https://preview.redd.it/4d383q0k8ia81.png?width=696&format=png&auto=webp&s=6abc388dc86f0caca804bfa8dd7ba3cfa2c7aa50
I'm in the following situation:
i took a simple image containing one object
i traced the objects boundary using the moore traacing algo
now i have the coordinates of all the boundary points
my goal is the impliment the curvature scale space algorithm and for that i need to have the parametric equation of the shape curve.
i will really appreciate any kind of help, thanks in advance.
hey guys! how do you tell whether the graphed circle is counter clockwise or clockwise without using a graphic calculator?
for example x=cos(t), y=sin(t) is clockwise yet x=cos(pi-t), y=sin(pi-t) is counter clockwise. (both ranges are 0<=t<=pi)
i’m completely lost right now :( will appreciate the help!! thank you in advance <3
Find the equations of the tangents to the curve x=6t^2+2,y=4t^3+2 that passes through the point (8,6)
y=(smaller slope)
y=(larger slope)
I just need help finding the equation for the smaller slope.
I can't understand why r=cost and r=sint form a circle. I tried to convert those to cartesian coordinate which I already know I should use (x^2)+(y^2)=r^2 and tant=y/x. But it seems like a dead end after I wrote (x^2)+(y^2)=cos^2(t) or sin^2(t) Any hints...?
Is there a general method to convert implicit equations into parametric equations?
For example, here is a 3D heart shape implicit equation, How to get its parametric equation? so that this surface can be displayed in GGB?
"(x^2 + 9/4 y^2 + z^2 - 1)^3 - x^2 z^3 - 9/80 y^2 z^3 = 0"
Very much appreciated!
https://preview.redd.it/ecguhrnuq8g71.png?width=1429&format=png&auto=webp&s=28cbc62026c6b2b922acb013aa141d7edbfee0f4
Not exactly a controls questions. But is more on the mathematics side which then heads towards kalman filters.
This is related to representing lane lines mathematically.
I have equations available to represent the lane line (x,y) points parameterized on Length (L)
Parametric equation. L = Length of the lane line from 0 to some value l
The lane line are also represented as clothoids as explained here in section II B starting part till equation (3)
http://www.cs.cmu.edu/~youngwoo/doc/fusion-14-ywseo.pdf
https://preview.redd.it/wlilo2ii4df71.png?width=722&format=png&auto=webp&s=8e257723b6432515b42d1c436d3a87929c8158c5
How would I go about converting the parametric equation to the cartesian type x = f(y) clothoid?
My first thought was, L in the 1st parametric equation can be substituted as a function of heading angle(beta) and y. Does that make sense?
Hello,
I am working on an engineering design project and wanted to create a spreadsheet to graph a cycloidal rotor so I can see its shape before modelling on SolidWorks. The rotor is governed by the equation below. In this case, theta is the variable. I have made a column of integers from 1 to 360 (though I can make more increments if required). I also have cells for each of the variables. How would I proceed in parametrically graphing the equations X and Y?
Excel version: 2019
https://preview.redd.it/r5mdnb5ttsg71.png?width=1782&format=png&auto=webp&s=4626a7c4cd458401337ab3600e9c1040692ec35c
hi, how do i get the cartesian equation in terms of y from these parametric equations?
x(t) = t^2 - 1
y(t) = t + 1
i've tried eliminating the parameter but...
x = t^2 - 2
x + 2 = t^2
t = ±sqrt(x + 2)
which sign is the real solution for t?
EDIT: Grammar.
Any pointers or lesson links would be extremely helpful, trying to catch up on missed work and I'm struggling.
Given a particle moves in the xy plane when t≥0. x(t)= sqrt(2t+1) and dy/dx= (2t+1)^(3/2)
a. Find y'(t)
(I got y'(t)= 2t+1 though I doubt I did this question correctly)
I first found x'(t), then substituted it into dy/dt/dx/dt and I solved for dy/dt..
b. Find y(t) given that y(1)=4
(I got y(t)= (2t+1)^(3/2) (t-1) +4, doubt I did this question correctly either)
I wasn't sure how to do this problem so I just plugged it into the point-slope formula. y(t)-4=dy/dx(t-1)
c. Determine the concavity of the particles motion through the xy plane
(I solved for d^2y/dx^2 and got 6t+3 and wrote that because it is positive for all t≥0, the particle's motion is concave up through the xy plane)
https://math.stackexchange.com/questions/461547/whats-the-equation-of-helix-surface
I don't understand the last steps in the last answer in this link... How do we go from the binormal, normal and tangent vectors to the surface area equation?
Thanks!
my guy Childs wrote this test with the intention of anally pounding your GPA
View the full paper presentation here which includes a time-stamped outline:
Numerical solvers for Partial Differential Equations are notoriously slow. They need to evolve their state by tiny steps in order to stay accurate, and they need to repeat this for each new problem. Neural Fourier Operators, the architecture proposed in this paper, can evolve a PDE in time by a single forward pass, and do so for an entire family of PDEs, as long as the training set covers them well. By performing crucial operations only in Fourier Space, this new architecture is also independent of the discretization or sampling of the underlying signal and has the potential to speed up many scientific applications.
Abstract:
The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For partial differential equations (PDEs), neural operators directly learn the mapping from any functional parametric dependence to the solution. Thus, they learn an entire family of PDEs, in contrast to classical methods which solve one instance of the equation. In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on Burgers' equation, Darcy flow, and the Navier-Stokes equation (including the turbulent regime). Our Fourier neural operator shows state-of-the-art performance compared to existing neural network methodologies and it is up to three orders of magnitude faster compared to traditional PDE solvers.
Authors: Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar
why are there an infinite number of ways to choose a set of parametric equations for a curve defined as a rectangular equation
This is related to representing lane lines mathematically.
I have equations available to represent the lane line (x,y) points parameterized on Length (L)
Parametric equation. L = Length of the lane line from 0 to some value l
The lane line are also represented as clothoids as explained here in section II B starting part till equation (3)
http://www.cs.cmu.edu/~youngwoo/doc/fusion-14-ywseo.pdf
https://preview.redd.it/4kfg1frb3df71.png?width=722&format=png&auto=webp&s=7ff2ba017f01d643defe14dfd845a9e7d156c0d1
How would I go about converting the parametric equation to the cartesian type x = f(y) clothoid?
My first thought was, L in the 1st parametric equation can be substituted as a function of heading angle(beta) and y. Does that make sense?
