Extending Space Colonization Tree Modeling for Artistic Control and

Environmental Interactions

Owen Patrick

, Manjeet Rege

and Reynold Bailey

Department of Computer Science, Rochester Institute of Technology, Rochester, New York, U.S.A.

Department of Graduate Programs in Software, University of St. Thomas, St. Paul, Minnesota, U.S.A.

Keywords:

Tree Modeling, Space Colonization.

Abstract:

There are a growing number of modeling techniques and algorithms for creating and modifying tree structures,

both quickly and realistically. Many of these tools are part of larger software packages used for architecture

or landscaping designs. In these tools the tree models are static and come from a library selection. In other

areas, such as 3D modeling and design in ﬁlm and animation, the tree creation tools are more open for artistic

creativity and freedom of control. Much research has also been done on growing trees that are sensitive to some

environment. That is, growing tree models where genus type, and natural and artiﬁcial environment factors

are taken into heavy consideration. In this paper, we present an approach that facilitates user creativity while

still providing a realistic response to environment factors. Our system adapts the Space Colonization Tree

Modeling approach to allow for continued branch addition as well as environmental interaction. Feedback

from experienced modelers who participated in a user study revealed that our approach generated the tree

skeleton structures they intended and also provided realistic interaction with the environment.

1 INTRODUCTION

Though often overlooked by consumers of most

forms of computer generated imagery, botanical tree

models are used in many different applications in-

cluding gaming, movies, urban modeling, and land-

scape and architecture design. Tree modeling is there-

fore well-researched in different areas of computer

graphics as their creation is not a trivial task in most

respects. There are many variations of tree shapes,

structures and canopies all of which are controlled or

modiﬁed by both endogenous information (individual

plants genetics) and by exogenous inﬂuences (the sur-

rounding environment) (Pirk et al., 2012). These fac-

tors must be kept in mind by artists and modelers as

different tree systems and algorithms may have limi-

tations on the types of trees and branches that can be

simulated. Also the context of the application must

be considered as not all instances require a highly de-

tailed or interactive model.

Many existing tree modeling systems have either

focused on providing artistic control or on generating

realistic response to natural and artiﬁcial environment

factors. However there has been very little work to

bridge the gap between these two approaches. In this

paper, we present an approach that facilitates user cre-

Figure 1: Tree modeled using our modiﬁed space coloniza-

tion technique adapts to the addition of an obstacle to the

environment.

ativity while still providing a realistic response to en-

vironment factors. Our system adapts the Space Col-

onization Tree Modeling technique (Runions et al.,

2007) to allow for continued branch addition as well

as environmental interaction. We invited modeling

students to use our system and they reported that our

approach generated the tree skeleton structures they

intended and also provided realistic interaction with

the environment.

The remainder of this paper is organized as fol-

128

Patrick O., Rege M. and Bailey R..

Extending Space Colonization Tree Modeling for Artistic Control and Environmental Interactions.

DOI: 10.5220/0004690501280135

In Proceedings of the 9th International Conference on Computer Graphics Theory and Applications (GRAPP-2014), pages 128-135

ISBN: 978-989-758-002-4

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 2: Space Colonization. Initial point cloud in a deﬁned volume (left). Resulting tree model using standard Space

Colonization technique (middle). Tree modeled using our modiﬁed space colonization technique adapts to the addition of

obstacles to the environment (right).

lows: background and related work is presented in

section 2, implementation details are presented in sec-

tion 3, the results of a user study involving experi-

enced modelers is presented in section 4, and the pa-

per concludes in section 5 with a summary of the con-

tributions and potential avenues of future research.

2 BACKGROUND

Direct modeling of trees using NURBS or other para-

metric techniques allow the user to manually create

and position branches until the desired tree structure

is attained. Although such approaches offer a high

level of artistic control, they are too time consum-

ing to be practical for most applications. To over-

come this problem, procedural techniques arose to au-

tomatically create less artistically dependent models

quickly based on the traversal and application of spe-

ciﬁc rules that were created and modiﬁed by the mod-

eler. These rules controlled things such as branching

behavior, branch length, and branch angles (Smith,

1984). Various biological studies of tree structure

helped to lay the foundation for these rule-based sys-

tems (Lindenmayer, 1968; Honda, 1971; Kawaguchi,

1982; Bloomenthal, 1985; de Reffye et al., 1988).

