Continuous Collision Detection for Virtual Environments: A Walkthrough of Techniques

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electronic Journal of Computer Science and Information Technology (eJCSIT), Vol. 3, No. 1, 2011

H. A. Sulaiman and A. Bade, Continuous Collision Detection for Virtual Environments: A Walkthrough of Techniques 1

Continuous Collision Detection for Virtual Environments:

A Walkthrough of Techniques

Hamzah Asyrani Sulaiman

Universiti Teknikal Malaysia Melaka 76109 Durian Tunggal, Melaka

[email protected]

Abdullah Bade

Universiti Malaysia Sabah 88999 Kota Kinabalu, Sabah

[email protected]

Abstract –Continuous Collision Detection (CCD) has been widely accepted as the common tool to detect collision between dynamic collisions of rigid and deformable models, especially for use as an accurate collision method. Performing a computationally intensive technique for detecting between two configurations that focuses on accuracy always slows detection as compared to discrete collision detection (DCD). CCD algorithms focus on the motions toward objects regarding any interpolation as long as it can be detected before it can penetrate the object. While DCD requires backtracking after collision has been detected, CCD does not suffer the same problems as DCD. CCD also avoids the tunnelling problem that exists in DCD algorithms where penetration always occurs to the object (missed the collision). This paper will provide current and future research of CCD algorithms, which eventually will become the framework of our CCD algorithm technique for our research.

Keywords – Continuous Collision Detection; Collision Detection; Bounding-Volume Hierarchies

I. INTRODUCTION

Collision detection (CD) has been widely use in various types of applications such as robotics, computer graphics and physically based modelling. For those types of applications, reliable and fast collision detection algorithms are required for such simulation in order to bring realistic force of non-penetration constraints. Collision detection has been widely studied over the past two decades based on various types of research that have been conducted in order to increase the performance of simulation especially in computer games and other virtual simulations such as avatar for motion movements and urban simulation for wide-scale interactive simulations. At the earlier age of CD approach, most prior works were on static scenes where their intersection needs to be determined. However, current research areas have focused on dynamic scenes where objects are moving. The object movement may be known in advance, as it requires determining the possible collision with certain other objects. In sampling-based robot motion planning, robot movement may need to determine its future directions in order to find the possible collision with certain objects around the robot’s area movement and eventually use the data that has been collected by sensors in order to compute a continuous collision-free path from its current position until the end of the robot’s movement position.

At an initial level of collision detection, there are two subparts of dynamic collision detection algorithms which are discrete collision detection (DCD) and continuous

collision detection (CCD). Discrete collision detection only detects collisions at discrete moments in time; see examples in [3-18]. The consequence is, it may miss the collision between two successive configurations. This is also known by researchers as the tunnelling problem. Continuous collision detection performs a higher-order check to find out if there are any intersections between two objects through the distance defined by configuration points. It happens a lot when the object has thin surfaces or fast affecting objects that eventually missed the collision. It is important for high-fidelity simulations even though it is not required for fast response simulations such as in computer games or animations. Meanwhile continuous collision detection (CCD) algorithms resolve the tunnelling problem by first using the interpolated motions to check for continuous movement in collisions, motion interpolation between successive configurations, and use the interpolated motions to check for continuous movement collisions. Thus, CCD hardly misses any potential collision between those configurations.

Most CCD algorithms are used in sampling-based motion planning [9], and robotics collision to find the first intersection to apply responsive forces [19-21]. However, the drawback of CCD algorithms is that they are slow compared to DCD algorithms because they constantly check for collisions between configurations. That is the reason why most researchers seem to put more attention on DCD algorithms compared to CCD algorithms. Most researchers that use CCD algorithms limit their attention to polyhedral or articulated models. Others just use DCD to perform collision detection as there is no connectivity information except like that of polyhedral and articulated models.

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II. COLLISION DETECTION OVERVIEW

A. Overview

Detecting object interference in 3D applications is always a challenging problem for researchers. Compared to the real world, performing fast and accurate collision detection is never an easy task, as each object that contains triangles must be checked for interactions. For example, when a collision occurs between two geometric models that have 1000 triangles for each of them, the corresponding system must check every triangle on one object between triangles in another object. Thus, it is very expensive just to detect collision between only two objects that have only 1000 triangles. Any application that has a collision detection system must be aware of this limitation and find a solution to overcome it. Apart from that, memory management in any 3D application must be considered. Furthermore, there are some other criteria and important issues that need to be measured when designing a 3D application. For instance, in 3D games, animation and simulation, there is a need to maintain the application’s speed running with suitable frame rates of 30-60 fps [25-27]. Apart from that, there is a need to balance between the realism and the complexity of the applications as well [3, 28].

