Chapter 2  Perspective Drawing by F. Gilly

2.2  Lecture on perspective

      F. Gilly is known that he built young architects' group, and educated mutually(9). On that occasion, the design subject was shared and training of perspective was also performed. Moreover, he served as a professor of architectural drawing in the Architectural Academy (Bauakademie) just founded in Berlin, and taught the exercise for "Optics and Perspective" (10). The memorandum on the outline of the lecture is left and it is found there that he showed concern not only in the geometrical perspective method as a part of architectural drawing technology but also in the perspective as an artistic pictorial expression (11). Its first part is on the geometry of perspective, the second part is on the shade and shadow theory and the third part is on the color theory, and the still more detailed items were discussed in each volume, showing synthetically the theoretical and artistic guidelines in total. This outline of the lecture is a precious material to know what kind of points one should focus on in order to analyze his method of perspective.

     A practice subject work to answer the basic problem of the perspective is left behind which is said that Gilly drew himself (photo. 2)(12). It is a perspective drawing which lays on the foreground a form of solids just like a range of building blocks, and sets a background with a water surface like a lake and a mountain range. The central form consists of pieces of cubic form including four slopes which are probably supposed as the outdoor stairs, and surrounding five pieces of rectangular parallelepiped of various size. Although the central form makes one symmetric figure glued together, other rectangular parallelepiped are arranged at random, and also with slightly different heights. The standing point of two-point perspective and the vanishing points (serving as measuring points simultaneously) in the right and left direction of 45 degrees are specified, and moreover, a sketch in three dimensions showing the relation between the viewpoint and the picture plane of perspective is thinly found out at the left end of the lower part of the figure, and therefore it is guessed that this figure was probably used for the educational purpose. The trace of having taken the level size on the horizontal measuring line is shown in this perspective, and that makes checkerboard on the ground, which define the position of each solid. The trace of the same size is found also on the vertical measuring line located at the center, and the height of central form is simplified on the basis of the square root of the level size. Moreover, it also turns out from such size picking that an abstract modeling method is used performing combination of geometrical solids directly on the perspective drawing, and not that the perspective is drawn after having created a plan and elevations beforehand.

     This perspective is represented by CG picture of the ray tracing method as CG photo :G1, and the voluntary perspective view from the infinite upper viewpoint equivalent to a roof plan is CG photo :G2. On the original perspective drawing, the direction of lighting is so simple as from true left and in 45 degree vertical angle against the solids, and the exact shade and shadow expression was tried on it. But it turns out that there are several mistakes in the position and outline of the shadow in the original perspective drawn by Gilly as compared with CG picture. However, the depth of the color and the depth of the shade and shadow seen in each plane of the solids are colored comparatively correctly, and that shows the accuracy of Gilly's knowledge on the perspective method, especially concerning optical expression. By the way, the background picture is not following as same depth image as that of the form on the foreground at a glance, and it seems that the depth of the color of the mountains is determined by means of the aerial perspective method independently. The creation procedure of this perspective drawing is understood here clearly. Namely, only the form of solids as the main subject is processed by the three-dimensional geometry, and the background is processed freehand as a two-dimensional picture in harmony to the picture of the foreground.

     Because of the attitude to try to illustrate directly the theory and the simple setting of the conditions about volumes, positions, angles, etc., it becomes clear that Gilly was a kind of perspective painter who thinks basic theory as important, although this figure is only an exercise for an educational purpose.

 2-3  CG representation of the project for "Monument for Frederick II"

2-4  Evaluation of Gilly's perspective method

      The important feature of Gilly's perspective is in the space expression using a very clear outline. It reveals how he understood and utilized the perspective method.

(a) Linear expression

     In regard to the Gothic architecture of the above-mentioned Malbork Castle, it was characterized by vertical lines and also arch lines made of ribs showing vertical character, and clear edge lines of the geometrical form in neo-classic style was emphasized in the "Monument for Frederick II" project and the “National Theater” project. However, they are common in the linear composition of such clear outlines in spite of the difference of the style, and it showed the more universal modeling technique.

     On the other hand, his perspective drawings made generally use of the two-point perspective method, and many of them emphasized the comparatively dynamic motion of space rather than expressing the sense of stability using one-point perspective. This point can be referred to as showing the artistic sensitivity of this time that inherited the expression technique of Bibiena family or Piranesi.

     The simple and clear outline, which appeared since the linear geometrical processing of a perspective method built the base, as mentioned as "linear graphics" in Gilly’s lecture items, had a role to display the virtual frame of the space on a perspective screen. It is considered that to the features mentioned above, such as the streaminess, layer composition, and openness of the space, the character of abstract modeling carried by such linear space structure had influenced strongly. The more delicate expression technique will be developed in the 19th century, and therefore such character to express the virtual frame will be lost instead. The "Monument for Frederick II" project can be said having shown a kind of the style of epoch, in the meaning that it has embodied such a sense of modeling in the 1790s.

(b) Method of shade and shadow

     It seems that the time is assumed around from 2 to 3 o’clock p.m., judging from the solar shadow although the solar position is influenced also by the season. Then, the viewpoint position is taken to the southeast side in order to express clearly the silhouette of the Greek temple on the podium. It shows that, in connection also with the way how to take a viewpoint position in order to express the assembly of the total form as clearly as possible, the light source of sun was set up from the intention to express the form intelligibly.

