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Questions tagged [b-spline]

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Grid Data Interpolation

What are the most sophisticated methods for interpolating a scalar field say Electric or Magnetic Field on a 3-D grid? I have scalar data on a meshgrid with equal spacing. I would like to use an ...
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Cardinal B-Splines with derivative information

Have Schoenberg's cardinal B-splines been extended to accept derivative information at each knot, similar to how Lagrange interpolation can be improved by Hermite interpolation?
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B-splines least squares with equality constraints

Can someone recommend the best way to solve a least squares fitting problem with B-splines, with additional equality constraints? I want to solve: $$ \min_x || b - A x ||^2, \textrm{subject to: } C x =...
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1answer
157 views

Integrating/Implementing NURBS-related calculations

Recently, I started to develop some codes that use NURBS (general things I intend to use/already using: spline generation, interpolation, grids, isolines, closest-point find, and many others), both ...
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Are planar 2nd order NURBS curve segments exactly the segments of conic sections?

I think it is well known that 2nd order NURBS curve can describe any segment of a conic section. Such a segment has 7 degrees of freedom, take an ellipse arc for example: the ellipse itself has 5 ...
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1answer
138 views

B-Splines Matlab Package

I'm looking for a good Matlab package/library for B-Splines approximation. Ideally, it would take knots $t_1, \ldots , t_n$, and data points $g(t_1),\ldots , g(t_n)$, and Produce $$Vg :\,= \sum\...
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Find B-spline coefficients from values on collocation points

The context of my question is how to compute high order derivates on direct numerical simulation of turbulent channel flow. It is of particular interest for fluid dynamics and turbulence research. I ...
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1answer
79 views

Is a B-spline curve uniquely defined by one set of coefficients?

Let $C(u)$ be a B-spline curve depending on the parameter $u\in[0,1]$ $C(u) = \sum_{i=0}^n c_i \, B_i(u)$ with $n+1$ coefficients $\{c_i\}$ and B-spline basis functions $\{B_i(u)\}$. Edited based ...
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2answers
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Parametrized spline - oscilating second derivative

I am using a parametrized natural spline to interpolate 2D curves. For example something like this: Where I parametrize both the x and the y coordinate with a parameter that increases by one between ...
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C1 continuous spline on regular 2D-grid with quadratic 1D cuts

I want some scalar spline function defined on regular 2D grid $F(x,y)$ with continuous first derivative which is easy to intersect with arbitrary ray/line ${\vec l}(t) = (c_x t,c_y t,c_z t)$. ...
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NURBS-based isogeometric analysis using Nutils [closed]

How can one construct non-uniform rational B-splines (NURBS) in Nutils, and use them for NURBS-based isogeometric analysis?
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End conditions on cubic splines interpolation

I'm currently working on cubic splines interpolation. My question has to do with the end conditions. Instead of using natural or clamped cubic splines, I am asked to use the following condition : $S_{...
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How to interpolate a set of points with a continuous closed B-spline curve?

I have been learining the NURBS theory by the classical textbook "The NURBS Book" this year. In the chapter 9, the author introduced the method of non-rational B-spline curve interpolation with a open ...
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3answers
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Is my Restricted (Natural) Cubic Spline equation wrong?

I am trying to fit a restricted cubic spline (natural cubic spline) with 4 knots to toy data, attempting to follow Hastie, Tibshirani, Friedman 2nd ed. 5.2.1 p.144-146, Eqs 5.4 and 5.5. Data: Is ...
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interpolate the circle going through three points using splines

It is known from Geometry that any 3 points determine a circle. This is the problem of Appolonius Programming solutions try to approximate using Bezier curves. Can you not draw conics as Bezier ...
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1answer
255 views

Piegl's algorithm in calculating B-spline basis function

The B-spline basis function is given by one recursive formula. However,I hope to obtain popular expression: a0x^n + a1x^(n-1) + ... + an. From the answer How to build a recursive spline function in C++...
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1answer
209 views

How to connect two fitted B-spline curve?

I use B-spline curve fitting to obtain one smooth curve. If I obtain two smooth B-spline , how can I connect then smoothly. For example, I have 59 points((x0,y0,z0),...,(x58, y58, z58)) and I have two ...
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1answer
303 views

Number of control points for B-spline curve

I am trying to use B spline curve fitting. The order of B-spline curve is 4. When I have many control points, it works well. However if the number of control points is small such as two, my program ...
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1answer
175 views

What spline functions are used in Section 13.9 of “Numerical Recipes in C”?

I asked a similar question on MathSE but with more added fluff, but didn't really get any straight answers, so I figured I'd ask here. Computing Fourier coefficients of a function using the FFT is ...
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0answers
163 views

NURBS surface fitting for a closed region on mesh

I'm developing a tool that allows users to select a closed boundary (a polygon) on the triangle mesh and then from this boundary, generate a NURBS surface fitting the original mesh surface. My idea ...
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0answers
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How should I choose the knot sequence when using B-splines as a basis for solving a PDE?

I'm looking to solve the Schrödinger equation with a basis made of a tensor product of basis splines. A number of papers describe calculations made with a program designed this way, but they never ...
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2answers
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SciPy interpolation with Univariate Splines

I have coded a routine for interpolation with B-splines, only to discover later that this functionality is already included in Python's SciPy. However, I do not understand one parameter in the SciPy ...
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3answers
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How to build a recursive spline function in C++

At the moment I am working on a differential equation solving method called basis-spline collocation. What I am having trouble with is building a method to build an arbitrary order spline, with the ...