Several user assisted systems have emerged that

attempt to balance the procedural approaches with

that of direct modeling. Many of these systems of-

fer the modeler an extensive array of parameters to

ﬁnely control the characteristics of the tree structure.

Weber and Penn (Weber and Penn, 1995), and more

recently Deussen and Lintermann (Deussen and Lin-

termann, 2010), present user assisted tree modeling

systems that rely on basic geometric principles rather

than trying to adhere to botanical rules. We adopt a

similar approach in this work.

To achieve visually accurate models, some re-

searchers have designed techniques that utilize im-

ages of trees and tree branch structures. The images

can be either registered (Reche-Martinez et al., 2004)

or unregistered (Neubert et al., 2007). In both cases,

the modeler still has to specify certain parameters for

the branches. Other systems combine image-based

approaches with rule-based techniques or directly use

sketch-based techniques to provide additional con-

trol (Chen et al., 2008; Longay et al., 2012).

Researchers have also studied physically-based

approaches for tree modeling. Various systems have

attempted to simulate the effect of either endogenous

inﬂuences, exogenous inﬂuences, or both. Some of

the factors considered in these systems include inter-

nal water ﬂow of the plant, the tendency for climb-

ing plants to latch on to structures, the effect of grav-

ity, competition for resources, phototropism, and the

presence of obstacles in the environment (M

ech and

Prusinkiewicz, 1996; Hart and Baker, 1996; Bene

and Mill

an, 2002; Bene

s et al., 2009; Pirk et al.,

2012). While these physically-based systems typi-

cally produce visually pleasing results and allow for

realistic (and in some cases computationally efﬁcient)

response to changing environmental factors, they of-

fer limited creative control. In this paper, we adapt the

Space Colonization Tree Modeling approach to facil-

itate user creativity while still providing a realistic re-

sponse to environment factors

2.1 Space Colonization

The Space Colonization Algorithm for modeling

trees (Runions et al., 2007) is a procedural tech-

nique that serves as the backbone for our approach.

The method itself is much like other procedural al-

gorithms. It uses a simple rule-based approach and

mimics the ﬁght for resources that trees and other

plants engage in for growth. A volume is ﬁrst deﬁned

in space with a speciﬁed number of randomly placed

points (see Figure 2). This represents an initial point

cloud structure that is placed around a set of starting

branch nodes. Each point in the cloud has two pri-

mary values; an inﬂuence radius i

and a kill radius k

The inﬂuence radius deﬁnes the effect a given point

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Figure 3: Screenshot of user interface showing two overlapping initial point clouds.

may have on branches nearby. This represents the re-

source that branches in the system would be attracted

to. The kill radius is an area that removes the point

from the system once a branch has overlapped with

it - representing both the depletion of resources for

branch growth and the algorithm’s terminating case.

Branches in the system are all of unit length and

each has a general grow direction. The algorithm cy-

cles through all branches and computes a direction

vector to all points whose inﬂuence radii it may fall

in. When ﬁnished it adds a new branch to the sys-

tem in that direction. It then checks all new branches

against the kill radii of points still in the system. Once

a branch enters the kill radius of a point, that point

is removed from the point cloud. This process is re-

peated until there are no more points in the cloud. The

technique produces attractive and, in general, physi-

cally plausible results.

Pirk et. al. (Pirk et al., 2012) noted that one of

the drawbacks of the Space Colonization technique is

the need to regrow the entire tree structure to adapt

to changing external factors. In their approach, they

instead take a fully formed tree skeleton as the base

model and compute its method of growth. In do-

ing this they have the total span of branches that

could possibly be created and so can adapt the tree to

varying surroundings. Their system provides visually

pleasing results, however their system is still locked

into the set of branches that are initially provided and

adding more is not possible. Furthermore, the pre-

computation required for their models is quite expen-

sive. In our approach we augment the space coloniza-

tion technique by way of parametrization and present

it in context for user assisted modeling. This enables a

greater amount of artistic freedom while still provid-

ing realistic response to the surrounding environment.

