The following example shows various levels of parametric control that can be achieved using the proposed histogram-based design interface. We resample a given point-cloud model by projecting a grid through its points and finding the closest point to each of the grid points. The result is an ordered point-cloud matrix where each point has a location address that can be used for identification.

The first level of parametric control is over the point-cloud geometry. The X, Y, and Z coordinates of each point can be documented in a tabular form following a sequential order. The coordinate values of each point can also be represented as three separate matrices providing the point location within the point-cloud. This way we can create mathematical or graphical relationships between the coordinate values and transform the point-cloud geometry parametrically. For example, we can introduce a parametric sine wave equation to the X-coordinate values and alter the design according to the amplitude and frequency parameters. We can also assign relationships to a selection set of points by simply identifying them in the unfolded schematic layout and change the values assigned. The histogram provides a simplified representation of the parameters values and allow for graphic manipulations that can be directly imposed on the spatial point-cloud.

When populating the point-cloud model with cellular components, the points act as place holders defining the component size and orientation. A schematic layout of the components can be used to control the distribution pattern over the point-cloud geometry. Applying a numeric naming convention allows to create a histogram representation of the distribution pattern and to control it parametrically.

For example, we can create a series of cladding panels and name them according to the opening ratio where “10″ is a fully closed panel and “19″ is a fully open panel (do not name components with “0″ or “1″). The schematic layout can be represented as a histogram where the numeric value defines which panel component is to be placed. This histogram can be used as an abstract design interface providing a schematic visual representation of the façade design. This method can also be used as a framework for a performance driven design process. For example, we calculate the solar exposure of each panel and scaling the numeric results between 0-9. The rescaled solar exposure values can be used as a components distribution pattern populating the point-cloud geometry according to performance values.

When populating point-cloud geometry with components, the bounding-box of each component inherits its x-y size and its orientation from the point-cloud. Another layer of parametric control can be applied to the bounding box of the cellular-components. For instance, the z-scale values of each component can be represented schematically in a tabular form providing an unfolded histogram representation of the components height values. The histogram interface provides both uniform and non-uniform control over the height parameter of the components. By creating graphic or numeric relationships between the histogram values a uniform control can be achieved while changing an individual value results in a non-uniform transformation. This method simplifies the modeling process by providing a 2.5-dimensional interface for a complex design model.

• Histogram Matrix Tools
• ParaCell Components System
• Populating Components with Performance Matrices
• Behavior Modeling: Generative DNA Example
• Re-Fit 4-Corner Points Components