Hi-
I'm new here- so pardon me if my question has just been discussed or is inappropriate to this forum.
I have done different murals of fake "windows" and prefer to have the "storybook" type window where it opens vertically from the center, like shutters. (Doe sthat make sense?)
I'm clear on the one point perspective of having all the panes correctly aligned, and able to have the windows open to any degree without difficulty. Heretofore, I have always "eyeballed" the depth of the outside window edge. That is to say, how far "into" the drawing/painting the vertical plane of the window pane or shutter extends. And it is convincing enough for clients. But there seems to me there ought to be a way of knowing EXACTLY where that plane stops relative to it's known width from outer edge to center of the window.
I'm pretty good with geometry and get into the technical aspects of drawing in perspective, and I have to admit, I've driven myself nuts with this question. I even went to a friend who is a professional architect for an answer. he confessed finally that he hadn't drawn anythign with a pencil since college and had no clue.
I've considered it mathmatically, considering the problem as a calculus/geometry where you know the x and Y axis values, and must calculate the Z, but that doesn't work because of the perspective. I've used ratio of the depth vertically to the depth of the perspective length. That didn't work either. I've tried everythign I can think of!
I have finally found one way to make my particular drawing work, but I think there must be something I"m missing! What I'm doing is "projecting" a square into the plane, and using its bounds to sketch in an ellipse. The projection begins with the known width of the shutter, so I know what I come out with is in fact square and the correct size. But it's quite a pain, leaves lots of lines on my paper and I just KNOW there's some simple way of knowing where that line stops!!
Can anybody help?
Thanks-
T

can you post a picture. I'm thinking the window opens with an arc and would need to be figured with diameters and arcs. does that help?
paulette

this is so a question for jeanette .. here let me try and yell for her ....JEANETTE !!!!!! lets see if she hears that .. she will be able to help you I am sure .

Thanks so much- the method I thought was working isn't. So now I"m really confused. :-(
I don't know how to post a picture??
You're right about the arc and diameter, which would be simple IF you were looking at it head-on. But you're not. You're looking from the side, at a circle (the outer edge of the "shutter" pivoting around the hinge) that will be skewed into an ellipse by the perspective.
Rather than the circle/ellipse, I've tried to just do a square and sketch the ellipse within that. That would be close enough. But I can't figure out how to make the square "square" by just knowing the length of the front edge, when the back edge recedes into the picture. :-(
<sigh>

[quote name='TLBarrett' date='Nov 14 2006, 06:02 PM' post='5123']
Hi-
I'm new here- so pardon me if my question has just been discussed or is inappropriate to this forum.
I have done different murals of fake "windows" and prefer to have the "storybook" type window where it opens vertically from the center, like shutters. (Doe sthat make sense?)
I'm clear on the one point perspective of having all the panes correctly aligned, and able to have the windows open to any degree without difficulty. Heretofore, I have always "eyeballed" the depth of the outside window edge. That is to say, how far "into" the drawing/painting the vertical plane of the window pane or shutter extends. And it is convincing enough for clients. But there seems to me there ought to be a way of knowing EXACTLY where that plane stops relative to it's known width from outer edge to center of the window.
I'm pretty good with geometry and get into the technical aspects of drawing in perspective, and I have to admit, I've driven myself nuts with this question. I even went to a friend who is a professional architect for an answer. he confessed finally that he hadn't drawn anythign with a pencil since college and had no clue.
I've considered it mathmatically, considering the problem as a calculus/geometry where you know the x and Y axis values, and must calculate the Z, but that doesn't work because of the perspective. I've used ratio of the depth vertically to the depth of the perspective length. That didn't work either. I've tried everythign I can think of!
I have finally found one way to make my particular drawing work, but I think there must be something I"m missing! What I'm doing is "projecting" a square into the plane, and using its bounds to sketch in an ellipse. The projection begins with the known width of the shutter, so I know what I come out with is in fact square and the correct size. But it's quite a pain, leaves lots of lines on my paper and I just KNOW there's some simple way of knowing where that line stops!!
Can anybody help?
Thanks-
T
In the picture, draw an ellipse on a horizontal plane that touches the bottom of the shutter. Make the center of the ellipse coincide with the bottom edge of shutter's rotation axis (hinge line). Any line drawn at any angle from the ellipse's center will intersect this ellipse. The distance between ellipse's center point and the intersection point represents the width of the shutter. The more foreshortened this line is, the shorter it is.

