[Dr. Bang]

bump!

[aquamire]

Damn,why didn't I think of that? Hmm, probably because my knowledge of geometry and trig is piss poor, but I use to love coding. Will give it a try! Thanks Pierre! Where do you come up with all this?

[[Shizo]]

bump
(i didn't read all that calculator mumbo jumbo though)

[pierre]

Linear perspective theory is a good way to learn and understand the principles of how humans see things and how to translate a 3D realm them into two dimensions. The disadvantage of it though, is often alot of lines and vanishing points, most often outside the paper.

The following is only a tip on how to draw with mathematical correct perspective, without the use of vanishing points and measure lines. This is the same type of algoritm that 3D Studio Max, Softimage, Maya, Lightwave, Houdini, you name it, uses. That is, the algoritm of course can take on different coding, but the end result is always the same.

NOTE! You should not use this method before understanding the basics of linear perspective. You will not understand it if you do not know the basics and you will be unable to use the program.

You will need:

a programmable calculator or you can sit at your computer using any programming language that supports the mathematical functions that the soon to be explained algoritm uses.

two rulers

do I need to say you need a paper? (you can use a photoshop canvas, you have the rulers there too!)


====================================
BEGINNING OF PROGRAM
====================================

10 INPUT "height angle=";ALFA
20 INPUT "rotation angle=";BETA
30 INPUT "eyes distance to 3D axis origo=";D
40 INPUT "eyes distance to picture plane=";K
50 INPUT "horisontal coordinate of focus=";Q
60 INPUT "vertical coordinate of focus=";W

70 INPUT "x=";X
80 INPUT "y=";Y
90 INPUT "z=";Z
100 N=X*SIN BETA+Y*COS BETA
110 A=X*COS BETA-Y*SIN BETA
120 B=N*COS ALFA+Z*SIN ALFA
130 C=N*SIN ALFA+Z*COS ALFA
140 H=K*A/(D+B)+Q
150 V=K*C/(D+B)+W
160 print H, print V
170 GOTO 70

====================================
END OF PROGRAM
====================================

In the first part of the program (10-60) you define your cone of vision in relation to origo and its position on the paper.

The remaining part (70-170) asks for x, y and z and translates them into a point on your paper. After you get the point (line 160) the program loops back to line 70 which query you for an additional set of values for another point.

On the paper place a ruler horisontally on the bottom, this is coordinate H.

Place the other ruler vertically towards the horisontal ruler. Origo should thus be found at the paper's lower left corner. On this vertical ruler, we will place our coordinate V.

Give the program the following values (x,y,z)=(0,0,0) and you will get the position of focus on the paper.

Draw one axis through the aquired point and give some additional values, e.g (100,0,0) and (-100,0,0). You will get a line that is 200 units across with the correct perspective. (NOTE! the values you use in the program reflect the units on your ruler, in my case millimeters).

For example, a cube with 80 units at each side with its center in origo has the coordinates:
(-40,40,40)
(40,40,40)
(40,-40,40)
(-40,-40,40)
(40,40,-40)
(-40,40,-40)
(40,-40,-40)
(-40,-40,-40)

Once you get comfortable with the practice of using this method, drawing for example a mathematically correct 3D grid can be a very quick process. Eventually you may skip the 3D grid part and directly construct roughs of your objects.

The program can be extended to calculate circles and other geometrical complexities. But that would be to many confusing lines of code. Just bake cirklis into your squares.

Anyway, this was a tip on how to draw with mathematical correct perspective. Personally, I wouldn't use this method as I love to draw with a "feeling". I like to feel where this and that line goes and where my vanishing points are. It is good to rough out your perspective and your large forms. To actually draw everything using this method is terrible. Think big with the calculator and do the rest manually.

This was just a tip for those who may be interested in a different approach on how to draw with mathematical exactness.

Pierre

[ December 19, 2001: Message edited by: pierre ]

[BooMSticK]

lol Shizo.. you really crack me up from time to time!!!

but besides that... I surely didn't get a 1/10 of what Pierre just said... In through one ear - out the other... so to speak!
,boom

[[Shizo]]

hehe.. it's true.
PS: lemme give you a 5-star rating, because konjak that i'm drinking is 5-star also!

[Ian Jones]

Hmmm, I didn't get much of that either.

If anyone actually creates the program for this, then it would be great if they could provide it for everyone to use. Don't forget a tutorial on how to use it aswell!!

[Ian Jones]

Hey do you reckon you could program it in Flash? Therefore you could put in dimensions like your paper size, cone of vision, and the calculations and it could render a simple vector drawing for you, that shows you where to measure and put points in relation to your paper size you entered.

that would be cool. *nudge nudge, wink wink*

[Ian Jones]

or you could just use a 3D program! what a revelation! LOL

[Ian Jones]

or you could just use a 3D program! what a revelation! LOL

I'm an idiot.

[lazydead]

Wow.
I didn't know it was that simple.
No...really.

Ian Jones:
"Hey do you reckon you could program it in Flash?"
I don't know about Flash5 but I'm used to Flash4 so...You could recreate this in JavaScript and use it as the engine to process the variables you send it with an FS command. I think that's what I remember.

I could see this written in JS to do a whole crapload of stuff.
Thanks for sharing it.

[edit]
I just remembered that way back in the day I wrote script for Flash to draw a line between two points. I never got around to using it for anything though. I gotta go find it and do a little updating...
[/edit]

[ December 21, 2001: Message edited by: lazydead ]

[edible snowman]

is there a book or text that explains this in more detail? i hate knowing how to do something without knowing why it works.

[Queezy]

Well, it's nice to know, but I'm more artist than I am mathematician. So I'll stick with good old guess, and the not so old 3D Studio Max.

[pierre]

well,

I have no book about it.

Actually, the whole purpose of this method is that you don't have to sit at a computer, just at your paper and a programmable calculator.

Those who whave constructed a correct a perspective grid with the rotation and height angel higher than 0 (sometimes incorrectly called "three point perspective") knows that you need to have the vanishing points very very far away from the paper inorder to get a satisfying drawing area. You could of course draw the points and grid in photoshop, resize the drawing area and print it out to draw on if you desire.

But there are other advantages with this "numerical" method that it would be too painstaking to do with the graphical method.

Further more, you don't have to be a matematician to use this method, just as little you have to be one using 3D studio max.

Why would we use 3D studio max when we can draw our own perspective grid? Isn't that one part of the creative process, creating your perspective? It is fascinating that you can generate a grid that easy and fast and that is something all artists should take advantage of. After all, before computers, illustrators bought or made their own 3D grids to use over and over again. But, I don't think it would be wise to generate a 3D software grid before one thouroughly knows the basics.

A software can easily create primitives today. But what happens when a software can create anatomically correct humans at your desire, with just some inputs by you, with acceptable speed. Would we give up that aspect of our creative process too? I know I wouldn't.


In conclusion,
this method doesn't require a computer and it doesn't require you to spread your paper out on your backyard inorder to create a 3D grid.




[ December 23, 2001: Message edited by: pierre ]

[KeLLuSioN]

hmmm that's really something pierre, though i'm to really sure how it all relates to the linear perspective... could u perhaps show a diagram or something? i'm sure lots of people would be able to make more sense of it that way, or at least i would. i like trig tho