APPLICATION

This component is designed to simulate the growth of a single magnolia tree. All relevant algorithm parameters, such as the attraction distance, kill distance, and segment length, have been seamlessly integrated into the internal code of this component. Extensive testing has been conducted to ensure the optimal configuration of these parameters, resulting in a highly accurate representation of magnolia tree growth.

Furthermore, the user interface of this component features user-friendly functions that are intuitive and easy to comprehend. These functions offer customization options, empowering users to personalize their simulations according to their specific preferences and requirements. With the emphasis on simplicity and flexibility, users can effortlessly modify various aspects of the growth simulation, enhancing their overall experience and enabling them to achieve their desired outcomes.

Enviroment Influenced Growth Growth Stages

b. If there is an obstacle, decrease the density of attractors within the shaded zone, which is coherence with the fact that the shaded enviroment is not suitable for plant to grow.

c. Set the weight of each attractor according to the raletive position of the attractor and the obstacles, as well as between the attractor and plant seed position. The weight of attractors is a crucial parameter to simulate different tree spicies.

The most important aspect of tree growth is the sunlight, which is determined by the surrounding condition where the tree is rooted. This simulation considered this property of the growth and implemented it into the environment setup.

C. Build spacial Index of nodes

a. RTree is used to calculate the spacial index of nodes to avoid the massive amount of calculation between nodes and attractors.

2. GROW ITERATION

A. Associate attractors with nearby nodes a. Find nodes that within the searching range of an attractor using RTree index. b. Calculate distance between those nodes and the attractor.

Showing different tree appearances of various ages, providing a straightforward customer experience of the growing process of trees.

Season

A more realistic rendering of the tree can be achieved by rendering leaves and flowers.

Left: Magnolia in spring

Middle: Magnolia in summer

Right: Magnolia in winter

Space Colonization Algorithm

Space colonization algorithms are computational techniques used in the field of computer graphics and simulation to simulate the growth of natural structures like trees, rivers, or even galaxies. These algorithms are often used in procedural generation to create realistic, branching structures.

The framework of the algorithm are described visually by this diagram provided in the 2007 paper by Runions et al in which attractors are shown as blue dots and nodes as black dots:

(a) place a set of attractors.

(b) figure out which attractors are influencing each node

(c) for each node, calculate the average direction towards all of the attractors influencing it.

(d) calculate the positions of new nodes by normalizing this average direction to a unit vector, then scaling it by a pre-defined segment length.

(e) place nodes at the calculated positions.

(f) check if any nodes are inside any attractors’ kill zones.

(g) remove attractors that fit the criteria.

(h) begin the process over again from step (b)

Attractors represent the enviroment condition that are influencing the growth of the plants. Nodes represent tree branch that is reaching out to the attractors c. If the distance is less than the attraction distance, add this attractor to the list of attractors that is affecting this node. The attraction distance is not a constant, it reduces along with the iteration count, because as the tree grow, the space around each branch are smaller. d. If the distance is less than the kill distance, set the attractor property to kiledW.

B. Grow the next node a. For each node in this tree, is inluenced by attractors, and the attractor is not too lower than the node, calculate the average direction of the attractors, b. Because magnolia tree has a charactor of having vertical stern closing to the center, and horizontal branch reaching out, a sternRation is caltulaed to empasize this charactor by calculating the horizantal distance between the root and the node. c. Get the length of how long this branch is going to be by multiplying the segment length which is also changing along iteration, because trees tend to have longer sterns and shorter branches. d. Create new node at this position e. For each new nodes added, increase the all parenting nodes' radius

C. Remove the reached attractors

D. Rebuild the spacial index of current node

3. RENDER

A. Draw tree sterns with the updated radius a. Connect each node with its parent node(if it has any) by loft a tube using their raius.

B. Draw flowers and leaves on tree branches a. Input the flower or leaf to allow alteration. b. For each get the stalk vector of the flower of radding a random vector to the branch direction c. Orient the flower or leaf to the stalk, randomize the size and number of elements

2. EXAMPLES

Tree growth simulation Tree interaction with surroundings Tree interaction with trees

Future Works

1. One aspect of improving the tree modeling algorithm involves addressing the connection between branches to achieve a more natural and realistic appearance. This may include refining the algorithm's branch attachment mechanism to ensure smooth transitions and visually coherent branching patterns. By enhancing the connection between branches, the algorithm can generate tree structures that closely resemble those found in nature.

