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        riddles >> easy >> Point of view
        
(Message started by: Noke Lieu on Feb 8^th, 2010, 8:57pm)

Title: Point of view
Post by Noke Lieu on Feb 8^th, 2010, 8:57pm

I'm stumped.

I'm thining of one point perspective drawings.
The axioms are, as far as I know:

All parallel lines converge in this projection.
The points at which they converge (Vanishing Points) lie on the Horizon Line.

and that's about it (for one point perspective, in a handwavy way).

I'm perfectly comfortable with parallel lines running horizontally across the page converging at a vanishing point that's infinitely far along the horizon line. In fact, thinking about it makes me happy.

My question is "Where do parallels that run vertically on the page converge?"

Title: Re: Point of view
Post by towr on Feb 9^th, 2010, 3:23am

I'm not sure what you're asking. Lines that are parallel on the page aren't parallel in the scene you're drawing. (Except when they're also parallel to the horizon.)

Title: Re: Point of view
Post by Immanuel_Bonfils on Feb 9^th, 2010, 5:30am

Couldn't find the beginning of thuis riddle...

Title: Re: Point of view
Post by Grimbal on Feb 9^th, 2010, 6:23am

This is about a projection of 3d space on a 2D plane.

The line of sight is the axis going from your eye through the plane, perpendicularly.

If that line aims at the horizon, then it is horizontal, the projection plane is vertical and all vertical lines remain parallel on the projection.

If that line of sight is going upwards, then there is a vanishing point over the horizon. That is the point where a line going up vertically from your eye meets the projection plane. All verticals converge to that point. Imagine looking at a skyscraper from the street.

If the line of sight is going down, you have a vanishing point below the horizon. Imaging looking down an elevator shaft.

Title: Re: Point of view
Post by Immanuel_Bonfils on Feb 9^th, 2010, 6:44am

Thanks, but I knew this stuff about prespective or/and projective. I thought it was a continuation of som riddle (it's looks like) but seems its the starting of...

Doesn't vertical lines in the scene be represented by verical lines in the page?

I mean, with the line of view being horizontal, the vertical lines are parallel...

Title: Re: Point of view
Post by Grimbal on Feb 9^th, 2010, 4:56pm

yes, when the line of sight aims at the horizon, it is horizontal and the verticals are parallel.

Title: Re: Point of view
Post by Noke Lieu on Feb 9^th, 2010, 8:10pm

It is the continuation of some sort of riddle, one that I've been playing with. I'm writing teacher support notes on perspective.
And as I'm working on it on my own, I thought I'd consult better brains than mine.

I'm going to use fairly layman language to describe what I'm struggling with...

Imagine a square grid on the floor, stretching off into the distance.

There are parallel lines running perpendicular to the image plane. Ther converge at the "Vanishing Point".

There are other parallel lines, for example those of the diagonals of the squares.

They also converge, but at a diagonal vanishing point.

There are an *ahem* rather large number of diagonal vanishing points. The closer to being parallel to the plane lines are, the further from the vanishing point the DVP is.

The parallel lines running parallel to the image plane therefore converge at a spot infinitely far along the horizon line.

(and now I can't remember what my point was... :'()
It was struggling with the distinction between 1 and 2 point perspective., and representation of dimensions, how they didn't match...

Title: Re: Point of view
Post by rmsgrey on Feb 10^th, 2010, 8:27am

With a horizontal line of sight, horizontal parallel lines meet on the horizon, vertical parallels never meet, and parallel lines which are neither horizontal, nor perpendicular to the line of sight, meet at some random point on the viewing plane.

The difference between 1-point and 2-point perspective lies in how many sets of parallel lines not perpendicular to the line of sight are allowed to exist in the picture - in one point perspective, parallel lines are either perpendicular to the line of sight, or parallel to each other (and often to the line of sight); in 2-point perspective, there are two sets of mutually parallel lines not perpendicular to the line of sight.

In general, you can have arbitrarily many vanishing points, each representing a set of parallel lines with a different direction in object-space.

Title: Re: Point of view
Post by JohanC on Feb 10^th, 2010, 9:09am

Google points to pages such as this one (http://www.khulsey.com/perspective_basics.html) where fig. 12 demonstrates a 3 point perspective.
Also wikipedia has an interesting discussion (http://en.wikipedia.org/wiki/Perspective_%28graphical%29) , and an example of a satirical false perspective (http://en.wikipedia.org/wiki/File:Hogarth-satire-on-false-pespective-1753.jpg). Curious is a topic about
reverse perspective (http://en.wikipedia.org/wiki/Reverse_perspective).