VARIABLE SHAPING FORM

Abstract

A variable shaping form (10) includes a variable frame (12) and a variable support (16) extending within or across the frame. The shaping form (10) is selectively adjustable to vary the shape of the support (16) to define a variety of differently shaped contours, each of which approximates a doubly-ruled curved surface. The variable frame (12) may be defined by a plurality of frame portions (18, 19, 20, 21).

Claims

1. A variable shaping form including: a variable frame; and a variable support extending within or across the frame, wherein the shaping form is selectively adjustable to vary the shape of the support to define a variety of differently shaped contours, each of which approximates a doubly-ruled curved surface.

2. The variable shaping form as claimed in claim 1 wherein the doubly-ruled curved surface is a hyperbolic paraboloid.

3. The variable shaping form as claimed in claim 2 wherein the variable frame is four-sided and of equal side lengths such that the doubly-ruled curved surface is a rhombus hyperbolic paraboloid.

4. The variable shaping form as claimed in claim 1 wherein the variable frame comprises a plurality of frame portions which have any one or more of the following features: straight rods or bars; fixed i.e. non-variable length; all frame portions are of equal length; 4 frame portions; adjacent frame portions are relatively pivotable; adjacent frame portions are either interconnected or discrete.

5. The variable shaping form as claimed in claim 1 wherein adjacent frame portions are pivotally interconnected with a multi-axial joint.

6. (canceled)

7. The variable shaping form as claimed in claim 1 wherein the variable support is defined by a series of spaced rods or bars extending between two opposite frame portions.

8.-10. (canceled)

11. A variable shaping form including: a variable frame defined by a plurality of frame portions; and a variable support extending within or across the frame, wherein the frame portions are selectively relatively moveable to vary the shape of the support to define a variety of differently shaped contours.

12. The variable shaping form as claimed in claim 11 wherein the variable frame is four-sided and of equal side lengths to define a rhombic frame.

13. The variable shaping form as claimed in claim 11 wherein the plurality of frame portions have any one or more of the following features: straight rods or bars; fixed i.e. non-variable length; all frame portions are of equal length; adjacent frame portions are relatively pivotable; and adjacent frame portions are either interconnected or discrete.

14. The variable shaping form as claimed in claim 11 wherein adjacent frame portions are pivotally interconnected with a multi-axial joint.

15. (canceled)

16. The variable shaping form as claimed in claim 11 wherein the variable support is defined by a series of spaced rods or bars extending between two opposite frame portions.

17.-19. (canceled)

20. A method of shaping formable material, the method including: a) providing a variable shaping form as claimed in any one of claims 1 to 19; b) adjusting the variable shaping form such that the variable support defines a desired contour; c) either before or after step b, supporting the formable material on the variable support; d) allowing the formable material to fully or partially set or cure to substantially conform to the desired contour of the variable support; and e) removing the formable material from the variable shaping form.

21. The method as claimed in claim 20 further comprising a batch process of repeating steps b) to e) with the same selected contour or a different selected contour.

22.-25. (canceled)

26. A forming apparatus including: a variable shaping form as claimed in any one of claims 1 to 19; a support apparatus to adjust the variable shaping form, wherein the support apparatus includes a motorized adjustment mechanism.

27. (canceled)

28. The forming apparatus as claimed in claim 27 further including a control system to receive configuration data for the variable shaping form, wherein the control system controls the motorized adjustment mechanism to conform the variable frame in response to the configuration data.

29. The forming apparatus as claimed in claim 28 wherein adjustment of the variable frame is driven from the vertices of the variable frame.

30. The forming apparatus as claimed in claim 29 wherein there is one adjustment actuator for each vertex for the variable frame.

31. The forming apparatus as claimed in claim 30 wherein diagonally opposite first frame vertices are associated with respective actuators ( actuators) to adjust skew of the variable frame while diagonally opposite second frame vertices are associated with respective actuators ( actuators) to adjust the fold angle (beta) about an axis through the first frame vertices.

32. (canceled)

33. The forming apparatus as claimed in claim 31 wherein each actuator is connected to the associated vertex in a manner which allows for intersection of the longitudinal axis of the actuator and two adjacent frame portions at a single point.

34.-59. (canceled)

60. A formed part when formed using the apparatus of claim 1.

61. A formed part when using the apparatus of claim 11.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0079] In order that the invention may be more fully understood, one embodiment will now be described, by way of example, with reference to the figures in which:

[0080] FIG. 1 is a perspective view of a forming apparatus in accordance with a preferred embodiment of the present invention;

[0081] FIG. 2 is a perspective view of the forming apparatus shown in FIG. 1, except illustrating a second configuration of the apparatus;

[0082] FIG. 3 is a perspective view of the forming apparatus shown in FIG. 1, except showing the apparatus in a third configuration;

[0083] FIG. 4A is a perspective view from above of the forming apparatus illustrated in FIG. 1;

[0084] FIG. 4B is a detailed view of the forming apparatus illustrated in FIG. 4A;

[0085] FIG. 5A is a perspective view of one of the actuators forming part of the forming apparatus illustrated in FIG. 1;

[0086] FIG. 5B is a side elevation of the actuator of FIG. 5A;

[0087] FIG. 5C is an end elevation of the actuator of FIG. 5A;

[0088] FIG. 6 is an exploded view of the actuator shown in FIG. 5;

[0089] FIG. 7 is a perspective view illustrating one of the actuators forming part of the apparatus of FIG. 1;

[0090] FIG. 8 is an exploded view of the actuator illustrated in FIG. 7;

[0091] FIG. 9 is a side elevation of the actuator illustrated in FIG. 7;

[0092] FIG. 10 is an end elevation of the actuator illustrated in FIG. 7;

[0093] FIG. 11 is a flow chart of the process from the geometry of a desired free form surface to moving the apparatus into the forming apparatus into a required forming configuration;

[0094] FIG. 12 is a descriptive geometry model showing translation of physical parametric model into trajectories of motion;

[0095] FIG. 13 is a panelised wall free from surface (right) and geometry generated using Kangaroo Physics (left);

[0096] FIG. 14 is descriptive parameters of symmetric hyperbolic paraboloid panels;

[0097] FIG. 15A is descriptive geometry showing translation of symmetric hyperbolic paraboloid panel to position of mould frame vertices;

[0098] FIG. 15B is a diagram showing limits of current machine (left) and a diagram showing asymmetrical panel trimmed from symmetrical panel (right);