Theoretically, in order to simulate or design our 3D application, certain criteria and important issues need to be considered. For instance, in 3D games, animation and simulation, there is a need to maintain the application’s running speed of suitable frame rates as high as 30-60 fps [4, 11, 29]. To achieve that goal, the applications developed should undergo appropriate construction techniques to minimize memory consumption using some optimization method. Furthermore, it is necessary to balance between the realism and the complexity of the applications [4, 29].

B. Discrete Collision Detection and Distance Calculation

The virtual world differs from the real world in many terms such as how the geometric object in the virtual world behaves (physics effects, etc.), how the gravity in the real world differs from the virtual world and so on. Moreover, the big differences between the real world and the virtual environment are the objects themselves where the real world contains unlimited objects whereas the virtual environment can only generate a certain number of objects. However, the limitations of the virtual environment bring researchers to continue to produce high quality virtual worlds where the experiences in the virtual world are almost the same as the real world. Various virtual world applications such as computer games (first person shooter, racing car, etc.), online games (Second Life, World of Warcraft, etc.) and walkthrough city simulation, for example, have been developed to satisfy people using new ways of entertainment.

One of the important aspects that greatly affects the realism of the virtual world which we can experience is

the limitation of two or more objects that cannot share the same space at the same time. The constraint of this aspect will definitely result in some restrictions to our movement and this limitation has a great impact on the virtual world. However, objects that have impenetrability will enable us to perform tasks such as stacking a pile of cards and grabbing things in the virtual world.

In the virtual world, geometric objects do not have impenetrability on their own after being modelled using 3D tools. However, we are able to create a mechanism to handle impenetrability by introducing a technique called collision detection. Collision detection has a broad meaning and covers many applications; for instance in 3D simulation and animation, engineering (e.g., robotics), virtual reality environments, and even networking. According to Moller et al. [30], collision detection can be divided into three main parts: collision detection, collision determination, and collision response. Collision detection occurs when two or more solid objects (simple or complex) come into contact (e.g., cars collide with each other). Collision determination will try to find the exact contact between colliding objects. Next, collision response will react after the collision has been detected either by appointing new positions or by changes of shape for both objects.

C. Continuous Collision Detection

CCD is almost the same with DCD except in terms of how the detection process is implemented. There are various types of CCD algorithms that have been proposed in the literature. Figure 1 shows the difference between DCD and CCD algorithms.

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H. A. Sulaiman and

One of the advantages of CCD from the tunnelling

missed if the simulation has low frame Furthermore, CCD is

detection data collection, such as point of contact, time of contact, and normal of contact.

and DCD methods.

accepted because of the requirement to deal with the dynamic nature of 3D applications. It has received attention from various research communities because it offers robust handling of non

rigid bodies. CCD based on

Figure 1.Differences between DCD method (a) and CCD method (b). DCD check

Figure 2.

and A. Bade, Continuous he advantages of CCD tunnelling effect,

missed if the simulation has low frame Furthermore, CCD is perfect

detection data collection, such as point of contact, time of contact, and normal of contact.

methods. Recently, CCD has become widely accepted because of the requirement to deal with the dynamic nature of 3D applications. It has received ttention from various research communities because it offers robust handling of non

rigid bodies. Readers are encourage n figure 2.

Differences between DCD method (a) and CCD method (b). DCD check calculation technique that continuously checks for intersection

Figure 2. CCD techniques

ronic Journal of Computer Science and Information Technology (eJCSIT), Vol. 3, No. 1, 2011

Continuous Collision Detection for Virtual Environment he advantages of CCD is it does not suffer

and no collision is going to be missed if the simulation has low frame

perfect for accurate collision detection data collection, such as point of contact, time of contact, and normal of contact. Figure 1 depicts the CCD Recently, CCD has become widely accepted because of the requirement to deal with the dynamic nature of 3D applications. It has received ttention from various research communities because it offers robust handling of non-penetration constraints fo

are encouraged to read paper

echniques and implementation

Collision Detection for Virtual Environment it does not suffer

and no collision is going to be missed if the simulation has low frame-rates. for accurate collision detection data collection, such as point of contact, time of Figure 1 depicts the CCD Recently, CCD has become widely accepted because of the requirement to deal with the dynamic nature of 3D applications. It has received ttention from various research communities because it penetration constraints fo

to read paper

mplementations

Collision Detection for Virtual Environment it does not suffer

and no collision is going to be rates. for accurate collision detection data collection, such as point of contact, time of Figure 1 depicts the CCD Recently, CCD has become widely accepted because of the requirement to deal with the dynamic nature of 3D applications. It has received ttention from various research communities because it penetration constraints for to read papers on