     As compared with the CG picture by the ray tracing method, the shadow in each portion of the original perspective was indeed added pursuing preciseness, but there are found some places which have certainly exaggerattion in order to express  solid effect. Especially the shadow of the eaves of the temple is actually deeper (In the CG picture created here another light source is added and it is partly rectified in order to imitate the original perspective.).

     In another perspective sketch of Gilly painting the interior of naos, stand type votive lights are found at the right and left of the Friedrich II’s figure, and their effect is reflected on the surface of walls, pillars, etc. Although it seems that only the right one is on in this sketch, it is represented in the CG photograph G20 in a situation that both are turned on. Here is found the practice corresponding to what was mentioned in the lecture items, namely, not only the solar parallel light but also "Various lights of lighting objects (Verschidene Strahlung leuchtender Körper)".

     Since in the shade, which is made by the brightness attenuation according to the degree of light incidence angle, infinitely various reflective lights and dispersion lights overlap intricately actually and indefinite elements such as a shadow of clouds are involved, in fact, it is impossible to reconstruct it completely correctly by a CG picture which is performed only by a setup of the light source position of sun. In the original perspective, brightness was suitably adjusted with artistic sense of a painter in order to assume it as a natural scene, and so we have decided to set several light sources in the CG picture in order to imitate it as similar as possible. Moreover, on the original perspective, the buildings of the city area behind the square and roadside trees have dropped saturation using aerial perspective method. As known from the lecture items, it is found that Gilly seems to have examined the artistic quality of the shade and shadow effect deeply and pursued it in high grade exceeding a materialistic expression of architectural design, .

(c) Color

     That the three-layer composition of the monument is distinguished like the upper layer's white, the middle layer's ocherous and the lower layer's dark brown suggests that the contrast effect of design using the color was intended (19). The building with a pediment on the right hand edge and the city gate of rectangular parallelepiped on the left has a beige color similar to the color of the middle layer, and distinction of color was also made with the form element. Moreover, in the original perspective, bright white clouds are allotted behind the temple form in the sky of the background, and it seems giving the underlining composition of pyramid form at the whole, and therefore there could be found an intention to make central brightness high in the total screen structure and to express a feeling of a rise. In short, it is guessed that the composition theory of picture was probably used here.

     It turns out that one of three chapters in the lecture items is set for "color theory(Lehre von den Farben)", and color expression is thought considerably as important. The title about "phenomenon, attributes and general effect of color (Erscheinung, Eigenschaften und Wirkung der Farben im Allgemeinen)", "the pure color as the inherent and different individuality of various objects observed from the aspect, the proportion and the mutual relation (Die reinen Farben als eigenthümliche und unterscheidende Eigenschaft der verschiedenen Körper nach Art, Verhältnis und Verwandtschaft gegeneinander betrachtet)", and the items including a mixed color, etc. are seen there, and it is also guessed that Gilly was inquiring in detail about color expression. It is known that in the same 1790s Goethe wrote "Beiträge zur Optik (Contributions to Optics)" (1791, 92) and criticized the theory of Newton, and also made research which was published as "Farbenlehre (Color Theory)" (1810) (20). It solved the phenomenon about color through scientific experiments, and discussed it in relation also to the artistic expression. Although the meanings of the optics in natural science and the optics in graphics differ, it can be said that Gilly's perspective theory was also a symbolical thing of the general concern of those days.

　Chapter 3  Architectural Painting by K. F. Schinkel

3.1  Foreword

     Karl Friedrich Schinkel (1781-1841) was an architect who studied architecture under the influence of F. Gilly, and was a person who belonged to the young architects group which gathered around Gilly, and inherited his technique under his instruction of the perspective. He is known for having drawn much fictitious architectural pictures of oil painting, and having created much stage scenery paintings, such as Mozart's "Magic Flute" etc. (21). Especially he showed outstanding feature that he drew in the time of Neo-Classicism not only with classic style but also with Gothic style, having deep romantic yearning to Gothic style. Here, his perspective drawing "Gothic cathedral at the water" (1823) which shows a unique church of the Gothic style is selected for an analysis object, also for the sake of comparison with Gilly's neo-classic work (photo.6 and 7). (22)

3-2  CG representation of "the Gothic cathedral at the water"

     This oil painting is assumed that Schinkel painted as a landscape painting, designing a fictitious cathedral and setting also fictitious environment. Therefore, it might be said an ideal architectural project which Schinkel held.

     As for this painting a draft drawing for the preliminary design based on the perspective method is left and it is possible to reconstruct from it the outline of the plan and reproduce the architectural form (Fig. 4)(23).

(a) Analysis of the working situation of perspective drawing

     In the draft drawing which Schinkel left is found the main drawing of the perspective view in the upper part, and in the lower part, the auxiliary perspective drawing of the cathedral's plan, the quay at the water and the large stairs, and also the plan for an arch bridge built toward the opposite bank. This is the trace which is left during the work for the dummy perspective in order to determine the level position of each point to draw the total perspective. Such perspective technique was used to make the scenery painting for the stage of the baroque age, as is presented in "Civil Architecture (24)" (1711) etc. by the Ferdinand Galli-Bibiena in detail with the model figure. Piranesi, a prominent architectural painter, was also supposed to be under its influence. Schinkel, who was also tackling with stage scenery painting as mentioned above, is considered to refer to these publications by Bibiena, and to have been well versed in this projection method.