[0099] FIG. 16 is a diagram of a square;

[0100] FIG. 17 is the square of FIG. 16 when skewed;

[0101] FIG. 18 is a diagram of the Cartesian axes for the skewed square of FIG. 17;

[0102] FIG. 19 is a diagram of the skewed square with rotation;

[0103] FIG. 20 is a diagram of the hyperbolic paraboloid with rulings;

[0104] FIG. 21 is a diagram of curvature matching;

[0105] FIG. 22 is a diagram of parabolas describing the curvature of the hyperbolic paraboloid surface;

[0106] FIG. 23 is a diagram showing three estimates of the frame vertices;

[0107] FIG. 24 is a diagram of the distance between the centre point of the panel and one of the three estimated frames;

[0108] FIG. 25 is a diagram of the solution for the abscissa of the frame vertex;

[0109] FIG. 26 is a diagram of the required centre point correction; and

[0110] FIG. 27 is a diagram of a computer system upon which one or more of the various steps may be performed.

DETAILED DESCRIPTION OF THE EMBODIMENTS

1 Forming Apparatus

[0111] FIG. 1 illustrates a forming apparatus 10 according to a preferred embodiment. The forming apparatus 10 includes a variable shaping form 12 which is comprised of a variable frame 14 and a variable support 16 extending across the frame 14.

[0112] The frame 14 is comprised of four frame portions 18, 19, 20, and 21 (see FIG. 4). The frame portions 18 and 19 are opposite each other, while frame portions 20 and 21 are opposite each other. Each frame portion 18, 19, 20 and 21 is pivotally interconnected to the adjacent frame portion at a joint 22, 24 as will be explained subsequently. Diagonally opposite corners of the frame 14 define first frame vertices (V.sup.f.sub.0, V.sup.f.sub.2) at the centre of the joint 24. The position of the first frame vertices is determined by the position of the actuators 26, 28.

[0113] The other diagonally opposite corners of the variable frame 14 define second frame vertices V.sup.f.sub.1, V.sup.f.sub.3 at the centre of the tri-axial joint 22. The position of the second frame vertices is determined by respective actuators 29, 30 and the position of the first frame vertices.

[0114] Both the actuators 26, 28 and the actuators 29, 30 are linear actuators. However, the actuators 26, 28 are of a different form than the actuators 29, 30 as will be explained.

[0115] The forming apparatus 10 is arranged with the variable form 12 and variable support 16 in a substantially level configuration. However, this will vary as the shape of the variable form is changed to suit different moulding requirements. With the variable frame 14 configured as a flat square at a rest position, the variable support 16 will be substantially horizontal. In this configuration of the forming apparatus 10, the 13 actuators 29, 30 are arranged in a substantially upright configuration. The actuators 26, 28 have their longitudinal axes oppositely inclined. The actuators extend upwardly in the direction away from the centre of the variable support 12. The actuators 26, 28 are supported in this ramped orientation by means of support ramps forming part of a support substrate (not shown). The actuators 29, 30 are also mounted to the support substrate by means of the bi-axial joints 32, 34 as will be explained subsequent in connection with FIGS. 5 and 6.

[0116] The inclination of the actuators 26, 28 exists to prevent collision of the joints 24 against the frame 14. The precise angle of the slope is not important but the gradient employed here is 4 across by 3 up.

[0117] The variable frame 14 is movable into a number of configurations by support apparatus 11. The variable frame 14 is configured to vary the support 16 to define any number of differently shaped contours, each of which approximates a doubly-ruled curved surface. Thus, the curved surface 16 can be used as a form to mould or shape formable material. In one preferred embodiment, the preferred material is concrete and thus, a silicon tray 36 is provided to contain the concrete. The tray 36 is flexible and thus conforms to the shape of the support 16. Thus, the shape of the moulded concrete panel (not shown) when set will substantially conform to the shape of the variable support 16. Therefore, by changing the shape of the variable support 16, a variety of differently shaped contours may be achieved and thus differently shaped parts or panels may be created using the same apparatus, thereby eliminating wastage.

[0118] Whereas FIG. 1 illustrates the variable frame in the level square configuration, FIG. 2 illustrates a second configuration providing a second shape contour on the support 16 following the necessary movement of the actuators. FIG. 3 illustrates a third configuration of the apparatus which creates a third configuration of the variable form to define a third contour on the support 16.

[0119] 1.1 Variable Frame

[0120] FIGS. 4A, 4B and 8 illustrate the structure of the variable frame 14 in greater detail. As mentioned, the variable frame 14 comprises four frame portions, 18, 19, 20, 21 which are of equal length and are pivotally interconnected by means of tri-axial joints 22 at the diagonally opposite second vertices and second joints 24 at the diagonally opposite first vertices. The frame portions 18, 19 are spaced across from each other on opposite sides of the frame 14. Extending between the frame portions 18, 19 is a series of parallel spaced rods 40. This series of spaced parallel rods 40 makes up the variable support 16. The rods 40 move relative to the frame portions 18, 19 through the range of permitted movement of the variable frame. One end 42 of each of the rods 40 is constrained more than the other end 44.

[0121] As shown in FIG. 8, each end 42 is mounted to the frame portion 18 by means of a spherical joint 46 which comprises a ball 48 threadingly engaged at the end of the rod 42. Each ball 48 is captured between two plates 50, 52 which seat the ball therebetween and allow for three degrees of freedom (rotation about 2 axes and rotation about the longitudinal axis of the rod 40). The plates 50, 52 have inwardly facing spherical seats to seat the ball 48. Additionally, plate 52 has a circular hole 54 permitting passage of the rod 40 therethrough. The two plates 50, 52 are housed within a sleeve 56 having a series of circular holes 58 on both side walls of the sleeve 56. The series of holes 58 in each side wall align with each other and with the balls 48 and rods 40. Each rod 40 extends through a corresponding set of aligned holes 54, 58.

[0122] At the other end of the rods 44, the frame member is made up of an identical sleeve 56 with a series of spaced holes 58. An insert 60 is received within the sleeve 56. The insert 60 comprises a series of spaced holes 62 which align with the holes 58. The arrangement of holes 62 in the frame member 19 is such to permit a greater degree of freedom for the second end 44 of the rod 40 compared to the first end 42. Each end 44 is permitted to pivot about two axes, rotate about the longitudinal axis and translate along the longitudinal axis of the rod 40 (4 degrees of freedom). Thus, the second end 44 of the rod is less constrained than the first end 42.

