Examples of Using Regulators to Explore Design Configurations:

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· Architectural Design: Plan Layout

· Architectural Design: Transformation across Styles

· Architectural Design: Early Layout and Mass

· Architectural Design: Façade and Massing Design

· Mechanical Engineering: Gear Assembly

· Industrial Design: Car Form Design

· Graphic Design: Pattern Generation.

Architectural Design: Plan Layout

1 - Initial plan layout

It consist of one reflection regulator (blue line) and a few of grid regulators red lines). The reflection regulator controls both the walls and the grid regulators.

User manipulation

1 – The layout after the user rotates one side of the façade regulator

The façade regulator realigns all walls and windows according to its new orientation. The mirror regulator ensures that the change is properly reflected on both sides.

User manipulates the regulator’s curvature

2 – Plan layout after the user changes the curvature of the two lower regulators

The regulator re-configures the walls, doors and windows such that they follow the curve. The façade regulator also automatically reconfigures the grid regulators that are perpendicular (to the curve).

User manipulation

3 – Plan layout after the user changes the orientation of the side grid line regulator.

The mirror regulator ensures that the change is properly reflected on both sides.

Architectural Design: Transformation across Styles

1 - Initial configuration: a modern style two story linear building.

It consist 2 reflection regulators (green planes), two translation regulators (blue lines) an area regulator (not shown), and an adjacency regulator (not shown).

Use decreases the building footprint.

2 – The configuration after the user decreases the footprint of the building.

The area regulator adds floors to ensure that the area requirement remains the same. The adjacency regulator ensures that the roof is resized to follow the new building footprint. The translation regulator ensures that the windows remain within the same spacing.

Use decreases the building footprint.

3 – The configuration after the user decreases the footprint of the building (again).

User manipulates the windows on one floor

4 – The configuration after the user updates the number and size of the windows on one floor.

The floor translation regulator, (blue line) ensures that all floors are updated equally.

User manipulates one window

5 – The configuration after the user changes the form of the windows

User replaces the regulators

User replaces the roof

6 – The configuration after the user replaces the form of the roof.

The adjacency regulator ensures that the dimensions of the roof remain consistent with the footprint. The user also replaces the two reflection regulators by a rotation regulator (red line).

User adds a sub–roof

7 – The configuration after the user adds one sub-roof to the first floor

The floor translation regulator, (blue line) propagates the change to all the floors.

User manipulates the regulator. By changing the rotation degree.

8 – The configuration after the changes the rotation degree from 90 to 60.

The plan changes from a square to a hexagon. The regulators ensure that the all floors and the roof are updated

User manipulates the regulator by introducing a scale factor

9 – The configuration after the user introduces a scale factor into the translation regulator.

User manipulates a floor

10 – Final configuration: A Chinese pagoda. The user selects a floor and disassociates it from the translation regulator, and then applies a scale transformation to make it more prominent.

Architectural Design: Early Layout and Mass

1 - Initial configuration

It consist three reflection regulators and two pairs of translation regulators

User manipulates on window

2 – The configuration after the user changes the form of the window

The translation regulators associated with the wall, ensures that all window forms are updated. The reflection regulators ensure that windows in all the walls are updated.

User manipulates the regulator’s curvature

3 – The configuration after the user changes the curvature of the central axis, which is also a reflection regulator.

The translation regulator changed its form as well. The regulator ensures that all the external walls follow the curve and all internal walls remain perpendicular to the central axis.

User inserts splitting planes

4 – The configuration after the user splits up the mass.

The user inserts split regulators then moves the resulting masses.

User replaces the form of an element

5 – The configuration after the user replaces the form of the left mass.

The containment regulators (not shown) ensure that the number of floors, spaces, and windows remain the same.

6 – The configuration after the user rotates one of the splitting regulators. The regulator ensures that the both resulting sides of the splitting operation are redefined with respect to its new position.

Architectural Design: Façade and Massing Design

1– Initial configuration.

It consists of two reflection regulators and a few of translation regulators (blue lines), which act as horizontal axes that control the window alignment as well as the roof orientation.

User manipulates the regulators

2 – The configuration after the user rotates the horizontal axes.

The regulator aligns the windows along a slanted line, and updates the roof orientation creating a gable roof. Containment regulators (not shown) ensure that the number of windows remain the same.