     From the drawing of the auxiliary lines the standing point, two vanishing points, the center of vision, and from such information the position of the picture plane can be correctly identified. The standing point is on the terrace in the foreground of the painting and the center of vision is at the position where the large stairs under the cathedral touch the terrace at water. The height of the man's eye who stands at the tip of the terrace in the foreground matches the height of the center of vision exactly. It seems that Schinkel had set the viewpoint after performing prudent examination considering the appearance of the cathedral, as discussed below. The left vanishing point is at the left edge scarcely inside of the draft, and the right vanishing point is far right out of the draft.

     Since another rough free hand sketch is left, it seems that Schinkel had drawn the outline sketch first and then shifted to geometrical processing after defining the center of vision and the vanishing points. There is a trace of a circle in the draft which makes the distance between right and left vanishing points a diameter, and the standing point is defined from the intersection with the perpendicular line taken down from the center of vision. Then, it seems to have progressed to the creation of the perspective of the plan form.

     By the method of Bibiena, a plan is prepared under the dummy plan perspective, and vertical lines are drawn from the edges of the plan toward the baseline. If thought as the same, Schinkel might have prepared a plan, but he could also work without a plan dotting the points on the baseline assumed as the measuring line calculating the length. Anyway, many points are dotted on the baseline drawn from right to left crossing the plan perspective, and auxiliary lines are drawn toward the center of vision from there, and each point on the plan perspective is defined further by connecting to the vanishing point, as it is in the method of Bibiena. Furthermore, starting from each point defined as such, each vertical line is settled in the main perspective.

     Thus from the perspective draft the plan and the elevations of the cathedral and its surroundings are reconstructed in outline (25) (Figs.5 and 6). In this case, the draft drawing includes some difference in some parts from the completed oil painting, and therefore Schinkel might have performed some amendment on the way.

     There is no material left which can define actual dimensions about size, and so it was processed as the relative size here. If  sizes are computed from the size of human body guesses very roughly, the upper surface of the podium of rock bed which makes the ground for the cathedral is about 20m from the water surface, and from the ground line to the top end of the central nave of cathedral is about 41m, and the height of the twin towers at the west facade is about 85m, the width between both ends of the aisle's outer walls of the basilica is about 30m, and the width between the right and left ends of twin towers is about 38m, all of which make a remarkable scale.

     The three-dimensional coordinates to make CG picture are defined here based on the numerical value acquired from the draft figure, and were readjusted in part according to the oil painting. CG picture drawn from the viewpoint as same as the original perspective is given as CG photo.: S1. For the sake of simplification of data, the architectural form of the cathedral and the surrounding urban buildings, etc., are expressed simplified restricting to volume expression here.

(b) Simulation

     The simulation pictures in which the viewpoint are changed using the same three-dimensional coordinates data are following CG photo.: S2-S20. Here, it is assumed that the cathedral has the general form of eastern apse, and the central axis matches the global east-and-west axis.

b-1  Viewpoint position simulation

<north-south movement of viewpoint>

- northeast (S2)

- northeast (the viewpoint is at the symmetrical position of the original perspective) (S3)

- east (S4)

- southeast (S5)

<viewpoint height movement>

- height of the ground of the cathedral (S6)

- height of the eaves on the top of the wall of the nave (S7)

b-2  Solar position simulation

 (here, the longitude and latitude, season, and time are not specified strictly.) 

- early morning (S8)

- morning (S9)

- noon (S10)

- afternoon (S11)

b-3  Form simulation

- trimming of the original CG (S12)

- a variation where the bridge between the twin towers at the west facade is removed (S13)

b-4  Figures for reference

- infinite far viewpoint  = an equivalent to a roof plan (S14)

- infinite far viewpoint  = an equivalent to an east elevation (S15)

- infinite far viewpoint  = an equivalent  to a north elevation (S16)

- infinite far viewpoint  = an equivalent to a west elevation (S17)

- a view from the north opposite shore (S18)

- a view of the west facade looking up (S19).

- a view from northwest looking down (S20)

(c) Evaluation of the work based on simulation pictures

c-1 Cubic composition by a three-dimensional coordinate system

     While Gilly tried to develop the three-layer composition which is the tradition of Classicism, and to apply it to the whole square space, Schinkel showed further on its extention a wide range space structure based on the layer composition which includes natural landscape and urban scape. That is, the polygonal rock bed modeled geometrically as the podium for the cathedral and the large outdoor stairs is equivalent to the lower two layers of Gilly's monument, and a Gothic cathedral was placed instead of a Greek temple. The presence of the podium is strengthened more than the cathedral by daring to take a low viewpoint position, and the exaggerated view of looking up at the cathedral in extraordinary situation is selected, and the perspective effect is heightened dramatically (26).

     In spite of being a Gothic church which generally emphasizes vertical lines, the feature of layer composition emphasizing the horizontal lines is remarkable here, and the horizontal elements are strongly shown in the edge line of the high podium on which a cathedral is built, the eaves of the roof in high level, the bridge connecting the twin towers on the height of the west facade, etc. In addition, in the perspective draft, the height of each part is adjusted using the measuring line of height, and then horizontal elements such as the articulation lines of west towers, lines of eaves running at the top of the aisle's outer walls, etc. become included. Indeed the horizontal lines as reference lines are also included in the church architecture of the Gothic style which is generally characterized by the vertical feature, but it is clear that the inherent nature of the perspective method has brought about the horizontal composition including even the surrounding space such as a rock bed and an arch bridge, especially here. Therefore, it can be said that the perspective method influenced the architectural form of the church in this picture.

c-2 The west facade

     When the architectural form was reconstructed from the perspective drawing, it turned out that weste facade in particular is not a usual Gothic cathedral, that is, its height of the central part of the facade is low, and twin towers rise from its upper end immediately (27).

