以下為嘗試翻譯稿，請謹慎閱讀。如有誤導，概不負責。

十九世紀二十年代，最終導致風格派特奧·凡·杜斯堡與彼?！っ傻吕锇矝Q裂的主要爭論在于，凡·杜斯堡在畫布上將內(nèi)在直角關系傾斜45度，從而打破了最初與畫布邊界平行的90度關系。

菱形項目是在建筑中探索上述形式可能性的首次嘗試。一系列的問題浮現(xiàn)出來。不過，在進入這些討論之前，關于立體主義空間轉(zhuǎn)譯到建筑，有幾點需要說明。其中包括，立體派畫家們對畫布上圖形的強烈集中，而隨著圖面的深淺畫布邊緣的活動逐漸減少感興趣；對正90度、60度、30度、45度軸網(wǎng)以及平面圖形的聯(lián)結(jié)關系感興趣。建筑師勒·柯布西耶在空間問題上認識到立體主義的理念。哈佛大學的卡朋特中心是將立體主義空間問題轉(zhuǎn)譯到建筑的最佳詮釋。在19世紀早期的哈貝住宅和蘭格住宅中，密斯·凡·德·羅對抽象的平面概念和將平面作為二維（圖形）問題處理所涉及的空間矩陣的概念表現(xiàn)出了同等的興趣。

對于蒙德里安極力主張的直角關系的重要性，這一動作引發(fā)了一系列形式爭論。蒙德里安對凡·德斯堡45度內(nèi)部關系的回答是傾斜畫布，但對觀察者而言仍舊保持90度內(nèi)部直角關系。這一動作的形式結(jié)果是令人震驚的：邊緣和輪廓的外圍張力被加強，領域的延伸被暗示超出畫布之外。就建筑的空間意義而言，這一觀點的理念還還沒有得到試驗。

蒙德里安一開始是一位立體主義者，后來又從立體主義轉(zhuǎn)向了新造型主義。他不斷地敦促建筑師們研究他繪畫中的空間概念；然而，他那個時代的建筑師顯然對采用菱形“構型”并不感興趣。當今建筑學的主要爭論之一仍然是關于二維空間和三維空間概念之間的辯證關系。

勒·柯布西耶早期的建筑，如加歇別墅，是建筑形式二維平面化的宏偉構想，但由于堅持單一的優(yōu)先視角而顯得有些奇怪；立面以平面構圖的形式呈現(xiàn)在觀察者的眼前，與平面圖非常相似。其立面，有對文藝復興式外部形式視圖的回溯，即在二維表皮上構圖的問題。

建筑的獨特之處不僅僅在于呈現(xiàn)完美的平面式立面，或創(chuàng)造在傾斜、夸張的深透視中盤旋的精致建筑體量。

如果說立體主義繪畫為（20世紀）20年代的建筑師提供了思想，那么蒙德里安的菱形繪畫對今天的建筑師來說可能會有一些意義。在菱形項目中，探求以一種新的投影和分解空間形式的初始空間演化。另一種空間和形式的觀察方式可以被采用。文藝復興式的透視空間是一種事實；蘊含流動空間的后立體主義淺-平空間也是一種事實。

當平面圖中的菱形被等軸測投影時，它就變成了正方形。這似乎是一個不言自明的事實。但在這些探索之前，這種投影，即把菱形投影到正軸測，從未出現(xiàn)在建筑圖紙中。而反向的操作卻已經(jīng)存在和使用了，也就是，正方形在等軸測中繪制成菱形。

當平面上的一個正方形用軸測畫出來時，在眼睛看來它就像是一個三維投影。當一層以上的平面以等軸測投影時，它會非常自然地建造起來，并且仍然呈現(xiàn)為三維表現(xiàn)。當菱形以等軸測繪制且平面不止一層時，就會出現(xiàn)一種非常特殊的現(xiàn)象。這些形式看起來像是二維的；這些樓層在先在的二維視圖中相互重疊。在等軸測中，形式向畫布平面傾斜；它們是三維的，但更強的二維讀解卻占據(jù)主導地位。（這里不理解的可以去看特奧·凡·杜斯堡《不和諧音對位構圖》）二維圖形相互咬合堆疊是我們最熟悉不過的現(xiàn)象了。