Diquimugs wrote:
In the picture, draw an ellipse on a horizontal plane that touches the bottom of the shutter. Make the center of the ellipse coincide with the bottom edge of shutter's rotation axis (hinge line). Any line drawn at any angle from the ellipse's center will intersect this ellipse. The distance between ellipse's center point and the intersection point represents the width of the shutter. The more foreshortened this line is, the shorter it is.

Thank you, Diquimugs!
I still don't get how I know where the sides of the ellipse touch at front and back?? I see the center is the hinge, and the horizontal center is the "sill" of the window, and I see the plane those two points form with the vanishing point. But the depth has to be relative to the width of the "shutter", which we know to be the distance between hinge and center, when closed. The arc of the line represented by the bottom edge of the "shutter" will be skewed shorter in the "background" and longer in the "foreground".
What am I missing?

Good news!
My method IS working <whew>
I just had something messed up in the particular drawing I was doing, aside from that. As if I need any other challenge, right?
So I'm not as frantic, but this really does bug me and the advice is MOST appreciated.
As I said earlier, I dunno how to post pictures , but here is a link to the general idea of the method I'm using:
http://studiochalkboard.evansville.edu/lp-square.html
I did it a bit backward, starting with the "front" edge of the square in perspective, since it's our "known". I constructed the axis and points like the website. Once I had the front side UNprojected up into the right side, I just chose any place at random, drew a horizontal line, and made a square based on that distance. I used its other two corners to get the back two corners in the projected view, thus providing a "stopping point" that should be relative to the front side. Having the square, I sketched the ellipse based on the centers of the 4 sides of the "square" and darned if it doesn't look just perfect :-)
This is a laborious way of doing it, tho. And I'm not 100% sure it's really accurate. I've done this so many ways, everything starts to look goofy to me.
So keep the ideas flowing, PLEASE!

Well now, here's a question and it seems you have some solution already.

I'm not 100% sure if I understand your question. Is it the depth of the window itself you're trying to calculate? I'd love to see what you are trying to achieve as I'm more an image person than a mathematical person. I looked at the link but still am not quite sure what you're trying to do.

Perhaps another person can have a look and add some more suggestions here.

T,
re:posting picture
When you "add reply" at the bottom of the forum, you get your message area. Scroll down and you will see "file attachments", click the browse button. This will bring up your files, open the correct folder, then open your file. Next click "add this attatchment", Then click add into post. Scroll down "Preview post" then if all is good "add reply". I hope this will do it for you.
Paulette