BVH

geometric models with specific bounding volumes. It works like a tree that has a root (

of leave node has it

The main idea of the BVH is to build a tree that has a primary and secondary root which each of the secondary nodes store

hierarchy is shown in Figure

Figure 3.

the right hand side image shows binary type hierarchy

BVH allow for

example, given two objects root

will not be done for both objects. However, when the root

intersection between one root of the hierarchies’ tree and the othe

it recursively checks again whether there is intersection between both objects at

correct intersection. Figure partitioned into several par

basic algorithms for detecting collision between two hierarchies

Collision Detection for Virtual Environments: A Walkthrough of Techniques III. BOUNDING

BVH is simply a tree structure that represents geometric models with specific bounding volumes. It works like a tree that has a root (

of leaves (middle division) and a leaf (last division). Each node has its bounding

The main idea of the BVH is to build a tree that has a primary and secondary root which each of the secondary nodes stored as a leaf.

hierarchy is shown in Figure

Figure 3. The left hand side image show the right hand side image shows binary type hierarchy

BVH allows the intersection for non-colliding

example, given two objects roots of the hierarchies

will not be done for both objects. However, when the roots of both hierarchies intersect, it checks for intersection between one root of the hierarchies’ tree and the other children of objects hierarchies’ tree. In this case, it recursively checks again whether there is intersection between both objects at

correct intersection. Figure partitioned into several par

basic algorithms for detecting collision between two hierarchies [37-38]

Differences between DCD method (a) and CCD method (b). DCD checks for certain time steps, while CCD uses calculation technique that continuously checks for intersections which are more

Walkthrough of Techniques

OUNDING-VOLUME

simply a tree structure that represents geometric models with specific bounding volumes. It works like a tree that has a root (

s (middle division) and a leaf (last division). Each bounding-volumes that cover t

The main idea of the BVH is to build a tree that has a primary and secondary root which each of the secondary

as a leaf. An example of bounding hierarchy is shown in Figure 3.

The left hand side image show

the right hand side image shows an unbalanced hierarchical f

the intersection

colliding pairs from the hierarchy tree. For example, given two objects with their BVH, when

of the hierarchies do not intersect, the calculation will not be done for both objects. However, when the of both hierarchies intersect, it checks for intersection between one root of the hierarchies’ tree and r children of objects hierarchies’ tree. In this case, it recursively checks again whether there is intersection between both objects at the middle level until i

correct intersection. Figure 3 partitioned into several parts w

basic algorithms for detecting collision between two 38].

tain time steps, while CCD uses more computationally intensive ronic Journal of Computer Science and Information Technology (eJCSIT), Vol. 3, No. 1, 2011

OLUME HIERARCHIES

simply a tree structure that represents geometric models with specific bounding volumes. It works like a tree that has a root (upper division), a group s (middle division) and a leaf (last division). Each

volumes that cover the child node The main idea of the BVH is to build a tree that has a primary and secondary root which each of the secondary

xample of bounding .

The left hand side image shows a BVH with Sphere BV while unbalanced hierarchical f

the intersection to occur without searching pairs from the hierarchy tree. For

with their BVH, when not intersect, the calculation will not be done for both objects. However, when the of both hierarchies intersect, it checks for intersection between one root of the hierarchies’ tree and r children of objects hierarchies’ tree. In this case, it recursively checks again whether there is intersection

middle level until i 3 shows how ts while Figure

basic algorithms for detecting collision between two

tain time steps, while CCD uses an advance computationally intensive [1]

3 IERARCHIES

simply a tree structure that represents geometric models with specific bounding volumes. It upper division), a group s (middle division) and a leaf (last division). Each he child nodes The main idea of the BVH is to build a tree that has a primary and secondary root which each of the secondary xample of bounding-volume

s a BVH with Sphere BV while unbalanced hierarchical form using

without searching pairs from the hierarchy tree. For with their BVH, when the not intersect, the calculation will not be done for both objects. However, when the of both hierarchies intersect, it checks for intersection between one root of the hierarchies’ tree and r children of objects hierarchies’ tree. In this case, it recursively checks again whether there is intersection middle level until it finds the shows how the object is igure 4 depicts the basic algorithms for detecting collision between two

advanced motion

3

simply a tree structure that represents geometric models with specific bounding volumes. It upper division), a group s (middle division) and a leaf (last division). Each s. The main idea of the BVH is to build a tree that has a primary and secondary root which each of the secondary volume

s a BVH with Sphere BV while orm using

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A.