[0123] Additionally, as shown in FIG. 4B the centre rod 40 is more constrained compared to the other rods 40. Each end of the centre rod 40 is pinned by a pin 41 which extends through an axis transverse to the longitudinal axis of the frame portion 18, 19. This allows the rod 40 to pivot about an axis aligned with the centre of the pin 41. Given that the arrangement of the spherical joints 46 and the joints 22, 24 will permit the frame portions 18, 19 to pivot relative to the rods 40, the pinning of the central rod 40 constrains the relative movement to limit potential interference between the frame portions 18, 19 and the rods 40.

[0124] The frame portions 20 and 21 may be in a similar form to frame portion 19, with or without the insert 60.

[0125] 1.2 Actuator

[0126] FIGS. 5 and 6 show the form of the actuator 29. The actuator 30 is substantially the same.

[0127] The actuator 29 is in the form of a linear actuator with a threaded drive rod 64 driven by stepper motor 66. The drive rod 64 is driven to rotate about its longitudinal axis. The drive rod 64 is externally threaded and engages with an internally threaded mount 68. The mount 68 is supported at a fixed level in the bi-axial joint 32 mounted on the fixed support structure (not shown). The mount 68 is also constrained against rotation about the longitudinal axis of the drive rod within the bi-axial joint 32. Thus, rotation of the drive rod 64 by the stepper motor 66 will cause the drive rod 64 to move either up or down relative to the support structure, depending upon the direction of rotation of the drive rod 64. Thus, the second vertex of the two adjacent frame portions 19, 21 which is located at the tri-axial joint 22, will be driven up and down.

[0128] The mount 68 is mounted in the bi-axial joint 32 for rotation about two axes 70, 72 which lie substantially parallel to the plane of the support structure on which the bi-axial (gimbal) joint 32 is mounted. The mount 68 is received within a complementary recess in a hub 74. The mount 68 is attached to the hub 74 by screw fasteners.

[0129] A guide rod 76 extends alongside the drive rod 64 in a parallel and spaced manner. The guide rod 76 is received within a slide block 78. The slide block 78 has a keyway 80 having a complementary profile to the guide rod 76. As the drive rod 64 is driven up and down relative to the mount 68, the guide rod 76 slides within the keyway 80 to guide the motion. The slide block 78 is received within a complementary recess 82 in the hub 74.

[0130] The hub 74 is mounted within an annulus 84 which surrounds the hub 74. The hub 74 is pivotable about axis 70 by means of a pin connection between the hub 74 and the annulus 84 by means of pins 86 and 87.

[0131] The annulus 84 is mounted between two trunnions 90 and is thereby pivotable about axis 72. Axes 70 and 72 extend transversely to each other. The bi-axial (gimbal) joint 32 minimises the constraint imposed by the connection of the actuator 29 to the support structure.

[0132] If the support structure is a table then the lower ends of the drive rod 64 and the guide rod 76 extend through a hole or aperture in the table.

[0133] At the upper end of the actuator, the tri-axial joint 22 joins the actuator 29 to the frame portions 19 and 21. At the upper end of the drive and guide rods 64, 76, is an actuator bracket 92 which houses the stepper motor 66. The actuator bracket 92 defines two spaced trunnion arms 94. A pin 96 extends between the trunnion arms 94 to define a first pivot axis 98.

[0134] Pivotally mounted to rotate about the pivot axis 98 defined by the pin 96 is a first inverted U-shaped bracket 100. A second U-shaped bracket 102 is also pivotally mounted for rotation about the pivot axis 98 by the pin 96. The U-shaped bracket 102 is offset from the location of the U-shaped bracket 100. An L-shaped bracket 104 is pivotally connected to the inverted U-shaped bracket 100. The downwardly turned leg of the L-shaped bracket 104 is pivotally connected to the frame portion 21 for pivotal movement of the frame portion 21 about the longitudinal axis of the frame portion 21. The L-shaped bracket 104 pivots relative to the inverted U-shaped bracket 100 through an axis which is aligned with the longitudinal axis of the drive rods 64.

[0135] The U-shaped bracket 102 is pivotally attached to a second L-shaped bracket 106. The pivotal axis is also aligned with the longitudinal axis of the drive rods 64. The upturned end of the L-shaped bracket 106 is pivotally connected to the frame portion 19 for relative pivotal movement about the longitudinal axis of the frame portion 19. The configuration of the tri-axial joint 22 is such that the longitudinal axis 65 of the drive rod 64, the longitudinal axis 103 of the frame portion 21 and the longitudinal axis 107 of the frame portion 19 intersect at a single point. The tri-axial joint 22 is considered superior to a ball joint.

[0136] 1.3 Actuator

[0137] FIGS. 7 and 8 illustrate the form of the actuator 26. The actuator 28 is a mirror image of the actuator 26.

[0138] The actuator 26 includes a drive rod 110 driven by stepper motor 112 to rotate in either direction. A carriage 114 is driven by the drive rod 110 up and down the incline. The carriage 114 includes an internally threaded mount 116 which interacts with the drive rod 110 in a similar manner as described above for the actuator 29. Two spaced parallel guide tracks 118 are provided on either side of the drive rod 110 in spaced parallel orientation. The guide tracks 118 are complementary to keyways 120 provided in the carriage 114 enabling the carriage to slide up and down the guide tracks 118.

[0139] A mounting plate 122 is provided on top of the carriage 114 and is angled relative to the inclination by a wedge 124. The wedge 124 has an upper surface with the complementary angle of inclination of the ramped actuator to present the mounting plate 122 at substantially horizontal orientation.

[0140] The joint 24 is mounted on the mounting plate 122 and includes two spaced trunnions extending upwardly from the mounting plate 122 and defining an axis for rotation for the inverted U-shaped bracket 128 and the offset U-shaped bracket 130. The inverted u-shaped bracket 128 is connected to the frame portion 20 by means of an L-shaped bracket 132. The U-shaped bracket 130 is connected to the frame portion 19 by means of a similar L-shaped bracket 134. The longitudinal axes of the frame portions 19, 20 intersect at a single point within joint 24.