Thanks for responding, Islander.
It is rather hard to say concisely. It's not the thickness of the window pane that I'm after. The window opens from the center out, more like "shutters" than a window. It's what i think of as a "storybook" window. With the panes or shutters extended out toward the horizon, I know how to make the pane/shutter appear to go in whatever direction I want it to. But when drawing those lines back toward the horizon, away from the hinges, I cannot figure how to determine wher ethey "stop". If, for instance, the window itself is 2 ft wide, then the shutter is 1 ft wide when closed (or completely open back against the outside wall). As it opens out away from you, it is no longer 1 ft actual length. It appears to shorten. If looking from the top, the outside edge of the window pane/shutter will go in a circle around the hinge. From the top, the circle would have a radius of 1 ft. Once you begin to tip that circle, it becomes an ellipse. The ellipse is tipped to the plane created by the line from the vanishing point to the window.
So when drawing, I start from the corner of the window and strike lines out toward the vanishing point for the top and bottom of the "shutter/pane", and any divisions or individual panes I want in between. The question is: "How far do those lines extend?" One ft, of course. But one foot is no longer one foot when viewed from "perspective".
Rather than try to create the ellipse or circle, I've been trying to create a square and draw the ellipse within that square. I've doen this because squares are easier for me to work with. So the link you looked at shows how to take a known square shape and project it into any plane toward any horizon line/vanishing point. Not knowing what size or placement to start with to get the right size an dplacement I needed, I started with that known 1 ft line and did a little backtracking to create the square, then created the rest of the projected square. In theory, this oughta work, and it sure looks like it does. But it requires lots of lines and time and aggravation and there's just got to be an easier way.
I'm thinking my "math tendencies" are maybe what's fowling me up here. I'm hoping some good visual perspective artist will give me a "duh!" and show me the EASY way to know where that line ends in the depth of the picture.
If someone can show me how to post a picture, I'll post my sketch and maybe that'll help.
Thanks for trying
Tami

T, you must have been writing when I posted, look back re:Posting picture.
Paulette

Duh! I guess I could've read where it said "attachments". Thanks for pointing that out.
All right- here is the drawing.
First of all, ignore the circular part on the left- that's a stain from my soup at lunch <ahem>
Now,
what your'e looking at is a window- that's the rectangle. You are inside and the window swings outside.
The "shutter" is on the right side in this drawing, tho the left one would be there too in reality. It is drawn in 3 different positions.
The lower edge of the window is labelled "sill". The horizon line, vanishing point, and "lower point" are also all labelled, as are "hinges" on the right.
The link I posted earlier http://studiochalkboard.evansville.edu/lp-square.html shows how to take a known square, labelled "actual square" in the upper right of my drawing, and "project" it into a plane of perspective down below.
The line of hinges creates a vertical axis and defines the right edge of the pane/shutter when closed. The center of the window would be it's left edge. I need to be able to swing that window out, not only having the horizontal lines in perspective, but also stopping them at the appropriate length such that it marries with the idea that it was originally 75mm long, or whatever it is.
the chalkboard instructions from the website begin with a large circle "field of vision", which I've found to be largely irrelevant for this application, and a vertical and horizontal axis. I'm using the horizon line as the horizontal axis. The vertical axis is the vertical line from my randomly chosen vanishing point.
Chalkboard draws an actual square of any size above the horizon line. Lines are drawn from the 4 corners, down to the "lower point" (don't ask me why, I dunno).
They cross the horizon line in 4 spots. From these points, drop vertical lines. Here they tell you how to determine, based on 2 other points of perspective, where the front of the plane stops. For my application, I don't care, because I am beginning with that front of the plane being the distance from the center of the sill to the hinge point on the right.
Because I am beginning there, I draw two lines up from the lower point through the two known points. At some random place above the horizon line, I drew a horizontal line from one to the other, measured it, and constructed a square, using it as the bottom line.
Then I used the upper two corners just as the instructions show. Where their vertical lines intersect the perspective lines from the front two points, defines the back edge of the plane. I now have a "square" in perspective. I have quadrupled that square in order to have a complete ellipse. I drew diagonal lines from each of the rear points to the center of the front line and beyond to where they intersected the opposite side. This defines the front of the plane. I extended the original line the same distance past the edge of the window as it was from the center to the edge, effectively doubling it. From that point, I struck a line to the vp, which is the right edge of the now quadrupled square, now being one big square with 4 quadrants.
The ellipse touches the 4 sides of the square. This is slightly skewed as real ellipses don't hit the center exactly, but that's as good as I've been able to get it.
Having that ellipse, I use it as where to "stop" such that my pane remains the same width or depth from hinge to outer edge, no matter what perspective it's drawn in.
I hope that makes sense.


y.for


just noticed that the pic got cut off- only the bottom of the "actual square" in the upper right is visible.

