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

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2
votes
3answers
173 views

BSpline or other curve through arbitrary ordered sequence of two-dimensional points

How does one create a BSplineCurve or other smooth curve passing through each point in an ordered list, where the curve may be non-simple, i.e., can double-back ...
6
votes
2answers
424 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 ...
11
votes
3answers
245 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)= ...
13
votes
1answer
887 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 ...
10
votes
3answers
769 views

Getting a custom Bézier curve function to work

In general, the $nth$-degree Bézier curve is defined as: $$\vec{C}(u)=\sum_{i=0}^{n} B_{i,n}(u) \vec{P_i} \qquad 0\leq u\leq1$$ where $B_{i,n}(u)$ is the classical Bernstein polynomial, ...
12
votes
5answers
570 views

Joining ordered set of points with splines in spiral

I have a collection of points ...
7
votes
2answers
469 views

How to create an adjustable Bézier curve?

I tried to create an adjustable Bézier curve with the following simple code. However the curve didn't show up. What is the problem? Please help. ...
2
votes
0answers
195 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
133 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
votes
2answers
480 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: ...
3
votes
1answer
145 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
votes
1answer
185 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
170 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 ...
11
votes
3answers
898 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
188 views

Problems with BSplineFunction vs. BSplineSurface

Why are those surfaces different? ...
1
vote
0answers
147 views

How to write my own interpolation method [duplicate]

I was comparing results of spline interpolation in Mathematica and C++/gsl-library Results of interpolation are different if I use ...
23
votes
4answers
914 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 ...
1
vote
2answers
1k views

Cubic Splines Functions

I have this set of three data points and want the natural cubic spline functions for them: dat = {{-.0247500, .5}, {.3349375, -.25}, {1.101000, 0}}; I tried: ...
5
votes
2answers
510 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 ...
7
votes
1answer
170 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 ...
19
votes
5answers
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: ...
1
vote
1answer
268 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. ...
15
votes
5answers
564 views

BSplineFunction derivatives wrong if using weights?

Bug introduced in 7.0 and persisting through 10.4 In my work, I make heavy use of non-uniform rational B-spline (NURBS) functions, defined using the function ...
15
votes
3answers
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 ...
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 ...
1
vote
2answers
408 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? ...
13
votes
2answers
168 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 ...
14
votes
2answers
185 views

Color Blend in BezierCurve

How can I color a BezierCurve from Red into Green just as ...
8
votes
2answers
571 views
0
votes
1answer
463 views

Exporting BSplineFunction 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 ...
4
votes
3answers
1k 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
345 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
415 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
474 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
460 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
916 views

Parametric differentiable interpolation of a 2D data set

I have a set of data ...
6
votes
2answers
409 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
205 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
858 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
552 views

BSplineCurve Interpolation

Can I get interpolated values from this B-spline, (shown in red)? ...
26
votes
2answers
3k 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 ...
12
votes
1answer
2k 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
271 views

SplineDegree->1 does not work with BezierFunction?

This works (SplineDegree -> 2) ...