自由形體表皮製造改進

Abstract

電腦科技以及新媒材在建築的發展，激發了設計者的想像力，在製造上建築更帶領新形式的解放，光滑的曲面成為數位建築的象徵。CAD/CAM製造自由形體建築的施作方法，分為曲面表皮以及骨架的製作。而在玻璃的曲面表皮製作通常使用：1.CNC數值控制，製造曲面的單元(Kolarevic,2003) 2.三角化及攤平，(Welch, 1994; Turkiyyah, 1997; Lee, 2005 ) 3.平面化四角面等方法( Glymph, 2002; Shelden, 2002; Schmiedhofer, 2008)。在自由曲面的製造複雜且昂貴的，因此為了節省經費，我們會希望一定數量的表皮單元是重複的，以減少玻璃單元開模的數量。而美學上，自由形體的表現上會希望盡量與原始設計一樣，並且充分表現曲面光滑的表面。但是製造上與美學上往往是難以兼顧的。 例如：CNC數值控制，可以有效且忠實的表現設計的形體，曲面單元精準且光滑，但未經模矩化的曲面使得，每一塊單元都不一樣大，美學上呈現了光滑的特性，但是造價太過於高昂(LIM, 2006; Lee,2005; Turkiyyah,1997)。再者三角網格及平面四邊形網格法使用雷射切割平面單元，雖然有效的將低了造價以及施工的困難。但是使用平面的單元簡化自由曲面成為多面體的近似形體外觀，卻使得自由曲面不光滑而且不連續 ，違反了美學觀感。( Shelden, 2002 ; Schmiedhofer, 2008; Baldassini, 2008)

因此為了同時兼顧施工以及美學，我們的主要問題及目標是：為了使更容易建造曲面單元，在最小限度的改變原始設計的形體，同時保持自由形體曲率連續而且光滑的特性的條件下，我們如何增加重複的表皮單元數目？ 基於問題本文透過實際案例的玻璃帷幕，展示基本且實用的幾何原理，並且整合成為可應用的步驟。最後將方法及步驟整理為玻璃自由曲面表皮分割的流程。在本文中自由形體的曲面，會具有以下條件。1. 為自由形體的玻璃帷幕2.面為雙向度曲面3.表皮單元為曲面，並且曲率連續。曲率本文的幾何方法，使用有幾何規則的曲面逼近原始設計形狀，使得表面單元可以分割為可具有相同單元的曲面。可整理為以下步驟：

步驟 1:提取原始設計曲面上的兩條(U,V)向結構線 步驟 2:簡化、重新描繪上一步中兩條不同向度（U,V向）曲線，使這兩條曲線成為對稱的二階曲線所組成的曲線；這些曲線可能有幾段曲線組合成。 步驟3:控制這兩條曲線掃略（sweep）成新的NURBS曲面。 步驟4:藉由調整這兩條曲線來控制曲面以進行Form Finding （Shelden, 2002），以逼近原始的形狀。 步驟5:再依照兩條曲線對稱規則來分割曲面取出曲面單元。 步驟6: 特徵重繪。將無法模矩化的單元去除，以原始表面取代。

在我們操做的實際案例中，原始設計的表皮單元數目由53塊完全不同的單元，下降至41塊不同的單元，有24塊單元是有模矩的，而且單元和單元間的曲率是完全連續的。使用此方法產生的新表面會擁有光滑的表面，而且可以得到一些重複的曲面單元，但不可避免的，此方法會改變一些原始設計的形狀。在最理想狀況下，此方法最多可將曲面單元數目減少至原始設計50%

The development of computer technology and new media in architecture has given new rise to the creativity of designers and lead architecture to new break through in construction. The making of CAD/CAM free-form structures, can be divided into the making of curved surfaces and the skeleton. In using curved glass as the skin, methods often used are: 1. CNC for the making of curved components (Kolarevic, 2003) 2. Triangulating curved faces and then flattening (Welch, 1994; Turkiyyah, 1997; Lee,2005) 3. Quadrilateral Planar Facets. (Glyph , J.2002;Shelden, 2002 ;Schmiedhofer,2008) This research paper proposes a new method for curved-glass construction using a simple and robust geometric method.Presently, problems encountered while making CAD/CAM surfaces are view in two dimensions: 1. Manufacturing issues: In present manufacturing, each unit is unique and needs to be made individually. Such complexity leads to problems like mounted expenses and difficulties in construction. ( LIM , 2006 ;Lee,2005 Turkiyyah ,1997) 2. Aesthetic issues: Triangulating , and parallelogram framing techniques form shapes out of planar components. This constructs a non-smooth surface for the exterior causing it lose aesthetic values. ( Shelden,2002 ;Schmiedhofer,2008 ;Baldassini,2008)Therefore, the main problem is: in order to minimize changing the original design during construction and to construct in a simpler fashion, how do we maximize the amount of repeated components but at the same time keep the smoothness of the free form design? According to the problems mentioned above, we review actual cases on curtain glass, and then demonstrate the geometric method through procedure. At the end process and steps will be categorized and organized into a framework for free-form glass dividend. Free-form surfaces mentioned in this paper are to meet the restrictions: 1. free-form surface must be a glass curtain 2. curved surface must be curved in both directions. 3. the surface component is to be a curved surface which has a constant radius of curvature. The geometric method proposed in this research, uses a curved surface to meet the original designed shape allowing surface components to divide surfaces into repeated components. Procedure can organized as below:

Step 1:To use a double dimension (U,Vdimension) degree 2 curve as a control element for NURBS. Step 2:By adjusting the control element we execute form-finding on the “ main 3D model”for a shape-closure to the original form. The new shape will come close to the original and thus replace it. Step 3:Then, divid the curved surface to while conforming these two control elements. Step 4:Part of the new curved component will grow symmetrically due the the symmetry of the curved line. Resulting from this symmetric, paired and identical curved components will be found in the new shape.

The new surface constructed using this method will result in a smooth surface along with a few repeated curved components. However, this inevitably will slightly change the shape of the original design. Under ideal circumstances, curved components can be reduced to half the original design.