EndConditions 2D/3D• EndConditions is an option for SplineFit that is used to specify the end conditions of the spline. • EndConditions can be set to Natural, Closed, or a list of two vectors {{x1, y1}, {x2, y2}} (2D) or {{x1, y1, z1}, {x2, y2, z2}} (3D) specifying the tangency direction at the beginning and end of the spline, respectively. • If a list of two vectors is given, both their magnitude and direction are significant. • The default setting is EndConditions->Natural. • See also: SplineFunction. Further Examples Load the Modeler2D package. Create a SplineFunction representing the path between a sequence of 2D points, and evaluate it halfway between the first and second points. Each end of the spline will have zero curvature.
Out[3]= | ![](/applications/mechsystems/FunctionIndex/HTMLImages/EndConditions.en/EndConditions.en_3.gif) |
Out[4]= | ![](/applications/mechsystems/FunctionIndex/HTMLImages/EndConditions.en/EndConditions.en_4.gif) |
The spline is a 2D parametric function, and can be plotted as such.
Out[5]= | ![](/applications/mechsystems/FunctionIndex/HTMLImages/EndConditions.en/EndConditions.en_7.gif) |
Here is a spline with the ends closed upon themselves.
Out[6]= | ![](/applications/mechsystems/FunctionIndex/HTMLImages/EndConditions.en/EndConditions.en_9.gif) |
Here is a spline with specific direction vectors at the ends.
Out[7]= | ![](/applications/mechsystems/FunctionIndex/HTMLImages/EndConditions.en/EndConditions.en_11.gif) |
Here are all three splines shown together.
Out[8]= | ![](/applications/mechsystems/FunctionIndex/HTMLImages/EndConditions.en/EndConditions.en_14.gif) |
Here is a SplineFunction with values given for the independent variable at each knot point.
Out[9]= | ![](/applications/mechsystems/FunctionIndex/HTMLImages/EndConditions.en/EndConditions.en_16.gif) |
Out[10]= | ![](/applications/mechsystems/FunctionIndex/HTMLImages/EndConditions.en/EndConditions.en_18.gif) |
Here is the arc length of the spline, also expressed as a function of the independent variable.
Out[11]= | ![](/applications/mechsystems/FunctionIndex/HTMLImages/EndConditions.en/EndConditions.en_20.gif) |
Out[12]= | ![](/applications/mechsystems/FunctionIndex/HTMLImages/EndConditions.en/EndConditions.en_21.gif) |
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