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So you tell us we're mathematically wrong and then proceed to make the same point we are making?.. I'm confused here.
Of course there is no VP in 3D space...that is so elementary as to be an unnecessary and possibly confusing point of semantics.
As I said, linear perspective is a constructive formula/approach which has developed to allow the artist to accurately represent what we see on a 2D surface, ie: the picture plane. What we see are vanishing points. That is no more the purvey of math than it is of optical phenomena.
Edit: IMHO the important thing to keep in mind when trying to understand perspective theory is to keep it simple. Maybe this will help:
Vanishing points are simply the points at which parallel edges appear to converge. They can occur anywhere in the distance, and thus anywhere on the drawing/picture plane depending on the orientation of the parallel edges.
Last edited by JeffX99; August 22nd, 2012 at 02:36 PM. Reason: clarity
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Its a very basic problem like, in a scene I am trying to plot boxes at different depth, some near , some very far, some overlapping each other.
Then I am trying to duplicate the drawing with changed horizon line/ changed view point. This gives rises to all sorts of confusions.
This lead me back to basic question, what else can I use except my intuition, to analyze the rate of convergence of these parallel lines.
Iamcreasy
Yes, a scene in 2-point perspective assumes a vertical picture plane. And even if you're hesitant, it's much easier for us to help if you show us your efforts. It's very hard to guess from your words exactly what is confusing you.
It wasn't a mistake of fact, just a mistake of terminology: the term "vanishing point" refers specifically to points on the picture plane, that's all. Important though if you want to avoid confusing beginners.
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Because everything converges at your eye level, which you see as a horizon line.
What you should realize is that artistic perspective is just a set of tools for making believable pictures. It uses a ton of tricks and abstract devices to do it, which often correspond to nothing you can observe directly. You can't see a vanishing point, but you can use it to plot a set of lines that would look like they are parallel in a picture. That's it.
Problem is, a lot of this stuff is closely related to mathematics (projective geometry) and a lot of formal methods you can find in advanced books are really convoluted - while what you need are the practical and quick ones.
Get Ernest Norling's "Perspective Made Easy". It's practical and straightforward.
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