All Questions
Tagged with cubics interpolation
25
questions
2
votes
0
answers
70
views
Finding rational coefficients of a cubic polynomial that fits 4 data points that have been floored to an integer
I have 4 data points:
(204, 5422892)
(205, 5722486)
(207, 6343357)
(213, 8386502)
I have information that these data points were generated with a cubic polynomial
$y = ax ^ 3 + bx ^ 2 + cx + d$
with ...
- 119
0
votes
0
answers
52
views
Numerical Analysis - natural cubic spline and clamped cubin spline
a question from first exam period (A).
True or false ( it is false, but I want to understand ).
Given the following intersection points $x_0, x_1,...,x_n$ (interpolation nodes ) and the values of ...
- 179
0
votes
1
answer
104
views
How to get the coefficients in a parametric cubic function
Let's say I have 4 points with x and y coordinates. And I want to determine the parametric cubic function:
$x(t) = a_x t^3 + b_x t^2 + c_x t^3 + d_x$ and $y(t) = a_y t^3 + b_y t^2 + c_y t^3 + d_y$
So, ...
1
vote
1
answer
88
views
Solve for x given formula for cubic interpolation
Given formula for a linear interpolation, I can solve for $x$ as follows:
\begin{align}
y = a(1-x)+bx\\
y = a+x(b-a)\\
x = \frac{y-a}{b-a}
\end{align}
How do I solve for $x$ given formula for cubic ...
- 647
2
votes
0
answers
306
views
4-Point Cubic Spline Solution?
Consider a 4-point natural spline. I want to use the spline for interpolation between two points $y_1,y_2$, when having access to four equidistant points (w.r.t $x$ axis).
Is the solution for the ...
- 2,706
0
votes
1
answer
227
views
Interpolation of a function at 4 points
Assume that the cubic polynomial a + bx + cx^2 + dx^3 interpolates a function f(x) at the four points (0,2), (1,-1), (2,1), (3,3). I'm trying to do a question that asks me to write down a system of ...
- 3
1
vote
1
answer
528
views
cubic Hermite interpolation
Professor gave us this little bastard of a question and I'm at a complete loss about what to do. Some help or hints would be immensely appreciated, translated to the best of my abilities.
Let $x_0=0$,...
- 13
1
vote
1
answer
660
views
Converting to cartesian equation from parametric equation for a Cubic curve
Considering the Cartesian form of the cubic equation:
$$y(x)= ax^3 + bx^2 + cx + d $$
And considering the parametric equation of this above equation:
$$x(t)=et^3 + ft^2 + gt + h \\ y(t)=pt^3 + qt^2 +...
- 11
2
votes
1
answer
534
views
Converting polynomial interpolations to Bézier splines
The search
I needed to convert some quadratic interpolation plots (from PiCTeX) to
quadratic Bézier splines (for SVG). I saw this question asked several times
elsewhere but never with the kind of ...
5
votes
3
answers
2k
views
Cubic Spline Interpolation - Solve X from Y
I'm a programmer, not a mathematician, but I've got a real-world problem I'm trying to solve that's out of my league, and my Google skills so far have failed me.
I have an analog waveform that's been ...
- 151
0
votes
1
answer
785
views
Polynomial interpolation with data points from derivative of original polynomial
Question:
What is a polynomial g(x) no more than degree 3 (including 3) s.t.
$$g(0) = 1, g(1) = 0, g′(0) = 0, g′(−1) = −1$$
Solution is: $$g(x) = −\frac3 5x^3 − \frac2 5x^2 + 1$$
My attempt: I was ...
- 1,913
4
votes
1
answer
906
views
Is Monotonicity-preserving cubic spline interpolation continuous to the second derivative?
I need to use cubic splines to interpolate between data points (sets of x-y-coordinate pairs). The problem is that there is the well-known "overhooting" of the spline that occurs every now and then (...
1
vote
1
answer
765
views
Natural Spline - Determining Coefficient
A practice problem (not homework/assignment).
Given a natural spline
S(x) where
a1 + 25x + 9x^2 + x^3 where x is [-3, -1]
26 + a2x + a3x^2 - x^3 where x is [-1, 0]
26 + 19x + a4x^2 + a5x^3 where ...
- 279
4
votes
1
answer
1k
views
Unique Cubic Polynomial Hermite Interpolation.
A practice problem from my textbook (not homework/assignment).
Show that there is a unique polynomial $P_{3}(x)$ where
$p_{3}(x_{0}) = f(x_{0}),\space
p_{3}(x_{2}) = f(x_{2}),
p'_{3}(x_{1}) = f'(...
- 279
0
votes
1
answer
112
views
Why this parametric function for an explicit cubic form?
I'm trying to understand a statement here. It states that the parametrisation of a cubic function is:
$$\begin{align}
x(t)&=a_xt^3+b_xt^2+c_xt+d_x\\
y(t)&=a_yt^3+b_yt^2+c_yt+d_y\\
\end{align}$$...
- 117