Vec` Returns: `float`
`Vec.angle2PiInXY (a, b)` Full Usage: `Vec.angle2PiInXY (a, b)` Parameters: a : `Vec` b : `Vec` 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 Zaxis. Range: 0.0 to 2 Pi ( = 0 to 360 Degrees) Extended Type: `Vec` a : `Vec` b : `Vec` Returns: `float`
`Vec.angle360InXY (a, b)` Full Usage: `Vec.angle360InXY (a, b)` Parameters: a : `Vec` b : `Vec` Returns: `float` Modifiers: inline	Returns positive angle of two 3D vector projected in X-Y plane. In Degrees. Considering positive rotation round the World Z-axis. Range: 0 to 360 Degrees. Extended Type: `Vec` a : `Vec` b : `Vec` Returns: `float`
`Vec.angle90 a b` Full Usage: `Vec.angle90 a b` Parameters: a : `Vec` b : `Vec` Returns: `float` Modifiers: inline	Returns positive angle between two 3D vectors in Degrees. Ignores vector orientation, Range: 0 to 90 Degrees. Extended Type: `Vec` a : `Vec` b : `Vec` Returns: `float`
`Vec.angleDiamondInXY (a, b)` Full Usage: `Vec.angleDiamondInXY (a, b)` Parameters: a : `Vec` b : `Vec` 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: `Vec` a : `Vec` b : `Vec` Returns: `float`
`Vec.angleHalfPi a b` Full Usage: `Vec.angleHalfPi a b` Parameters: a : `Vec` b : `Vec` Returns: `float` Modifiers: inline	Returns positive angle between two 3D vectors in Radians. Ignores vector orientation, Range: 0.0 to Pi/2 ( = 0 to 90 Degrees) Extended Type: `Vec` a : `Vec` b : `Vec` Returns: `float`
`Vec.anglePi a b` Full Usage: `Vec.anglePi a b` Parameters: a : `Vec` b : `Vec` Returns: `float` Modifiers: inline	Returns positive angle between two 3D vectors in Radians. Takes vector orientation into account, Range 0.0 to Pi( = 0 to 180 Degree). Extended Type: `Vec` a : `Vec` b : `Vec` Returns: `float`
`Vec.areParallel other v` Full Usage: `Vec.areParallel other v` Parameters: other : `Vec` v : `Vec` Returns: `bool` Modifiers: inline	Checks if Angle between two vectors is Below 0.25 Degree. Ignores vector orientation. Fails on zero length vectors, tolerance 1e-12. Extended Type: `Vec` other : `Vec` v : `Vec` Returns: `bool`
`Vec.areParallelAndMatchOrientation other v` Full Usage: `Vec.areParallelAndMatchOrientation other v` Parameters: other : `Vec` v : `Vec` Returns: `bool` Modifiers: inline	Checks if angle between two vectors is below 0.25 degrees. Takes vector orientation into account. Fails on zero length vectors, tolerance 1e-12. Extended Type: `Vec` other : `Vec` v : `Vec` Returns: `bool`
`Vec.arePerpendicular other v` Full Usage: `Vec.arePerpendicular other v` Parameters: other : `Vec` v : `Vec` Returns: `bool` Modifiers: inline	Checks if angle between two vectors is between 89.75 and 90.25 degrees. Ignores vector orientation. Fails on zero length vectors, tolerance 1e-12. Extended Type: `Vec` other : `Vec` v : `Vec` Returns: `bool`
`Vec.asPnt v` Full Usage: `Vec.asPnt v` Parameters: v : `Vec` Returns: `Pnt` Modifiers: inline	Convert 3D vector to 3D point. Extended Type: `Vec` v : `Vec` Returns: `Pnt`
`Vec.asPt v` Full Usage: `Vec.asPt v` Parameters: v : `Vec` Returns: `Pt` Modifiers: inline	Convert 3D vector to 2D point by ignoring Z value. Extended Type: `Vec` v : `Vec` Returns: `Pt`
`Vec.asVc v` Full Usage: `Vec.asVc v` Parameters: v : `Vec` Returns: `Vc` Modifiers: inline	Convert 3D vector to 2D vector by ignoring Z value. Extended Type: `Vec` v : `Vec` Returns: `Vc`
`Vec.bisector a b` Full Usage: `Vec.bisector a b` Parameters: a : `Vec` b : `Vec` Returns: `Vec` Modifiers: inline	Returns a (not unitized) bisector vector in the middle direction. Code : a.Unitized + b.Unitized. Extended Type: `Vec` a : `Vec` b : `Vec` Returns: `Vec`
