Questions tagged [spline]
A smooth piecewise-defined curve formed by joining segments together, end-to-end. The segments are usually described by polynomial or rational functions. Splines are typically used for approximation or data fitting.
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What is a natural cubic "B-spline"?
I recently learned that natural cubic splines are strictly distinct from natural cubic B-splines while studying spline methods. It appears that natural cubic B-splines are obtained by adding ...
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Finding Basis for specific Spline Space
Let $S = \{s \in S: s'(a) = s'(b) = 0 \}$ be the spline space that holds all cubic splines with derivate at startpoint (a) and endpoint (b) =0. I want to find a basis for this vector space. I looked ...
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Motion with parabolic blends problem. Seems easy but feels impossible!
I'm trying to calculate multi segment trajectories between points in a plane where the trajectory follows a linear function, but in order to keep continuous speed and position parabolic blends are ...
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Optimal knot placement for approximating this function with B-spline.
I have the following data points, which all lie along a smooth, unknown, function (it looks sigmoidal but might not be):
I want to approximate it rather accurately with B-splines, either quadratic or ...
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Calculating an Inverse Matrix of a Matrix with variables
I am trying to understand a part of an article regarding quaternions spline interpolation, where the situation folded into the equation:
$$
(\vec{a}\cdot\hat{e})\hat{e}+\frac{\sin\Delta\theta}{\Delta\...
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truncated power basis elements expressed as linear combination of bsplines
Given the truncated power series basis, e.g. the following functions: $1, x, x^2, ((x-\eta_0)^{+})^{2}, ((x-\eta_2)^+)^2, \dots ((x-\eta_{l+1})^+)^2$ there is a set of bspline-functions $s_1, \dots $ ...
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Reducing the number of natural cubic spline interpolation points
Say we have cubic curve $\vec{C}(t)_ = (C_x(t), C_y(t), C_z(t))$ which approximates some parametric function $\vec{F}(t)$ within error less than $\epsilon$. The cubic curve is $C^2$ continuous and is ...
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Why is the middle segment of a 4 points cubic spline not matching a 100 points cubic spline?
Let's say I have x0, x1, ..., x99 and y0, y1, ..., y99
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How to make arithmetic function continuous?
Suppose that we have an arithmetic function $f(x)$ defined as follows:
What are the methods in the literature that will make this function continuous and differentiable? However, it should be noted ...
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Quantifying the "curviness" of a spline
I'm developing an optimization problem that requires me to quantify the "curviness" of a spline. The spline is defined in a software library, and the only input to generate a spline with ...
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Singular Matrix with Closed B-spline Interpolation when Degree and Number of Data Points are Both Even
I have written an algorithm to perform closed B-spline interpolation on a set of $N$ data points for a given degree $p$. I first generate a cyclic, uniform knot vector, and also use uniform ...
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B-Spline with increasing knot distance
I'm trying to approximate a function $f(x)$ on $[0, M]$ that, in some sense, begins to rapidly "vary slower" as $x$ increases, i.e. its modulus of continuity (or the variation of its ...
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cubic spline interpolation - spline interval
The k function values are to be interpolated by a piecewise cubic spline. The k-1 cubic polynomials are defined on the intervals [xi,xi+1],i ∈ {1,...,k-1}. Indicate which of the following statements ...
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Defining a Quad Spherical Cube Tile as a Uniform NURBS Surface?
I am trying to create NURBS surface that perfectly fits one face of a Quadrilateralized Spherical Cube (QSC) [also called a Cobb sphere in some contexts, I believe]. I have seen some visualizations of ...
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Reparametrization of rational Bézier curve
I am trying to solve the following task
Using rational Bézier curve find the control points and weights of one sixth of a circle $c_1$, such that $$c_1(0)=\{3,0\},c_1(1)=\{\frac{3}{2},\frac{3\sqrt{3}}{...
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