Questions tagged [spline]

Question 1

If we know the value of a function $f$ at a set of points (usually regularly spaced, but that is not necessary) $x_1, x_2, \dots, x_k$, we can approximate the integral $\int_{x_1}^{x_k} f(x) dx$ via ...

Question 2

I am trying to proof this by induction Proposition (Boundary values under clamped knots): Let $\{t_i\}_{i=1}^{m=n+k}$ be a clamped knot sequence of order $k$ on the interval $[a,b]$, that is, $$ t_1 = ...

Question 3

I am inquiring about a particular result shown in section 2.1 of Grace Wahba's book (pages 23-24), Spline models for observational data. The setup is as follows. We consider the data model $$y_i = f\...

Question 4

Let $I=[0,1]$ be the unit interval, and $f:I\to\mathbb R$ be a $C^2$ function. For $n\ge1$, denote by $PL(n)$ the set of continuous, piecewise linear functions with $n$ pieces defined on $I$. It is a ...

Question 5

Let be $[a,b]$ an interval and $\Delta$ a partition of $[a,b]$ where $a=\xi_0<\xi_1<\dotsc<\xi_n=b$ and $I_j:=(\xi_{j-1},\xi_j)$. Further, let be $l,m\in\mathbb{N}$. We define the space of ...

Question 6

Background: I am resizing image dimensions to powers of two for practical purposes in an image compression scheme. Then I need to switch back to the previous size. For example an image of dimensions ...

Question 7

I have a set of data consisting of water levels [$m$] and volumes [$m^3$] that I want to fit a function to while fulfilling some constraints over the defined region of volumes. An example of a dataset ...

Question 8

Book on archive.org: https://archive.org/details/practicalguideto0000debo In Carl de Boor's A Practical Guide to Splines (2001/revised edition), page 89, definition of the BBform, corresponding to B-...

Question 9

In Carl de Boor's A Practical Guide to Splines (2001), page 90, proof for the B-spline property (i): (archive.org: https://archive.org/details/practicalguideto0000debo) Apply Leibniz' formula I(iv) ...

Question 10

I am interested in solving the following problem. Let's say we have a quintic bezier curve p(t) = {p0, p1, p2, p3, p4, p5}. I also have some curvature bound Kc. How can I find that the maximum ...

Question 11

Let $s\in \left(0, 1\right)$, and consider the task of finding the 'nicest-possible' function $f$ such that $f(0) = 0, f^\prime (0) = s$, and $f(1) = 1, f^\prime (1) = 0$, where 'niceness' is framed ...

Question 12

I'm a newer to NURBS curves and surfaces stuff. Here is my (naive) question regarding related definitions, and I just want to check my understandings: Is a parametric curve $\gamma(t)=(x(t),y(t),z(t))...

Question 13

I am looking for a formula to make a curve that could mimic loosened thread (from P to Q in the above figure) in 2D. The thread need not be slanted. Wrt x axis I can plot the loosened thread. Which ...

Question 14

I have an equation that converts three points $p_0,p_1,p_2$ into a parametric circle where $o$ is the center of the circle and $R$ is the radius. $$ f(t)=(o_x+Rcos(t),o_y+Rsin(t)) $$ this part works ...

Question 15

I was reading through a section in the textbook ESL2 Sec.5.2 (P.144) under Basis Expansions and Regularization when I came across this line: "More generally, an order-$M$ spline with knots $\xi_j$...

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Questions tagged [spline]

Is it possible to improve on the trapezoidal rule if we have derivative data available?

Boundary values for b splines under clamped knots

Penalized spline on the circle

Faster approximation for piecewise linear functions in $L^2(\rho)$

Dimension of polynomial spline space

How to derive analytic formula or efficient computational scheme for function underlying pseudoinverse to linear interpolation matrix?

Fit nonlinear, increasing and concave function

Carl de Boor's "A Practical Guide to Splines" (2001), page 89, BBform definition

Carl de Boor's "A Practical Guide to Splines" (2001), page 90, particular product

Maximum curvature of a Quintic Bezier curve

Finding an optimal interpolation subject to some boundary constraints

Is a parametric polynomial curve always a Bézier curve?

What formula could mimic loosened thread

Draw line along parametric circle intersecting points in order

Orders and Degrees - Piecewise Polynomial functions

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