View Full Version : Some doodlings and explanations on perspective...

05 May 2005, 10:52 AM
I started doing this for another forum. Will complete it in due time ^_^ So be patient. Pardon the crappy rushed images, but they were done during midterms as an emergency help for a pal. All this is built from old 2000- architecture notebook annotations taken at class.

Part I: Getting Started

The Horizon Line.

The utmost important thing about perspective is stablishing the eye level line or horizon line- it is the line were our two limits, sky & ocean meet. YOU MUST KNOW WHERE IT IS AT ALL COSTS.

Visualization through Positioning the Horizon.

Depending on your Horizon Line you will give your work a different atmosphere. From sharing the experience and integration (A.), to the observing position and distancing (b.) to a feeling of independence and importance (c.) Very much alike looking up to someone, as you did when you were a little child to looking down on someone as tall people/adults do or being at the same level.

Cone of Vision

Even though we may be aware of the whole space- our f vision doesn't really allow us to see everything clear. Many say that our cone of vision (measured from the standing point) is from 55 degrees to 65 degrees (I guess wide eye people see more goatish ); +/- 60 degrees to be exact. Anything further than that *must be distorted. However if you choose to stay within the 60 degrees limit working with basic perspective should be easy.

05 May 2005, 10:56 AM
Part II: Vanishing Points

The basic perspective constructions are done in relation of the subject to the imaginary picture plane. Visualize yourself as if looking from behind a crystal (PP). After identifying the horizon and the Central Line of Vision then we can study the objects and interpret their relation to the horizon. When we see a common building we can think of it as a cube whose surfaces are composed of plane rectangles. But if we observe them we notice that even though we know that the sides are quite the same and rectilinear the angles don’t look as they should. Here is where we come to the vanishing points and their relation to objects. We can resume the types basically in three: One (Vanishing)-Point Perspective (# 1), Two-Points Perspective (# 2-4) and Three Point Perspective (Not done yet).

A. When we look to an object straight ahead (Fig. 1)it is a One Point Perspective Type- the most basic and simple one to do.

B. Two point perspective only changes because of the angle in which we look at the object. Notice how I played with the positioning of the PP(canvas, etc. in relation to the diagrams at the right. While #2 seems more normal/centered in reality it isn’t, instead it is very similar to Fig. 4. While #3 seems more to be like #4 this one does have symmetrical vanishing points and the angles in realtion to the horizon angle (180 degrees) are at 45 degrees in relation to the CLV (90 degrees). It’s just that the end result of the PP is not centered- when it could be. Moving the visible field about and around is a good way of making interesting pictures using simple techniques.

Here the angle of the object changes and the vanishing points as well giving us another option and example using the Two Point Perspective.

Vanishing Points is almost finished here. I'll explain the Three Point Perspective in full- starting from the three vanishing points. After I go more in depth with the next two parts: One Point Perspective and Two Point Perspective.

05 May 2005, 10:59 AM
Part III: One Point Perspective

The credits for this exercise can be traced back to Leon Battista Alberti (1404-1472) to whom we should be thankful! A moment of silence for Alberti....:sad:

Imagine that A. is a pavement grid divided into identical squares and placed on the floor in front of you. The front edge of this pavement grid is positioned at the edge of the PP.
To establish the VP, we put in the HL which must be at the same level of the viewer’s eye.

After we establish the angled guiding lines all parting from the same source- the SP/ the eyes of the viewer- we can easily make up a 1PP piece. This is done through the use of Orthogonal & Transversal(horizontal) Lines. If you're confused don't worry about names...I'll explain further on.

This is one way of doing IPP using a plan. This is called the Pavement Method (which is really the Alberti Method looked from another angle).

1) Establish the SP.

2) Establish the PP***, GL & HL( ***the unnamed green horizontal line between the Sp & GL- no need to name it for it is not that important for this exercise- the PP is the same as the lower edge of the pavement grid)

3) Establish the VP

4) Make the Plan* of the Pavement Grid (grey square)

5) Establish the measurements for the nearest edge which is exactly the same as the diameter of the pavement grid and extend lines diagonally towards the VP

6) From the superior corner a. trace a line to the SP

7) Notice how that line passed through b.