2 Operation of Forming Apparatus

[0141] The operation of the forming apparatus will now be described. A control system (not shown) generates the control signals for the and actuator 26, 28, 29 and 30 to drive the vertices of the variable frame 14 to the desired position. This will cause the variable support 16 to adopt the desired contour approximating a doubly-ruled curved surface. Concrete is then poured into a silicon tray 36 supported on the variable surface 16. The concrete is leveled and partially set prior to the support 16 being moved to adopt the desired contour. Because of the flexible nature of the silicon tray 36, the silicon tray will adopt contour of the support 16. Once set, the silicon tray 36 is removed from the support 16. The concrete panel can then be removed from the silicon tray 36 and the tray re-used. GRC concrete mix enables casting of a thin concrete shell. Calcium sulfoaluminate (CSA) added to the concrete mix will allow the mix to achieve early strength and permit the panel to be moved within 15 minutes and demoulded within 5 to 6 hours.

[0142] The silicon tray 36 may be of any perimeter shape and any size provided within the boundaries of the frame 14 and need not be straight-sided. For example, where the perimeter shape is irregular and therefore not a quadrilateral, a four-sided or rhombus hyperbolic paraboloid (RHP) may be defined within the perimeter shape and thus within the panel. The vertices of the RHP serve as reference points to determine the frame vertices for the frame configuration 14 required to obtain that RHP within the perimeter of the mould, while the perimeter shape is obtained from the mould perimeter. In any case, any panel whether four-sided or not may be defined by reference to an RHP within or extrapolated from the panel shape and thus defined by reference points instead of its vertices.

[0143] FIG. 2 shows how a second shape may be obtained using the same forming apparatus. While FIG. 3 illustrates how a third shape may be achieved by the same forming apparatus. Thus, this invention eliminates the need to produce individual moulds for doubly-ruled curved panels through a single variable mould apparatus 10 which is computer numerically controlled, thereby reducing cost and waste in the production cycle.

3 from CAD Model to Control Signals

[0144] FIG. 11 illustrates the steps to produce the control signals or numerical outputs for the and actuators to achieve a desired panel geometry, starting with a desired free form surface geometry. Firstly, the descriptive geometry of the panels will be explained.

[0145] 3.1 Descriptive Geometry of the Panel

[0146] The panels are a hyperbolic paraboloid with quadrilateral boundaries of equal length, otherwise known as rhombi. Thus their diagonals intersect at right angles. The transformation of the panel surface between its potential forms can be understood as follows: the trajectory at opposing corners of the panel edge is the intersection of two spheres (radius=edge length), where the centre is based on the remaining two corners of the panel (see FIG. 12).

[0147] The model of the hyperbolic paraboloid panel surface has three parameters: (A) an edge length (predetermined and constant), and two parameters measured as a change in geometry from a flat square lying on the xy plane: (B) the skew ( or alpha) relative to the perfect square; and (C) a change of angle in degrees ( or Beta) about the x-axis. The change in skew resulting in a change along the y-axis results in the change of angle about the X-axis (change in ), provided the panel edge lengths are all equal.

[0148] 3.2 Summary of Steps from CAD Model to Control Signals

[0149] The goal of the following description is to take a geometric model of a free form surface which is desired to be constructed and break it down into individual panels that can be moulded using the forming apparatus 10, then, knowing the desired individual panel geometry, ultimately calculate the numerical outputs to the and actuators of the forming apparatus 10. More particularly, this is achieved by the following steps with reference to FIG. 11: [0150] (a) Obtain CAD model of a free form surface. [0151] (b)(i) Break the free form surface into hyperbolic paraboloid panels of equal side length and determine the vertices of such panels. [0152] (b)(ii) Orient individual panels to X and Y axes as illustrated in FIG. 12. [0153] (b)(iii) Once the vertices of a desired panel are known, calculate alpha and beta for the panel. The variety of different contours achievable by the variable frame 14 can also be described by corresponding descriptors alpha and beta. Thus, it is desired to map alpha and beta of the panels onto alpha and beta of the frame 14. However, the translation of alpha and beta to alpha and beta is without a deterministic solution. [0154] (c) Instead, map the vertices of the desired panel onto the vertices of the frame using initial estimates of the frame vertices, with the error resulting from the estimates being used in the process to solve for the correct vertices of the frame. This can be done using 3 estimates of the vertices to solve a quadratic correction function. [0155] (d) Now having the vertices of the frame which are required to make the desired panel, the target travel distances .sub.action and .sub.action of the frame vertices from a known starting point can be calculated. The control signal or numerical output to the and actuators is derived directly from .sub.action and .sub.action. The methods and techniques described here may be implemented on one or more special purpose computing devices as defined below in the Hardware Overview in connection with FIG. 27, with the various different steps and even sub-steps above performed on the same special purpose computing devices, on linked special purpose computing devices or special purpose computing devices linked with a control system of the apparatus 10, such as an NC numerical control. [0156] For example, the CAD model may be developed on a desktop computer system. Step (b)(i) may be performed on the same desktop computer in the same or another software module. Optionally steps (b)(ii) and (b)(iii) may be performed on the same desktop computer in another software module. Preferably the software module for steps (b)(ii) and (b)(iii) is discrete from the module for the preceding steps. [0157] The output of (b)(iii) (alpha and beta) may be then transferred to another special purpose computing device or another software module on the same desktop computer in order to perform step (c) to obtain the frame vertices. Alternatively steps (c) and steps (b)(ii) and (b)(iii) may be combined. [0158] Step (d) may be performed on the same or another special purpose computing device as step (c) to obtain .sub.action and .sub.action for the frame movements. Preferably, the output of step (d) may be the input to the control system of the apparatus 10. However, the control system may incorporate steps (c) and (d) on receipt of alpha and beta for the panel. Other combinations of these arrangements may also be implemented. Such special purpose computing devices may be networked as set out in the example of FIG. 27 below. [0159] The control system may be incorporated into or associated with the forming apparatus 10. Thus, alpha and beta (the minimum descriptive information of the panels) may be communicated between modules and converted back to panel vertex information as required.

[0160] 3.3 Step (b)(i) Panelise a Desired Free Form Surface

[0161] We can take most freeform curve surfaces, e.g. modelled in CAD or any other mathematical model of a freeform surface and panelise them. Taking one corner of the freeform surface as a starting point (point W illustrated in FIG. 13), we can iterate the process using custom script in McNeel Rhinoceros, with Grasshopper v0.9.0076 to find the intersection of equal edge lengths on the surface (point Y & Z followed by point X). These known points (W, Z, X and Y) are thus the vertices (V.sub.0, V.sub.1, V.sub.2, V.sub.3) of the panel in the mathematical model of the panel discussed below.

