Go Back   Physics Help Forum > College/University Physics Help > General Physics

General Physics General Physics Help Forum

Reply
 
LinkBack Thread Tools Display Modes
Old Nov 29th 2012, 04:34 AM   #1
Junior Member
 
Join Date: Nov 2012
Posts: 1
Deriving the equation of points for exact fitting and shape analysis

Hello,

I would like to ask you some questions.

1) I've a closed curve (for example an ellipse, which may represent the contour of an object) represented by the set of its (known) points. I need to find the equation of that curve to pass through all and every point (exact fit). I think that to do this I need a polynomial whose grade is equal to the number of points less 1.

Something like this:

a0+a1 x1+a2 x1^2+ ...+ an x1^n = y1
a0+a2 x2+a2 x2^2+ ...+ an x2^n = y2
...
a0+a2 xn+a2 xn^2+ ...+ an xn^n = yn

This argument is right? Do you have suggestions (or anything else relevant) for me in this regard for which is the best way to solve my problem? This equation can be made in parametric form?

2) After I got the exact equation of this curve. Suppose we have a set of curves very similar to each other (represented by their equation), I would like to find the equation that represents the shape which best approaches to all previous curves, a sort of average curve created from those previously acquired.
Do you know if this thing can be done and how? What is the best way (most efficient and / or mathematically more correct) to do this?

Best Regards,

Giusy
odiosetta is offline   Reply With Quote
Old Nov 29th 2012, 06:18 AM   #2
Physics Team
 
ChipB's Avatar
 
Join Date: Jun 2010
Location: Morristown, NJ USA
Posts: 2,352
See: http://www.askmehelpdesk.com/mathema...is-719761.html
ChipB is offline   Reply With Quote
Reply

  Physics Help Forum > College/University Physics Help > General Physics

Tags
analysis, deriving, equation, exact, fitting, points, shape



Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
III newton ball shape and cubic shape !? MMM Advanced Mechanics 28 Mar 15th 2015 07:38 AM
Deriving an equation from 4 simple equations blaZkowicZ Advanced Mechanics 1 Oct 25th 2009 09:41 PM
Deriving the drag equation? revolution2000 Kinematics and Dynamics 2 Apr 5th 2009 09:02 AM
Deriving Equations zobe2500 Kinematics and Dynamics 2 Feb 13th 2009 06:44 AM


Facebook Twitter Google+ RSS Feed