     As to the west facade, the influence from the Halle Cathedral, the Prague Cathedral, or northern Gothic architecture, etc. is already pointed out (28). Anyway, it is a strange facade which does not have an example historically. In order to consider why Schinkel came to design such a strange facade, it is useful to investigate about how the visual angle of the oil painting was determined. CG pictures drawn from the viewpoints moving from north to south show how the composition changes in accordance with the spatial relationship with the sun (S2, S3, S4, S5).

     In the oil painting, a truly dramatic arrangement of light was performed that the halo is radiating from some gap of the structure of the cathedral against the background of the setting sun. Such composition is the technique which a painter of Romanticism Caspar David Friedrich often used, and it is found that Schinkel had tried to take out a similar effect getting inspiration from it (29).

     Probably Schinkel has built such original architectural form, without persisting in the customary style of facade so that the effect of light which leaks from the gap between the thin twin towers of a Gothic style is performed. Schinkel drew some other visionary works of the similar Gothic churches. One of them, "the Gothic church on the rocks at the see (30) " (1815, photo.8) , which set the afternoon sun in the background similarly, has the twin Gothic arches at the west facade just like a standing screen similarly, but has no deep gap or unusual facade. Besides, in "the medieval town at the river (31) " (1815) , the height of facade was secured so that the roof gable of the nave might be hidden clearly, and it followed a historical form in general. It means that the form of the west facade of "the Gothic cathedral at the water" shows unique form even if compared with these, and Schinkel had adhered to the gap from which light leaks so much. If there were no twin arches of the west facade, the distance between the towers might have become large and left some silly-looking architectural form (S12, S13).

     A rough preliminary sketch in which Schinkel examined freehand the form of the cathedral and the composition of its surroundings is left behind, in which such gap incised keenly is not found, and it turns out that some form change was made later to extend the interval of twin towers at the west facade so that a gap could be seen (32). The visual angle of perspective here was almost the same as that of the final work, and in this rough sketch, rocks, urban scape, etc. around the cathedral are illustrated and overall composition was already decided. Although the operation of modeling was added there which emphasizes the spectacle of the cathedral, especially that with soaring twin towers of the west facade, it was made a little bit wider in the final work, and it became to seem spatially spread emphasizing the light effect of the setting sun which leaks from the gap between towers.

     Thus, it can be probably said that Schinkel's intention was not in a church design of mere Gothic revival, and was rather in a design on the more abstract level, namely just the modeling of form and the effect of light. It doesn’t have to do with the problem of style theory whether it is Classic or Gothic, but the problem of more universal modern modeling.

c-3 Composition of the cathedral with four towers

     The word "composition of the cathedral with four towers" is the word which Schinkel had written down in the travel diary, and he claimed strongly that they should be four at all(33). It was because he aimed at for the the visual effect in the scenery against the setting sun at the back. Considering that the three-dimensional lattice could not be drawn in the space if not four, it turns out that it is a thing equivalent to four obelisks in Gilly's perspective. For Schinkel, then, the towers of Gothic style will make the vertical axes of the three-dimensional lattice.

    When a side elevation has been reconstructed, it turned out that the height differs between twin towers of the west facade and those which touch the transept wing remarkably in this "Gothic cathedral at the water". It is understood that he did not intended to create the perfect three-dimensional lattice arranging the heights of the tips of towers. However,  in the rough preliminary sketch sheet mentioned above, a small sketch which scribbled only four towers is also included, and it proves that he had examined what kind of scene four towers build. The composition which this preliminary sketch shows is the same as final composition and the viewpoint position was already decided. In this small sketch the scene that the twin towers at the west facade looked slightly higher than the twin towers at the transept was changed so that the perspective shows that the twin towers at the transept appear a little bit higher which were actually a little bit lower. It means that Schinkel paid careful attention to the mutual relation of four towers in apperance. Furthermore, although the helms appeared at the tip of twin towers of the west facade in the former sketch, in this revised sketch, they were changed into the towers without pointed head so that it is changes into the scenery that different towers were seen instead that four sharp pointed towers stand simply together, and is taken over to the final work. That is, the operation on a two-dimensional picture made correction to the three-dimensional spatial modeling there.

     Though simulation with CG in which viewpoint heights are changed, such delicate correlation of four towers can be compared and examined. If the viewpoint height is raised, the tip's height of the eastern pinnacles will sink relatively than the the tip's height of twin towers of the west facade, hence the emphasis is moved to the west twin towers and the balance of four towers will collapse gradually (S6, S7). Schinkel's effort becomes clear here again, who paid mind to the delicate relation of four towers.

c-4 Performance using backlight

     The composition of the halo, which is the general technique for the paintings of Romanticism, is rather a technique for showing by light the space than showing architecture. It makes a clear contrast to that, when the sun as light source is set at the front , the picture shows the building's formal composition clearly and yields completely different impression (solar position simulation =S8, S9, S10, S11). The position of the setting sun on the original painting could be defined following the emitting light conversely. According to it, the sun is located on the line which extended downward along the left edge of the north tower at the west facade, around the crossing of the ambulatory and the transept, and a little bit under the eaves of the ambulatory. The direction of the solar position is calculated through connecting the viewpoint and this point,  and it turns out that it is about 15 degrees north slippage from west and about 8 degrees altitude, supposed that the main axis line of the cathedral is in accordance with the east and west axis.