[0162] 3.4 Steps (b)(ii) and b(iii)

[0163] Before moving to the subsequent steps, a little more description of the mathematical model of the panel is provided.

[0164] Mathematical Modelling

[0165] A. Detailed Description of Mathematical Model of the Panel

[0166] The resulting rhombi hyperbolic paraboloid panels require tensor (self-referencing) parametric descriptors. The most intuitive and minimal number of parameters are used: skew and beta (FIG. 14).

[0167] Skew (or ) is a ratio which describes the amount by which the quadrilateral is skewed from a perfect square. A skew of greater than one means the panel is stretched along the x-axis (and subsequently contracted through the y-axis) and vice versa for a skew of less than one.

[0168] Beta (or ) is the fold angle about the x-axis (of the rotationally translated vertices which correspond to the y-axis).

[0169] The panel surface geometry can be regenerated from the two parametric descriptors if required (an edge length must also be specifiedthough this is predefined and unaltered for a set of panels).

[0170] The two chosen parametric descriptors (skew and beta) intuitively correspond to the actual frame geometry of the forming apparatus 10 and the mechanical movement of the and actuators required to achieve the desired frame geometry. The two linear actuators 26, 28 control the amount of skew and the other two linear actuators 29, 30 control the degree of beta rotation. All four actuators can move independently of one another within the physical bounds of the apparatus 10. This drastically simplifies the mechanical drive routine.

[0171] The main challenge (as discussed in (b)(iii) above) within the mathematical model for the apparatus 10 is the translation of the panel geometry (defined as alpha and beta) to the frame geometry (defined as alpha and beta) and thence to the necessary actuator actions (.sub.action, .sub.action). See FIG. 15A.

[0172] The translation functions from the panel geometry (alpha and beta) to frame geometry (alpha and beta) are indeterminate. Instead, a method using a quadratic convergence function solver is used to map the panel vertices onto the frame vertices (step c)).

[0173] Firstly, the determination of alpha and beta within the context of the mathematical model for the panel is discussed.

[0174] B. Initial Note about Step (c) Mapping of Panel Geometry to Frame Geometry

[0175] The mathematical procedure discussed below needs to be defined in such a way to accommodate bidirectional calculations to map the panel geometry onto the frame geometry required to make the panel, and also the reverse. For example, the frame geometry may need to be mapped onto the panel, such as where the frame has defined outer limits of movement which place constraints on the available panel shapes. Thus, the same process can be used to go from frame to panel and also from panel to frame. The process is the same, merely the edge length changes in the calculations.

[0176] FIG. 15B also shows the limits of skew and beta for the current prototype forming apparatus 10.

[0177] C. Mathematical Procedure to Describe any Hyperbolic Paraboloid Surface for Frame Mapping

[0178] The mathematical procedure to describe the hyperbolic paraboloid surface was created through defining an edge length for a square then translating that simple shape into a skewed hyperbolic paraboloid surface. The process of translating the square into a hyperbolic paraboloid requires three steps each with their respective descriptive parameters.

[0179] Step 1: Define a square with a chosen edge length (x), (FIG. 16).

x.sub.p====

[0180] The origin is defined as the mid-point between V.sub.0 and V.sub.2

O=(V.sub.0+V.sub.2)

[0181] where V.sub.0 and V.sub.2 (and subsequently V.sub.1 and V.sub.3) are defined in a coordinate system.

[0182] Step 2: Skew the square using the skew parameter (), (FIG. 17).

[00001]$=\frac{.Math.\stackrel{.Math.}{{\mathrm{OV}}_0^{}}.Math.}{.Math.\stackrel{.Math.}{{\mathrm{OV}}_0}.Math.}$

[0183] Where the vertices defined along the x-axis are simply scaled accordingly:

=

[0184] With symmetrical condition

=

[0185] Given the edge lengths must remain constant i.e.

x====

[0186] The translations of the vertices along the y-axis are found by the following:

[00002]$\stackrel{.Math.}{{\mathrm{OV}}_1^{}}={\left(x^2-{\left(.Math.\stackrel{.Math.}{.Math.{\mathrm{OV}}_0.Math.}\right)}^2\right)}^{\frac{1}{2}}.Math..Math.$

[0187] With symmetrical condition

=

[0188] Step 3: The vertices defined along the yz-plane are rotated () about the x-axis:

[0189] By firstly defining the Cartesian axes at O as in FIG. 18, the rotational translation about the x-axis was performed to resolve the definition of the hyperbolic paraboloid as in FIG. 19.

==

===

[0190] Rulings are then applied at increments from points along to equivalent increments along for the spacing between rulings required in FIG. 20.

[0191] That completes the process of determining the description of the hyperbolic paraboloid as defined by the three parameters (edge length (x), skew () and beta ()).

[0192] Step (b)(iii) Calculate and for the Panel

[0193] Following on from step a) above, skew and beta can be calculated from the known vertices (V.sub.0, V.sub.1, V.sub.2, V.sub.3).

[0194] Fortunately, the three stage process described can also be reversed so that when a hyperbolic paraboloid surface is defined by its vertices, the edge-length, skew and beta parameters can be extracted from the surface. This is achieved as follows:

[00003]$=\frac{\sqrt{2}.Math..Math.\stackrel{.Math.}{V_0^{}.Math.V_2^{}}.Math.}{2.Math.x_p}$

[0195] Where x.sub.p refers to the edge length of panel

O=(V.sub.0+V.sub.2)

==

[0196] Beta can simply be solved using trigonometry.

[0197] 3.5 Summary of Data Workflow

[0198] The summary of the data workflow is illustrated in FIG. 11.

[0199] This provides a consistent method of defining the hyperbolic paraboloids for the panel and the frame. The alpha, beta and edge length can be extracted from the panels located at various positions on the larger curved surface (FIG. 13) one wishes to fabricate.

[0200] This methodology allows for data extraction from a large very complex CAD model into individual panels that can be manufactured by the forming apparatus 10. By defining such panels simply by alpha, beta and edge length (step b), the panel geometry can be oriented relative to the variable frame geometry 14. Additionally, such simple panel definition allows a determination of whether the panel can be fabricated within the limits of the variable frame 14 as per FIG. 15B.

