Cubic interpolating plane curve or space curve

**Library:**Curves and Surfaces

This block represents a continuous spline curve based on cubic interpolation between the points specified. The curve can be two-dimensional, such as a planar cam profile, or three-dimensional, such as a roller coaster track. Depending on the end conditions selected, the curve can be either open or closed.

**Cam profile — An Example of a 2-D Spline Curve**

Whether a spline curve is two- or three-dimensional depends solely on the coordinate
matrix dimensions. A two-column matrix specifies a two-dimensional curve in the
*xy* plane. Each row in this matrix provides the
[*x*, *y*] coordinates of a point. A three-column
matrix specifies a three-dimensional curve. Each row in this matrix provides the
[*x*, *y*, *z*] coordinates of a
point. All coordinates are resolved in the local reference frame of the block.

The spline curve is a piecewise function of third-order polynomial segments connected end-to-end. The curve is built such that adjacent polynomial segments have the same first and second derivatives at the shared end point. If the curve is periodic, an additional curve segment connects the last point specified to the first point. The first and second derivatives of this segment matches those of the adjacent segments at the shared end point.

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