     Thus, the sun is located in the center of the silhouette of the cathedral and the cathedral is seen only as a shadow picture. Although the exact architectural form is assembled in the draft and it is actually conscientiously drawn on the perspective on the final painting, it is smeared away with deep black and the three-dimensional composition of the cathedral is hardly in sight of the appreciating person. In spite of being able to display his ability of design as an architect if the light source is placed on this side, he dared to draw a cathedral only as a silhouette. There could be observed a certain expression of his spirit of Romanticism.

     The sunlight toward morning could have the effect of raising the cathedral up simply in the painting, and could display clearly the structure of architectural articulation. Compared to it, a dramatic spectacle is created in Schinkel's painting, while the brightness of the background sky and the deep black silhouette of the cathedral overlapped, the light escaped from the gap served as a medium expressing an effect of solidity of the air. The usual aerial perspective as Gilly showed was reversed here, and it was made bright in the depth and dark in this side, which became, so to speak, the reversed aerial perspective (34).

3-3   Positioning of Schinkel's perspective method

      It turns out through the CG representation of two perspective drawings that there are the following fundamental common features and differeces as to Schinkel's perspective when compared with Gilly's perspective.

<common feature>

- two-point perspective method with unstable impression

- exaggerated expression emphasizing the existence of the auxiliary lines of perspective method

- the flat level surface (ground or water surface) and the cubic composition which utilized the advantage of the three-dimensional coordinate system assembled on it

- the basic pyramidal shape of the monument and the surrounding space wrapping it

<difference>

- the visual angle making the shape of the central building appear as distorted, versus the visual angle making it clearly

- positioning of  the light source at the background making a silhouette conspicuous, versus frontal light visualizing the object lucidly

- the complicated townscape with landscape mingling various architectural forms, veusus the standardized and unified artificial townscape

- ambiguity of contour versus its lucidity 

     These common features and deffernces verify the establishment of the fundamental technique of the perspective on the one hand, and on the other hand it shows the process of transition from Gilly's neo-classic sense of expression to Schinkel's romantic sense of expression.

     Generally among Schinkel's architectural paintings, certain number of the works have similar composition to the paintings of C. D. Friedrich, where the front is dark and the background is bright. They were drawn contrasting a deep black figure of architecture with the background of the setting sun outdoors, or dark interior space against bright outdoor view indoors. That shows the way of viewing which does not look at the structure as an object illuminated brightly, but consider it as a mystical one with the hidden power.

     Even if expressed darkly, the structure was not necessarily obscured vaguely, and after being conscientiously drawn from the precise line drawing, it was smeared away black. The detailed ornament of the Gothic style was also drawn there according to the exact perspective method. Therefore, it seems to have become a difficult painting method wasting more time and effort technically. That is, the technique of the perspective of romantic paintings made architects to progress in the direction searching for more impressive architectural form, and here can be found out the influence which the perspective method had to the architectural design.

     Moreover, there are certain number of paintings by Schinkel which are in relation to Neo-Classicism, including "View of Greece in prosperity" (1825) painting ancient Greek temples and the surrounding townscape, or the perspective drawings illustrating his own design works in neo-classic style, etc. It means that he had also the skill to express classic order, and was well versed in the various expression techniques. The systematic method of formal composition such as the composition using three-dimensional coordinate space and layer composition, etc., was established there as a common technique to both Classic and Gothic styles. It is found here as a result that a universal modeling technique exceeding a conventional modeling of style was enacted through the perspective technique in this age.

     It is verified from such two architectural perspective drawings by Gilly and Schinkel that the expression technique which Gilly reclaimed was steadily inherited by Schinkel, and developed on the basis of still newer sensibility. The method of three-dimensional cubic composition was extended to the expression of the surrounding space, natural environment and urban environment beyond the formal system buildings. While the method of a subtle cubic expression depending on the technique of shade and shadow expression, and color expression by Gilly had textbookish exactness, Schinkel used it in inversion and raise even to a spiritual expression of Romanticism. Thus it is to say that the technique of a perspective influenced even the characteristic romantic design method of Schinkel who is named generally as an architect of Neo-Classicism but also liked the Gothic style at the same time.

　Chapter 4  Conclusion

 4-1   Change of the architectural design method affected by the perspective method

     From the middle of the 18th century in Germany the architects stained with the philosophy of the Enlightenment like F. W. V. Erdmannsdorff of Dessau appeared and the new architectural style of Neo-Classicism was developed, but there was a certain lag in respect of the quality of architectural expression. The architectural image by the simple form which Erdmannsdorff showed was inherited by D. Gilly, and also raised for the first time to the leverl of space design by his son F. Gilly, and came finally to the stage that each volume of building were related with one orthogonal three-dimensional coordinate system. The design process of the "Friedrich II Monument" project showed that, and the technique of the perspective had played a big role there. The process observed there, that the former feature of architectural form with a group of distorted and swinging forms in the baroque style was replaced by the new feature of simple form, which in turn farther integrated to the unified space system governing the whole space, showed one big stream which should be described as a formation of a new style. There was a developmental process on the level of modeling such as a new establishment of the formal processing method and the formal system in which the architectural perspective as an artistic expression became the power to promote it. It brought this new style formation that two levels as the formation and expression, that is, the modeling and the rendering in the terminology of CG, influenced each other mutually, and feed each other back. F. Gilly aimed at the systematization of a new modeling technique and achieved it successfully. The emergence itself of such gifted perspective painter and perspective method theorist was what the historical process of the formation of a new style needed.

