Re: [PATCHES] Re: Harp Pedals?

[Trevor Daniels]

Carl

Why not use an ellipse that just fits _inside_ the rectangle?

Then a^2/xrad^2 = 1; so xrad = a
and  b^2/yrad^2 = 1; so yrad = b

The values of x-extent and y-extent of the grob are also given
immediately.

Trevor, puzzled ||%-/

----- Original Message ----- 
From: "Carl D. Sorensen" <address@hidden>
To: "Reinhold Kainhofer" <address@hidden>; "Valentin Villenave" 
<address@hidden>
Cc: <address@hidden>
Sent: Friday, August 29, 2008 4:17 AM
Subject: Re: [PATCHES] Re: Harp Pedals?


I want the equation of an ellipse that circumscribes a box 2a by 2b.

x^2/xrad^2 + y^2/yrad^2 = 1 (ellipse)

needs to pass through the points (a,b), (-a,b), (a,-b), (-a,-b).

Because of the squared terms, all four points have the same equation.

a^2/xrad^2 + b^2/yrad^2 = 1  (1)

There is an infinite number of ellipses that circumscribe the ellipse.

I want one with the aspect ratio being the same as the box.  So my second
equation is

q/b = xrad/yrad

Solve for a.

a = b* xrad/yrad

substitute into equation (1)

b^2*xrad^2/(yrad^2*xrad^2) + b^2/yrad^2 = 1

2b^2/yrad^2 = 1

yrad^2 = 2b^2

yrad = sqrt(2) b.

By symmetry, xrad = sqrt(2) a.

Your counterexample didn't apply because of the 0 in the denominator.

HTH,

Carl

On 8/28/08 3:42 PM, "Reinhold Kainhofer" <address@hidden> wrote:

> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>
> Am Donnerstag, 28. August 2008 schrieb Valentin Villenave:
> > 2008/8/19 Carl D. Sorensen <address@hidden>:
> > > I've been looking at ellipse code.  Once I can get rhythms.itely off my
> > > plate (which is waiting on the beatGrouping patch, one way or the other)
> > > I'll add an ellipse in place of the circle.
> >
> > I've been looking at a way to draw ellipses, but I've just seen you
> > have pushed a much better-looking implementation than mine; I hope the
> > docs will be recompiled soon so we can appreciate your nice ellipse in
> > the documentation!
>
> Yes, I saw that, too. I even generalized it to allow different paddings in 
> X-
> and Y-direction. However, what I don't understand about the ellipse code 
> in
> ellipse-stencil is the factor 0.707 (supposedly from sqrt(2)/2) for 
> x-radius
> and y-radius. If that factor comes from scaling the ellipse so that it
> surrounds the stencil, then it only works for square stencils, for all 
> other
> stencils it will be too large. As an extreme case consider a line stencil
> ("box" from (0 . -1) to (0 . 1) ). The ellipse will have half-axes of 
> length
> 1.414 and 0 (without padding), so in X-direction it will overshoot by far.
>
> For a square, of course, the ellipse will degenerate to a circle, touching 
> all
> corners, but for stencils with other rectangular extents, the ellipse will
> not touch the corners of the bounding box any more.
>
> Cheers,
> Reinhold
>
>
> - --
> - ------------------------------------------------------------------
> Reinhold Kainhofer, Vienna University of Technology, Austria
> email: address@hidden, http://reinhold.kainhofer.com/
>  * Financial and Actuarial Mathematics, TU Wien, 
> http://www.fam.tuwien.ac.at/
>  * K Desktop Environment, http://www.kde.org, KOrganizer maintainer
>  * Chorvereinigung "Jung-Wien", http://www.jung-wien.at/
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