Construct a spline from its three control points. This is the same as just using the CubicSpline3d constructor directly;

CubicSpline3d.bezier p1 p2 p3 p4

is equivalent to

CubicSpline3d ( p1, p2, p3, p4 )

Construct a spline in Hermite form, from the position and derivative values at its start and end points, like so:

The spline is based on a parameter that ranges from 0 to 1; as a result, in most cases the length of each derivative vector should be roughly equal to the length of the resulting spline.

Get the control points of a spline as a tuple.

( p1, p2, p3, p4 ) =
    CubicSpline3d.controlPoints exampleSpline




--> p1 = Point3d ( 1, 1, 1 )
--> p2 = Point3d ( 3, 1, 1 )
--> p3 = Point3d ( 3, 3, 1 )
--> p4 = Point3d ( 3, 3, 3 )

Get the start point of a spline. This is equal to the spline's first control point.

CubicSpline3d.startPoint exampleSpline
--> Point3d ( 1, 1, 1 )

Get the end point of a spline. This is equal to the spline's last control point.

CubicSpline3d.endPoint exampleSpline
--> Point3d ( 3, 3, 3 )

Get the start derivative of a spline. This is equal to three times the vector from the spline's first control point to its second.

CubicSpline3d.startDerivative exampleSpline
--> Vector3d ( 6, 0, 0 )

Get the end derivative of a spline. This is equal to three times the vector from the spline's third control point to its fourth.

CubicSpline3d.endDerivative exampleSpline
--> Vector3d ( 0, 0, 6 )

Get a point along a spline, based on a parameter that ranges from 0 to 1. A parameter value of 0 corresponds to the start point of the spline and a value of 1 corresponds to the end point.

CubicSpline3d.point exampleSpline 0
--> Point3d ( 1, 1, 1 )


CubicSpline3d.point exampleSpline 0.5
--> Point3d ( 2.75, 2, 1.25 )


CubicSpline3d.point exampleSpline 1
--> Point3d ( 3, 3, 3 )

Get the deriative value at a point along a spline, based on a parameter that ranges from 0 to 1. A parameter value of 0 corresponds to the start derivative of the spline and a value of 1 corresponds to the end derivative.

CubicSpline3d.derivative exampleSpline 0
--> Vector3d ( 6, 0, 0 )


CubicSpline3d.derivative exampleSpline 0.5
--> Vector3d ( 1.5, 3, 1.5 )


CubicSpline3d.derivative exampleSpline 1
--> Vector3d ( 0, 0, 6 )

Note that the derivative interpolates linearly from end to end.

Scale a spline about the given center point by the given scale.

CubicSpline3d.scaleAbout Point3d.origin 2 exampleSpline
--> CubicSpline3d
-->     ( Point3d ( 2, 2, 2 )
-->     , Point3d ( 6, 2, 2 )
-->     , Point3d ( 6, 6, 2 )
-->     , Point3d ( 6, 6, 6 )
-->     )

Rotate a spline counterclockwise around a given axis by a given angle (in radians).

CubicSpline3d.rotateAround Axis3d.z (degrees 90) exampleSpline
--> CubicSpline3d
-->     ( Point3d ( -1, 1, 1 )
-->     , Point3d ( -1, 3, 1 )
-->     , Point3d ( -3, 3, 1 )
-->     , Point3d ( -3, 3, 3 )
-->     )

Translate a spline by a given displacement.

displacement =
    Vector3d ( 2, 3, 1 )


CubicSpline3d.translateBy displacement exampleSpline
--> CubicSpline3d
-->     ( Point3d ( 3, 4, 2 )
-->     , Point3d ( 5, 4, 2 )
-->     , Point3d ( 5, 6, 2 )
-->     , Point3d ( 5, 6, 4 )
-->     )

Mirror a spline across a plane.

CubicSpline3d.mirrorAcross Plane3d.xy exampleSpline
--> CubicSpline3d
-->     ( Point3d ( 1, 1, -1 )
-->     , Point3d ( 3, 1, -1 )
-->     , Point3d ( 3, 3, -1 )
-->     , Point3d ( 3, 3, -3 )
-->     )

Project a spline onto a plane.

CubicSpline3d.projectOnto Plane3d.xy exampleSpline
--> CubicSpline3d
-->     ( Point3d ( 1, 1, 0 )
-->     , Point3d ( 3, 1, 0 )
-->     , Point3d ( 3, 3, 0 )
-->     , Point3d ( 3, 3, 0 )
-->     )

Take a spline defined in global coordinates, and return it expressed in local coordinates relative to a given reference frame.

localFrame =
    Frame3d.at (Point3d ( 1, 2, 3 ))


CubicSpline3d.relativeTo localFrame exampleSpline
--> CubicSpline3d
-->     ( Point3d ( 0, -1, -2 )
-->     , Point3d ( 2, -1, -2 )
-->     , Point3d ( 2, 1, -2 )
-->     , Point3d ( 2, 1, 0 )
-->     )

Take a spline considered to be defined in local coordinates relative to a given reference frame, and return that spline expressed in global coordinates.

localFrame =
    Frame3d.at (Point3d ( 1, 2, 3 ))


CubicSpline3d.placeIn localFrame exampleSpline
--> CubicSpline3d
-->     ( Point3d ( 2, 3, 4 )
-->     , Point3d ( 4, 3, 4 )
-->     , Point3d ( 4, 5, 4 )
-->     , Point3d ( 4, 5, 6 )
-->     )

Project a spline into a given sketch plane. Conceptually, this projects the spline onto the plane and then expresses the projected spline in 2D sketch coordinates.

CubicSpline3d.projectInto SketchPlane3d.yz exampleSpline
--> CubicSpline2d
-->     ( Point2d ( 1, 1 )
-->     , Point2d ( 1, 1 )
-->     , Point2d ( 3, 1 )
-->     , Point2d ( 3, 3 )
-->     )