Figure 4. BVH traversal algorithm proposed by

A. BVH Construction

There are multiple types of BVH construction

be used to represent hierarchical representation. Among the popular ones

definitions:-

a) Nodes

condition that represents a separate data structure or a tree of its own. In BVH, it contains bounding

may become computer science tree

the root is at the top of the tree). The node that gives

or a

height of the tree is determined by the length starting from root node down to the leaf no The depth of the tree is the length of the path to its root.

b) Root Nodes

tree is called

not have any parents. It is the starting node where all the operations of

norm

child nodes downward of a branch or

tree connect

c) Leaf Nodes

binary tree

have any child nodes and mostly contain the last value or conditions. In BVH,

contain

d) Internal Nodes

both parent

node as it still has child nodes and parent node.

e)

Sub-can be viewed as a complete tree in itself. It repres

manipulated by

Beginning at the root nodes of two given trees

1. Check for intersection between two parent nodes 2. If there is no intersection between two parents 3.

4. Else check all children of one node against all children of the other node

5. If there is intersection between any children 6.

7. 8.

9. Else

Figure 4. BVH traversal algorithm proposed by detection between two BVH

BVH Construction

be used to represent hierarchical representation. Among ones is binary tree. Binary tree has some node

Nodes – A node may contain specific value or a

condition that represents a separate data structure or a tree of its own. In BVH, it contains bounding-volume with their tree ID. Each node may become a parent, child or leaf node (in computer science tree

the root is at the top of the tree). The node that s birth to a child node

a superior node

height of the tree is determined by the length starting from root node down to the leaf no The depth of the tree is the length of the path to its root.

Root Nodes – The topmost node in tree is called the

not have any parents. It is the starting node where all the operations of

normally. The root node is child nodes downward of

branch or sub-tree connecter is connects each node

Leaf Nodes – The bottommost node

binary tree are call

contain a few triangles or

Internal Nodes –

both parent nodes and child nodes. It is not node as it still has child nodes and parent node.

-tree – A portion of a tree data structure that can be viewed as a complete tree in itself. It represents some other part

nipulated by the

Check for intersection between two parent nodes If there is no intersection between two parents

Then stop and

lse check all children of one node against all hildren of the other node

If there is intersection between any children Then if at

Else go to Step 4 Else stop and report

Figure 4. BVH traversal algorithm proposed by detection between two BVH

be used to represent hierarchical representation. Among is binary tree. Binary tree has some node

A node may contain specific value or a condition that represents a separate data structure or a tree of its own. In BVH, it contains

volume with their tree ID. Each node parent, child or leaf node (in computer science trees grow downward where the root is at the top of the tree). The node that

child node is called superior node (or an ancestor node height of the tree is determined by the length starting from root node down to the leaf no The depth of the tree is the length of the path to

The topmost node in the root node. The root node not have any parents. It is the starting node where all the operations of the

The root node is connected to each child nodes downward of the root node by using

tree connector.

connecter is an important element that s each node with their parent nodes.

The bottommost node called leaf nodes.

few triangles or perhaps – The functional node nodes and child nodes. It is not node as it still has child nodes and

A portion of a tree data structure that can be viewed as a complete tree in itself. It ents some other part of the tree that can be

the user in programming.

Then stop and report “no collision” lse check all children of one node against all hildren of the other node

If there is intersection between any children f at a leaf node

Report “possible collision” Else go to Step 4

and report “no collision”

Figure 4. BVH traversal algorithm proposed by [38] for collision detection between two BVH

There are multiple types of BVH constructions that can be used to represent hierarchical representation. Among is binary tree. Binary tree has some node

A node may contain specific value or a condition that represents a separate data structure or a tree of its own. In BVH, it contains

volume with their tree ID. Each node parent, child or leaf node (in

downward where the root is at the top of the tree). The node that

called a parent node ancestor node). The height of the tree is determined by the length starting from root node down to the leaf no The depth of the tree is the length of the path to

The topmost node in the binary The root node not have any parents. It is the starting node

the tree will begin connected to each root node by using connector. A branch or

important element that with their parent nodes. The bottommost nodes in

leaf nodes. They do not have any child nodes and mostly contain the last value or conditions. In BVH, leaf nodes

perhaps one triangle. The functional node that nodes and child nodes. It is not a node as it still has child nodes and is linked by

A portion of a tree data structure that can be viewed as a complete tree in itself. It of the tree that can be user in programming.