3 IMPLEMENTATION DETAILS

We implemented our system in two different environ-

ments to allow usability testing on both a portable lap-

top and a stand-alone desktop. The speciﬁcation of

each system is shown in the table below:

Laptop Desktop

OS Ubuntu 12.04 Windows 8

CPU Intel Core i5

(2.50 GHz)

Intel Core i5

(3.8GHz)

GPU Nvidia GeForce

GT 540M

Nvidia GeForce

GTX 660 Ti

RAM 4GB DDR3 8GB DDR3

To ensure cross-platform capabilities, we use Qt

IDE - Qt Creator for user-interface development. Our

software is written in C++ and utilizes OpenGL as the

rendering agent.

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3.1 Approach

Our approach can be split into three main processes:

1. Growing the tree model using the space col-

onization approach proposed by Runions et

al. (Runions et al., 2007).

2. Ensuring the model conforms to external physical

factors. To accomplish this we emulate the ap-

proach proposed by Pirk et al. (Pirk et al., 2012).

3. Providing a mechanism for continuing tree growth

based on user input. The additional growth also

conforms to the external physical factors.

The user interface provides the modeler with sev-

eral options to create point clouds of varying sizes

based on four basic shapes; sphere, ellipse, cone, and

cube. The modeler can create any number of starting

point clouds and position them in the scene as needed

(see Figure 3). Each cloud will have its own inﬂuence

and kill radius applied if needed. These point clouds

are placed around an initial set of branches that rep-

resent the starting trunk (or root) of the branch sys-

tem. For this project, we have implemented an initial

trunk that grows perpendicular to the ground-plane.

The user has the ability to modify the width and num-

ber of starting branches (recall that all branches are

unit length). An initial point cloud and starting trunk

setup is shown in Figure 2 on the left and the result-

ing tree structure is shown in the middle. The user can

then specify different obstacles in the scene or chose

to add on to current set of branches by specifying ad-

ditional point clouds. This process can be repeated

until the user is satisﬁed with the result.

The space colonization growth process is compu-

tationally intensive and even with preprocessing to

speed this up, the modeler has no way of predict-

ing what the ﬁnal tree structure will be beyond the

general space the branches will occupy (based on the

point cloud they specify). To overcome this prob-

lem and provide ﬁner artistic control, we extend the

basic space colonization technique by providing a

parameter called step size which allows the user to

specify how many nodes should be processed before

pausing the growth algorithm. The modeler can set

small step sizes to periodically pause and preview the

tree’s growth. They can also modify, remove, or add

new point cloud information or change kill radius or

inﬂuence radius parameters to affect the subsequent

growth of the branches. Note that since we maintain

age information of the branches that the modeler can

also reverse branch-growth to return to an earlier stage

of the tree where they can also make changes.

For every iteration of growth (i.e. whenever new

branches are added to the existing tree) we cycle

Figure 4: Octree spatial data structure used to speed up col-

lision testing between branches and obstacles in the envi-

ronment.

through the tree, starting from the branch tips (any

branches without children) and add girth going to-

wards the root node. This girth is changed at each

age step and also when the user dynamically alters

the tree’s age, environment, or the girth value itself.

At any step of the growth process, the modeler can

add obstacles to the scene. The addition (or modiﬁ-

cation) of obstacles triggers an intersection test that

checks each branch in the tree against each obstacle

in the scene. Furthermore, once the obstacle is in

place, the test must be conducted for each subsequent

iteration. To speed up this process, we use an octree

spatial data structure to store and retrieve branch po-

sition information as shown in Figure 4. If a branch is

found to be in a space occupied by an obstacle, an iter-

ative function is called which systematically disables

that branch and all children it may have, the results of

which can be seen in Figure 2 (right).

