With all due respect, you're answering a question I'm not asking, and Dr. Wright was answering a question by guessing.
On Sep 10, 2010 4:57 AM, "Louis Schultz" <[email protected]> wrote: > George, > > Dr Wright was sending you in the correct direction. Perspective assumes a fixed distance from a fixed eye point to a fixed picture plane. The view that eye has is perpendicular to the picture plane, and an object to be represented on that picture plan is some distance behind that plane. > > The apparent effect of moving an object away is a function of its distance from the eye AND the distance from the eye to the front of the picture plane. Perhaps the attached image will help to make that more clear. > > > If we let DP = distance from eye to picture plane; DO = distance from eye to the object, then a plane or line parallel to the picture plane would appear to be (DE/DO) x (absolute size of the line or plane) > > You can also use that same formula and a bit of trigonometry to figure out how to make a plane or line appear to tilt in relation to the picture plane. In the attached image, imagine the hypotenuse of the blue 45 deg. right triangle as an edge view of a 1 unit square (that square being perpendicular to the diagram plane). If the edge at A were projected onto a picture plane 2 units from the eye position, then it would measure 2/3 = 0.667 units. If the line at B were project to the same plane, it would measure 2/(3+sqrt0.5) = 0.54 units. > > To make it clear where those numbers come from, The hypotenuse is 1 unit, and the square root of 0.5 is the hypotenuse length x cosine 45, which is the angle of the plane in relation to the perpendicular view of the eye. > > In that case, two edges remain parallel to the picture plane, but with a little work you can figure out how to make a plane appear at any distance and at any angle to the picture plane. If it gets confusing, all you should really need get it figured out are some quick sketches of top and side views (picture plane appears as a line). > > One final note, perspective is a useful tool, but not a true depiction of reality (whatever that is). The further an object in that system moves from the line of the view, the more distortion creeps in. Consider a 1 unit square 8 units behind the picture plane and parallel to it. The square is centered on the line of view. The picture plane is 2 units from the view point. That square would be 10 units from the eye. If it were moved it 10 units away from the line of view in the same plane it would actually then be 14 units from the eye point. It would project the same size though based on our formula. That contradicts what we know to happen. > > We actually see in something more like spheres of vision rather than planes. The distance between the eye and the picture plane has to be zero for that to really work though, which is, to state the obvious, how you do see the world. > > I mention that both as a warning to keep things somewhat centered if you don't want them to look weird, but also as an encouragement to play with the notion of curved picture "planes" if it strikes your fancy. The artists Victor Vasarely and of course Escher might be inspirational for that. > > > > > > > On Sep 9, 2010, at 8:38 PM, George Toledo wrote: > >> So, just so I know where this is at, the statement that there is no way to do this 100% accurately in QC is valid? >> >> -George Toledo >> >> On Thu, Sep 9, 2010 at 2:05 PM, Christopher Wright < [email protected]> wrote: >>> I basically want to know the exact number, from Apple (or really, from anyone, but not a visual comparison/kinda close thing, like this). >> >> >> There isn't an exact number -- this sort of thing requires passing the coordinates through the projection matrix QC uses (undocumented, but it's been investigated on the list before in the past) as well as the model view matrix (which can be arbitrarily configured via Trackball and 3D Transformation). >> >> i'm going to assume this is for faking Z on a Billboard? If so, why not just use a sprite? If not, what other reason is there to fake Z positioning like this? (I'm not saying there isn't a reason, I'm just not able to think of one off the top of my head :). >> >> -- >> Christopher Wright >> [email protected] >> >> >> >> >> _______________________________________________ >> Do not post admin requests to the list. They will be ignored. >> Quartzcomposer-dev mailing list ([email protected]) >> Help/Unsubscribe/Update your Subscription: >> http://lists.apple.com/mailman/options/quartzcomposer-dev/lulu%40vt.edu >> >> This email sent to [email protected] >
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