[0201] Once the panel geometry has been extracted as alpha, beta and edge length, it can be converted back to vertices information (V.sub.0, V.sub.1, V.sub.2, V.sub.3) to allow mapping of the panel vertices onto the required frame vertices V.sup.f.sub.0, V.sup.f.sub.1, V.sup.f.sub.2, V.sup.f.sub.3. (step c).

[0202] This simplified data extraction (as per step b) and a method to map each panel onto the frame (as per step c) allows separation of the two processes (steps b and c) from each other and furthermore separation of the steps b and c from the large very complex CAD model and thus provides an effective workflow from design to manufacture.

[0203] 3.6 Step c) Translation of Panel Geometry to Frame Geometry

[0204] Overview

[0205] A method of translation between panel and parametric mould (and vice versa) is required.

[0206] It is desired to map a panel (as described above) with a defined edge length (x), skew () and beta () onto the hyperbolic paraboloid support 16 of the frame 14 to determine and . However, the solution to the translation appears to be without a deterministic solution. Hence, an optimised curvature matching correction function was used to solve for the hyperbolic paraboloid translation.

[0207] The translation of panel geometry to frame geometry is done through curvature matching of scaled hyperbolic parabolas as will be described. In short, the parabolas extending between diagonally opposite vertices of the panel are extrapolated to estimate the location of the frame vertices, with the error resulting from the estimates being used to solve a quadratic correction function for the correct vertices of the frame.

[0208] Detailed Description of Translation of Panel Geometry to Frame Geometry

[0209] Referring to FIG. 22, the parabolas describing the curvature of the hyperbolic paraboloid surface are (for a Cartesian coordinate system located at CP):

CP=(V.sub.0+V.sub.1+V.sub.2+V.sub.3) [0210] The xz plane parabola is: z.sub.x=a.sub.xx.sup.2 [0211] The yz plane parabola is z.sub.y=a.sub.yy.sup.2

[0212] where a.sub.x and a.sub.y can be determined from the location of the panel V vertices and CP point.

[0213] Three points V.sup.s.sub.0,0, V.sup.s.sub.0,1, V.sup.s.sub.0,2 along the xz-plane parabola are chosen to formulate the curvature matching correction function. The location of the three points should be reasonable estimates of the vertices of frame 14, as per FIG. 23.

[0214] A spherical intersection between a sphere centred at each estimated vertex and the yz-plane parabola was performed to locate the vertices on the yz-plane parabola i.e. V.sup.s.sub.3,0; V.sup.s.sub.3,1 and V.sup.s.sub.3,2satisfying the frame equal edge length (x.sub.f) criteria i.e.

x.sub.f===

[0215] There are a number of different methods for spherical intersections. However using a direct algebraic method is the preferred method:

[00004]$x_i^2+{\left(z_y-V_{0,z}^{}\right)}^2\frac{z_y}{a_y}=x_f^2$

[0216] Where x.sub.i was the i.sup.th estimate of the xz-plane parabola abscissa where i=0,1,2.

[0217] Having now determined V.sup.s.sub.0,0, V.sup.s.sub.0,1, V.sup.s.sub.0,2, it is possible to directly derive V.sup.s.sub.2,0, V.sup.s.sub.2,1, V.sup.s.sub.2,2. Likewise, having determined V.sup.s.sub.3,0; V.sup.s.sub.3,1 and V.sup.s.sub.3,2, it is possible to directly derive V.sup.s.sub.1,0; V.sup.s.sub.1,1 and V.sup.s.sub.1,2.

[0218] Thus, 3 estimated frames are defined by this process, each having a respective centre point CP.sub.1, CP.sub.2, CP.sub.3.

[0219] As per FIG. 24, the distances (.sub.0, .sub.1 and .sub.2) between the centre-point of the panel and the centre point of the three estimated frames are defined:

.sub.i= where i=0,1,2

[0220] A quadratic correction function relating the distance between the centre-points and the abscissa x.sub.0, x.sub.1 and x.sub.2 of the three estimates along the parabola in the xz-plane was used to determine the abscissa x.sub.sol of the correct location of the vertex V.sup.f.sub.0. The quadratic correction function takes the form:

.sub.i=ax.sub.i.sup.2+bx.sub.i+c [0221] where i=0, 1, 2

[0222] The coefficients a, b and c change values based on skew and beta states of the parametric mould. Hence, the coefficients needed to be solved very efficiently. A method to solve simultaneous equations using matrix inversions was used to solve the system of the three equations for a, b and c.

[0223] The solution of x.sub.sol occurs when distance is zero (=0). This is when the surface curvature described by the mould frame rulings will match the curvature of the panel. Thus:

0=ax.sub.sol.sup.2+bx.sub.sol+c

[0224] Once x.sub.sol was foundit was used to locate the first frame vertex solution on the xz-plane parabola, as FIG. 25.

z.sub.x,sol=a.sub.xx.sub.sol.sup.2

V.sup.f.sub.0={x.sub.sol,0,a.sub.xx.sub.sol.sup.2}=V.sup.f.sub.2 where CP={0,0,0}

[0225] V.sup.f.sub.1 and V.sup.f.sub.3 can be found using the same sphere-parabola intersection technique required for finding x.sub.sol.

[0226] Thus the frame vertices V.sup.f.sub.0, V.sup.f.sub.1, V.sup.f.sub.2, V.sup.f.sub.3 are determined by the above process.

[0227] The above modelling has been done with CP at the centre of the panel. However, in a global coordinate system, a change in will result in a change in CP since the and actuators are fixed to the support structure of the apparatus 10. Therefore, when defining positions of the vertices within a global, static coordinate system, a slight vertical correction must be made to CP.

[0228] A suitable fixed origin is defined when the apparatus 10 was at its rest state i.e. when =1 and =0.

O.sub.st(,)={0,0,0}=CP(1,0)

CP(,)={0,0,a.sub.xx.sub.sol.sup.2}.sub.O.sub.st

V.sup.f.sub.st,i=V.sup.f.sub.i{0,0,a.sub.xx.sub.sol.sup.2} for i=0,1,2,3

[0229] 3.7 Step d) Calculate Target Travel Distances for the and Actuators

[0230] The actuator motion can be calculated from the frame vertices V.sup.f.sub.0, V.sup.f.sub.1, V.sup.f.sub.2, V.sup.f.sub.3.

[0231] The actuators act symmetrically as do the actuators. Therefore, only two coordinates are required to describe the positional state of the apparatus 10. This is further simplified with the gimbal 32 and tri-axial jointing systems 22 which maintain point singularities for rotational nodes. The actuation control system only requires two numerical values to operate the four linear actuators 26, 28, 29, 30.

