Perspective
Constructions
Outdoor Assignments
Special Courses
Publications
¤ "A New Methodological Approach for Teaching"
¤ Street Drawings
(Thirdyear students of Buda Castle)
¤ Lecturing in Illinois as a Fulbright Scholar
¤ "Contourside Opposites of Tone
 the Local Contrast"
¤ Chaos and Order 


"A NEW METHODOLOGICAL APPROACH
for TEACHING
ARCHITECTURAL FREEHANDDRAWING"*


Keywords: basic structure of linear web, convergence, extreme oblique line, foreshortening, framing shape, judgement by naked eye, main direction, master picture plane, perspective distortion, projection, proportion measuring, proportion meter, reduction, target of observation, sense of proportion, simple line, sight from above, sight from below, viewpoint, Yshaped junction.

In teaching the basic structure of Architectural FreehandDrawing, most problems are due to the correct presentation of illusion of depth. It's about the determination of oblique lines which are principally responsible for the perspective effect that means about their inclination compared to main directions. Within the frames of the "Master Picture Plane", converging lines of the perspective create a system of lines appearing to be inclined.
To a given viewpoint only one kind of perspective distortion may correspond. Most of typical structural errors in perspective drawings might be traced back to mistakes committed in this field. 



Blackboard figures explaining
The "Propotion Measuring Method"
(Central projection through orthogonal pictures;
A stepbystep picture about the birth of the oblique line;
Metering "sightfromabove"ratio with lengthened measuring arm.)



I propose the introduction of my new methodological approach called "proportion measuring" in the initial phase of teaching of Architectural FreehandDrawing, when the teacher needs absolutely the possibility for convincing demonstration of certain critical connections in the view  observed through the pupil's angle of vision.
The name of the help developed for this method is "proportion meter". The educative role of my device is to devide the mental process of presentation of space in plane into some decisive steps. This auxiliary instrument supports the development of the sense of proportion and the correct judgement by naked eye through selfcontrol and it proves the critical comments by impartial demonstration.
With the help of the "proportion meter" the drawer can temporarily fix certain points or lines by covering them on his "master picture plane" which he imagines to be joint to the top edge of his drawing board. During the measuring process he follows the target of observation on this master picture plane, accomplishing the needed comparisons and projections in a suitable chronological order. Who has mastered to transmit in an appropriate proportion the data of his virtual picture plane to his drawing plane, has essentially solved the secret of basic structure of perspective depicting. 
Although the "proportion meter" seems to be adequate for controlling any oblique lines appearing on our picture plane, yet in the first place we should use it for teaching how to present the phenomena of convergence and foreshortening within the spatial modul system of basic lines.
My methodological experiments were carried out in the initial phase of teaching freehanddrawing at the Department for Drawing and Design at the Technical University of Budapest, among Hungarian and foreign students for Architecture and Civil Engineering (199898). In 1997, I tested my new approach also at the Ecole d'Architecture de Strasbourg, France. 



Teaching of basic elements of linear perspective by reductive methods

The way to the oblique lines appearing in the picture plane leads through the simple lines. The subject is: the space, we represent it by the method of projection; the result we produce is: a drawing in plane.
We reduce the limiting walls of space to vertical and horizontal planes. We relieve the objects by their framing shapes. Curves should be represented by tangents or chords, curved surfaces should be substituted by covering planes.
For the sake of teaching, basic components of our surrounding should be reduced to a simplified "basic structure of linear web". We substitute objects and volumes by simple cubes; we change spaces into an enlarged cube's interior subdivided by quadratic network. The teaching aim of this initial phase is the correct presentation of the basic web  distorted according to the given viewpoint. 

Teaching perspective freehanddrawing, we first show how to depict the virtual deformation of the quadratic web on basic planes. Subdivisions, surfaces and other details which differ from the basic web remain to be elaborated in the next phase of presentation process, being adjusted outside or inside of the shellstructure, considering it as scaffolding.
We analyse in the core of the linear web (at the socalled Yshaped junction) the largest distortions. We disassemble the objectcube and the spacecube into their typical components: positive and negative corners, "sights from above and from below". We observe in a central meeting point the relation between the oblique lines and the main directions, evaluating them successively.


Most important basic phenomena for us are the convergence and the foreshortening (appearing here as sights from above and from below); plus the case of hiding. Examining their effect on the line, we understand that convergenceforeshortening cause mainly an increasing density of lines; and hiding results an absence of lines.

An instinctive approach to basic phenomena of perspective

If an architectteacher like me, creatively dealing also with arts, becomes really immersed in the scientific theory of perspective, he schrinks soon back from the mass of complicated demonstrations in which the working process (that means the chronological order of construction) can hardly be followed.
We, draftsmen, stick less to a scientific background and prefer more instinctive observations, individual experiences aquired with a lot of practice: we better study famous predecessors and work with other patterns. Who can draw a cube even by heart, according to a given viewpoint, masters really the science of perspective. The minimal level of Architectural FreehandDrawing is the skill of correct presentation of the main directions of space which converge in the cube's corner.
We approach to the simulation of depth's illusion from the side of instinctive observation. We delimit ourselves from the omnipotence of vanishing points  because they are often far off from the drawing surface. We shall control convergences afterwards only! 
My principal goal is to make perspective perceptible as a phenomenon. The perspective is an illusion, the experience of depthsensation in space. Rendering perspective is a graphical mode of presentation, by which we produce pictures about real or imaginary objects which are similar to pictures originating of normal sight. Practising perspective is a twoway action: we let see what exists already, what has been and what it becomes! Thus perspective serves both imagination and surveying. The task of a perspective picture is to make the spectator believe that lines on the paper may express "depth"  thanks to oblique lines!
The sensation of perspective depth on a picture reduced to simple lines is mainly due to the convergence of parallel edges of the basic structure of linear web, as well as to foreshortenings of its intermediate spaces. We register this phenomenon in the picture plane as line slantins, compared with main directions.




