Spline

Cubic interpolating plane curve or space curve

Library:
Simscape / Multibody / Curves and Surfaces

Description

This Spline block creates a continuous spline curve based on cubic interpolation between the specified points. The curve can be two dimensional, such as a planar cam profile, or three dimensional, such as a roller coaster track. The dimension of the spline depends on the dimension of the coordinate matrix. An N-by-2 matrix specifies a 2-D curve in the xy plane. An N-by-3 matrix specifies a 3-D curve. All the coordinates are resolved in the local reference frame of the block. Moreover, according to the specified end conditions, the curve can be either open or closed.

An Example of a 2-D Spline Curve

Ports

Frame

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`R` — Reference frame
frame

Spline curve reference frame. Connect this frame port to another block to specify the location and orientation of the spline curve in a model.

Geometry

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`G` — Spline curve representation
geometry

Geometry data associated with the representation of a 2-D or 3-D continuous spline curve. It provides the spline curve specification to other blocks to which it connects, such as the Point on Curve Constraint block.

Parameters

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`Interpolation Points` — Coordinates of interpolation points for specifying spline curve
[6 -2 9; -6 5 -4; -6 -7 9; 6 0 -4; -3 6 9; -3 -8 -4] m (default) | N-by-2 matrix | N-by-3 matrix

Matrix that includes the coordinates of the interpolation points for defining the spline curve. Use an N-by-2 matrix to specify a 2-D spline and an N-by-2 matrix to specify a 3-D spline. Each row of the matrix specifies the Cartesian coordinates of an interpolation point with respect to the reference frame of the Spline block. An error occurs if the matrix has any repeated rows.

Tips

You can use the unique function to remove repeated rows from an input matrix.

`End Conditions` — Treatment of the curve endpoints
`Periodic (Closed)` (default) | `Natural (Open)`

End conditions of the spline curve. The Periodic (Closed) end conditions correspond to a closed curve. For this condition, the block joins the first and last data points with a continuous curve. The Natural (Open) end condition corresponds to an open curve.

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 endpoints.

Graphic

`Type` — Spline visualization setting
`From Geometry` (default) | `Marker` | `None`

Visualization setting for this spline. Use the default setting, From Geometry, to show the spline. Select Marker to show a graphic marker such as a sphere or frame. Select None to disable visualization for this spline.

`Visual Properties` — Parameterizations for color and opacity
`Simple` (default) | `Advanced`

Parameterizations for specifying visual properties. Select Simple to specify diffuse color and opacity. Select Advanced to specify more visual properties, such as Specular Color, Ambient Color, Emissive Color, and Shininess.

Dependencies

To enable this parameter, set Type to From Geometry or Marker.

`Diffuse Color` — True color as [R,G,B,A]
[0.0 0.0 0.0] (default) | three-element vector | four-element vector

True color under direct white light, specified as an [R,G,B] or [R,G,B,A] vector on a 0–1 scale. An optional fourth element specifies the color opacity on a scale of 0–1. Omitting the opacity element is equivalent to specifying a value of 1.

Dependencies

To enable this parameter, set Type to From Geometry or Marker.

`Opacity` — Graphic opacity
1.0 (default) | scalar in the range of 0 to 1

Graphic opacity, specified as a scalar in the range of 0 to 1. A scalar of 0 corresponds to completely transparent, and a scalar of 1 corresponds to completely opaque.