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Description
A spline is a piecewise, parametric curve defined by polynomial segments. Please see a full definition here.
Navigation
A spline curve can be generated in the following ways:
•Create a new curve, then select "Spline (polynomial segments)" from the type drop-down list.
Controls
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Control
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Inputs / Description
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Defaults
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Logical Parent
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Name of Custom Element containing this curve.
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Selected custom element at the time of curve creation.
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Name
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Name of the curve.
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Curve n
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Description
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Description of the curve.
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Type
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Curve type. Select "Spline (polynomial segments)" from the drop-down list.
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Circular Arc
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Spline Curve Options
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Degree
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Polynomial degree of spline curve. Each segment of the spline will have Ndegree+1 coefficients.
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1
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Breakpoints
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The breakpoints define the number of segments in the curve (Nbreakpoints-1) and the range of the parametric variable for each segment. For example, a breakpoint list of [0,2,3] defines two segments and the parametric variable ranges from 0 to 2 over the first segment and 0 to 1 over the second segment.
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0,1
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Segment(n)
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The columns X, Y and Z define the parametric polynomial coefficients having the form, a + bt + ct2 + dt3 + ...
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(0,1) (0,0) (0,0)
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OK
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Accept settings and close the dialog box.
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Cancel
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Discard settings and close the dialog box.
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Apply
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Apply settings and keep the dialog box open.
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Help
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Access curve Help.
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Application Notes
Example: Simple spline curve
The task is to produce X and Y components of the position vector P such that they correspond to the desired shape. The X-segment is represented by x(t) = t - t2 + t3 - 2t4 and the Y-segment is given by y(t) = t + 2t2 -2t3 - t4. The dialog box shown below creates a 4th degree (5th order) spline with breakpoints at 0 and 1 with position vectors (0,1,-1,1,-2) for the X-segment and (0,1,2,-2,-1) for the Y-segment. Note that x(t=0) = 0, x(t=1) = -1 and y(t=0) = 0, y(t=1) = 0. The curve is also shown below.
.png)
.png)
Example: Closed spline curve
This example creates a closed spline curve, which corresponds to x(t=0) = x(t=1) = y(t=0) = y(t=1) = 0. The X-segment is represented by x(t) = t - 2t2 - t3 + t4+ t5. The Y-segment is given by y(t) = t + 3t2 -2t3 - t4 - t5. The dialog box shown below creates a 5th degree (6th order) spline with breakpoints at 0 and 1 with position vectors (0,1,-2,-1,1,1) for the X-segment and (0,1,3,-2,-1,-1) for the Y-segment.
.png)
.png)
Related Topics
Introduction to Curves
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