Fwd: Re: button-hole problem

D=E9but du message r=E9exp=E9di=E9 :

> De: Jacques Vernin <[email protected]>
> Date: 24 avril 2005 08:09:23 GMT+02:00
> =C0: Larry Siebenmann <[email protected]>
> Objet: R=E9p : [metafont] Re: button-hole problem
>
> Quaesturam una petiit et sum ego factus prior. Non est respondendum ad=20
> omnia.  Neque enim uestrum quelquam fugit, cum multi pares dignitate=20
> fiant, unus autem primum locum solus possit obtinere, non eundem esse=20
> ordinem dignitatis et renontiationis proptera quod renuntiatio gradus=20
> habeat, dignitas autem sit perseape eadem omnium. Sed quaestura=20
> utriusque prope modum pari momento sortis fuit. Habuit hic lege Titia=20
> prouinciam tacitam et quietam, tu illam qui, cum quaestores=20
> sortiuntur, etiam adclamari solet, Ostiensiem non tam ....
>
>
> Le 24 avr. 05, =E0 05:21, Larry Siebenmann a =E9crit :
>
>>
>>
>> Hi Laurence F.
>>
>>  Me> For example, if the
>>> projection point is on the target plane, which happens to be
>>> disjoint from the circle, then the projected circle is the
>>> EMPTY SET.
>>
>>  You> Wouldn't it be a point, namely the projection point
>>
>> You are quite right, I boobed; as Peter Vanroose further
>> explained, a cone on an empty set is not empty but the cone
>> point.  Unfortunately, programmers usually have to
>> pay attention to degenerate cases -- they are like
>> accidents waiting to happen.
>>
>>> occlusion of two polygons
>>
>> ??? whazzat?
>>
>> I mentioned radial projection of objects in R^3 onto
>> the spherical retina of an imaginary eye. You answered:
>>
>>> This is interesting, but I think it may not be of
>>> practical importance for 3DLDF.
>>
>> You can ignore it.  But it is helpful to consider
>> because the sphere (eye) with opposite points
>> identified is a model of projective 2-space RP^2.  One
>> in which no particular line at infinity is has privilege
>> and in which the compactness of RP^2 is obvious. It is
>> natural since God gave your users spherical eyes and a
>> preception of projective geometry through them.
>>
>>> it might be useful to just store the center of an
>>> object and a transformation matrix.
>>
>> I favor 3-dimensional scenes which one can journey through
>> with a computer.
>>
>>> What I do is the following:  A `Focus' contains a
>>> `Point' representing the position of the "camera" in
>>> space
>>> ....
>>> `Focus::position'
>>
>> This would be the center C of my eye.
>>
>>> and another representing the direction of view.
>>> ....
>>> `Focus::direction'
>>
>> This is direction CP, where P is the center of the pupil
>> of my eye.
>>
>>> The "up" direction is determined somehow, I don't
>>> remember how,
>>
>> It is determined by gravity via the inner ear, I
>> believe.
>>
>>> and can be modified by using a `real'
>>> value for an angle of rotation.
>>
>> OK. But, my eye tends to resist that modification.
>> Stand in front of a mirror and tilt your
>> hear to one side.  Do not your eyes not stay upright?
>> Of course this mechanism is switched off sometimes
>> for astronauts and athletes.
>>
>>> These values are used to determine a transformation
>>> which would place the position point and the
>>> direction point on the z-axis and the plane of
>>> projection into the x-y plane.  This transformation
>>> is then applied to all of the objects in the space
>>> before applying the perspective transformation.
>>
>> Let me try to understand using a model eye or camera.
>>
>> Are you, in other words, introducing a new oriented isometric
>> coordinate system on 3-space: origin at the center C
>> of the eye, the z-axis running from that center out
>> through the center of the 'pupil' P? The y-axis
>> 'vertical', and the x-axis 'horizontal'.
>>
>> The retina or film F  can be thought of as the
>> translate of the xy plane distance m in the positive
>> z-direction. This m is zoom magnification if we think of
>> the eye as a *simplified* camera.
>>
>> Then a "view" or "photo" of 3-space is obtained by
>> radial projection through C onto F.
>>
>>> Objects that can't be projected are culled in
>>> `Picture::output()'
>>
>> The projection can be restricted to map only
>> objects in the half-space of positive z, onto the
>> film F. The film can be cut down to a finite part
>> F0 of F, presumably a neighborhood of the origin.
>> The cut-down film then sees just scenery in the
>> positive cone on F0 with center C. Occultation is a
>> major problem I won't explain. Also color
>> luminosity texture shadow, reflection, transparency
>> -- gasp.=20
>> If one is to be able to tour through 3D scenes, a
>> model of this complexity seems necessary.
>>
>> All this is guesswork.  Is is consistent with *some*
>> 3D graphics system?
>>
>> Cheers
>>
>> Laurent S.
>>
>> PS. As in photography, the center C can move far
>> from the scenery of interest, though F0 will stay
>> relatively close.  The projection onto F
>> then becomes parallel to the z-axis.  But it seems
>> advisable allow freedom for C to tour
>> in all 3-space.
>>
>>
>>
> Jacques Vernin
> piR2
> 10, Boulevard de Brazza
> 13008 Marseille
>
>
Jacques Vernin
piR2
10, Boulevard de Brazza
13008 Marseille