report “no collision” lse check all children of one node against all

If there is intersection between any children

eport “possible collision”

for collision

that can be used to represent hierarchical representation. Among is binary tree. Binary tree has some node

A node may contain specific value or a condition that represents a separate data structure or a tree of its own. In BVH, it contains a volume with their tree ID. Each node parent, child or leaf node (in downward whereas the root is at the top of the tree). The node that parent node . The height of the tree is determined by the length starting from root node down to the leaf node. The depth of the tree is the length of the path to

binary The root node does not have any parents. It is the starting node tree will begin connected to each root node by using sub-important element that

in the do not have any child nodes and mostly contain the last may one triangle.

that has a leaf linked by a

A portion of a tree data structure that can be viewed as a complete tree in itself. It of the tree that can be

There are few common operations involved in construction and implementation of binary tree for BVH construction. Among them are enumerating all the items, searching for an item which is bounding

removing a

area when performing collision dete traversing

to the root, and report

two intersected BVH that possibility

B. BVH Splitting Rules

The first step of BVH construction is choosing the splitting rules that will divide the root node into two equal parts using

axis

at the longest axis at the splitting point based on the splitting rules. According to

common solution construction:

The details will be explained more the condition:

Figure 5. (a) Object median splitting, (b) Object mean splitting,

Meanwhile,

top-primitives by

recursively partitioned the bounded objects using a There are few common operations involved in construction and implementation of binary tree for BVH construction. Among them are enumerating all the items, searching for an item which is bounding

removing a whole section of a tree for area when performing collision dete

traversing down from the root to leaf nodes or leaf nodes to the root, and report

two intersected BVH that possibility

BVH Splitting Rules

The first step of BVH construction is choosing the splitting rules that will divide the root node into two equal parts using the binary type tree. Then, by using

axis-separating plane technique, the object will be divided at the longest axis at the splitting point based on the splitting rules. According to

common solution construction:

a. Median of the object coordi

– split at the object median (evenly distributed parts) resulting

b. Mean of object coordinates (object mean) at the object mean

c. Median of the bounding extent (spatial median) into two equal parts

The details will be explained more the condition:-

Meanwhile, [32, 40]

-down approach. The first procedure enclosed all primitives by using

recursively partitioned the bounded objects using a

Figure 6. Splitting along the farthest axis of object bounded with

whole section of a tree for area when performing collision dete

down from the root to leaf nodes or leaf nodes to the root, and reporting any intersected area between two intersected BVH that possibility

BVH Splitting Rules

The first step of BVH construction is choosing the splitting rules that will divide the root node into two equal

binary type tree. Then, by using

separating plane technique, the object will be divided at the longest axis at the splitting point based on the splitting rules. According to

common solutions of choosing the splitting rules for BVH

Median of the object coordi

split at the object median (evenly distributed parts) resulting in a well

Mean of object coordinates (object mean) at the object mean.

Median of the bounding extent (spatial median) into two equal parts.

The details will be explained more

Figure 5. (a) Object median splitting, (b) Object mean splitting, (c) Spatial median splitting

[32, 40] constructed OBB trees using down approach. The first procedure enclosed all

using an oriented bounding

recursively partitioned the bounded objects using a

Figure 6. Splitting along the farthest axis of object bounded with OBB using centre points

whole section of a tree for a non

area when performing collision detection (called pruning), down from the root to leaf nodes or leaf nodes any intersected area between two intersected BVH that possibility in collision.

The first step of BVH construction is choosing the splitting rules that will divide the root node into two equal

binary type tree. Then, by using

separating plane technique, the object will be divided at the longest axis at the splitting point based on the splitting rules. According to [8, 39], there

of choosing the splitting rules for BVH

Median of the object coordinates (object median) split at the object median (evenly distributed

a well-balanced tree. Mean of object coordinates (object mean)

Median of the bounding-volume projection extent (spatial median) – splitting the volume

The details will be explained more later. Figure 5 depicts

Figure 5. (a) Object median splitting, (b) Object mean splitting, (c) Spatial median splitting

constructed OBB trees using down approach. The first procedure enclosed all

an oriented bounding-box, and then it recursively partitioned the bounded objects using a

Figure 6. Splitting along the farthest axis of object bounded with OBB using centre points [32]

There are few common operations involved in the construction and implementation of binary tree for BVH construction. Among them are enumerating all the items, searching for an item which is bounding-volume, a non-intersected ction (called pruning), down from the root to leaf nodes or leaf nodes any intersected area between

in collision.