Sorry,
Your math sense is way further along than mine and my art sense is nil. Maybe now that Jeanette has a picture she can help. By the way if you could rotate your picture and keep them below 200kb you will have a larger group of people that can look at them.
Paulette

I think this is a perspective problem that may not be as difficult as it appears.

If the shutter is one foot wide, it still will be one foot wide no matter how you draw it. BUT to the human eye it will APPEAR to be shortened due to the foreshortened view point.

If you convert your drawing into realtime measurements - on a much smaller scale of course and divide the window into say 1/8 inch increments, then you can do the same with the bottom edge of your shutter. At the required length (1 foot for example) that is the stop point for your vertical line and the rest is down to simple one point perspective to get the angles correct.

That's MY theory anyway. I'll try to do a sketch and see if that theory works in reality later.

Sorry about it being big and sideways-

If I understand you right, you're saying if it's 1 ft on the horizontal axis, then it'll be one foot on the "depth" or "z" axis (that being the line from the hinge point to the vanishing point). I tried that and it didn't work. At least it didn't look like it to me.
Then I tried comparing the length of the line from hinge to vp, to the line fromthe sill edge directly vertical to the vp, and creating a ratio to use. That didn't work because it doesn't stay the same all the way back- units get smaller as they go "deeper".
Then I tried making a rectangle of any size starting at the sill and reproducing it over and over, back many times. It gets smaller each time of course, yet each one represents the original depth in that perspective. So if that first depth was say 5mm, and the total length of the line from ctr to hinge was 20 mm, then that's 4 "units", and I then counted 4 of the "receding" units and got that point on the z or receding axis. Still no dice. UG
I think you're right that it must be a simple perspective issue. I just can't see what that is!
Does the drawing look "right" to you, the way it came out?
Thanks for your help-
Tami

OH MY GOSH!!!
Check this out: http://www.mathaware.org/mam/03/essay6.html
This guy teaches math for artists- how cool is that?
His explanation of how far back the back line of a cube falls, blows me absolutely away. And "answers" my question, but in a frustrating way!!! it still seems so "random".
I emailed him and asked for some advice on my specific drawing- will post if he replies.

[quote name='TLBarrett' date='Nov 14 2006, 11:08 PM' post='5153']
Diquimugs wrote:
In the picture, draw an ellipse on a horizontal plane that touches the bottom of the shutter. Make the center of the ellipse coincide with the bottom edge of shutter's rotation axis (hinge line). Any line drawn at any angle from the ellipse's center will intersect this ellipse. The distance between ellipse's center point and the intersection point represents the width of the shutter. The more foreshortened this line is, the shorter it is.

Thank you, Diquimugs!
I still don't get how I know where the sides of the ellipse touch at front and back?? I see the center is the hinge, and the horizontal center is the "sill" of the window, and I see the plane those two points form with the vanishing point. But the depth has to be relative to the width of the "shutter", which we know to be the distance between hinge and center, when closed. The arc of the line represented by the bottom edge of the "shutter" will be skewed shorter in the "background" and longer in the "foreground".
What am I missing?
I'm not sure I understand what you think you're missing. The horizontal width of the ellipse (it's major diameter) is the width of the shutter. The "roundness" of the ellipse (whether it's long and skinny or nearly circular) will depend on how far the ellipse is above or below the horizon line of your picture. The closer it is to eye level (the picture's horizon line), the skinnier it will be, getting thicker (rounder) as it moves away (up or down) from the horizon line. You have to judge by eye how thick the ellipse should be for its location relative to the horizon line of your picture. To see this, hold a dinner plate horizontally out in front of you and move it up or down until it look like a thin line. That's your eye level, which coincides with the picture's horizon line. Moving the plate up or down, away from the horizon line, reveals more of the bottom or top of the plate, and the ellipse of the plate becomes "rounder," thicker, or however you want to think of it.