[0232] All four actuators 26, 28, 29, 30 are able to act independentlythey are not over-restrainedallowing for further simplification of the relative motion of each actuator during manipulations of the frame 14 that include the motion of all actuators at the same time. Each actuator does not need to move at a specific rate. Therefore, standard acceleration curves for actuator motion could be employed. The actuators 26, 28, 29, 30 act in such a way that each actuator will arrive at its target at the same timeeven if the travel distances are different. Hence, the control system only requires the two target travel distances (.sub.action, .sub.action) to be mapped onto the four actuators.

[0233] By maintaining the point singularities at rotational joints where axes intersect, the derivation of the two numerical values for actuator motion is greatly simplified. The positioning of the actuators on the base of the static structural frame support for the apparatus 10 system is optimised for maximum actuator motion range.

[0234] The simplest version of the horizontal actuation system is two horizontal actuators acting symmetrically along the axis which can be described by:

x.sub.hori,0=V.sup.f.sub.0,x(,)V.sup.f.sub.0,x(1,0)=x.sub.hori,2 [0235] where x.sub.hori,0 is the abscissa for V.sup.f.sub.0 and x.sub.hori,2 is the abscissa for V.sup.f.sub.2

[0236] However, we opted for a slanted configuration

[00005]$\left(\frac{\mathrm{rise}}{\mathrm{run}}=\frac{3}{4}\right)$

that solved both of these challenges. Giving a final sloped actuation target () calculated as (from the rest position where =1 and =0):

.sub.action=5/4x.sub.hori,0

[0237] The beta actuator controls the degree of curvature of the frame 14.

[0238] For the beta actuator connected to V.sup.f.sub.1:

.sub.st,1={0,y.sub.st,z.sub.st}

[0239] and the beta actuator connected to V.sup.f.sub.3:

.sub.st,3={0,y.sub.st,z.sub.st}

[0240] The beta actuation arm travel distance .sub.action relative to the rest position (=1 and =0) can be derived from the position of V.sup.f.sub.st,1 or V.sup.f.sub.st,3 (with vertical correction to compensate for the sloped alpha actuator):

[00006]${}_{\mathrm{action}}={\left({\left(V_{\mathrm{st},1,y}^f\left(,\right)-y_{\mathrm{st}}\right)}^2+{\left(V_{\mathrm{st},1,z}^f\left({}_{,}.Math.\right)+\frac{3}{4}.Math.x_{h.Math.o.Math.r.Math.i,0}+z_{\mathrm{st}}\right)}^2\right)}^{\frac{1}{2}}-{\left({\left(V_{\mathrm{st},1,y}^f\left(1,0\right)-y_{\mathrm{st}}\right)}^2+z_{\mathrm{st}}^2\right)}^{\frac{1}{2}}$

[0241] The above methodology is incorporated into the control system which operates the forming apparatus 10.

[0242] It will be understood that the invention disclosed and defined in this specification extends to all alternative combinations of two or more of the individual features mentioned or evident from the text or drawings. All of these different combinations constitute various alternative aspects of the invention.

4 Hardware Overview

[0243] According to one embodiment, the techniques described herein are implemented by one or more special-purpose computing devices. The special-purpose computing devices may be hard-wired to perform the techniques, or may include digital electronic devices such as one or more application-specific integrated circuits (ASICs) or field programmable gate arrays (FPGAs) that are persistently programmed to perform the techniques, or may include one or more general purpose hardware processors programmed to perform the techniques pursuant to program instructions in firmware, memory, other storage, or a combination. Such special-purpose computing devices may also combine custom hard-wired logic, ASICs, or FPGAs with custom programming to accomplish the techniques. The special-purpose computing devices may be desktop computer systems, portable computer systems, handheld devices, networking devices or any other device that incorporates hard-wired and/or program logic to implement the techniques.

[0244] For example, FIG. 27 is a block diagram that illustrates a computer system 600 upon which one or more steps described above may be implemented. Server computer 102 and/or user computer 112 may be computer systems such as 600.

[0245] Computer system 600 includes a bus 602 or other communication mechanism for communicating information, and a hardware processor 604 coupled with bus 602 for processing information. Hardware processor 604 may be, for example, a general purpose microprocessor.

[0246] Computer system 600 also includes a main memory 606, such as a random access memory (RAM) or other dynamic storage device, coupled to bus 602 for storing information and instructions to be executed by processor 604. Main memory 606 also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor 604. Such instructions, when stored in non-transitory storage media accessible to processor 604, render computer system 600 into a special-purpose machine that is customized to perform the operations specified in the instructions.

[0247] Computer system 600 further includes a read only memory (ROM) 608 or other static storage device coupled to bus 602 for storing static information and instructions for processor 604. A storage device 610, such as a magnetic disk or optical disk, is provided and coupled to bus 602 for storing information and instructions.

[0248] Computer system 600 may be coupled via bus 602 to one more output devices such as a display 612 for displaying information to a computer user. Display 612 may, for example, be a cathode ray tube (CRT), a liquid crystal display (LCD), a light emitting diode (LED display), or a touch screen display. An input device 614, including alphanumeric and other keys, may be coupled to bus 602 for communicating information and command selections to processor 604. Another type of user input device is cursor control 616, such as a mouse, a trackball, or cursor direction keys for communicating direction information and command selections to processor 604 and for controlling cursor movement on display 612. This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), that allows the device to specify positions in a plane. Additional and/or alternative input devices are possible, for example touch screen displays.

[0249] Computer system 600 may implement the techniques described herein using customized hard-wired logic, one or more ASICs or FPGAs, firmware and/or program logic which in combination with the computer system causes or programs computer system 600 to be a special-purpose machine. According to one embodiment, the techniques herein are performed by computer system 600 in response to processor 604 executing one or more sequences of one or more instructions contained in main memory 606. Such instructions may be read into main memory 606 from another storage medium, such as storage device 610. Execution of the sequences of instructions contained in main memory 606 causes processor 604 to perform the process steps described herein. In alternative embodiments, hard-wired circuitry may be used in place of or in combination with software instructions.