`Vec.create (x, y, z)` Full Usage: `Vec.create (x, y, z)` Parameters: x : `float` y : `float` z : `float` Returns: `Vec` Modifiers: inline	Returns a new 3D vector from X, Y and Z parts. Extended Type: `Vec` x : `float` y : `float` z : `float` Returns: `Vec`
`Vec.create (start, ende)` Full Usage: `Vec.create (start, ende)` Parameters: start : `Pnt` ende : `Pnt` Returns: `Vec` Modifiers: inline	Returns a new 3D vector from start and end point. Extended Type: `Vec` start : `Pnt` ende : `Pnt` Returns: `Vec`
`Vec.createFromMembersXYZ vec` Full Usage: `Vec.createFromMembersXYZ vec` Parameters: vec : `^T` Returns: `Vec` 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: `Vec` vec : `^T` Returns: `Vec`
`Vec.createFromMembersxyz vec` Full Usage: `Vec.createFromMembersxyz vec` Parameters: vec : `^T` Returns: `Vec` 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: `Vec` vec : `^T` Returns: `Vec`
`Vec.createFromPnt pt` Full Usage: `Vec.createFromPnt pt` Parameters: pt : `Pnt` Returns: `Vec` Modifiers: inline	Create 3D vector from 3D point. Extended Type: `Vec` pt : `Pnt` Returns: `Vec`
`Vec.createFromUnitVec v` Full Usage: `Vec.createFromUnitVec v` Parameters: v : `UnitVec` Returns: `Vec` Modifiers: inline	Create 3D vector from 3D unit-vector. Extended Type: `Vec` v : `UnitVec` Returns: `Vec`
`Vec.createFromVcWithZ z v` Full Usage: `Vec.createFromVcWithZ z v` Parameters: z : `float` v : `Vc` Returns: `Vec` Modifiers: inline	Returns a 3D vector from z value and 2D vector. Extended Type: `Vec` z : `float` v : `Vc` Returns: `Vec`
`Vec.cross (a, b)` Full Usage: `Vec.cross (a, b)` Parameters: a : `UnitVec` b : `Vec` Returns: `Vec` Modifiers: inline	Cross product, of a 3D unit-vectors and 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 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: `Vec` a : `UnitVec` b : `Vec` Returns: `Vec`
`Vec.cross (a, b)` Full Usage: `Vec.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 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: `Vec` a : `Vec` b : `UnitVec` Returns: `Vec`
`Vec.determinant (u, v, w)` Full Usage: `Vec.determinant (u, v, w)` Parameters: u : `Vec` v : `Vec` w : `Vec` Returns: `float` Modifiers: inline	Returns three vector's 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: `Vec` u : `Vec` v : `Vec` w : `Vec` Returns: `float`
`Vec.difference a b` Full Usage: `Vec.difference a b` Parameters: a : `Vec` b : `Vec` Returns: `float` Modifiers: inline	Returns the distance between the tips of two 3D vectors. Extended Type: `Vec` a : `Vec` b : `Vec` Returns: `float`
`Vec.differenceSq a b` Full Usage: `Vec.differenceSq a b` Parameters: a : `Vec` b : `Vec` Returns: `float` Modifiers: inline	Returns the squared distance between the tips of two 3D vectors. This operation is slightly faster than Vec.difference and sufficient for many algorithms like finding closest vectors. Extended Type: `Vec` a : `Vec` b : `Vec` Returns: `float`
`Vec.direction2PiInXY v` Full Usage: `Vec.direction2PiInXY v` Parameters: v : `Vec` Returns: `float` Modifiers: inline	Returns positive angle of 3D 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: `Vec` v : `Vec` Returns: `float`
`Vec.direction360InXY v` Full Usage: `Vec.direction360InXY v` Parameters: v : `Vec` Returns: `float` Modifiers: inline	Returns positive angle of 3D 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: `Vec` v : `Vec` Returns: `float`
`Vec.directionDiamondInXY v` Full Usage: `Vec.directionDiamondInXY v` Parameters: v : `Vec` Returns: `float` Modifiers: inline	The diamond angle. Returns positive angle of 3D 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: `Vec` v : `Vec` Returns: `float`
`Vec.dot (a, b)` Full Usage: `Vec.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: `Vec` a : `UnitVec` b : `Vec` Returns: `float`