Digimugs-
You must be a way better "visualizer" than me- or maybe I"m just too dependent on the other side of my brain. Be it a blessing or a curse, I'm as strong (or weak) on one side as the other. So my left brain insists there must be a way to calculate where that ellipse goes, as far as depth.
I'm very excited about finding the art math instructor- we must be kindred spirits! He's in the UK and I'm in the US so my husband needn't worry I guess ;-)
I have since found another site http://www.wetcanvas.com/ArtSchool/Drawing...ective/Lesson2/ that affirms my theory by using a similar method to produce an exact "cube" in perspective. I was only doing the "top" or the "bottom" of the cube as I only need one plane, but this page is specifically addressing why it's hard to know how far back that cube goes in various perspectives.
As pleased as I am to be ABLE to do it, I still think there's gotta be a more direct way of going about it. But the more people I talk to, the more it looks like the "more direct way" is just as you describe: eyeball it from experience.
Thank you for your help-
Tami

Tami, do yourself a favor and train your eye rather than rely on mechanical projection. In my haste yesterday, I mistakenly said that the major diameter of the ellipse is the width of the shutter. Actually it's TWICE the width of the shutter. If you're interested in learning more about perspective, a great little book I'd recommend starting with is Perspective Made Easy by Earnest Norling. It's been out of print for a long time but your local library may have a copy. Bookfinder.com may have a copy for sale if you want to consider purchasing it.

One of these days I guess I'll have enough experience to eyeball things better. But because I don't yet have it, and maybe even more so because I really enjoy the technical aspects of precision drawing, I'll rely more on the math for now.
I will make an effort to learn as I go, so that I'm not so dependent on the math stuff. it does take up time!
It's been interesting for me to take drawings or paintings where others had eyeballed the measurements and do the math to see how close they are.
That one site about it all depending on how far your eye was from the page or board or whatever, just amazed me.
Thanks again-
Tami

Tami, I've been making my living as a technical illustrator for over 30 years. I'm self-taught and, like you, I relied heavily on projection and mathematical formulae to create the "perfect" image, having studied these topics in college, preparing for an engineering degree that didn't materialize. I thought myself clever for having avoided the whole painful process of developing my eye to see and my hand to obey, relying instead on "accuracy" to create the drawing. Then something happened to change my mind. I became bored with it all. Drawing became a chore because I thought I had to follow certain rules I had established for myself. I began doodling in my boredom and I discovered what I had been afraid to find out. I could actually draw, not as well as I wanted, but I could draw! I've since studied independently, practiced, experimented, and developed my skill to the point that I feel comfortable with it, and I enjoy teaching the basics to anyone who wants to learn. So, don't be like me. Don't allow a lot of time to go by before you discover yourself through drawing. And never be afraid of what you'll see on your paper and never judge yourself through your drawings. They aren't art, they're only a record of your continuing progress. Give yourself permission to make mistakes and be grateful you can see them. Without them, how would you know what you need to improve? Celebrate your work like Hal did in the book entitled, Drawing You Can Do It by Greg Albert.

Lest I be misunderstood, and I hurt Tami's feelings, I need to expand my comment that Tami's work isn't art. I certainly was not intending to be critical of Tami's work, though some have gotten that idea from the emails I've received. What I WAS saying, and what I mistakenly assumed everyone understands, is that art can only happen AFTER the means of bringing it forth has been developed. Until then, all efforts are mere records of progress in acquiring skill. When does "art" happen? When people are moved by the work, when it speaks to them personally on a non-verbal level, when it doesn't have to be explained to be understood. How does that happen? When the creator of the work has something to say and is completely free of technical distractions, when the use of the medium is so well understood that it becomes an extension of oneself. I use the word "medium" in the broadest sense; it can even be the emotional and physical act of drawing. Until that can happen, a drawing is only a record of where the student is in his/her development. It's not to be judged as art, but much can be learned from it.