Pulling down the perspective to simple linear web

From the viewpoint of our rendering goal, we may separate (1) scientific drawing (constructed mainly by ruler and belonging to Descriptive Geometry) and (2) freehand drawing, related to fine arts.
Next we carry out the reduction of the perspective picture, leading to simple lines. Let's devide the requisits of our graphical store in two groups: "linear" and "other" means for expressing of distance! Linear drawing might be a contourdrawing, made of simple lines only, enriched later by surfacesubdivision and material rendering.
Teaching of "lines" is indispensable in drawingteaching. We analyse the optimal chronological order of weblayers woven of lines, grouping them accordingly to their depthexpressing function. Let's disregard all kinds of "other" depthcreating graphical means, and let's walk backwards from the finished picture to the empty paper! First we take leave of colours, tones; next of other details, surfacesubdivisions and material renderings  at last remains the essential basic structure of linear web only! Here the illusion of depth might be mainly expressed by direction and length of lines: operating with condensing or abandoning of lines.
In his manual on lines and perspectives, J.P. JUNGMANN calls a picture made entirely of lines as "white graphic". He considers architectural rendering as an optical mechanism, grouping all kinds of graphical effects in drawings according to the mutual mechanism between diverse light conditions, distances, materials, styles and adapted graphical means.
In my opinion, we may most economically (with less investment) reach the illusion of depth if we use the simple line web  measuring the result by the total length of lines drawn on correct places within a given time! Our task remains to find these appropriate places only. My present study tries to focus the Reader's attention to this special method for "catching" of oblique lines which express uttermost the illusion of depth.



Traditional Inclination Measuring of Oblique Lines

The traditional "pencil" method for observing of oblique lines and for making realize their virtual inclination could be described as "measuring by straight arm, holding a pencil". In the simple line phase of freehanddrawing, we attach importance to certain linesections of the sight, compared with each other in an apprpriate chronological order. The advantage of the classic method is that the pencil is always close at hand and stretching one's arm is easily accomplished. Its disadvantage is that it involves many uncertain elements: the distance between the head and the picture plane traced out by pencil is unstable, the linesegment marked with the thumb's nail on the pencil is limited, and thus the sightdetail remains tiny.


The New Approach

The "Proportion Measuring" method can temporarily fix and increase the characteristic data of the observed foreshortening. This happens on the surface of the "Master Picture Plane" which we imagine to be attached to the upper edge of the drawing board. On the Master Picture Plane we exactly accomplish the needed comparison of segments in order to quantify proportions. (That means we find out differences between horizontal and vertical components of the "diagonal"  hypotenuse  in question.)


My "Proportion Meter" developed for this methodological approach is a teaching help for measuring of oblique lines within the basic structure of linear web. By visualizing the (master) picture plane, it clearly surmounts the uncertainties of the "pencil" method.
By introducing this help, the connection between the masterpicture plane and the correct position of the drawing board, can be understood.
If we succeed in developing the special capacities of realizing the comparing choice and the quantifying of proportions in the early stage of teaching; and if we succeed in instructing our students how to "catch" the oblique lines, we may step forward to the next chapter.

The ability to judge proportions with naked eye is more or less an inborn aptitude, which can, nevertheless, be spectacularly improved with practice. Its development is one of the important tasks of freehanddrawing instruction. At the beginning, my teaching help should also participate in the training, when students still have an open and receptive mind for all kind of new approaches.
My experiments proved that the Proportion Measuring Method is suitable for:
• Checking of convergence and foreshortening,
• Developing awareness for target areas of observation,
• Disintegrating of oblique lines in the basic structure of linear web,
• Comparing of (enlarged) perpendicular sides.
The method has proved as a suitable help for finding the picture's frame and for determining the vanishing point occasionally falling outside the paper. Lines inside the paper could be outwardly extended  short segments could be enlarged. With the help of the "Proportion Meter" we may discover further important intersections and demonstrate many characteristic features of the basic structure of linear web. It has a role in simplifying outlines, in determining important intersections, in substituting lines and it identifying axes. By adjusting the device's hand we evidently show the position of the masterpicture plane. 
On basis of experiences gained by testing my "ThreeHandMeasuringDevice", the prototype of my "SingleHandTeachingHelp" was completed in January 17, 1997.


This observation method of dissecting the picture plane, also teaches some kind of chronological order. The teacher can help even his weakest pupil to realize the basic phenomena of perspective,  even without touching his drawing!  when, from the student's viewpoint, he prepares the help's measuring hand by which he determines the virtual position of extreme oblique lines.
Auxiliary devices for perspective construction, having been discovered until now, were either too complicated to be ready for practical use, or too simple. The greatest efforts have been made  before the computer's appearance on the scene  in the mechanization of perspective reconstructions using their orthogonal pictures.
Freehanddrawing requires few instruments only: the proportion measuring device could complement these at the beginning of the instruction. Its educative role lies in demonstrative guiding and in practising of observation, to sum it up: in teaching how to see.
In my opinion, nothing can substitute one's inborn ability to judge proportion by naked eye: however, in order to develop and to improve it, any new method promising some success should be allowed.



*Revised in 2oo4 for Freehand Drawing Course ont he basis of my article published in the "Új Magyar Építőművészet" ("New Hungarian Art of Architecture"), a Cultural Periodical of the Society of Hungarian Architects, Budapest, Hungary  1998/6, p. 5961, column "Teaching"



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