`Vec.dot (a, b)` Full Usage: `Vec.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: `Vec` a : `Vec` b : `UnitVec` Returns: `float`
`Vec.equals tol a b` Full Usage: `Vec.equals tol a b` Parameters: tol : `float` a : `Vec` b : `Vec` Returns: `bool` Modifiers: inline	Checks if two 3D vectors are equal within tolerance. Identical vectors in opposite directions are not considered equal. Use a tolerance of 0.0 to check for an exact match. Extended Type: `Vec` tol : `float` a : `Vec` b : `Vec` Returns: `bool`
`Vec.flip v` Full Usage: `Vec.flip v` Parameters: v : `Vec` Returns: `Vec` Modifiers: inline	Negate or inverse a 3D vectors. Returns a new 3D vector. Same as Vec.reverse. Extended Type: `Vec` v : `Vec` Returns: `Vec`
`Vec.flipToPointUp v` Full Usage: `Vec.flipToPointUp v` Parameters: v : `Vec` Returns: `Vec` Modifiers: inline	Flips the vector if Z part is smaller than 0.0 Extended Type: `Vec` v : `Vec` Returns: `Vec`
`Vec.getX v` Full Usage: `Vec.getX v` Parameters: v : `Vec` Returns: `float` Modifiers: inline	Gets the X part of this 3D vector. Extended Type: `Vec` v : `Vec` Returns: `float`
`Vec.getY v` Full Usage: `Vec.getY v` Parameters: v : `Vec` Returns: `float` Modifiers: inline	Gets the Y part of this 3D vector. Extended Type: `Vec` v : `Vec` Returns: `float`
`Vec.getZ v` Full Usage: `Vec.getZ v` Parameters: v : `Vec` Returns: `float` Modifiers: inline	Gets the Z part of this 3D vector. Extended Type: `Vec` v : `Vec` Returns: `float`
`Vec.isAngleAbove cosineValue a b` Full Usage: `Vec.isAngleAbove cosineValue a b` Parameters: cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vec` b : `Vec` Returns: `bool` Modifiers: inline	Checks if the angle between two vectors is bigger than a threshold angle specified as a precomputed cosine value. Considers the vector orientation too. So the angle is between 0 to 180 degrees. Use the Euclid.Cosine module to get some precomputed cosine values Fails on tiny vectors shorter than 1e-12. Use Vec.isNotParallelWithin to ignore vector orientation. Extended Type: `Vec` cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vec` b : `Vec` Returns: `bool`
`Vec.isAngleBelow cosineValue a b` Full Usage: `Vec.isAngleBelow cosineValue a b` Parameters: cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vec` b : `Vec` Returns: `bool` Modifiers: inline	Checks if the angle between two vectors is smaller than a threshold angle specified as a precomputed cosine value. Considers the vector orientation too. So the angle is between 0 to 180 degrees. Use the Euclid.Cosine module to get some precomputed cosine values Fails on tiny vectors shorter than 1e-12. Use Vec.isParallelWithin to ignore vector orientation. Extended Type: `Vec` cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vec` b : `Vec` Returns: `bool`
`Vec.isHorizontal v` Full Usage: `Vec.isHorizontal v` Parameters: v : `Vec` 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: `Vec` v : `Vec` Returns: `bool`
`Vec.isNotParallelWithin cosineValue a b` Full Usage: `Vec.isNotParallelWithin cosineValue a b` Parameters: cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vec` b : `Vec` Returns: `bool` Modifiers: inline	Checks if the angle between two vectors is bigger than a threshold angle specified as a precomputed cosine value. Ignores vector orientation. So the angle is between 0 to 90 degrees ignoring their orientation. Use the Euclid.Cosine module to get some precomputed cosine values Fails on tiny vectors shorter than 1e-12. Use Vec.isAngleAbove for considering vector orientation. Extended Type: `Vec` cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vec` b : `Vec` Returns: `bool`
