How Do I Draw 6x6 Tiles in 1-Point Perspective?

[Blahness]

Need a bit of help with Art(:sad:)

(Okay, if this isn't in the right location, feel free to move it and inform me.)


I'm doing a 1-point perspective drawing on a 18x12 inch piece of paper. My vanishing point is directly at (9,6) and my back wall is 1.5 inches left and right, and 1 point up and down. I made marks every 3 inches along the bottom, and connected them to the center(dotted lines past the 7 inch point, which is where the bottom floor meets the back)

Now, what I am trying to do is, I am trying to make a floor that is made of 6 by 6 tiles. How would I make it in perspective, yet make it seem evenly spaced? (Is there/what is the ratio of distance between the tile edges as it decreases over a distance of 5 inches?)

Thank you in advance!
(P.S. Clarification given on request )

 

[zoobyshoe]

Hmmmm. Yes. I know exactly what you're asking, but my brain won't lock onto the answer. I believe there's a simple formula. It's the same way you generate the spacing when you shade a cylinder by means of incrementally closer spaced lines as you approach the edges.

 

[tribdog]

I believe that if you draw a line from the front corners of your tile through the center of the back edge to where it intersects the line of your side edges to the vanishing point you get the back edge of the next tile.

 

[zoobyshoe]

Here, I think this explains how to do it:

http://www.artic.edu/aic/students/sciarttech/2d1.html

From the first paragraph:

Once these basic elements have been set in place, the artist may add further elements to create a more complicated, yet more realistic, space. For example, to represent a square-tiled floor, the artist chooses another point on the horizon line, called the distance point, and draws a line through the orthogonals to a point at the bottom of the picture plane. The points at which this line bisects the orthogonals establish the points at which horizontal lines, called transversals, may be placed. These lines represent the perspectively correct regression of the square tiles into space (see diagram). These elements of linear perspective link the science of three-dimensional geometry with the art of illusionistic representation.

 

[tribdog]

is that what I said?

 

[zoobyshoe]

is that what I said?

Well, let's have another look at what you said:

Maybe it's real maybe it isn't. but if they've really managed to get 6 hydrocoptic marzyl veins feeted to the ambithazion lunar wang shaft they are genius, because every single retro encabulator I've come across has suffered from terrible side fumbling.

So, yes, more or less.

 

[Blahness]

Argh

I'm sorry, but I'm probably not getting it; How do I know how big to make my first row of tiles? (I'm horrid at visualizing, due to a lack of practice )

Since the 6x6 tiles have to cover an area much, much wider than they are wide, I'm going to have to use rectangular tiles to keep it even.

But still, at least, how tall do I make my first row of tiles?

 

[zoobyshoe]

I'm sorry, but I'm probably not getting it; How do I know how big to make my first row of tiles? (I'm horrid at visualizing, due to a lack of practice )

Since the 6x6 tiles have to cover an area much, much wider than they are wide, I'm going to have to use rectangular tiles to keep it even.

But still, at least, how tall do I make my first row of tiles?

The diagonals sort that out for you: no calculations necessary.

What you're trying to do is exactly like the illustration at the link I posted with one difference. The tiles at the link are 7 across x 6 deep. If your drawing has one less line radiating from the vanishing point that automatically reduces it to your 6 x 6 tiles.

You start by drawing a horizontal line through the vanishing point. Then mark off two points on that horizontal evenly spaced on each side of the vanishing point. Draw diagonals from those two points to the outer edges of the floor at the front (bottom) of the paper.

Where those diagonals intersect the original radial lines you draw horizontals. These are automatically spaced at the proper incrementally increasing distance from each other to appear "right" to the eye.

 

[Blahness]

Oh! I get it!

Thank you.

EDIT: My two end "distance" points are off the page... is this normal? :S

(Basing it on how far the illustration is. Are the placements arbitary?)

 

[zoobyshoe]

Oh! I get it!

Thank you.

You're welcome, sir.

EDIT: My two end "distance" points are off the page... is this normal? :S

I've never actually done it myself, but it looks to me that the more of your page that is taken up by the floor the more likely you are to have reference points off the page.

(Basing it on how far the illustration is. Are the placements arbitary?)

I can't tell without doing it. You have stipulated the location of your vanishing point but not the distance of the back wall from the front of the paper. It could be you have a range that will work, or it could be there is only one distance that will work.

Realize, too, that if you have a t-square or any means of easily striking horizontal lines you don't really need two diagonals. A horizontal from any point the diagonals intersect the radial lines will intersect them automatically where the "mirror" diagonal would intersect them.

The diagonal has, in any event, to create a situation where the first row in front of the back wall is the thinnest of all, with the rest getting incrementally thicker as you approach the bottom of the page.

 

[Yonoz]

It all depends on the perspective you want to give. As a matter of fact, to be truly realistic-looking, your schematic needs to have a slight fisheye effect, relative to the distance between the point of view and object.
Imagine your field of view as a square pyramid of infinite height, the apex of which is your point of view. You are trying to project a view looking from the apex to the center of the "base". As different points along the straight lines formed by 3D objects are at a varying distance from the apex, they will not project on a 2D plane as straight lines. This is the fisheye effect.
It does not matter whether some point falls on the page or not, as it is simply a matter of the FOV you chose.

 

[zoobyshoe]

Three days since we've heard from Blahness.

Blahness, how'd your thing turn out?