Construct a spline from its start point, inner control point and end point:

exampleSpline =
    QuadraticSpline3d.fromControlPoints
        (Point3d.meters 1 1 1)
        (Point3d.meters 3 2 1)
        (Point3d.meters 3 3 3)

Construct a 3D spline lying on a sketch plane by providing a 2D spline specified in XY coordinates within the sketch plane.

QuadraticSpline3d.on SketchPlane3d.xz <|
    QuadraticSpline2d.fromControlPoints
        (Point2d.meters 1 1)
        (Point2d.meters 3 4)
        (Point2d.meters 5 1)
--> QuadraticSpline3d.fromControlPoints
-->     (Point3d.meters 1 0 1)
-->     (Point3d.meters 3 0 4)
-->     (Point3d.meters 5 0 1)

Construct a B-spline from a list of knot values and a list of control points, and return the individual segments of that B-spline as a list.

The number of knots should be one greater than the number of control points; any extra knots or control points will be dropped. In most cases the first and last knots will be repeated two times; for example, the knots

[ 0, 0, 1, 2, 3, 4, 4 ]

could be used along with 6 control points to form 4 spline segments.

Note that a popular alternate convention uses two extra 'dummy' knot values at the start and end, so if you see an example where the number of knots is three greater than the number of control points (especially if you also notice that the first and last knots are repeated three times instead of two!) then you should drop the first and last knot values.

Knot values should be given in ascending order but will be sorted if necessary.

For a given set of B-spline knots, return the corresponding intervals between knots that correspond to individual spline segments.

Get the start point of a spline. Equal to firstControlPoint.

Get the first control point of a spline. Equal to startPoint.

Get the second control point of a spline.

Get the third and last control point of a spline. Equal to endPoint.

Get the end point of a spline. Equal to thirdControlPoint.

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

QuadraticSpline3d.startDerivative exampleSpline
--> Vector3d.meters 4 2 0

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

QuadraticSpline3d.endDerivative exampleSpline
--> Vector3d.meters 0 2 4

Compute a bounding box for a given spline. It is not guaranteed that the result will be the smallest possible bounding box, since for efficiency the bounding box is computed from the spline's control points (which cover a larger volume than the spline itself).

QuadraticSpline3d.boundingBox exampleSpline
--> BoundingBox3d.from
-->     (Point3d.meters 1 1 1)
-->     (Point3d.meters 3 3 3)

Get the point along a spline at a given parameter value.

Represents a nondegenerate spline (one that has finite, non-zero length).

Attempt to construct a nondegenerate spline from a general QuadraticSpline3d. If the spline is in fact degenerate (consists of a single point), returns an Err with that point.

Convert a nondegenerate spline back to a general QuadraticSpline3d.

Get the tangent direction to a nondegenerate spline at a given parameter value.

Get both the point and tangent direction of a nondegenerate spline at a given parameter value.

Approximate a quadratic spline by a given number of line segments. Note that the number of points in the polyline will be one more than the number of segments.

Approximate a quadratic spline as a polyline, within a given tolerance. Every point on the returned polyline will be within the given tolerance of the spline.

Reverse a spline so that the start point becomes the end point, and vice versa.

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

Rotate a spline counterclockwise around a given axis by a given angle.

Translate a spline by a given displacement.

Translate an arc in a given direction by a given distance.

Mirror a spline across a plane.

Find the orthographic projection of a spline onto a plane.

Convert a spline from one units type to another, by providing a conversion factor given as a rate of change of destination units with respect to source units.

Convert a spline from one units type to another, by providing an 'inverse' conversion factor given as a rate of change of source units with respect to destination units.

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

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

Project a spline into a given sketch plane. Conceptually, finds the orthographic projection of the spline onto the plane and then expresses the projected spline in 2D sketch coordinates.

Split a spline into two roughly equal halves. Equivalent to QuadraticSpline3d.splitAt 0.5.

Split a spline at a particular parameter value, resulting in two smaller splines.

A spline that has been parameterized by arc length.

Build an arc length parameterization of the given spline, with a given accuracy.

Find the total arc length of a spline, to within the accuracy specified when calling arcLengthParameterized.

Get the point along a spline at a given arc length.

Get the midpoint of a spline. Note that this is the point half way along the spline by arc length, which is not in general the same as evaluating at a parameter value of 0.5.

Get the tangent direction along a spline at a given arc length.

Get the point and tangent direction along a spline at a given arc length.

Get the original QuadraticSpline3d from which an ArcLengthParameterized value was constructed.

Get the first derivative of a spline at a given parameter value. Note that the derivative interpolates linearly from end to end.

Get the second derivative of a spline (for a quadratic spline, this is a constant).

Get the bounds on the first deriative of a spline.

Determine the number of linear segments needed to approximate a quadratic spline to within a given tolerance.