2. To expand the capabilities of the tree modeling algorithm, is crucial to test with various tree types beyond the existing ones. This involves incorporating different species of trees and their distinctive growth patterns into the simulation. Additionally, introducing realistic leaves and flowers to the algorithm can enhance the visual fidelity of the generated trees, further increasing their resemblance to real-world counterparts.

3. Improving the interaction behavior between trees is a significant area of development in the modeling algorithm. This entails refining the way trees interact and influence each other within a simulated environment. By considering factors such as shading, competition for resources, and physical proximity, the algorithm can simulate more accurate interactions between neighboring trees, resulting in a more realistic and ecologically informed representation of tree growth and development.

4. To enhance the realism of the tree modeling algorithm, incorporating seasonal changes is essential. By simulating the effects of changing seasons on tree growth, including factors like foliage color variation, leaf shedding, and blooming periods, the algorithm can accurately represent the dynamic nature of trees throughout the year. Integrating seasonality into the growing simulation allows for a more comprehensive and lifelike portrayal of tree development and adaptation to environmental changes.

CLOUD CITY:

Imaginary Futuristic City Senerio

This project illustrates a futuristic city where aircraft is the commen transportation. The project is completed in a 10 day workshop led by Jan Pernecky, developer of the Grasshopper plugin Monoceros. Monoceros is a suite of tools for optimally occupying an Envelope with discrete Modules, where the spatial relationship between those Modules can be constrained by a set of user-defined Rules. By using the Wave Function Collapse algorithm, it provides an innovative and fast solution to the emerging architectural problem of Discrete aggregation for purposes of design, architecture and urban planning.

Only one type of roof in this model which allows free transpassing of passangers with their personal aircrafts. The rule is simply that it must be on the top of each tree tower.

Stairs House Pillar

The stairs represents the vertical connections in the cloud city, the components itself doesn’t allow horizontal transpassing of any kind of transport and only allow vertical flow. The house units represents the residential volumn. The different openings showed in the model are abstractions of how residential area is opened to the public transportations.

Pillars are the vertical support of the tree house colony. The transparency feature of the pillars allows the transpassing of both fast traffic shafts and pedestrain trajectories.

Fast Traffic Shaft

Consistant with any 2d city planning, fast transportation lanes are crucial elements of a habitat. The traffic shaft here represents the regulated traffic road of the city where the speed of aircraft is less limited.

Flight Trajectory

The pedestain route design in a 3d town planning is almost impossible with traditional design tools and methods. However, with Monoceros, the connection of spaces can be generated following simple rules and modules.

The dotted lines showed in the pictures represents possible pedestrain aircraft movements in the habitat.

October 3rd

Introduction to grasshopper and Monoceros

October 10th

Combining the ideas of each members, made a preliminary vision for the work. Sketching, monoceros exercises, etc..

The first iteration of the project, the housing units are not intersecting with the pipe lines. Made a draft rendering in enscape, tried diffenent housing units.

October 11th

The second iteration of the design. Pipes are able to go though the housing units. However the housing units requires finer controls to avoid unconnected pillars and components.

October 13th

The third iteration of the design. Adding different type of pipes to represent the regulated traffic shafts and the random path of passengers. The envolpe of the city is designed as a tree shape colony in a valley like landscape.

October 16th

The final iteration of the design. Refine the rules of house generation to ensure the residential units has sufficent sunlighting, also refined the traffic shafts and the trajectory pipes. Lastly, render the model and presented in class.

October 17th

SELF FORMING FORMWORK FOR DOUBLY CURVED SHELL STRUCTURE:

This continuous research endeavour explores the feasibility of autonomous additive manufacturing, employing various materials. The core concept revolves around harnessing the self-shaping capabilities enabled by a 3D-printed pattern, effectively manipulating the shape-altering attributes of elastic materials and shape-memory polymers. Leveraging cutting-edge simulation tools, we have devised procedural frameworks for pattern generation and subsequent self-shaping simulations. The implications of this study hold promise for potential applications in molding intricate doubly curved geometries in the future.

The elasticity of cotton mixed lycra is the weekest, eventhough the fabric is thick and offers better support to printings, the shape forming is merely visiable.

Nylon mixed lycra shows best elasticity and good binding performance. The medium density of the fabric brings out the most obivious shape forming effect.