正如立體派畫家在他們的繪畫中將物體向繪畫平面（畫面）傾斜一樣，菱形的等軸側(cè)投影也為建筑圖紙?zhí)峁┝祟愃频囊暯?。菱形的等軸側(cè)投影正是建筑中的立體投影，從而完善了繪畫中的立體投影與建筑中的立體投影的形式關系。

使用菱形等距軸測，摒棄古老過時的透視投影形式，將把空間的質(zhì)量傳遞給觀察者。平面圖的二維性投射到三維等軸測后，仍然保持二維，但更接近平面圖的二維抽象，或許也更接近建筑空間的實際的二維性。

關于菱形構型的實際三維空間，引發(fā)了一些的問題，并帶來了側(cè)向邊界的延伸和視角。二維表皮和立面的呈現(xiàn)并不是唯一的，它意味著正面和單一的視角。也許，建筑空間的歷史可以用圖7來表示，其中a表示過去，b表示現(xiàn)在，c表示未來。

未來只能靠推測。當觀察者站在菱形外部，從頂點的外側(cè)觀察(圖8)，則其兩條邊（面）會有向前展平的趨勢，從而產(chǎn)生了一個側(cè)邊延展的擴展透視視圖。在內(nèi)部(圖9)，觀察者也面臨非常相似的現(xiàn)象，盡管它是情境的內(nèi)化；他再次被展平的兩個面所環(huán)繞。這里體現(xiàn)出內(nèi)部與外部體驗的一種協(xié)調(diào)。其中最重要的點在于相交的直角關系；曲面會弱化這一體驗和效果。張力來自垂直和水平直線的對立，蒙德里安在關于繪畫的討論中小心翼翼地指出了這一點；圓顯得有點可疑，但也不完全是；對立有時是必要的。

在菱形領域中引入直角，帶來了觀察者面對不斷延伸的邊界開始菱形“探索”的可能性。這一結(jié)論支持最大程度的“放松”源自最大程度的“收緊”的觀點；以及垂直于觀察者的視角觀看空間，而成角度地觀看側(cè)立面。以上是關于將菱形架構引入建筑空間生成“家族”的有些簡短的討論。

以下：英文原文

One of the major arguments which eventually caused the disengagement of the De Stijlists, Theo Van Doesburg and Piet Mondrian, during the nineteen twenties was when Van Doesburg tipped by 45 degrees the internal right angle relationships within the canvas, thereby destroying the original internal 90 degrees which ran parallel with the edge of the canvas.

The Diamond Projects are a first attempt to investigate the above formal possibilities in architecture. A number of problems emerge; however, before going into these, a few points as the Cubist space translated into architecture should be made. Among other things the Cubist painters were interested in the strong centralization of figures upon the canvas, with a decrease of activity towards the periphery of the field along with the problems of shallow depth; and the strong 90, 60, 30, 45 degree gridings and the interlocking of planar figures. The architect, Le Corbusier, was cognizant of the Cubist ideas as far as spatial problems. The Carpenter Center at Harvard is a prime rendition of the problems of Cubist space translated into architecture. Mies van der Rohe in the Hubbe and Lange houses of the eatrly part of the century shows equal interest in the idea of an abstract plan and the spatial matrix involved in the treatment of plan as a two-dimensional problem.

This act caused a serious formal disagreement with regard to the significance of right angle relationships in which Mondrian was actively and spiritually involved. Mondrian's answer to Van Doesburg’s 45 degree internal relationship was to tip the canvas, but still maintain the internal right angle 90 degree relationships as far as the observer was concerned. The formal ramifications of this action were shattering: the peripheric tension of the edge and contours were heightened and the extension of field was implied beyond the canvas. The ideas in this point of view were not experimented with as far as the spatial implications in architecture were concerned.