     It turned out, as stated above, that the position of viewpoint in the perspective was not real and actually impossible, but it was also understood that it was an expedient in order to express on the picture plane the beauty which is represented by the stable formal composition and the unific space system. It means that, in this stage, the level of rendering still served for the formation of the modeling system. Indeed the original purpose of the perspective expression was to make an architectural project understandable with reality by the observer, as is known from that F. Gilly had adopted the actually possible viewpoint assuming the real city area etc. in other designs such as "Hunde Brücke" project in Berlin. But here was an attitude willing to give independent value to the means of geometrical processing itself, for the sake of conceptual design consisting of the modeling method of building blocks and the consistent coordinate system.

     He aimed at systematization of perspective expression technique as is known by the lecture items in the Bauakademie (Architectural Academy). Soon, standing on his result and reversing the way of thinking, Schinkel became to paint architectural paintings giving emphasis on the perception as if a fictitious image is a reality, as stated above. That the viewpoint was set targeting dramatic composition and the light effect was also added in "the Gothic cathedral at the water" was simply the procedure for evoking a feeling in the observer's mind a three-dimensional virtual experience, and was the result of giving priority to rendering beyond modeling.

     Schinkel is known also having drawn many stage scenery paintings with fictitious setup, and having gathered spectators and got reputation through setting and exhibiting dioramas (35). It may be said that such experiences have affected the emergence of such architectural paintings. Schinkel also introduced his own architectural projects in "Sammlung Architektonischer Entwürfe (Collection of Architectural Designs) (36)" and involved in it many copperplate engravings of perspective drawing, which suggests certainly that such perspective feeling influenced the actual architectural design. For example, as for the architectural works of the Neo-Classicism which consist of very simple forms, such as "Altes Museum" and "Bauakademie", he drew perspectives with the surprising composition which give emphasis on the urban scape. It is concluded that to the Neo-Classicism architecture in early 19th century the rendering-oriented aesthetic value was applied, exceeding beyond the level of the stable modeling of individual building volumes.

4-2  Significance of the research method through CG representation

       The summary of the meaning of the CG as the means for the research of architectural history in the range relevant to this study is given as follows.

(a) Logicizing of the design language and procedure

     First of all, since it is possible to clarify the method of formal composition of the object work through reconstructing the working process of the perspectives, it become possible to attain precise form evaluation of the object work. And there, the designer's design language and design procedure become clear, and the process of form processing can be logicized. While the evaluation of an architectural work means generally to evaluate the result of the work realized, the historical evaluation will be carried out here paying attention to the process rather than the result. Although it is not to say that it is the research work which is impossible if CG is not necessarily used, the representation process by CG makes possible the simulation where conditions are changed, which urges a detailed verification.

     For example, in the case of architectural paintings like this study, generally the evaluation from the viewpoint of art history tends to become principal, but the evaluation as a substantial building project becomes possible by verification through reconstructing the design process here. By clarifying the process of trial and error of the design, the procedure of the modeling work of the architect to which its attention is paid here will be understood for the first time, and the architect's thinking itself will be directly understood. Generally, in the case of the successful architectural paintings, only the artistic expression as a result and a producer's talent will attract attention, but the fruit of historical development is contained in many cases in the procedure of the modeling found out in the method for the fundamental structure of form and the visual composition rather. Especially as to this study object, an architect’s unique technique different from the general freehand painting is utilized in the working procedure of architectural painting, and the historical important fruit can find there. Therefore this kind of research method became especially effective.

     As the mechanical perspective method starting in the early Renaissance developed gradually and affected the modeling technique of architectural work in each time, it seems that it is possible to rearrange them with the formal operation language of CG anew. In CG, the process to create the perspective is rearranged as an algorithm, and changed into the perspective creation method by a digital procedure by numerical computation and pixel units, which is different from the conventional geometric drawing, i.e., analog processing. Since this method inserts very strict logicalness into the art which is considered to be an intuitive thing, it can logicize and reconstruct the art work with technological means. That opens a new area of research different from the evaluation method of the historical work by an intuitive discerning eye.

     The lecture items which Gilly mentioned might be said to show the nearly perfect system of a general contemporary perspective technique, and it can be also said that the theory of the perspective method reached the completion stage by the end of the 18th century. Since based on CG technique of the surface model here, there was a missing portion in order to fulfill all the expression technique that Gilly mentioned. The more complicated and various expression techniques can be developed by CG technique of solid model and the additional expression technique of the aerial atmosphere, reflecting light or dispersion light, and the possibility of more perfect representation is left behind especially concerning shade and the shadow expression and the color expression.

(b) Reconstruction possibility

     Although the building which was built actually is generally thought as important in respect of historic meaning and social influence as a subject of research of the architecrural history, it cannot be said in many cases that all the ideal images that the designer had are expressed perfectly. An intellectual achievement has the base in the intellectual activity which was the source of an actual architectural work, and the historical result might appear at the level of only a pictorial image in many cases as it is clear in this study. This is a problem which should be focused when considering the information culture as is discussed today. That is, such as a dream of architecture, a utopian image of  architecture, and a beginning idea of project, should be observed in respect of information value, in the meaning that they leave historical influence without actually completed.

     This kind of informational value must never be seen lightly, if considered that the perspective of the unbuilt "Friedrich II Monument" project of F. Gilly, for example, left big influence on the architectural works which Schinkel realized later in Berlin, and also that it induced various reverberation including the work of "Walhalla" of L. v. Klenze and those of other architects, and that it gave important orientation for historical development. Of course, it is not a simple problem of imitation, and does not finish with the influential relation between individuals, either, but it shows that there was historical genealogy only at the level of information culture.

