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Full Discussion: Returns points of an ellipse
Top Forums Shell Programming and Scripting Returns points of an ellipse Post 302786381 by DGPickett on Wednesday 27th of March 2013 10:49:28 AM
Old 03-27-2013
Not an ellipsoidal solid (an ellipse spun on the line through its axes), then, just an ellipse in a plane.

I guess an ellipse reduced to a unit ellipse is a circle, so not so much scaling as rotation and translation. Do you start with just a few points? Takes three to set the plane, which sets the rotation need, and then I expect a couple more to fix the ellipse in position, size and orientation. Having the axes is so much more concise than having random edge points. Obviously, some points might be redundant in fixing the ellipse, such as 4 points of a rectangle, which the solution must be robust in detecting.

The characteristic of an ellipse is that the reflection angles of rays from one axis hit the other, but trig is processing expensive and not friendly for gauss-jordan reduction. More friendly is that all points have the same sum of distances from the two axes, and are in the surface of a cone. Three-D distance is not friendly, but after rotation it is 2d. The 2d distance calc is polynomial, but with the right scaling, separately for x and y, and translation, the first order terms might be zeroed, so the squares become substitute terms in the GJ. It is reminiscent of deriving the binomial theorem, if you recall back then!

There are colections of solutions for most geometric problems, but doing it yourself is so much nicer. I recall regenerating the binomial theorem while taking a math SAT (got 800), but since then for some reason it has stuck! I never liked the trig in calculus, as there were so many identities to memorize, but most Integral Calculus tests were open book.
Last edited by DGPickett; 03-27-2013 at 11:55 AM..
 

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LEARN ABOUT DEBIAN

ellipsecomp

EllipseComp(3U) 					    InterViews Reference Manual 					   EllipseComp(3U)

NAME

       EllipseComp, EllipseView, PSEllipse - ellipse component subject, view, and PostScript external representation

SYNOPSIS

       #include <Unidraw/Components/ellipse.h>

DESCRIPTION

       EllipseComp  is	a  GraphicComp	that  defines an ellipse.  It uses an Ellipse graphic to store its graphical attributes.  EllipseView is a
       GraphicView for displaying the ellipse.	PSEllipse is a PostScriptView that externalizes the subject's information in PostScript form.

ELLIPSECOMP PUBLIC OPERATIONS

       EllipseComp(SF_Ellipse* = nil)
	      The constructor takes an optional stroked-filled ellipse that defines the attributes of the ellipse.

       SF_Ellipse* GetEllipse()
	      Return the SF_Ellipse graphic that defines the ellipse's attributes.  GetEllipse is simply a more specific form  of  the	GetGraphic
	      operation.

ELLIPSEVIEW PUBLIC OPERATIONS

       EllipseView(EllipseComp* = nil)
	      Create an EllipseView, optionally supplying the subject.

       virtual void Interpret(Command*)
	      EllipseView interprets AlignToGridCmd to align its center to the grid.

       virtual Manipulator* CreateManipulator(
	  Viewer*, Event&, Transformer*, Tool*
       )

       virtual void InterpretManipulator(Manipulator*)
	      EllipseView redefines its response to manipulation with a GraphicCompTool.  The user clicks to specify the center of the ellipse and
	      then drags to vary its axes.  The center and the axes will be constrained by gravity, if any.

       EllipseComp* GetEllipseComp()
	      Return the subject.

PSELLIPSE PUBLIC OPERATIONS

       PSEllipse(EllipseComp* = nil)
	      Construct a PostScript external representation of the given subject, if any.

SEE ALSO

       GraphicComp(3U), GraphicCompTool(3U), GraphicView(3U), Grid(3U), PostScriptView(3U), align(3U), ellipses(3U)

Unidraw 							  22 January 1991						   EllipseComp(3U)
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