The first step of BVH construction is choosing the splitting rules that will divide the root node into two equal binary type tree. Then, by using the longest separating plane technique, the object will be divided at the longest axis at the splitting point based on the , there are three of choosing the splitting rules for BVH

nates (object median) split at the object median (evenly distributed

balanced tree.

Mean of object coordinates (object mean) – split

volume projection ng the volume

. Figure 5 depicts

constructed OBB trees using a down approach. The first procedure enclosed all

box, and then it recursively partitioned the bounded objects using a rule.

Figure 6. Splitting along the farthest axis of object bounded with

the construction and implementation of binary tree for BVH construction. Among them are enumerating all the items, volume, intersected ction (called pruning), down from the root to leaf nodes or leaf nodes any intersected area between

The first step of BVH construction is choosing the splitting rules that will divide the root node into two equal longest separating plane technique, the object will be divided at the longest axis at the splitting point based on the three of choosing the splitting rules for BVH

nates (object median) split at the object median (evenly distributed

split

volume projection ng the volume

. Figure 5 depicts

a down approach. The first procedure enclosed all box, and then it rule.

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H. A. Sulaiman and

Their ‘subdivide

splitting point with a plane orthogonal to either one of its axes and split it into two subsets. Objects

according to which side of the splitting point primitives are never cut. Figure

splitting example

C. Object Median

From figure

point. By calculating the median of each triangle, the object median point is equally distributed by finding the middlemost point between the median of all triangles. Then, it checks for the separating plane according to the median point of the triangle. According to

median requires O (n log n)

However, it is also reported that by using more sophisticated method

but this increase

[41]. This is because the median point of object median needs to be determine

take longer for the tree to be constructed.

D. Object Mean and O

Based on [5]

the centred coordinates. The object mean technique can result in tighter volume trees with

perform without splitting technique splits according into evenly spaced

find the best point. By using a brute force approach method finds

random subset of the primitive centre coordinates. However, due to the complex implementation

seldom use it.

IV.

Performing collision detection between rigid bodies using ‘primitive

expensive computation cost. Some buildings might have thousands of polygons

collision when some other objects intersection test

force approach, each primitive will be tested fo until the program fi

one of the way to handle this is to use a Bounding Volume (BV).

Figure 7.

and A. Bade, Continuous

subdivide’ rule is to find the longest axis of a box splitting point with a plane orthogonal to either one of its axes and split it into two subsets. Objects

according to which side of the splitting point are never cut. Figure

splitting example [32, 40].

Object Median

From figure 6, Object Median split

point. By calculating the median of each triangle, the object median point is equally distributed by finding the point between the median of all triangles. it checks for the separating plane according to the median point of the triangle. According to

median requires O (n log n)

However, it is also reported that by using more sophisticated methods, median can be found in O (n) time increases the heuristic usage at the earlier phase . This is because the median point of object median

to be determined using some heuristic take longer for the tree to be constructed.

Object Mean and Other

[5], the object is divided by using

the centred coordinates. The object mean technique can tighter volume trees with

perform without unbalancing splitting techniques, such as the splits according to BV projection. It sp

into evenly spaced points instead of using heuristic est point. By using a brute force approach finds the best possible

random subset of the primitive centre coordinates. However, due to the complex implementation

.

IV. BOUNDING

Performing collision detection between rigid bodies primitive-primitive’

xpensive computation cost. Some buildings might have thousands of polygons that

collision when some other objects

intersection tests with the buildings. By using force approach, each primitive will be tested fo

until the program finds the correct intersection point. So, one of the way to handle this is to use a Bounding Volume (BV).

Figure 7. Examples of common BVs as described in

Continuous Collision Detection for Virtual Environment rule is to find the longest axis of a box

splitting point with a plane orthogonal to either one of its axes and split it into two subsets. Objects

according to which side of the splitting point are never cut. Figures 5 and 6

, Object Median split

point. By calculating the median of each triangle, the object median point is equally distributed by finding the point between the median of all triangles. it checks for the separating plane according to the median point of the triangle. According to

median requires O (n log n) of time to sort all the points. However, it is also reported that by using more , median can be found in O (n) time the heuristic usage at the earlier phase . This is because the median point of object median

using some heuristic take longer for the tree to be constructed.

ther Splitting Rules

object is divided by using

the centred coordinates. The object mean technique can tighter volume trees with fewer

ing the tree by

such as the BV projection method BV projection. It sp

points instead of using heuristic est point. By using a brute force approach

possible splitting point between random subset of the primitive centre coordinates. However, due to the complex implementation

OUNDING-VOLUME (BV)