`Vec.isOppositeOrientation v other` Full Usage: `Vec.isOppositeOrientation v other` Parameters: v : `Vec` other : `Vec` Returns: `bool` Modifiers: inline	Checks if the angle between the two 3D vectors is more than 90 degrees. Calculates the dot product of two 3D vectors. Then checks if it is smaller than minus 1e-12. Fails if any of the two vectors is shorter than zeroLengthTolerance (1e-12). Extended Type: `Vec` v : `Vec` other : `Vec` Returns: `bool`
`Vec.isParallelWithin cosineValue a b` Full Usage: `Vec.isParallelWithin cosineValue a b` Parameters: cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vec` b : `Vec` Returns: `bool` Modifiers: inline	Checks if the angle between two vectors is smaller than a threshold angle specified as a precomputed cosine value. Ignores vector orientation. So the angle is between 0 to 90 degrees ignoring their orientation. Use the Euclid.Cosine module to get some precomputed cosine values Fails on tiny vectors shorter than 1e-12. Use Vec.isAngleBelow for considering vector orientation. Extended Type: `Vec` cosineValue : `float<MeasureProduct<cosine, MeasureOne>>` a : `Vec` b : `Vec` Returns: `bool`
`Vec.isTiny tol v` Full Usage: `Vec.isTiny tol v` Parameters: tol : `float` v : `Vec` Returns: `bool` Modifiers: inline	Check if the 3D vector is shorter than the tolerance. Also checks if any component is a NaN. Extended Type: `Vec` tol : `float` v : `Vec` Returns: `bool`
`Vec.isTinySq tol v` Full Usage: `Vec.isTinySq tol v` Parameters: tol : `float` v : `Vec` Returns: `bool` Modifiers: inline	Check if the 3D vectors square length is shorter than the squared tolerance. Also checks if any component is a NaN. Extended Type: `Vec` tol : `float` v : `Vec` Returns: `bool`
`Vec.isVertical v` Full Usage: `Vec.isVertical v` Parameters: v : `Vec` Returns: `bool` Modifiers: inline	Checks if 3D vector is parallel to the world Z axis. Ignoring orientation. Tolerance is 1e-6. Fails on vectors shorter than 1e-6. Same as ln.IsZAligned Extended Type: `Vec` v : `Vec` Returns: `bool`
`Vec.isXAligned v` Full Usage: `Vec.isXAligned v` Parameters: v : `Vec` Returns: `bool` Modifiers: inline	Checks if 3D vector is parallel to the world X axis. Ignoring orientation. Tolerance is 1e-6. Fails on vectors shorter than 1e-6. Extended Type: `Vec` v : `Vec` Returns: `bool`
`Vec.isYAligned v` Full Usage: `Vec.isYAligned v` Parameters: v : `Vec` Returns: `bool` Modifiers: inline	Checks if 3D vector is parallel to the world Y axis. Ignoring orientation. Tolerance is 1e-6. Fails on vectors shorter than 1e-6. Extended Type: `Vec` v : `Vec` Returns: `bool`
`Vec.isZAligned v` Full Usage: `Vec.isZAligned v` Parameters: v : `Vec` Returns: `bool` Modifiers: inline	Checks if 3D vector is parallel to the world Z axis. Ignoring orientation. Tolerance is 1e-6. Fails on vectors shorter than 1e-6. Same as ln.IsVertical Extended Type: `Vec` v : `Vec` Returns: `bool`
`Vec.length v` Full Usage: `Vec.length v` Parameters: v : `Vec` Returns: `float` Modifiers: inline	Returns the length of the 3D vector. Extended Type: `Vec` v : `Vec` Returns: `float`
`Vec.lengthInXY v` Full Usage: `Vec.lengthInXY v` Parameters: v : `Vec` Returns: `float` Modifiers: inline	Returns the vector length projected into X Y Plane. sqrt(v.X * v.X + v.Y * v.Y) Extended Type: `Vec` v : `Vec` Returns: `float`
`Vec.lengthSq v` Full Usage: `Vec.lengthSq v` Parameters: v : `Vec` 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: `Vec` v : `Vec` Returns: `float`
`Vec.lerp (start, ende, rel)` Full Usage: `Vec.lerp (start, ende, rel)` Parameters: start : `Vec` ende : `Vec` 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: `Vec` start : `Vec` ende : `Vec` rel : `float` Returns: `Vec`