     While only the very short time of Neo-Classicism is discussed in this paper, the historical change of architectural expression including perspective method is following the steady developmental process, in a level called the information generation method, and forms the history in the information level from the Renaissance to the present age at least. The CG representation technique has a possibility to become what reclaims new area of research in such an information level.

　Acknowledgement

     In this research, Mr. Shutarou Nagata, a graduate student of Hiroshima University at that time, has cooperated for the creation of CG data and pictures. I appreciate deeply his cooperation.

   Notes 

(1) About the history of perspective, Lawrence Wright, "Perspective in Perspective", London, 1983.

(2) Friedrich Weinbrenner, "Architektonisches Lehrbuch, Ester Theil, Geometrische Zeichnungslehre, Lichit- und Schattenlehre", Tübingen, 1810.　Klaus Lankheit, 'Friedrich Weinbrenner, Beiträge zu seinem Werk',"Fridericiana", Zeitschrift der Universität Karlsruhe, Heft 19, S.5-31.

(3) About the fundamental technique of CG some general books were referred to, including : Masataka Ohta, etc., "Applied Graphics", ASCII publication, 1986 (in Japanese).

(4) For example, to represent Leonard da Vinci's "Last Supper" or Masaccio's "Trinity", etc. in three dimensions has already been tried. See Wright, op.cit., p.96.　Piero Sanpaolesi, "Brunelleschi", Milano, 1962.（"Filippo Brunelleschi, la Naisasance de l'Architecture Moderne", p.73.） Here, the apparatus used for CG work is graphics workstation "COMTEC-4 DRPC-Elan", and application for perspective is "Softimage". In addition, another application for perspective "3D PERS" was used in personal computer "PC-9800" series as an early stage for data creation. The pictures are taken from RGB data with the film recorder.

(5) About the analysis of this work, see the following :  Toshimasa Sugimoto, 'Friedrich Gilly's project for "Frederick II Monument" - about form and society in the architectural monument at the end of 18th century', in "Transactions of Architectural Institute of Japan", No. 279 (1979-5), pp.161-169(in Japanese). It already pointed that the perspective method had played certain role in the design of this work. Including this point, more profound analysis is further achieved with CG technique.

(6) This was later published as a collection of prints. Friedrich Frick(Hrsg.), "Schloss Marienburg in Preussen nach seinem vorzüglichen aeussern und innern Ansichten dargestellt", Berlin, 1799.

(7) See Alfred Rietdorf, "Gilly, Wiedergeburt der Architektur", Berlin, 1943, S.20-37.

(8) Project for " Hunde Brücke"："Ansichit der so gennanten Hunde Brücke nach einem zum Bau derselben gemachten Entwurff"(1800).　See Alste Oncken, "Friedrich Gilly", Berlin, 1935, Tafel 76. Project for "National Theater"："Entwurf für das Berliner Schauspielhaus"(1798). See Ibid., Tafel 56.

(9) See Hella Reelfs, 'Friedrich Gilly als Lehrer. Die "Privatgesellschaft junger Architekten"', in: Berlin Museum, "Friedrich Gilly 1772-1800, und Privatgesellschaft junger Architekten", Berlin, 1987, S.174-178.

(10) Eytelwein, 'Nachricht von der Errichtung der Königlichen Bauakademie zu Berlin', in:"Sammlung nützlicher Aufsätze und Nachrichten, die Baukunst betreffend." Jahrgang 1799, zweiter Band, Berlin, S.30,36.

(11) "Vorlesungen über Optik und Perspektive, als Grundlage einer theoretisch artistischen Anweisung zur Zeichenkunst besonders für Architekten",　Preußisches Geheimes Staatsarchiv, Rep.76(alt), Abt.IV, Nr.31, in: Ibid., S.245-247.

(12) Ibid., S.178-179, 201.

(13) See Sugimoto, op. cit. Although the original painting was lost, a copy is in Schinkel Museum, Kupferstichkabinett, Berlin. Here were referred to the photos and a plan in Rietdorf, op.cit., S.51f.. and also the reconstructed elevations in Friedrich Mielke, 'Das Denkmal in seiner städtebaulichen Bedeutung - Die architektonischen Entwürfe', in: Jutta von Simson, "Das Berliner Denkmal für Friedrich den Großen", Berlin, 1976, S.27ff.. About the color according to the drawing （Nationalgalerie SMB(SZ n.5)） in Michael Snodin, "Karl Friedrich Schinkel, A Universal Man", New Haven and London, 1991, p.91. Although it should be directly carried out to data from the original work, it is thought here that the desired result for this study could be attained by using secondary data.

(14) For example, the spatial relationship how the Potsdam gate on the left hand contacts to the city wall is different in the perspective and in the plan.

(15) About the sketch on the directly preceding stage, see Oncken, op.cit., Tafel 26.

(16) Ibid. Tafel 28-b.

(17) See Sugimoto, op.cit.

(18) “Ich kenne keinen schöneren Effekt als von den Seiten umschlossen, gleichsam vom Weltgetümmel abgeschnitten zu sein und über sich frei, ganz frei den Himmel zu sehen.“, in: Rietdorf, op.cit., S.52.

(19) Although Wright wrote about the color of this work as gloomy and effective, it is considered as the result that Gilly had tried to give delicate difference of color to each portion, and aimed at a fine effect rather. See Wright, op.cit., p.201.