[0250] The term storage media as used herein refers to any non-transitory media that store data and/or instructions that cause a machine to operation in a specific fashion. Such storage media may comprise non-volatile media and/or volatile media. Non-volatile media includes, for example, optical or magnetic disks, such as storage device 610. Volatile media includes dynamic memory, such as main memory 606. Common forms of storage media include, for example, a floppy disk, a flexible disk, hard disk, solid state drive, magnetic tape, or any other magnetic data storage medium, a CD-ROM, any other optical data storage medium, any physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH-EPROM, NVRAM, any other memory chip or cartridge.

[0251] Storage media is distinct from but may be used in conjunction with transmission media. Transmission media participates in transferring information between storage media. For example, transmission media includes coaxial cables, copper wire and fiber optics, including the wires that comprise bus 602. Transmission media can also take the form of acoustic or light waves, such as those generated during radio-wave and infra-red data communications.

[0252] Various forms of media may be involved in carrying one or more sequences of one or more instructions to processor 604 for execution. For example, the instructions may initially be carried on a magnetic disk or solid state drive of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 600 can receive the data on the telephone line and use an infra-red transmitter to convert the data to an infra-red signal. An infra-red detector can receive the data carried in the infra-red signal and appropriate circuitry can place the data on bus 602. Bus 602 carries the data to main memory 606, from which processor 604 retrieves and executes the instructions. The instructions received by main memory 606 may optionally be stored on storage device 610 either before or after execution by processor 604.

[0253] Computer system 600 also includes a communication interface 618 coupled to bus 602. Communication interface 618 provides a two-way data communication coupling to a network link 620 that is connected to a local network 622. For example, communication interface 618 may be an integrated services digital network (ISDN) card, cable modem, satellite modem, or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, communication interface 618 may be a local area network (LAN) card to provide a data communication connection to a compatible LAN. Wireless links may also be implemented. In any such implementation, communication interface 618 sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information.

[0254] Network link 620 typically provides data communication through one or more networks to other data devices. For example, network link 620 may provide a connection through local network 622 to a host computer 624 or to data equipment operated by an Internet Service Provider (ISP) 626. ISP 626 in turn provides data communication services through the world wide packet data communication network now commonly referred to as the Internet 628. Local network 622 and Internet 628 both use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on network link 620 and through communication interface 618, which carry the digital data to and from computer system 600, are example forms of transmission media.

[0255] Computer system 600 can send messages and receive data, including program code, through the network(s), network link 620 and communication interface 618. In the Internet example, a server 630 might transmit a requested code for an application program through Internet 628, ISP 626, local network 622 and communication interface 618.

[0256] The received code may be executed by processor 604 as it is received, and/or stored in storage device 610, or other non-volatile storage for later execution.

[0257] A computer system as described herein may be configured in a plurality of useful arrangements. In one approach, a data processing method comprises using a server computer, obtaining from one or more non-transitory computer-readable data storage media a copy of one or more sequences of instructions that are stored on the media and which when executed using a particular user computer among a plurality of user computers cause the particular user computer to perform, using the particular user computer alone or in combination with the server computer, the techniques that are described herein; and using the server computer, downloading the copy of the one or more sequences of instructions to any user computer among the plurality of user computers.

[0258] In another approach, a computer system comprises a server computer comprising one or more non-transitory computer-readable data storage media stored with one or more sequences of instructions which when executed using a particular user computer among a plurality of user computers cause the particular user computer to perform: using the particular user computer, alone or in combination with the server computer, the techniques that are described herein; and in the server computer, stored downloading instructions which, when executed using the server computer, cause downloading a plurality of copies of the one or more sequences of instructions to the plurality of user computers.

[0259] The foregoing describes only one embodiment of the present invention and modifications may be made thereto without departing from the scope of the invention.

5 References

[0260] Adapa (2017), AdapaAdaptive moulds, www.adapa.dk. [Accessed 7 Sep. 2017] [0261] Block, P. (2017), Block Research Group, www.block.arch.ethz.ch. [Accessed 7 Sep. 2017] [0262] Block, P. (2016), Paramet Structu Congeni, Architectural Design, 68-70, John Wiley & Sons inc. [0263] Burry, M. (2011), Scripting Cultures: Architectural Design and Programming, John Wiley & Sons inc. [0264] Castaeda, E.; Lauret, B.; Lirola, J. M. & Ovando, G. (2015), Free-form architectural envelopes: Digital processes opportunities of industrial production at a reasonable price, Journal of Facade Design and Engineering 3(1), 1B13. [0265] Farshad, M. (2013), Design and Analysis of Shell Structures, Springer Netherlands. [0266] Gardiner, J. B.; Janssen & Steven, R.McGee, W. & Ponce de Leon, M., ed., (2014), FreeFab, Springer International Publishing, Cham, pp. 131-146. [0267] IBIS (2017), Electrical Equipment and Machinery Manufacturing in China (C2034), Technical report, IBIS World Industry Report. [0268] Kelly, A. (2016), Concrete Product Manufacturing in Australia (C2034), Technical report, IBIS World Industry Report. [0269] de Lagrange, F. (2016), Geometrical Conoids String Surface Model, in London Science Museum Group Online Collection. [Accessed 7 Jan. 2016] [0270] Lavery, C. (2013), Spencer Dock Bridge, Concrete International June, 28-31. [0271] Lee, G. & Kim, S. (2012), Case Study of Mass Customization of Double-Curved Metal Faade Panels Using a New Hybrid Sheet Metal Processing Technique, Journal of Construction Engineering and Management 138. [0272] O'Rouke, L. (2017), FreeFAB. www.freefab.com [Accessed 7 Jan. 2016] [0273] Oesterle, S.; Vansteenkiste, A.; Gramazio, F. & Kohler, M. (2012), Method for on-site casting of free-form concrete structures (EP2532808 A1). [0274] Pottman, H.; Asperl, A.; Hofer, M. & Kilian, A. (2007), Architectural Geometry, Bentley Institute Press. [0275] Scheurer, F. (2010), Materialising Complexity, Architectural Design, 86-91, John Wiley & Sons inc. [0276] Schipper, H. R. (2015), Double-curved precast concrete elements, PhD thesis, Technische Universiteit Delft. [0277] Verma, S. & Epps, G. (2013), Curved Folding: Design to Production, ACADIA, Adaptive Architecture. [0278] Wang, S.; Cai, Z.; Li, M. & Lan, Y. (2012), Numerical simulation on the local stress and local deformation in multi-point stretch forming process, The International Journal of Advanced Manufacturing Technology 60(9), 901-911.