`Vec.matchOrientation orientationToMatch vecToFlip` Full Usage: `Vec.matchOrientation orientationToMatch vecToFlip` Parameters: orientationToMatch : `Vec` vecToFlip : `Vec` Returns: `Vec` Modifiers: inline	Ensure that the 3D vector has a positive dot product with given 3D orientation vector. Extended Type: `Vec` orientationToMatch : `Vec` vecToFlip : `Vec` Returns: `Vec`
`Vec.matchUnitVecOrientation orientationToMatch vecToFlip` Full Usage: `Vec.matchUnitVecOrientation orientationToMatch vecToFlip` Parameters: orientationToMatch : `UnitVec` vecToFlip : `Vec` Returns: `Vec` Modifiers: inline	Ensure that the 3D vector has a positive dot product with given 3D orientation unit-vector. Extended Type: `Vec` orientationToMatch : `UnitVec` vecToFlip : `Vec` Returns: `Vec`
`Vec.matchesOrientation v other` Full Usage: `Vec.matchesOrientation v other` Parameters: v : `Vec` other : `Vec` Returns: `bool` Modifiers: inline	Checks if the angle between the two 3D vectors is less than 90 degrees. Calculates the dot product of two 3D vectors. Then checks if it is bigger than 1e-12. Fails if any of the two vectors is shorter than zeroLengthTolerance (1e-12). Extended Type: `Vec` v : `Vec` other : `Vec` Returns: `bool`
`Vec.moveX x v` Full Usage: `Vec.moveX x v` Parameters: x : `float` v : `Vec` Returns: `Vec` Modifiers: inline	Add to the X part of this 3D vectors together. Returns a new 3D vector. Extended Type: `Vec` x : `float` v : `Vec` Returns: `Vec`
`Vec.moveY y v` Full Usage: `Vec.moveY y v` Parameters: y : `float` v : `Vec` Returns: `Vec` Modifiers: inline	Add to the Y part of this 3D vectors together. Returns a new 3D vector. Extended Type: `Vec` y : `float` v : `Vec` Returns: `Vec`
`Vec.moveZ z v` Full Usage: `Vec.moveZ z v` Parameters: z : `float` v : `Vec` Returns: `Vec` Modifiers: inline	Add to the Z part of this 3D vectors together. Returns a new 3D vector. Extended Type: `Vec` z : `float` v : `Vec` Returns: `Vec`
`Vec.notEquals tol a b` Full Usage: `Vec.notEquals tol a b` Parameters: tol : `float` a : `Vec` b : `Vec` Returns: `bool`	Check if two 3D vectors are not equal within a given tolerance. Use a tolerance of 0.0 to check if the two vectors are not exactly equal. Extended Type: `Vec` tol : `float` a : `Vec` b : `Vec` Returns: `bool`
`Vec.orientDown v` Full Usage: `Vec.orientDown v` Parameters: v : `Vec` Returns: `Vec` Modifiers: inline	Reverse vector if Z part is bigger than 0.0 Extended Type: `Vec` v : `Vec` Returns: `Vec`
`Vec.orientUp v` Full Usage: `Vec.orientUp v` Parameters: v : `Vec` Returns: `Vec` Modifiers: inline	Reverse vector if Z part is smaller than 0.0 Extended Type: `Vec` v : `Vec` Returns: `Vec`
`Vec.perpendicularInVerticalPlane v` Full Usage: `Vec.perpendicularInVerticalPlane v` Parameters: v : `Vec` 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: `Vec` v : `Vec` Returns: `Vec`
`Vec.perpendicularInXY v` Full Usage: `Vec.perpendicularInXY v` Parameters: v : `Vec` 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: `Vec` v : `Vec` Returns: `Vec`
`Vec.projectToXYPlane v` Full Usage: `Vec.projectToXYPlane v` Parameters: v : `Vec` Returns: `Vec` Modifiers: inline	Project vector to World X-Y plane. Use Vc.ofVec to convert to a 2D vector. Extended Type: `Vec` v : `Vec` Returns: `Vec`
`Vec.reverse v` Full Usage: `Vec.reverse v` Parameters: v : `Vec` Returns: `Vec` Modifiers: inline	Negate or inverse a 3D vectors. Returns a new 3D vector. Same as Vec.flip. Extended Type: `Vec` v : `Vec` Returns: `Vec`