Yet Mondrian worked first as a Cubist, and then moved from Cubism into Neo-Plasticism. He continually urged architects to delve into the spatial ideas of his paintings; however, the architects of his time apparently were not interested in adopting the diamond configuration. One of the major architectural arguments of today still concerns the dialectic between the concepts of two-dimensional and three-dimensional space.

Le Corbusier's earlier buildings such as Villa Garches were magnificent conceptions of the flat two-dimensional aspect of architectural form, yet are curious because of the insistence of a single preferred point of view; the facade is presented as flat composition to the eye of the observer, very much like the plans. There is in the elevation a recall of the Renaissance vision of external form, the problem of composing upon a two-dimensional surface.

The uniqueness of architecture does not lie only in the presenting of a perfectly flat facade or in the creation of an elaborate volumetric building spiralling in oblique exaggerated deep perspectives.

If the Cubist canvas provided thought to the architects of the twenties, there may be some significance in the diamond canvases of Mondrian for architects today. The initial spatial evolution in the form of a new projected and exploded space were sought after in the Diamond Projects. Another way of looking at space and form can be adapted. The Renaissance space of perspective is a fact; the flat-shallow contained flux space of the post-Cubist canvas is a fact.

When a diamond form in plan is projected by isometric it becomes a square. This may appear to be a self-evident truth, but such projections, that is, the projections of diamond forms into isometrics, had not appeared in architectural drawings prior to these explorations. The converse has been in existence and use, that is, the square drawn in isometric which becomes a diamond.

When a square form in plan is drawn in isometric it appears to the eye as a three-dimensional projection. When more than one floor plan is projected in isometric, it builds up quite naturally and still appears as a three-dimensional representation. When the diamond is drawn in isometric and has a plan of more than one floor, a very special phenomenon occurs. The forms appear two-dimensional; the stories overlap each other in a primary two-dimensional vision. The forms tip forward in isometric towards the picture plane ; they are three-dimensional, yet a stronger reading of two-dimensionality predominates. A meshing together of two-dimensions pushing forward is the phenomenon we are most aware of.

As the Cubists in their paintings tipped objects forward towards the picture plane, the isometric projections of the diamond accomplished a similar point of view for architectural drawings. The isometric projections of the diamond are Cubist projections in architecture, therefore completing the formal relationship between Cubist projection in painting and Cubist projection in architecture.

The quality of space is transferred to the observer in the diamond isometrics without using the antique and outmoded form of perspective projection. The two-dimensionality of a plan, projected into the three-dimensional isometric, still appears two-dimensional, closer to the two-dimensional abstraction of the plan and perhaps closer to the actual two-dimensionality of the architectural space.

With regard to the actual three-dimensional space of the diamond configuration, certain problems arise and bring forth an aspect of encompassing lateral extension and vision. The presentation of a flat two-dimensional surface and facade is not unique, it implies frontality and a single point of view. Perhaps, the history of space in architecture can be represented in Figure 7, in which a denotes the past, b, the present and c, the future.? ? ??

Futures can only be speculated upon. When the observer is external to the diamond, looking at the outside of the apex (Fig. 8), there is a tendency of the two sides to come forward and flatten out, an extended perspective of lateral extension and vision is produced. Internally (Fig. 9), the observer is confronted with a very similar phenomenon although it is the internalization of the situation; he is again encompassed by the flattening out of the two sides; we have here the appearance of a coordination of external and internal experience. Of prime importance are the right-angle relationships of the intersections; a curvilinear surface would have the effect of softening the experience and impact. Tensions come from the opposition of straight lines, verticals and horizontals which Mondrian carefully points out in his discussions upon painting; the circle becomes somewhat suspect, but not entirely ; contradictions sometimes are necessary.

The introduction of the right angle within the diamond field permits the possibility of the observer to begin the trek of the diamond confronted with continual expanding encompassment. The conclusion permits the thesis of maximum extension from the maximum compression; that of seeing space perpendicular to the observer's vision; that is of seeing laterally the hypotenuse. The above is a somewhat compressed discussion for the admission of the diamond configuration into the family of architectural space generators.

1. 本篇英文原稿及插圖均來自Mask of Medusa，by John Hejduk；

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