# Tagged Questions

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

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### Problem with BSplineCurve 3D

I have a problem using the function BSplineCurve [ ] . I have to represent a line passing through about 3000 points in 3D. I managed to plot the points separately, but when I use the 3D BSplineCurve []...
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### How to integrate a Bézier function?

I have: points = {{0, 100}, {250, 0}, {0, 300}, {500, 500}} And I want to know the area below the curve, so I came to: ...
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### Move a point along a curve

I am trying to implement the de Casteljau algorithm to trace a point along a Bézier curve. I already have the Bézier curve in place given by the control points ...
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### Filling between two B-spline curves

I am trying to fill the space between two curves (curve1 and curve2) I generated since long but unable to do so. Can some one help on this please. The following is the code snippet. ...
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### Extracting control points from BezierFunction

given a Bézier surface, is there a simple way to express $g_{12}$ (from the First fundamental form) again in Bézier form? More precisely, I have control points and a Bézier function $f$: ...
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### 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, ...
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### 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 ...
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### 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....
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### 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 matrix(ls,ws,lx,bb,...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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: ...
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### 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: <...
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### Different results with BSplineSurface and BSplineFunction [closed]

There seems to be some differences when plotting a surface with BSplineSurface and with BSplineFunction. ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### Joining ordered set of points with splines in spiral

I have a collection of points ...
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 ...