Performing collision detection between rigid bodies ’ intersection checking require xpensive computation cost. Some buildings might have

that need to be checked for collision when some other objects

with the buildings. By using force approach, each primitive will be tested fo

the correct intersection point. So, one of the way to handle this is to use a Bounding

Examples of common BVs as described in

Collision Detection for Virtual Environment rule is to find the longest axis of a box

splitting point with a plane orthogonal to either one of its axes and split it into two subsets. Objects are partitioned according to which side of the splitting point it lies but the

5 and 6 depict

, Object Median splits at the median point. By calculating the median of each triangle, the object median point is equally distributed by finding the point between the median of all triangles. it checks for the separating plane according to the median point of the triangle. According to [39], o

time to sort all the points. However, it is also reported that by using more , median can be found in O (n) time the heuristic usage at the earlier phase . This is because the median point of object median using some heuristics that ma take longer for the tree to be constructed.

ules

object is divided by using the mean of the centred coordinates. The object mean technique can fewer operations to by too much. Other BV projection method BV projection. It splits the projection

points instead of using heuristic est point. By using a brute force approach, this

splitting point between random subset of the primitive centre coordinates. However, due to the complex implementation, researchers

(BV)

Performing collision detection between rigid bodies intersection checking require xpensive computation cost. Some buildings might have

need to be checked for collision when some other objects are undergoing with the buildings. By using a brute force approach, each primitive will be tested for collision the correct intersection point. So, one of the way to handle this is to use a Bounding

Examples of common BVs as described in [2]

Collision Detection for Virtual Environment rule is to find the longest axis of a box

splitting point with a plane orthogonal to either one of its partitioned lies but the depict the

at the median point. By calculating the median of each triangle, the object median point is equally distributed by finding the point between the median of all triangles. it checks for the separating plane according to the , object time to sort all the points. However, it is also reported that by using more , median can be found in O (n) time the heuristic usage at the earlier phase . This is because the median point of object median that may

mean of the centred coordinates. The object mean technique can operations to too much. Other BV projection method, lits the projection points instead of using heuristics to , this splitting point between a random subset of the primitive centre coordinates. researchers

Performing collision detection between rigid bodies intersection checking requires xpensive computation cost. Some buildings might have need to be checked for undergoing brute collision the correct intersection point. So, one of the way to handle this is to use a

Bounding-The purpose of using computational cost

the object performs primitive applying BV, it could consume check each triangle with However,

be reduced with

object in order to perform collision dete help perform

BVH provides a hierarchical represent split the single BV into certain level primitive

It can

at certain level respond, collide has others

At the present time, there are several as sphere

[43-Discrete Oriented Polytope (k Polyhedra

large

because of its response [47]

bounding volume

In this implementation, we performed an in development of

used for future development of continuous collision detection method

behaves

The collision detection module wa creating a virtual world space

University 3D repository objects. Then, we ha for three

method. We believe that this implementation of BVH could be introduced for

approach in order to reduce the pairs testing between object triangle

Figure

implemented the BVH construction using a Pentium Core 2 Duo 2.2

PC800MH

Collision Detection for Virtual Environments: A Walkthrough of Techniques The purpose of using computational cost

the object performs primitive applying BV, it could consume check each triangle with However, the time

be reduced through enveloping with a BV. Instead of using

object in order to perform collision dete

help perform collision detection better than a single BV. BVH provides a hierarchical represent

split the single BV into certain level

primitive-primitive testing for accurate collision detection. It can also be used for fast collision detection by stopping at certain levels using

respond, approximately collides. It depends heavily o has been developed as

others, accuracy.

At the present time, there are several as spheres [42], Axis Aligned Bounding Bo

-45], Oriented Bounding Box (OBB) Discrete Oriented Polytope (k

Polyhedra [2], and hybrid combination BV large scale 3D simulations use

because of its simplicity, response toward

[47]. Figure 7 bounding volume

V. I

In this implementation, we performed an in development of a

used for future development of continuous collision detection method

behaves in virtual environment

The collision detection module wa creating a virtual world space

University 3D repository objects. Then, we ha for three 3D models using

method. We believe that this implementation of BVH could be introduced for

approach in order to reduce the pairs testing between object triangles.

Figures 8 through

implemented the BVH construction using Pentium Core 2 Duo 2.2

PC800MHz, GeForce 85

Walkthrough of Techniques The purpose of using a computational cost of detecting the object performs primitive applying BV, it could consume check each triangle with the

time required to check for each collision can through enveloping

BV. Instead of using a single BV for one particular object in order to perform collision dete

collision detection better than a single BV. BVH provides a hierarchical represent

split the single BV into certain level

primitive testing for accurate collision detection. be used for fast collision detection by stopping

using a stopping function or criterion approximately, to the collision as the object . It depends heavily on what kind of application been developed as some application

accuracy.