`Vec.rotateByQuarterCircle numberOfQuarters v` Full Usage: `Vec.rotateByQuarterCircle numberOfQuarters v` Parameters: numberOfQuarters : `int` v : `Vec` Returns: `Vec`	Rotates a 3D vector around the Z-axis by a given number of quarter-circles (i.e. multiples of 90 degrees or Pi/2 radians). A positive number rotates counter-clockwise, a negative number rotates clockwise. The length of the vector is preserved. Extended Type: `Vec` numberOfQuarters : `int` v : `Vec` Returns: `Vec`
`Vec.rotateByQuaternion q v` Full Usage: `Vec.rotateByQuaternion q v` Parameters: q : `Quaternion` v : `Vec` Returns: `Vec` Modifiers: inline	Rotate by Quaternion. Extended Type: `Vec` q : `Quaternion` v : `Vec` Returns: `Vec`
`Vec.rotateOnZ90CCW v` Full Usage: `Vec.rotateOnZ90CCW v` Parameters: v : `Vec` Returns: `Vec` Modifiers: inline	90 Degree rotation Counter-Clockwise around Z-axis. Extended Type: `Vec` v : `Vec` Returns: `Vec`
`Vec.rotateOnZ90CW v` Full Usage: `Vec.rotateOnZ90CW v` Parameters: v : `Vec` Returns: `Vec` Modifiers: inline	90 Degree rotation clockwise around Z-axis. Extended Type: `Vec` v : `Vec` Returns: `Vec`
`Vec.rotateX angDegree v` Full Usage: `Vec.rotateX angDegree v` Parameters: angDegree : `float` v : `Vec` Returns: `Vec` Modifiers: inline	Rotate the 3D vector in Degrees around X-axis, from Y to Z-axis, Counter Clockwise looking from right. Extended Type: `Vec` angDegree : `float` v : `Vec` Returns: `Vec`
`Vec.rotateXBy r v` Full Usage: `Vec.rotateXBy r v` Parameters: r : `Rotation2D` v : `Vec` Returns: `Vec`	Rotate the 3D vector around X-axis, from Y to Z-axis, Counter Clockwise looking from right. Extended Type: `Vec` r : `Rotation2D` v : `Vec` Returns: `Vec`
`Vec.rotateY angDegree v` Full Usage: `Vec.rotateY angDegree v` Parameters: angDegree : `float` v : `Vec` Returns: `Vec` Modifiers: inline	Rotate the 3D vector in Degrees around Y-axis, from Z to X-axis, Counter Clockwise looking from back. Extended Type: `Vec` angDegree : `float` v : `Vec` Returns: `Vec`
`Vec.rotateYBy r v` Full Usage: `Vec.rotateYBy r v` Parameters: r : `Rotation2D` v : `Vec` Returns: `Vec`	Rotate the 3D vector around Y-axis, from Z to X-axis, Counter Clockwise looking from back. Extended Type: `Vec` r : `Rotation2D` v : `Vec` Returns: `Vec`
`Vec.rotateZ angDegree v` Full Usage: `Vec.rotateZ angDegree v` Parameters: angDegree : `float` v : `Vec` Returns: `Vec` Modifiers: inline	Rotate the 3D vector in Degrees around Z-axis, from X to Y-axis, Counter Clockwise looking from top. Extended Type: `Vec` angDegree : `float` v : `Vec` Returns: `Vec`
`Vec.rotateZBy r v` Full Usage: `Vec.rotateZBy r v` Parameters: r : `Rotation2D` v : `Vec` Returns: `Vec`	Rotate the 3D vector around Z-axis, from X to Y-axis, Counter Clockwise looking from top. Extended Type: `Vec` r : `Rotation2D` v : `Vec` Returns: `Vec`
`Vec.scale f v` Full Usage: `Vec.scale f v` Parameters: f : `float` v : `Vec` Returns: `Vec` Modifiers: inline	Multiplies a 3D vector with a scalar, also called scaling a vector. Returns a new 3D vector. Extended Type: `Vec` f : `float` v : `Vec` Returns: `Vec`
`Vec.slerp (start, ende, rel)` Full Usage: `Vec.slerp (start, ende, rel)` Parameters: start : `Vec` ende : `Vec` rel : `float` Returns: `Vec`	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: `Vec` start : `Vec` ende : `Vec` rel : `float` Returns: `Vec`
`Vec.slopeDegrees v` Full Usage: `Vec.slopeDegrees v` Parameters: v : `Vec` Returns: `float` Modifiers: inline	Returns positive or negative slope of a 3D vector in Degrees. This is the elevation angle from the World X-Y plane (not from the X-axis). Range -90 to +90 Degrees. Extended Type: `Vec` v : `Vec` Returns: `float`
