Procedural Modeling of Interconnected Structures

# Procedural Modeling of Interconnected Structures

### Lars Krecklau and Leif Kobbelt
### RWTH Aachen University, Germany

#### Presentation by: Markus Eger

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# Interconnected Structures

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# Shape Grammars

* As we have heard last week, we can use grammars to generate 3D structures

* Start with a box with a label

* A rule divides a box with a label into smaller boxes with potentially different labels

* These divisions are done by cuts along an axis

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# Interconnected Structures

* Starting with a large box, and cutting out pieces mirrors starting at a coarse level and adding detail

* However, in many cases we want to retroactively add things, like connections between parts

* For example, we add houses along a street and then want to add overhead wiring/a catenary

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# Challenges

* If we just subdivide boxes, we would have to take the connections into account while we perform the cuts

* However, a more natural/intuitive way of defining such connections would be to do so after the connectors have been created

* Krecklau and Kobbelt describe a method to perform such retroactive connections

* The challenges they address are how to find connectors, different types of connections, and avoiding obstacles while performing a connection
 
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# Creating Connections

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# Containers

* The basic idea when connecting structures is that every connector defines connection points

* While the grammar is being expanded, these connection points can be collected in so-called containers

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# Connections

* A grammar can contain an arbitrary number of containers

* Different parts of the geometry may populate the different containers

* When the evaluation of these parts is done, there may be extra rules that define how the containers are used to connect parts of the model

* These rules define two aspects: *Which* connection points are to be connected, and *how*

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# Patterns

The simplest way of connecting parts of the model is by defining which connection points are to be connected in code

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# Geometric Queries

Alternatively, a ray can be cast from a connection point to find a suitable surface to connect with.

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# FFDs

Instead of working on boxes, the grammars generate and use trilinear freeform deformations (FFDs). It is possible to define a mapping from FFDs to boxes, making them well-suited for grammars with more flexibility.

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# Splines

FFDs can be created along arbitrary splines. The rotation is defined by an additional normal vector on each control point.

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# Inverse Kinematics

Finally, two points may be connected with a given geometry that consists of rotational and translational joints. For example, to mount iron bars between two walls, we can define a connector with hinges and a bar of 
arbitrary length in the center.

To calculate the angles and length of the joints, homogeneous coordinates are used, which result in a non-linear equation that is solved using standard methods.

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# Use Cases

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# Sydney Harbor Bridge

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# Catenary

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# Rollercoaster

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# Discussion