Proportion Meter

 

A New Methodological Approach for Teaching Architectural Freehand Drawing

 

Key-words: basic structure (framing grid of cubes), extreme oblique line, Master Picture Plane, perspective distortion, target of observation, Y-shaped junction.

In teaching the basic structure of Architectural Freehand Drawing, most problems are due to how to make the illusion of depth.

It is about the determination of oblique lines principally responsible for perspective effect: about their inclination compared to verticals and horizontals insured by drawing paper’s edges.

Within the frames of the "Master Picture Plane", converging lines of the perspective create a system of lines appearing to be inclined.

To every viewpoint belongs a unique perspective distortion.

In the initial phase of teaching we often need the possibility for convincing demonstration of certain critical connections in the view – observed directly through the pupil's angle of vision.

The name of the tool developed for this personal method is: "Proportion Meter".

Its educative role is to devide the mental process of space presentation in plane into some decisive steps.

This auxiliary instrument improves the development of the sense of proportion and the correct judgement by naked eye through self-control.

It proves 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 drawing board’s top edge.

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 masters to transmit in an appropriate proportion the virtual picture plane’s data to the drawing plane, essentially solves the secret of perspective depicting’s basic structure.

Although the "Proportion Meter" seems to be adequate for controlling any oblique lines appearing on our picture plane, we should use it first of all for presenting the phenomena of convergence and foreshortening within the framing grid of cubes.

My methodological experiments were carried out in the initial phase of teaching Freehand Drawing at the Department for Drawing and Design at the Technical University of Budapest, among Hungarian and Foreign students for Architecture and Civil Engineering (1998-98). In 1997, I tested my new approach also at the Ecole d'Architecture de Strasbourg, France.

Early experiments with combined metering tools and Master Picture Plane.

Teaching linear perspective’s basic elements by the reductive method

The way to oblique lines appearing in the picture plane leads through simple lines. Our subject is the space, which we represent by the method of projection. The result we produce is: a drawing in plane.

Four-way reduction to pure lines

We reduce space’s limits to vertical  and horizontal planes. We relieve objects through framing cubic grids. Curves are replaced by tangents or chords. Curved surfaces are substituted by covering planes.

We substitute objects and volumes by cubes. The initial teaching aim is how to present correctly the framing basic grid - distorted according to our single viewpoint.

Subdivisions and other details which differ from the grid remain to be elaborated in the next phase of presentation process, being adjusted outside or inside of the shell-structure, considering it as scaffolding.

We analyse in the core (at the Y-shaped junction) the largest distortions. We disassemble the object-cube and the space-cube into their typical components: positive and negative corners.

Most important basic phenomena are: convergence, foreshortening  and hiding. Examining their effect on the line, we understand that convergence-foreshortening cause mainly increasing line density. Hiding results an absence of lines.

Outdoor experiment with the Proportion Meter mounted on easel.

An instinctive approach to perspective’s basic phenomena

If an architect-teacher like me, creatively dealing also with arts, becomes really immersed in the scientific theory of perspective, he soon schrinks back from complicated demonstrations in which the working process (the chronological order of creation) can hardly be followed.

We, draftsmen, stick less to a scientific background and prefer more instinctive observations, individual experiences aquired with many practices: 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 Freehand Drawing is the skill of correct presentation of main directions of space which converge in a cube's corner.

We approach to depth's illusion from the side of instinctive observation. We delimit ourselves from the omnipotence of vanishing points: they are often far off from the drawing surface. We control convergences afterwards only.

My principal goal is to make perspective perceptible as a phenomenon. The perspective is an illusion, the experience of depth-sensation 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 two-way 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 express "depth" - thanks to the oblique lines!

The sensation of perspective depth within a picture reduced to simple lines is mainly due convergence and foreshortening. We register this phenomenon in the picture plane as line slantins, compared with main directions.

Pulling down perspective to simple lines

From the viewpoint of our rendering goal, we separate scientific drawing (constructed by ruler and belonging to Descriptive Geometry) and fine arts related Freehand Drawing.

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 distance expression! Linear drawing might be a contour-drawing, made of simple lines only, enriched by surface-subdivision and material rendering later.

Teaching of "lines" is indispensable in drawing teaching. We analyse the optimal chronological order of web-layers woven of lines, grouping them accordingly to their depth-expressing function. Let's disregard all kinds of "other" depth-creating 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, surface-subdivisions and material renderings. Finally the essential basic structure of linear web remains only. Here the illusion of depth might mainly be expressed by lines’ direction and length: operating with line condensing or abandoning them.

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 length of correct lines within given time! Our task remains to find these suitable places only. My research intends to focus Reader's attention to this special method for "catching" extreme oblique lines which express uttermost the illusion of depth.

The traditional method for inclination measuring

The traditional “pencil” method for observing oblique lines, realizing their virtual inclination, could be described as "measuring by straight arm, holding a pencil in hand". In the pure-line phase of freehand drawing, we attach special importance to certain line-sections of the sight, compared with each other in an appropriate chronological order.

The advantage of the classic method is that a pencil is always close at hand and stretching arm is easy. Its disadvantage is that it involves many uncertain elements: the distance between head and picture plane (traced out by pencil) is unstable, the line-segment marked with the thumb's nail on the pencil is limited, and thus the sight-detail 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 drawing board’ upper edge. On the Master Picture Plane we exactly accomplish the 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 oblique lines within the basic structure of linear web. By visualizing the master picture plane, it clearly surmounts the uncertainties of the traditional “pencil” method.

By introducing this help, the connection between the Master Picture Plane and the correct position of the drawing board might be better understood.

If we succeed in developing special capacities of realizing comparing choice and proportion quantifying in the early stage of teaching; and if we succeed in instructing our students how to catch oblique lines, we may step forward.

After having tested the prototype Three Hand Meter, its successor the of Proportion Meter was completed January 17, 1997.

The ability to judge proportions with naked eye is more or less an inborn aptitude, which can, nevertheless, be spectacularly improved through practice. Its development is an important task of freehand drawing instruction.

Early experiments with the Three Hand Meter.

My teaching help plays a role in training at beginning, when students usually have an open and receptive mind for all kind of new approaches.

My experiments proved that the Proportion Measuring Method is suitable for: checking 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  vanishing points occasionally falling off 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 in identifying axes. By adjusting the device's hand we evidently show the position of the Master Picture Plane.

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 drawing’s touching – 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 for practical use, or too simple. Before the computer's appearance, the greatest efforts have been made in the mechanization of perspective reconstructions, using orthogonal pictures.

Architectural Freehand Drawing requires few instruments only: the Proportion Meter may complement these at the beginning. Its educative role lies in demonstrative guiding and in practising of observation - in teaching how to see.

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 success is allowed.

Published in: New Hungarian Art of Architecture (Új Magyar Építőművészet) Budapest, 1998/6, pp 59-61