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

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6
votes
0answers
61 views

Artefact at joints within BSplineCurve of low Opacity

I want to eliminate the dots of higher opacity that occur at the joints within a BSplineCurve of low opacity. Small rectangles of greater opacity, shown below, ...
11
votes
4answers
426 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 ...
5
votes
1answer
54 views

How to use BSplineFunction for calculating derivative

I have a set of data like the following data = {{x1,y1},{x2,y2},{x3,y3},......} Now I use ...
2
votes
1answer
182 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 ...
3
votes
2answers
263 views

Understanding polyharmonic splines

Rahul Narain and J.M. gives implementation of the thin plate polyharmonic splines in this post. Rahul Narain's method is clear. J.M.'s is convenient to reuse. But J.M. used too many ...
4
votes
1answer
67 views

More efficient method to implement knots instertion algorithm

Knots instertion algorithm of B-spline About the definition of B-spline, please see here. Suppose $\overline u \in [u_{k},u_{k+1})$initially has multiplicity $s$, and suppose it is to be inserted ...
3
votes
1answer
92 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 ...
1
vote
2answers
74 views

Creating B-splines using a For Loop

I'm very new to Mathematica (as will make itself clear with this question) and I'm trying to create a program that makes b-splines to fit n points. I'm not quite sure how to reference the i-th point ...
8
votes
1answer
157 views

How to discretize a BezierCurve?

Bug introduced in version 10.0 and persisting through 10.3 DiscretizeGraphics is new in 10.0. I need to create a discretized region from a ...
15
votes
2answers
447 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. ...
4
votes
1answer
125 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 ...
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
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: ...
1
vote
1answer
51 views

Different results with BSplineSurface and BSplineFunction [closed]

There seems to be some differences when plotting a surface with BSplineSurface and with BSplineFunction. ...
2
votes
3answers
162 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 ...
22
votes
4answers
823 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 ...
4
votes
1answer
90 views

How to get coordinate from spline interpolation

Hi, I would like to find 10 coordinates between each points of this spline interpolation. I have done some research, but cannot find an appropriate answer. Any help will be appreciated. ...
3
votes
1answer
179 views

Failed to create a special random-disturbed initial condition for partial differential equation [closed]

I try to use BSplineFunction to creat a initial condition for NDSolve which has periodic boundary condition, that is realized by ...
0
votes
0answers
39 views

How do I change a 3d bspline curve to a polygon based graphic? [duplicate]

I have a graphics image generated with bsplines: Graphics3D[Tube[BSplineCurve[pts], 2]] I want to export this to a .stl file. To do so I know I need to modify ...
12
votes
5answers
550 views
7
votes
1answer
97 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 ...
0
votes
0answers
41 views

Working with Piecewise functions - Hexsplines

I'm trying to use the convolution definition of hexsplines, that is, a hexspline is the convolution of the indicator function of a hexagon (of sidelength 1 and centre $(0,0)$ ) with itself. I'm ...
6
votes
2answers
190 views

What's the difference between Interpolation[pts, Method -> Spline] and BSplineCurve?

Last month, I answered a question about spline interpolation,please see here Now I do the following operations ...
11
votes
1answer
240 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 ...
2
votes
1answer
181 views

Interpolation of a NURBS curve

Known that NQ=P where N is the Bspline basis function, Q is the control point that we wish to locate, P is the data points given ( the curve must pass through it) is there any way to modify the "N" ...
1
vote
2answers
358 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
160 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 ...
0
votes
0answers
40 views

3D interpolation [duplicate]

I have four column data with first 3 column denoting x,y,z and fourth column energy. x variable is actually angle. Now I want to interpolate over all three indepdent variable (x,y.z) with ...
2
votes
1answer
172 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: ...
2
votes
1answer
68 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: ...
2
votes
1answer
117 views

How to find if x-y point falls within a closed BSplineCurve

Here's a simple Manipulate with a closed BSplineCurve, and a Locator. ...
14
votes
2answers
184 views

Color Blend in BezierCurve

How can I color a BezierCurve from Red into Green just as ...
11
votes
1answer
252 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 ...
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 ...
7
votes
2answers
399 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. ...
4
votes
3answers
444 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 ...
7
votes
0answers
92 views

Color Snapping When Using VertexColors with a Tube with BSplineCurve as an Argument

I think I've identified a bug in how VertexColors are treated when rendering a Tube object where the underlying data is a ...
6
votes
2answers
181 views

How do I get my spline based arrows to have rounded ends?

I would like to change the how the ends of the spline arrows in my figure are rendered to be "rounded", but ...
1
vote
1answer
79 views

Bspline weights

I change weigts of my points, but nothing has changed. What should i do to solve this problem? ...
1
vote
1answer
81 views

BSplineSurface problem

Why does the result of this function is straight line.If problem is in the order of my points, what order is correct? ...
4
votes
1answer
199 views

Find GeometricTransform from 3D object external surfaces to a positional point cloud data

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 ...
2
votes
1answer
230 views

What extrapolation method does Interpolation use by default? [closed]

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 ...
4
votes
2answers
416 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: ...
10
votes
3answers
219 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)= ...
6
votes
2answers
363 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
847 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 ...
2
votes
0answers
176 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
128 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: ...