Questions on the spline-related functions of Mathematica (BezierCurve[], BSplineCurve[], etc.).

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1
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0answers
40 views

Find GeometricTransform from 3D BSplineSurface to a point cloud

I am looking for another way to approach this problem. Any suggestion on how to optimize the computing speed is welcome. I have a BSplineFunction which accurately ...
1
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1answer
46 views

What extrapolation method does Interpolation use by default? [on hold]

As far as I can tell, Interpolation uses cubic spline interpolation by default - please correct me if I'm wrong. What does it use for extrapolation outside of the ...
3
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0answers
68 views

Understanding polyharmonic splines

Raul Narain and J.M. gives implementation of the thin plate polyharmonic splines in this post. Raul Narian's method is clear. J.M.'s is convenient to reuse. But J.M. used too many ...
6
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2answers
111 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 ...
7
votes
3answers
131 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)= ...
0
votes
1answer
92 views

PolarPlot works, ParametricPlot doesn't

Am new to Mathematica, so if this question has been asked already, apologies. Have a (polar) spline function and Mathematica did a fine job of calculating from my inputs and giving me the piecewise ...
10
votes
1answer
635 views

Curve fit based on minimal data

Inspired by the fantastic answers here and here, I would like to ask a questions along similar lines. I have 6 curve types that follow these rules: Type A: If point 1 is positive and point 2 is ...
12
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5answers
369 views

Joining ordered set of points with splines in spiral

I have a collection of points ...
2
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0answers
65 views

Exporting BSplineSurface to STL

I have encountered some difficulties getting BSplineSurface to export to STL. The following code works and generates a triangulated polygon mesh from the NURBS ...
2
votes
1answer
97 views

How to generate specific function using BSpline command/

I want to generate an approximation function that fits a curve to points. My goal is to obtain an actual formula. Is this possible with the BSpline function? Using the following code: ...
4
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2answers
199 views

How to get a uniformly distributed list of points from a B-spline function

I created a spline function from a list of points and made a plot as follows: ...
3
votes
1answer
95 views

How to color a BSplineSurface

I am trying to color a BSplineSurface in a complex way but not having any luck using ColorFunction. I can use ...
0
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2answers
118 views

How to fix problems solving for values of BSpline function?

I generated a spline function called f using the BSplineFunction with domain {t,0,1}. ...
0
votes
4answers
149 views

Minimization in single component of BSpline to extract points

I smoothed some data with a BSpline $B[t] = (x[t],y[t])$. I would like to extract certain points from this spline by their x-Values, $x_0$. The easiest way I came up with was to minimize ...
0
votes
0answers
42 views

How to approximate a computationally expensive 5-dimensional manifold?

I have a 4-parameter family of functions, which I'll refer to as y[a, b, c, d][x]. In this notation, a, b, c, d are the 4 ...
10
votes
3answers
620 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: ...
2
votes
1answer
102 views

Problems with BSplineFunction vs. BSplineSurface

Why are those surfaces different? ...
0
votes
0answers
90 views

how to write my own interpolation method

I was comparing results of spline interpolation in Mathematica and C++/gsl-library Results of interpolation are different if I use: ...
12
votes
2answers
242 views

Arbitrary precision spline interpolation

Current implementation of Interpolation does not allow arbitrary precision spline interpolation. Yu-Sung Chang say here that "it is not hard to implement it ...
5
votes
2answers
316 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 ...
0
votes
1answer
140 views

Plot hermite spline [closed]

I'm new to Mathematica and cannot figure out a way to plot a 2d hermite spline. My points are: $p_0=\{143.05;195.606\};$ $p_1=\{159.373;181.845\};$ $p_2=\{160.891;179.26\};$ $p_3=\{176.423;171.878\};$ ...
7
votes
1answer
141 views

Fixing Spline curves so as to not overlap with themselves - (Diagrams)

Statement of the problem: Conceptually, what I'm trying to achieve is pretty simple. I have some code that generates a set of diagrams from a list of sets of points using BSplineCurve. Certain ...
1
vote
1answer
169 views

BSplinefunction and its derivative

Hi I am trying to use curve fit some data using the BSplinefunction. I havent been using Mathematica long, so my questions might be quite basic. ...
5
votes
3answers
255 views

BSplineFunction derivatives wrong if using weights?

In my work, I make heavy use of non-uniform rational B-spline (NURBS) functions, defined using the function BSplineFunction with the option defining ...
2
votes
2answers
533 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 ...
6
votes
0answers
59 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 ...
5
votes
2answers
333 views

How to make BSplineFunction pass each data point and naturally smooth?

(Old package, works good) ...
0
votes
1answer
295 views

Exporting B Spline Function to Excel

I am trying to export the data from a B Spline Function to a table in excel. I have tried exporting as many different file types (.xls, .txt, .dat), but all of them show up in excel as all of the ...
4
votes
3answers
630 views

Inverting a Spline-Function (Bezier or BSpline)

I would like to use a Spline-Function to describe a transformation from one range of reals to another, that is I would like to have a function which maps a value $y$ on $x$ and for simplicity let us ...
2
votes
2answers
206 views

Evaluating Polynomials at Grid Points

I am continuing my quest on B-splines. The code below builds a 5x5 matrix out of B-splines, using the BSplineBasis[] routine. I now want to evaluate the polynomials that are stored in each matrix ...
1
vote
0answers
261 views

Plotting derivatives of B-splines

I am trying to solve an electrodynamics problem numerically by using B-splines a basis function. Please don't ask me why, but if you really wanna know, here is the assignment. Using the following ...
3
votes
0answers
350 views

How to make 3D object smooth?

This thread considers mathematical methods here to make the 3D object smooth but this question consider how to achieve the goal of smoothing a 3D object in Mathematica. I want to get smoother ...
4
votes
0answers
331 views

Cubic polynomial interpolation with velocities listed rather than some points

I am trying to use the function BSplineFunction[] to create a natural cubic spline. Normally what is done is that you specify "SplineDegree -> 3" and include a list of points and it will carry out ...
3
votes
2answers
683 views

Parametric differentiable interpolation of a 2D data set

I have a set of data ...
3
votes
2answers
264 views

Convert BSplineFunction into two Interpolating Functions

Is there a way to decompose a BSplineFunction output into two functions x[t], y[t] ...
2
votes
3answers
181 views

How can I find the points of B Spline functions for a specific range?

Based on this question: I have a list of bspline functions (nearly 1000) provided by applying BSplineFunction to a list of points. I want to get the points each of ...
1
vote
2answers
635 views

Derivative of a spline approximation

To approximate an experimental data function $f(t)$ with $t \in (t_{min},t_{max})$ I used a cubic spline $s(p)=(t(p),f(p))$ with the parameter $p \in (0,1)$ and $p = t/(t_{max}-t_{min})$ by using the ...
6
votes
1answer
391 views

BSplineCurve Interpolation

Can I get interpolated values from this B-spline, (shown in red)? ...
21
votes
2answers
2k 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 ...
11
votes
1answer
1k views

Fitting a spline to data with FindFit?

I am trying to find a function that fits my almost linear data. A high order polynomial model has too much residual. So I was hoping to use Mathematica to fit splines to the curve. This is what I ...
9
votes
1answer
246 views

SplineDegree->1 does not work with BezierFunction?

This works (SplineDegree -> 2) ...