8 ) From b. trace a vertical line towards the HL, you'll notice that on the way it will touch various angled lines- stop at the farthest to the edge (in this case the most to the left c.)

9) From c. trace a line towards the opposite corner at the ground line (d.)

10) Each point that line C-D touches will mark where the Transversals go. Trace the transversals parallel to the HL, Gl & PP and voilá!

Using Measuring Points

This is an extension of the Pavement Method.

1] Again: establish SP, PP & GL (in this case the same), HL, & VP.

2) From the SP trace a diagonal at 45 degrees toward the HL. Where this intersects the PP it will become the lower corners of the Pavement Grid. Where it intersects the HL it will be known as a Measuring Point..

3) Trace the diagonals towards the VP from the two points on the PP.
From the MP in the left trace a diagonal until it touches the right low corner. Do the same in the opposite way from MP in the right towards the point of the Pavement grid in the left.

4) You’ll notice that each diagonal intersects the lines that disappear in the VP in many places. The nearest intersecting point and the farthest will establish again the measurements of the figure of the pavement grid. The inner intersecting point will establish the crossing lines.

05 May 2005, 11:02 AM
I'll explain further, this time using cubes this time:

1) Establish the SP, VP & the HL. This time we are not working with ground lines- in fact we have two different one in this exercise.

2) Draw two different sized squares (preferably equally apart from the CVL) at different heights.

3) From the SP trace a diagonal at an angle of 45 degrees towards the HL to establish the MP 1 & 2.

4) trace all the disappearing lines that end in the VP from each corner of the squares.

5) From MP2 trace a diagonal towards the furthest and lowest opposite corner of the right square- a. The place where this intersects the diagonal that goes towards the VP will be b. Do the same from MP1- you’ll now have c. & d. too

6) From b. trace a vertical line parallel to the other vertical lines of the square. This one will end at the angled line. Where that touches trace a horizontal line towards the right, then a vertical line down. This will make a similar square to the one you already had drawn. Just finish tracing the rest of the cube now. Line b-a denotes the diameter of the side of the cube that is on the ground. Do the same with the other square and transform it into a cube.

We can use a plan & elevation in a similar way:

1) Draw a simple basic plan and elevation. be conscious of measurements*

2) Establish the main lines and Points- SP, CLV, HL and a MP to the left by intersecting the HL with a diagonal at an angle of 45 degrees. Draw a square for the *plain elevation (wall) of the plane using the same measurements as the original plan.

3) Starting from the central line of vision make an inverted replica of the points measured at the elevation a-f, they will be inverted to f-a. Notice that point b. determinates the beginning of the nearest wall of the Plan and that a. goes in further.

4) From the MP trace diagonals towards the lettered points.

5) From the intersections on the CLV you can now trace the rest of the 3d design.

To be continued...LATER (Finals are coming so be patient)

Oh, and if you have any questions so far, feel free to ask! ^_^

08 August 2005, 03:37 AM
you wrote all this hoping people would see it but unfortunately you chose an unpopular place XD

well, just so you know your hard work isnt all useless...i have read this and found it very useful

im going to test out some of this right now :thumbsup:

08 August 2005, 05:49 AM
oz haver,

Great tutorial, thank you for taking the time to do this! :thumbsup:


08 August 2005, 09:34 AM
Great stuff! Definitely stuff to munch on and you explained it very concisely. Thanks!

:thumbsup: :bounce:

08 August 2005, 05:13 PM
Heres a technique for foreshortening correctly. Simply find the middle of the square(You can do so by finding the intercept point in the transversals.) Then extending a line away from the square you are about to draw.

08 August 2005, 04:43 AM
Awesome stuff! Thanks so much for taking the time! I'll add this to the sticky page of tutorials.

08 August 2005, 09:18 PM
I saw this before, and it still rocks. :D Thanks so much, Oz!

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