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

learn more… | top users | synonyms

23
votes
3answers
991 views

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 ...
28
votes
2answers
4k views

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 ...
19
votes
4answers
2k views

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: ...
15
votes
2answers
1k views

ListSurfacePlot3D generates ugly artifacts

I have a list of $\{x,y,z\}$ pairs representing points in $R^3$. For every unique value of $z$ there are many $\{x,y\}$ pairs defining a polygon/contour in that particular $z$-plane. My dataset looks ...
8
votes
2answers
592 views
11
votes
3answers
259 views

How to deal with the condition $u_i=u_{i+1}$ in B-Spline basis function?

The defintion of B-Spline basis function as shown below: Let $\vec{U}=\{u_0,u_1,\ldots,u_m\}$ a nondecreasing sequence of real numbers,i.e, $u_i\leq u_{i+1}\quad i=0,1,2\ldots m-1$ $$N_{i,0}(u)= \...
12
votes
1answer
267 views

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 ...
6
votes
2answers
427 views

Convert BSplineFunction into two Interpolating Functions

Is there a way to decompose a BSplineFunction output into two functions x[t], y[t] ...
11
votes
3answers
949 views

Finding “Maxima” and “Minima” on a B-Spline

I need to find the "Maxima" and "Minima" on a B-Spline or more correct the points where the 2nd components of the derivate equal zero. For example: ...
5
votes
2answers
544 views

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 ...
3
votes
2answers
1k views

Generating x,y coordinates for an edge detection

I'd like to be able to process a number of graphics that have edge contours and output a list of $x$, $y$ coordinates to be used for generating a spline in another program, or in Mathematica, to make ...
12
votes
5answers
596 views

Joining ordered set of points with splines in spiral

I have a collection of points ...
9
votes
1answer
231 views

How to discretize a BezierCurve?

Bug introduced in version 10.0 and persisting through 10.4 DiscretizeGraphics is new in 10.0. I need to create a discretized region from a ...
9
votes
3answers
380 views

Implementation of tensor product formula

For the Bézier surface, which owns the following matrix definition: $$\begin{align*} \mathbf S(u,v)&=\sum_{i=0}^m \sum_{j=0}^n \mathbf P_{i,j} B_{m,i}(u) B_{n,j}(v)\\ &=\small \begin{pmatrix}...
5
votes
1answer
154 views

Multidimensional arbitrary precision spline interpolation on the grid

This question is a generalization of the previous one for multiple dimensions. In the answer to that question an implementation for the clamped spline interpolation for 1D case and arbitrary degree of ...
4
votes
3answers
646 views

How to find a length of a curve constructed using Spline?

By fitting the data using spline, I have created a curve. sp = SplineFit[data1, Cubic] I am trying to divide this curve into small segments of equal length. To ...
4
votes
2answers
515 views

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: ...
2
votes
1answer
185 views

Confusion with SplineFit (Angle calculation)

This question is continuation to this other one I am creating polymers (where each monomer is of equal length) using this method: ...
15
votes
2answers
507 views

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. ...
9
votes
2answers
162 views

How to optimize my own BezierFunction?

A few months ago, I asked a question about the implementation of Bezier surface. Please see here for a full detail. I also know that BezierFunction[] is built-in ...
11
votes
1answer
279 views

How to specify PDE Boundary condition on Bspline?

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 ...
6
votes
2answers
461 views

2D smoothing spline interpolation

Does Mathematica have 2D smoothing spline interpolation built in? I requires an interpolation method with smooth first derivatives and cubic bivariate splines fulfill this nicely. In python I would ...
13
votes
1answer
171 views

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 ...
6
votes
1answer
572 views

BSplineCurve Interpolation

Can I get interpolated values from this B-spline, (shown in red)? ...
3
votes
1answer
99 views

How to make the result of Piecewise be a closed interval?

Description This question comes from two questions. Namely Q1 and Q2 The defintion of B-Spline basis function as shown below: Let $\vec{U}=\{u_0,u_1,\ldots,u_m\}$ a nondecreasing sequence of real ...
3
votes
2answers
938 views

Parametric differentiable interpolation of a 2D data set

I have a set of data ...
10
votes
2answers
239 views

How to boost the performance of my own BSplineFunction

In my CAGD package, I implemented a CAGDBSplineFunction[] like built-in BSplineFunction[]. ...
9
votes
1answer
240 views

How to define a custom 2/3D graphic primitive like built-in?

There are lots of basic graphic-pimitive in Mathematica, such as 2D- pimitive: Line[], Circle[], Disk[] and 3D-pimitive: ...
8
votes
1answer
110 views

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 ...
3
votes
1answer
299 views

How can I make a pretzel shape using Bézier curves?

I am trying to make a pretzel shape,but I cannot seem to get the loops even. Eventually, I need to make the pretzel shape loop in 3D so I need to nail the 2D concept first. Here's what I have so far....
2
votes
1answer
73 views

Why are these methods giving me different results? (Trying to test SplineFit)

I am creating a polymer(where each monomer is of equal length) using this method: ...
1
vote
2answers
427 views

How to know form of plotted Bézier function

Simple scenario is to see the Bézier function, but how to know which polynomial approximate it? ...
0
votes
0answers
141 views

Converting a BSplinecurve to function [duplicate]

I am having two set of data. This is d000 and d001. The set d001 is a subset of d000. I am fitting the d000 data by using the BSpline of the d001 data according to the following commands: ...