(20) See the Japanese tranlation translated and edited by Yoshito Takahashi of Goethe "Nature and Symbol - collection of science theories - ", Fuzanbou, 1982(in Japanese).

(21) Schinkel is prominent also as a painter and his paintings have been sometimes exhibited in relation to the German Romanticists pictures even in Japan. See Tokyo National Museum of Modern Arts, and other, "Exhibition of 19th Century German Masterpiece Paintings", Asahi Shinbun Publishing, pp.42 - 47(in Japanese). Schinkel's paintings were discussed in many literatures, but it is omitted here which are referred to.

(22) About this "Gothic cathedral at the Water", there is no settled name and other names such as "Composition of four-tower Cathedral" are also used. The original is owned by Bayerische Staatsgemäldesammlung (München, Neue Pinakothek, Inv.-Nr.13422.), and a copy by Wilhelm Ahlborn (1823) is in Nationalgalerie Berlin (see "Exhibition of 19th Century German Masterpiece Paintings", p.47). See Rüdiger Becksmann,'Schinkel und die Gotik ― Bemerkungen zur "Komposition des viertürmigen Domes" von 1813', in: "Kunstgeschichtliche  Studien für Kurt Bauch zum 70. Geburtstag von seinen Schülern", München u.Berlin, 1967, S.263-276. Hermann G. Pundt, “Schinkel’s Berlin: A Study in Environment Planning”, Cambridge, Harvard University Press, 1972, (in Japanese translation by Toshimasa Sugimoto, Chuou-Kouron-Bijutsu-Shuppan, Tokyo, pp.120-122). Toshimasa Sugimoto, "Genealogy of Architectural Dream”, Kajima Institute Publishing, 1991, pp.120 - 4(in Japanese).

(23) Schinkel-Museum, M.XXb, 32. See Becksmann, op.cit., Abb.3, and Pundt, op.cit., Fig.49. The author has discussed about this draft once in  relation to "Composition of four-tower Cathedral" . Toshimasa Sugimoto, 'K. F. Schinkel’s project for “Memorial Cathedral for Liberation War” - about form and society in the architectural monument at the beginning of 19th century', in "Transactions of Architectural Institute of Japan", No. 279 (1979-5), pp.171-179(in Japanese).

(24) Ferdinando Galli-Bibiena, "Architettura Civile", Parma, 1711.　See Dunbar H. Ogden, "The Italian Baroque Stage", Los Angeles, 1978, pl.23,24. Pundt referred to "Architettura e Prospettiva", Augsburg, 1740, Ⅱ, p.10. Pundt, op.cit., p.120.

(25) The figure used here for reconstruction is in Pundt, op.cit., p.100. In addition, some errors on drafting work are found, for example, the right vanishing point of the perspective is somewhat different from that on the plan perspective, and so it is impossible to reach the  complete exact reconstruction. In addition, although not analyzed in detail, a remarkable difference about the city scenery of the background is found between the draft and the oil painting. Each building of the background is possibly drawn by improvisatorial after experimenting to a certain degree without deciding three-dimensional coordinates.

(26) Although Wright indicated that Schinkel took too large angle in the perspective for the colonnade of Altes Museum, and made a picture lacking stability, it should be said as the method which Schinkel used intentionally targeting the dramatic visual effect rather. See Wright, op.cit., p.203.

(27) Schinkel left a rough sketch of the west facade, which suggests it is planned that a gable is rising over the entrance gate of three openings, and a pier is standing upwards at the center axis assisting the twin-arch, and also a rose window is set to bring light into the basilica.  Becksmann, op.cit..

(28) Ibid..

(29) About the similarity and difference of C. D. Friedrich's paintings and Schinkel's paintings, see Sugimoto, "Genealogy of Architectural Dream", pp.98-108(in Japanese).

(30) "Gotische Kirche auf einem Felsen am Meer",(1815).　See Mario Zadow, "Karl Friedrich Schinkel", Berlin, 1980, S.23.

(31) "Mittelalterliche Stadt an einem Fluß"(1815). Nationalgalerie, Berlin, SMPK(SM A.2) See Snodin, op.cit., p.104.

(32) Schinkel-Museum,M.XXb,33　See Becksmann, op.cit., S.265, Abb.2.

(33) Alfred Freiherr von Wolzogen, "Aus Schinkel's Nachlaß, Reisebücher, Briefe, und Aphorismen", Bd.1, S.208.

(34) In relation to this aerial perspective a CG technology as an expression with the particles like fog is developed, but it is substituted with a simulated expression as the multi-purpose surface model is used as a perspective technique.

(35) When Ernst Gropius and Karl Gropius, parent and child, planed the event of the panorama or georama named "optics and perspective method picture", Schinkel produced for them. See Pundt, op.cit., pp.124-126. Incidentally, it might be said that it could be equivalent to "virtual reality" by means of today's computer technology in the level of a perspective technique of those days.

(36) Karl Friedrich Schinkel, "Sammlung Architektonischer Entwürfe", Berlin, 1873(orginal:1819-40).

　<Source of photograph, etc.>

・Rietdorf, "Gilly",　photo.3,4,5.

・Berlin Museum, "Fridrich Gilly 1772-1800", photo.2.

・"Exhibition of 19th Century German Masterpiece Paintings", photo.6,7.

・Zadow, "Karl Friedrich Schinkel", photo.8.

・Pundt, "Schinkel's Berlin",　pl.4(original drawing before addition).