# Tagged Questions

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

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### 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 ...
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 ...
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### 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 ...
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 ...
129 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)= ...
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### 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 ...
633 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 ...
366 views

### Joining ordered set of points with splines in spiral

I have a collection of points ...
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### 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 ...
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### 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: ...
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: ...
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### 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 ...
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}. ...
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### 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 ...
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### 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 ...
615 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: ...
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### Problems with BSplineFunction vs. BSplineSurface

Why are those surfaces different? ...
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### 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: ...
240 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 ...
315 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 ...
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### Plot hermite spline [closed]

I'm new to Mathematica and cannot figure out a way to plot a 2d hermite spline. My points are: $p_0=\{143.05;195.606\};$ $p_1=\{159.373;181.845\};$ $p_2=\{160.891;179.26\};$ $p_3=\{176.423;171.878\};$ ...
139 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 ...
168 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. ...
251 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 ...
528 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 ...
58 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 ...
333 views

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

(Old package, works good) ...
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### 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 ...
629 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 ...
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### 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 ...
258 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 ...
348 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 ...
329 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 ...
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### Parametric differentiable interpolation of a 2D data set

I have a set of data ...
264 views

### Convert BSplineFunction into two Interpolating Functions

Is there a way to decompose a BSplineFunction output into two functions x[t], y[t] ...
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 ...
633 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 ...
390 views

### BSplineCurve Interpolation

Can I get interpolated values from this B-spline, (shown in red)? ...
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 ...