3.2 Gravitropism

In our system, we have implemented an option for a

loose variation of gravitropism where the gravity in-

ﬂuences the direction of branch growth. Unlike the

work in TreeSketch (Longay et al., 2012), our im-

plementation does not modify existing branches as

this requires that the complete tree be regrown. Of

course we can go back in time and modify an earlier

stage of the growth process if that is the effect de-

sired by the artist. Our gravitropism effect is accom-

plished by further modifying the basic space coloniza-

tion method to grow new branches by taking in an ad-

ditional weighted direction vector to account for the

addition of gravity. The weight applied to each branch

is scaled by the distance from the current branch node

to the center of the branch system. This means that

the further a branch is from the tree center, the more

it will bend towards the ground plane. A more elab-

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Figure 5: Trees modeled with different amounts of gravitropism weights. As seen on the right, large weights can result in

unnatural looking tree structures.

Figure 6: Examples illustrating the level of control available to the artist with our system.

orate method could also be implemented to take into

account the summed weight of the children branches

supported by the current branch node. Figure 5 shows

some results using different amounts of gravitropism

weights. Note that large weights can result in unre-

alistic results however this is completely within the

artist’s control.

3.3 Artist control

As described above, the artist has the ability to pause

growth at any time and to modify the point cloud and

other parameters to inﬂuence the future growth of the

tree. With this level of control, the artist can of course

create unnatural looking trees. However, regardless

of how extreme the resulting models are, they will

still react in an appropriate manner to obstacles in the

environment. Figure 6 shows some examples which

illustrate the level of control that is available to the

artist.

Figure 7 shows how our tool can be used to gen-

erate tree structures that are visually similar to real

world scenes. The photographs on the left show the

front and side view of a tree between two bike sta-

tions. We did a rough mockup of the bike stations in

Maya and left space for the tree in the middle. The

Maya scene was imported into our tool which was

then used to generate the tree model to ﬁll the space.

4 USER STUDY

We conducted a user study in order to assess the use-

fulness of our tool in the workﬂow of experienced

modelers. Six modelers (4 males, 2 females) with at

least one year experience with packages such as Maya

and Maxon Cinema 4D volunteered to participate in

our study.

For each participant, the ﬁrst 10 minutes of the

study were for an introduction and tutorial about our

system. They then spent 20 minutes using the tool and

5 minutes completing a survey. During the 20-minute

session, they were tasked with setting up a scene with

a tree and one or more obstacles. We instructed the

subjects to only consider tree structure and to disre-

gard lighting/shading and other visual effects as that

was not the focus of our work.

The survey consisted of four statements and the

responses were based on a Likert scale ranging from

1 (strongly disagree) to 5 (strongly agree):

S1. The structure of botanical trees affects the visual

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Figure 7: Using our tool to generate trees that have the same structure and response to the environment as real-world trees.

Photographs on left show front and side view of tree between two bike stations. Images on the right show corresponding

rendered views.

Figure 8: Results of survey completed by six experienced modelers.

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appeal of digital imagery.

S2. When obstacles are present, the resulting tree

shape appears realistic.

S3. The controls provided allow you to create the tree

structure you intended.

S4. I would like to see this tree modeling approach

become part of the modeler’s work ﬂow.

The results of the questionnaire are shown in Figure 8.

Note that none of the subjects disagreed or strongly

disagreed with any of the statements. A notable ob-

servation from the survey results is that 67% strongly

agreed that our approach to tree modeling should be

part of the modeler’s workﬂow.

5 CONCLUSIONS

In this paper we presented a system that adapts the

Space Colonization Tree Modeling approach to allow

for continued branch addition as well as environmen-

tal interaction. Our approach facilitates user creativ-

ity while still providing physically plausible models.

The results of a user study with experienced modelers

demonstrates the usefulness of our system.

Our system does have several limitations which

we hope to address as part of our future work.

Our gravitropism implementation, for example, only

works well if the initial point cloud is roughly cen-

tered above the starting trunk. Unrealistically leaning

trees can result if this is not the case as our gravit-

ropism computation for each branch is based on dis-

tance from the trunk. Additional limitations include

the fact that our system does not yet consider light-

ing (phototropism) or curved trunks. We also plan

to further develop our data-structures for branch con-

trol. A branch container would allow us the ability to

implement our own branch clustering algorithms for

interactivity and subsequent balancing strategies. Fi-

nally, we would like to expand this tool to operate on

the GPU to give faster responses and open more doors

for real-time computation.

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