# Questions tagged [splines]

Questions on the spline-related functions of Mathematica (BezierCurve[], BSplineCurve[], etc.), or related to the theory and use of splines in Mathematica.

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### Arbitrary precision spline interpolation

The current implementation of Interpolation does not allow arbitrary precision spline interpolation. Yu-Sung Chang says here that "it is not hard to implement it ...
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### How to make BSplineFunction pass each data point and naturally smooth?

Old package, works good ...
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### Joining and interpolating data points

I wonder what is the best practice for interpolating curves? Usually, I'm using BSplineCurve and adjusting SplineWeights so it ...
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### Implementation of smoothing splines function

I have some problems in writing a module for spline smoothing. Actually, I have been trying for about two weeks. My listing is here: ...
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### How can I make FilledCurve smoother?

In How can I generate and randomly assign color to annular sectors? J.M. showed an interesting way to create a sector graphic using FilledCurve. Unfortunately it ...
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### Stiff BVP of nonlinear ODE, alternative/ enhancement to shooting method

Question: I have been trying to solve this coupled ODE set. \begin{align} ( \frac{ \mu^2}{B} +1 ) \Phi^2 + \frac{1}{A} {\Phi^{\prime 2}} + \frac{1}{2}\lambda \Phi^4 - \frac{A'}{r A^...
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### Extracting polynomials from a cubic spline function

I have this set of three data points and I want the natural cubic spline functions for them: dat = {{-.0247500, .5}, {.3349375, -.25}, {1.101000, 0}}; I tried: ...
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### How to speed up the plotting of B-spline curve?

Three months ago, I asked a quesion about B-Spline basis function here, Today, I used this function to plot B-spline curve. The definition of $N_{i,p}$ ...
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### Produce a spline from a set of {{x, y}, z} points and get its parameters/expression

I have produced a set of points in a variable of the type {{x1, y1}, z1},{{x2, y2}, z2}, ,... }, where {x, y} should be the ...
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### Intersection of two splines

I have a collection of sets of points, each set defining the segment of a (nice) curve on the unit sphere $S^2 \subset \mathbb{R}^3$. The points are computed numerically. I now want to compute the ...
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### Length of a curve parallel to a spline

I have constructed a BSplineFunction through a set of random points: ...
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### How to get a uniformly distributed list of points from a B-spline function [duplicate]

I created a spline function from a list of points and made a plot as follows: ...
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### SplineDegree->1 does not work with BezierFunction?

This works (SplineDegree -> 2) ...
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### BezierCurve in EdgeShapeFunction fails when used on multiedges graph

I would like to create a network graph with curved edges. To do this, I wrote this function: ...
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### How to know form of plotted Bézier function

Simple scenario is to see the Bézier function, but how to know which polynomial approximate it? ...
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### How to define a custom 2/3D graphic primitive like built-in?

There are lots of basic graphic-primitives in Mathematica, such as 2D- primitive: Line[], Circle[], Disk[] and 3D-primitive: ...
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### How to calculate the control points of a Bézier curve?

To plot a BezierCurve in Mathematica, I need control points. But, I do not know the control points; I only know the points through which the Bézier curve passes. ...
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### Joining ordered set of points with splines in spiral

I have a collection of points ...
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### Is there a way to get BSplineFunction beyond MachinePrecision?

I have been using BSplineFunction (Mathematica 8) to generate a smooth representation of some data, which I might then do some further processing on. As I ...
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### Manual ArcLength sampling on spline differs from MeshFunction sampling

Using Michael E2's answer, I performed a manual arclength parameterisation by solving the differential equation (or: finding the inverse of a function whose derivative is known). I compared the ...
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### Plot a bezier triangle

I have to construct a bezier triangle that interpolates these 4 points: $\qquad (0,0,1),\,(1,0,0),\,(0,1,0),\,(0.5,0.5,0.75)$ However, the surface that I get is so weird. Anyone please can help me to ...
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### BSplineFunction derivatives wrong if using weights?

Bug introduced in 7.0 and persisting through 12.0 or later In my work, I make heavy use of non-uniform rational B-spline (NURBS) functions, defined using the function ...
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### Color Blend in BezierCurve

How can I color a BezierCurve from Red into Green just as ...
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### How to specify PDE Boundary condition on a B-spline?

Context I would like to solve a PDE on a boundary which is parametrized as a BSpline. I am trying to solve the force-free Grad-Shafranov equation on a boundary ...
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### Why is DiscretizeGraphics missing points on my curve?

I have a graphics expression which renders nicely as a closed curve when put in Graphics, I don't understand why I can't get the lines from DiscretizeGraphics or ...
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### How to generate a closed B-spline curve?

I wrote a function called deBoor using the Cox-de Boor algorithm to generate a B-spline curve. ...
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### smooth spline through airfoil coordinates

I am trying to produce a smooth spline curve through a set of airfoil coordinates. An example for the data I am trying to use is here, and I am reading the file like so to get rid of some extraneous ...
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### Why is there a discrepancy between JoinedCurve/FilledCurve and the underlying BSplineCurve segments?

This may be related to How to discretize a BezierCurve?, but this question deals with BSplineCurves with specific SplineWeights, ...
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### Rendering PNG images to spline curves

I found something interesting on this page (Generic contour smoothing with shading) that could help me improve my images. Unfortunately, they can only be used with graphics generated by the software ...
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### Where is the other half of my fourth degree Bézier curve?

Bug introduced in 10.0.0 and fixed in 10.2 When I enter the following command, half of the fourth-degree spline is missing from the graph (i.e. it doesn't touch the last point). Is this a bug in ...
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### How to boost the performance of my own BSplineFunction

In my CAGD package, I implemented a CAGDBSplineFunction[] like built-in BSplineFunction[]. ...
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