# Questions tagged [b-spline]

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### B-Spline basis on a 3D mesh

I need to interpolate some (sparse) data scattered on a 3D manifold mesh. In other words, I have a scattered interpolation problem where the input values are defined for some vertices of the mesh. ...
• 301
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### BSplines from scipy not defined on whole range of the knots

I am looking at the construction of BSplines out of curiosity. I created a small code that uses scipy.interpolate.BSpline to create basic splines. I get the following basic splines for order 0, 1 and ...
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1 vote
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### in Finite Element, which approximation requires less number of unknowns: B-splines vs Shape functions vs Spectral Elements

In Finite Element Analysis, one requires to approximate the solution in terms of basis functions. My questions is, which method in general is better? by 'better', I mean which involves less number of ...
1 vote
68 views

### shape functions of interpolating a piecewise polynomial with continuous 0-th and 1-st derivatives

shape functions are the basis functions that interpolate a function in a subdomain using polynomials. linear interpolation is probably the most convenient approach which results in so-called "...
2k views

### Fitting a monotonically increasing spline function

I want to fit a monotonically increasing smooth spline function for a dataset Code: ...
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133 views

1 vote
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### Spline regularization

I am fitting some B-splines to data, but the data has a "gap" region where the spline is less constrained by the data. I want to devise a regularization scheme to help prevent the spline from ...
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1 vote
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### Accelerating Conjugate Gradients fitting for small localized kernel (like cubic B-spline)

Question: Is there some pre-conditioner for Conjugate-Gradient (CG) cheap enough, that it is worth using even if my operator is very local (i.e. already has a low number of non-zero elements), as it ...
1 vote
99 views

### 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 ...
54 views

### 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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1 vote
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1 vote
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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 ...
• 121
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### 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 ...
• 193
834 views

### 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 ...
• 301
1 vote
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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 ${\vec l}(t) = (c_x t,c_y t,c_z t)$. ...
1 vote
114 views

### 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?
1 vote
235 views

### 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 ...
• 71
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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 ...
139 views

### 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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1 vote
360 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++...
• 203
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### 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 ...
• 203
1k 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 ...
• 203
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### 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 ...
208 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 ...
• 121
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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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### 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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