`Vec.slopePercent v` Full Usage: `Vec.slopePercent v` Parameters: v : `Vec` 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 or input has length zero. Extended Type: `Vec` v : `Vec` Returns: `float`
`Vec.slopeRadians v` Full Usage: `Vec.slopeRadians v` Parameters: v : `Vec` Returns: `float` Modifiers: inline	Returns positive or negative slope of a 3D vector in Radians. This is the elevation angle from the World X-Y plane (not from the X-axis). Range -1.57 to +1.57 Radians. Extended Type: `Vec` v : `Vec` Returns: `float`
`Vec.transform m v` Full Usage: `Vec.transform m v` Parameters: m : `Matrix` v : `Vec` Returns: `Vec` Modifiers: inline	Multiplies a Matrix with a 3D vector Since a 3D vector represents a direction or translation in space, but not a location, the implicit the 4th dimension is 0.0 so that all translations are ignored. (Homogeneous Vector) Extended Type: `Vec` m : `Matrix` v : `Vec` Returns: `Vec`
`Vec.transformRigid m v` Full Usage: `Vec.transformRigid m v` Parameters: m : `RigidMatrix` v : `Vec` Returns: `Vec` Modifiers: inline	Multiplies (or applies) a RigidMatrix to a 3D vector. Since a 3D vector represents a direction or translation in space, but not a location, all translations are ignored. (Homogeneous Vector) Extended Type: `Vec` m : `RigidMatrix` v : `Vec` Returns: `Vec`
`Vec.unitize v` Full Usage: `Vec.unitize v` Parameters: v : `Vec` Returns: `UnitVec` Modifiers: inline	Returns 3D vector unitized as UnitVec type, fails on zero length vectors. Extended Type: `Vec` v : `Vec` Returns: `UnitVec`
`Vec.unitizeAsVec v` Full Usage: `Vec.unitizeAsVec v` Parameters: v : `Vec` Returns: `Vec` Modifiers: inline	Returns the 3D vector unitized, fails on zero length vectors. But as Vec type not as UnitVec Extended Type: `Vec` v : `Vec` Returns: `Vec`
`Vec.unitizeOrDefault defaultUnitVector v` Full Usage: `Vec.unitizeOrDefault defaultUnitVector v` Parameters: defaultUnitVector : `UnitVec` v : `Vec` Returns: `UnitVec` Modifiers: inline	Unitize 3D vector, if input vector is shorter than 1e-6 the default unit-vector is returned. Extended Type: `Vec` defaultUnitVector : `UnitVec` v : `Vec` Returns: `UnitVec`
`Vec.unitizeUnchecked v` Full Usage: `Vec.unitizeUnchecked v` Parameters: v : `Vec` Returns: `UnitVec` Modifiers: inline	Returns 3D vector unitized. If vector has zero length this wil return an INFINITY unit vector Extended Type: `Vec` v : `Vec` Returns: `UnitVec`
`Vec.unitizeWithErrMsg errMsg v` Full Usage: `Vec.unitizeWithErrMsg errMsg v` Parameters: errMsg : `string` v : `Vec` Returns: `UnitVec` Modifiers: inline	Returns 3D vector unitized, the error message is used in the Exception if the vector is too short. Extended Type: `Vec` errMsg : `string` v : `Vec` Returns: `UnitVec`
`Vec.withLength desiredLength v` Full Usage: `Vec.withLength desiredLength v` Parameters: desiredLength : `float` v : `Vec` Returns: `Vec` Modifiers: inline	Returns a new 3D vector scaled to the desired length. Same as vec.WithLength. Returns a new 3D vector. Extended Type: `Vec` desiredLength : `float` v : `Vec` Returns: `Vec`
`Vec.withX x v` Full Usage: `Vec.withX x v` Parameters: x : `float` v : `Vec` Returns: `Vec` Modifiers: inline	Returns new 3D vector with new X value, Y and Z stay the same. Extended Type: `Vec` x : `float` v : `Vec` Returns: `Vec`
`Vec.withY y v` Full Usage: `Vec.withY y v` Parameters: y : `float` v : `Vec` Returns: `Vec` Modifiers: inline	Returns new 3D vector with new Y value, X and Z stay the same. Extended Type: `Vec` y : `float` v : `Vec` Returns: `Vec`
`Vec.withZ z v` Full Usage: `Vec.withZ z v` Parameters: z : `float` v : `Vec` Returns: `Vec` Modifiers: inline	Returns new 3D vector with new z value, X and Y stay the same. Extended Type: `Vec` z : `float` v : `Vec` Returns: `Vec`