User manipulates the regulator

3 – The configuration after the user reduces the frequency of the windows by manipulating the translation regulator.

User manipulates the regulator

4 – The configuration after the user splits the primary mass. This step follows from figure 2.

The user also introduces another alignment regulator (slanted purple line in the middle) and rotates it until the resulting split masses are gradually recessed.

5 - The configuration after the user transforms. This step follows from figure 2. The user changes the curvature of the horizontal axes (blue lines), which realigns the windows and changes the curvature of the roof forming a vault.

Mechanical Engineering: Gear Assembly

1 - Initial gear configuration consisting of spur gears and bevel gears.

Rotation regulators, shown as red lines, control the teeth in each gear. Adjacency regulators are automatically assigned when gears are adjacent.

User manipulation

2- The gear configuration after the user manipulated a tooth of the bevel gear.

The rotation regulator updates all the teeth of this gear (changing it from straight to spiral). An adjacency regulator (not shown) propagate the change to the adjacent gear (also causing it to become spiral)

User manipulation

3 – The gear configuration after the user changed the number of teeth on the spur gear, by manipulating its regulator. The regulator updates the shape of the adjacent gear to fit properly with the new configuration. Adjacency regulators also propagate the change in number of gears, so that their circular motion remains synchronous.

Industrial Design: Car Form Design

1- Initial configuration

Mirror Regulator, shown as transparent planes, represents the car’s axes of symmetry.

Rotation regulators, shown as red lines, control the configuration of the wheels.

User manipulates the regulator

2- The car configuration after the user had moved the mirror regulator.

As the user moves the regulator plane, the latter preserves the mirror symmetry by re-computing the position of the car’s sides, causing the width to increase.

User manipulates the regulator

3- The car configuration after the user had rotated the mirror regulator.

As the user rotates the regulator plane, the latter preserves the mirror symmetry by re-computing the position/orientation of the car’s sides, causing the car ‘s sides to converge at an angle.

User deactivates the regulator

User manipulates the regulator

User manipulates the regulator

4- The car configuration after the user manipulates the number of elements in the wheel cover. This example follows from figure 1. As the user manipulates one wheel’s rotation regulator, the mirror regulator propagates the changes to all wheels. The user also changes the scale of the back wheel. To achieve this the user needs to deactivate the central mirror regulator.

User deactivates the regulator

User manipulates the curvature

5- The car configuration after the user changes the curvature of the car’s bodyshell.

The user updates the curvature in one corner of the car and the mirror regulators ensure that the curvature is updated all around the car’s lower bodyshell. The upper body shell is controlled by only one mirror regulator, which reflects the change in curvature as well.

User adds a row of seats

6- The car configuration after the user adds another row of seats in the middle.

A containment regulator, not shown, comes to play and ensures that the new component is aligned and follows the same form/style as the rest of the car, and repositions the mirror regulators to accommodate the new row of seats.

User deactivates the regulator

7- The car configuration after the user converts the car into a truck.

To achieve this, the user deactivates the central regulator and replaces the two components of the back-side with the truck’s open backside.

We note that the manipulations presented here can occur in any order.

Graphic Design: Pattern Generation.

Images in this section are generated by our prototype.

1 - Initial pattern generated by a 180˚ rotation regulator (red dot) and a horizontal glide regulator (blue line).

User manipulates the element

2 - Pattern generated when the user scales the triangular element. Both regulators propagate changes across all the related elements.

User manipulates the regulator

3 – Pattern generated as user rotates the glide regulator. The glide regulator imposes the change on all its related elements.

4 – P3 wallpaper pattern. This pattern has one 120˚ rotation regulator and two translation (horizontal and at 60˚). This pattern is derived from figure 3 through he following steps:

1. changing the rotation regulator’s degree from 180 to 120

2. replacing the glide regulator by a translation regulator

3. adding horizontal translation regulator.

5- P4 wallpaper pattern . This pattern is achieved when the user manipulates the above pattern in the following way:

1. changing the rotation degree from 120˚ to 90˚,

2. changing the 60˚ translation regulator to vertical.

Notice that both of these are members of two distinct wall paper groups (P3 and P4), and that our regulators allow the transformation across symmetry groups in just a few steps.