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Methods for creating topological patterns for form diagrams
The second tutorial session explores various methods for generating topological patterns of form diagrams. Each method has a direct influence not only on the topology of the shell structure, but also the type of application and interaction that is desired during the design process. Additionally, this tutorial session will cover how to set proper boundary condition constraints in order to create a form diagram object from a topological pattern.
What is covered in this tutorial session:
Exploration of various methods for generating patterns for form diagrams
Understanding the difference between "patterns" and form diagrams
Defining boundary condition constraints
There are many ways to generate a topological pattern. Each method has pros and cons, and the desired design or workflow will help determine which method is more appropriate.
Generating patterns from Rhino objects
In RV2, three types of Rhino geometries can be used to generate a Pattern
. These pattern generation features would be particularly useful when there is already an existing structure with a geometry that one would like to recreate the pattern for.
Photographs and diagrams of different rose windows with complex mullion geometries, showing from left to right an outside picture, the equilibrated and piped form diagram, and the reciprocal force diagram: (a) Notre Dame de Mantes, France; (b) Notre Dame de Chartres, France (Photo by Holly Hayes); (c) Durham Cathedral, England (Photo by Carcharoth on Wikipedia); (d) Notre Dame de Paris, France (Photo by Ellen Brown); (e) Bisshop’s Eye of Lincoln Cathedral, England (Photo from Cornell University Library); (f) Sainte-Chapelle Paris, France.
One of the simplest, and the most manual, way to make the Pattern is to draw the edges of the Pattern
as Rhino lines. Each edge of the Pattern should be an individual line; all lines should be broken at all line intersections. In other words, these lines may not be overlapping.
Pattern
is a COMPAS mesh object. A mesh datastructure is network of faces, where the connectivities of the faces are defined by halfedge adjacencies. Therefore, the input set of lines must consist of closed loops of lines representing the faces of the Pattern.
If there are closed loops of lines, a Pattern
will be generated and all lines that do not form a closed loop, such as the "leaf" edges will be omitted.
A Rhino mesh object can be used to create a Pattern
. Since a Pattern is also a mesh object, the vertices and edges can be directly used to create the vertices and edges of the Pattern
.
A non-trimmed Rhino NURBS surface can be used to generate a Pattern
. UV mapping of the surface is used to subdivide the Pattern,
based on a subdivision value for U and V. Please refer to the first tutorial example to see how this feature is used.
RV2pattern_from_surface
only works with untrimmed surfaces; the input surface cannot have more than four edges.
How to obtain a structured quad-mesh pattern mapping a surface including optional point features on it
RV2pattern_from_features
is based on the compas_singular
package. For more information on the package, please check out its online documentation.
Using the RV2pattern_from_features
command is a powerful and an effective way to generate quad mesh patterns from complex or irregular boundary conditions and point features, such as the British Museum Great Courtyard Roof.
This algorithm works for trimmed, planar, curved and non-heightfield NURBS surfaces, but not NURBS polysurfaces or meshes.
The first example takes into account only the input surface to produce a pattern align with the boundaries. This aspect is important in funicular form finding in the case of non-supported boundaries.
The second example also takes into account point features on the surface to include pole points in the pattern. The point features at the corner can integrate local concentration of thrust. The other point features can integrate point loads or nodal supports. All these aspects are important to design a suitable pattern for funicular form finding.
Follow the instructions in the command window, choose outer boundary, inner boundaries and constraint curves. For the last step enter a target triangle edge length. Triangulated force pattern will be generated.
outer boundary is a closed polycurve that represents the outline of the diagram.
inner boundaries are openings of the intended design pattern.
constraint curves are where the vertices and edges will be forced to snapped onto.
Triangulation is a method that is fast and robust for creating a Pattern from a set of complex boundary features. However, triangulated patterns have no clear direction or hierarchy of the edges, which make it difficult to interact with (for example, if you wanted to attract forces using the force diagram).
RV2pattern_from_skeleton
is a powerful new RV2 feature that provides easy and intuitive method for generating complex patterns for free form vaults with just a few clicks.
RV2pattern_from_skeleton
is a feature based on the compas_skeleton
package. Fore more detailed information on the package, please check out its online documentation.
Choose "Create Pattern" --> "From Skeleton" from the tool bar, select a group of lines from Rhino and press Enter.
Follow the instructions in the command window, for each step click on the corresponding vertex, move cursor to input skeleton node width, leaf width and end extension respectively.
After initialising the skeleton, there will be available editing methods showing up in the command window. try out these options, get your ideal pattern.
increase the subdivision level of skeleton and finish editing. by clicking on "Finish", a force pattern diagram will be automatically generated.
This feature allows you to modify the attributes of the vertices of a Pattern
.
constraints : Rhino object to which the vertex is referenced or constrained to (not yet implemented)
is_fixed : fixes the x, y, z coordinates of the vertex
x : x coordinate of the vertex
y : y coordinate of the vertex
z : z coordinate of the vertex
This feature allows you to modify the attributes of the edges of a Pattern
.
lmax : maximum length desired for the edge during relaxation/smoothing
lmin : minimum length for the edge during relaxation/smoothing
q : force density
This feature allows you to manually move selected vertices of a Pattern
.
This feature allows you to delete vertices of a Pattern
. By deleting interior vertices of a pattern, holes can be created.
Using the force density method, this feature relaxes the entire Pattern
.
Using area-based smoothing (every vertex is repositioned to the centroid of its neighboring vertices), the pattern is smoothed.
Supports are vertices of the FormDiagram
where reaction forces can be present. If there already are vertices of the Pattern
which was fixed during the modification of the Pattern
, they will be automatically defined as supports. Please refer to the to see how the vertices of a Pattern can be selected or unselected as supports.
Please refer to the to see how curvature can be introduced to unsupported boundaries of a Pattern.
A Pattern
object with identified supports and updated boundaries can be used to create the FormDiagram
. Any edges of the pattern, of which both endpoints are supports are removed from the FormDiagram
.
Depending on how the support vertices are defined, corners of the Pattern are automatically processed during the creation of the FormDiagram
.