At the present time, there are several , Axis Aligned Bounding Bo , Oriented Bounding Box (OBB) Discrete Oriented Polytope (k-DOP)

, and hybrid combination BV scale 3D simulations use

simplicity, lower collisions, and eas illustrates the bounding volume techniques.

IMPLEMENTATION OF

In this implementation, we performed an in a collision detection system in order to be used for future development of continuous collision detection methods. It was done

in virtual environment

The collision detection module wa creating a virtual world space.

University 3D repository objects. Then, we ha 3D models using

method. We believe that this implementation of BVH could be introduced for a continuous col

approach in order to reduce the pairs testing between

8 through 10 depict

implemented the BVH construction using Pentium Core 2 Duo 2.2

z, GeForce 8500 GT

a BV is to reduce the ing an object’s interference. If the object performs primitive-primitive testing without applying BV, it could consume more time as it needs to

the other object’s

to check for each collision can through enveloping a highly complex object single BV for one particular object in order to perform collision detection, BVH could collision detection better than a single BV. BVH provides a hierarchical representation that could split the single BV into certain levels before performing primitive testing for accurate collision detection. be used for fast collision detection by stopping

a stopping function or criterion o the collision as the object

n what kind of application some application value

At the present time, there are several popular , Axis Aligned Bounding Bo , Oriented Bounding Box (OBB)

DOP) [5], Oriented Convex , and hybrid combination BV

scale 3D simulations use a bounding box lower storage requirement

, and ease of implement the most commonly used

MPLEMENTATION OF BVH

In this implementation, we performed an in collision detection system in order to be used for future development of continuous collision It was done to show how the BVH in virtual environments.

The collision detection module was developed by We inserted

University 3D repository objects. Then, we ha

3D models using a spatial median splitting method. We believe that this implementation of BVH continuous collision detection approach in order to reduce the pairs testing between

10 depict the BVH approach. We implemented the BVH construction using a machine with Pentium Core 2 Duo 2.2 GHz, 5 GB DDR2 RAM

00 GT with GPU support.

5

BV is to reduce the interference. If primitive testing without time as it needs to ’s triangle set. to check for each collision can highly complex object single BV for one particular ction, BVH could collision detection better than a single BV. ation that could before performing primitive testing for accurate collision detection. be used for fast collision detection by stopping a stopping function or criterion and

o the collision as the object n what kind of application value speed while

popular BVs such , Axis Aligned Bounding Box (AABB) , Oriented Bounding Box (OBB) [32, 45-46]

, Oriented Convex , and hybrid combination BVs [11]. Most bounding box technique requirement, fast implementation most commonly used

In this implementation, we performed an initial collision detection system in order to be used for future development of continuous collision to show how the BVH

s developed by inserted three Stanford University 3D repository objects. Then, we had a BVH

spatial median splitting method. We believe that this implementation of BVH lision detection approach in order to reduce the pairs testing between

the BVH approach. We a machine with , 5 GB DDR2 RAM

GPU support.

5

BV is to reduce the interference. If primitive testing without time as it needs to triangle set. to check for each collision can highly complex object single BV for one particular ction, BVH could collision detection better than a single BV. ation that could before performing primitive testing for accurate collision detection. be used for fast collision detection by stopping nd o the collision as the object n what kind of application speed while

BVs such x (AABB) 46], , Oriented Convex . Most technique , fast ation most commonly used

itial collision detection system in order to be used for future development of continuous collision to show how the BVH

s developed by Stanford a BVH spatial median splitting method. We believe that this implementation of BVH lision detection approach in order to reduce the pairs testing between

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Figure 9.Teapots BVH level 8 and BVH level 9

VI. CONCLUSIONS AND FUTURE WORK

In this paper, we have described the current research of continuous collision detection (CCD) in virtual environments and bounding-volume hierarchies that will likely be used for the CCD approach. Simulating the environment with CCD is probably the hardest task for researchers, as it needs to continuously detect for collision, leaving behind the speed of intersection. However, it can provide a very accurate collision detection method compared to other techniques. Hence, this paper also provides a review of CCD research based on their current developments. In future, we hope to develop a framework based on the relevant literature in order to propose our own method in the continuous collision detection of the simulation of rigid bodies.

ACKNOWLEDGEMENTS

This research is supported by Universiti Teknikal Malaysia Melaka, and the Malaysian Ministry of Science, Technology and Innovation under their eScienceFund grant (VOT No. 79237).

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