3DArcLens: Interactive Network Analysis on Geographic Surfaces

Alberto Debiasi, Bruno Sim

oes and Raffaele De Amicis

Fondazione Graphitech, Trento, Italy

Keywords:

3D Geovisualization, Edge Congestion, Interactive Visualization, Graph Layout, Distortion Lens.

Abstract:

Geographic datasets such as international telecommunications trafﬁc, ﬁnancial ﬂows, trading patterns, and

national migration patterns describe the movement of entities between geographical locations. In spatial rela-

tions analyses the exact route of the connections is not important. Hence, one of the most preferred methods

for its depiction is a graph representation with data nodes layered over a geographical surface (such as a ﬂat

map or a virtual globe). However, a large number of arcs can produce dense visual clutters that make difﬁcult

the extraction of information from: occluded geographical surfaces, occluded nodes and occluded arcs. In this

work we present a novel focus+context technique for 3D virtual environments that interactively distorts and

ﬁlters arcs layouts, revealing underneath information about the three aforementioned visual elements: nodes,

arcs and geographical surface. Moreover, changing the camera does not affect the geographical focus of the

lens. In our use cases, we observed that such technique is an advantage for tasks that include the exploration

of geographical networks.

1 INTRODUCTION

A huge amount of geographical data is available

nowadays. Many of these datasets describe the move-

ment of entities from geographical locations, repre-

sented in form of origin-destination data. In such data

representation only the origin, the destination and

magnitude of the ﬂows are known. Examples of such

datasets are international telecommunications trafﬁc,

ﬁnancial ﬂows, trading patterns, and national migra-

tion patterns (Tobler, 1987). Representations based

on geographical maps can be useful to the study of

these datasets, e.g. allow users to reason about ge-

ographic patterns of the movement. In such case a

node-link structure is used to represent the informa-

tion over a ﬂat map or over a virtual globe. In such

context the exact route of the connections is not im-

portant, hence links are represented as straight lines,

arcs, or even curves drawn in 2D or 3D virtual envi-

ronment.

According to the ﬁrst law of Geography, ”Every-

thing is related to everything else, but near things

are more related than distant things” (Tobler, 1970)

the perception of the distance between the origin and

destination of a ﬂow is extremely important. There-

fore, the use of ﬂat map representations is not rec-

ommended if the dataset covers the entire world, e.g.

with the Mercator projection, nodes located in oppo-

site sides of a map appear very far, but in the real

world the physical distance is shorter. Also, ﬂat maps

can also increase the clutter problem, e.g. links that

connect nodes placed in North America with oth-

ers placed in the Asia stretch across the entire map,

occluding the network in Europe. Representing the

Earth as a virtual globe overcomes this limitation be-

cause distances are true to scale and the length of

the link (represented as a three-dimensional arc) that

connects the two points is proportional to the short-

est distance between them. The main limitation of

3D globes when compared to 2D maps is that only

one hemisphere is visible at a time. A technique that

works on a 3D space and that is not affected by the

aforementioned occlusion problem is ArcMap (Cox

et al., 1996). It is a geographic visualization that uses

a two-dimensional representation of the Earth com-

bined with three-dimensional arcs that connect the

nodes.

In both, virtual globe and ArcMap, the depiction

of considerable amount of links over an area often

causes visual clutter, either on the nodes and arcs that

are not visible or on the layered geographical map

(Figure 1). The latter is particular important due to the

geographical information encoded into the dataset.

For example, if the dataset to be analyzed describes

tourist ﬂows then it can be relevant to visualize the

layered map that contains the major touristic attrac-

tions in the world.

Although the user can move, pan, tilt and zoom

291

Debiasi A., Simões B. and De Amicis R..

3DArcLens: Interactive Network Analysis on Geographic Surfaces.

DOI: 10.5220/0005255202910299

In Proceedings of the 6th International Conference on Information Visualization Theory and Applications (IVAPP-2015), pages 291-299

ISBN: 978-989-758-088-8

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

(a) (b)

Figure 1: (a) Visual clutter in a virtual globe with arcs. (b)

Visual clutter in a ﬂat map with arcs. This visualization

shows Internet trafﬁc ﬂows between countries.

the camera, in some situations this in not enough to

reveal the hidden information. In addition, the re-

quired time to compute these interactions might not

be acceptable and performing the operations in 3D

space can be disorienting for the user (Kaur et al.,

1999). Since the nodes encode geographical informa-

tion, techniques that rearrange node positions, such as

graph layout approaches are not recommended.

In this paper, we introduce a novel focus+context

technique called 3DArcLens that interactively reduces

the occlusion problem without removing links or

moving nodes. We deﬁne a lens technique that acts

on the arcs depending on their position and incident

nodes. For example, if the interactive lens intersects

only with the arc and not with its incident nodes, then

the arc is replaced with an aesthetically pleasing curve

placed around the lens to be easily traced. If the arc

has an incident node inside the lens, the node is vi-

sualized as a sphere with an unique color, meanwhile

the segment inside the lens is not drawn and the rest is

colored accordingly with the node’s color. Due to the

fact that the arcs that depict origin-destination data do

not represent a real route, changing their shape or not

drawing a part of them does not affect the informa-

tion they represent. Combined, these two methods al-

low the visualization of elements inside the lens (map,

nodes and arcs) to be clutter free. This interactive lens

is speciﬁcally designed to support the identiﬁcation of

elements of geographical networks as well as the ex-

ploration of the layered map with 3D view preserving

the geographic context such as the virtual globe and

the ArcMap.

This paper is structured as follows. Section 2 de-

scribes the related work. Section 3 introduces the arc

congestion problem. Section 4 describes our theoret-

ical framework. In the Section 5 a comparison with

similar techniques is made, and a discussion on the

limitation of the proposed technique is done. We con-

clude with some remarks about the usability of the

technique in Section 6.

2 RELATED WORK

This section provides a brief overview of interactive

techniques for reducing the visual clutter in graph

drawing domain and in 3D space.

Interactive Techniques for Clutter Reduction

in Graph Drawing Domain. An approach to re-

duce visual clutter in graph layouts is through con-

tent ﬁlters (Wong and Carpendale, 2007). The down-

side of this approach is that we also lose information

about purged or less relevant edges (Furnas, 1986).

Becker (Becker et al., 1995) suggested an alternative

that does not required purging data. The idea is to

draw the arcs only half the way to their target. How-

ever, this approach requires more cognitive effort to

track or ﬁnd the edges destination.

Edge aggregation (i.e. edge bundling) is a well

adopted technique that became popular in the last ten

years. Holten et al. (Holten and Van Wijk, 2009)

presented a force-directed algorithm in which edges

are modeled as ﬂexible springs that can attract each

other while node positions remain ﬁxed. A force-

directed algorithm (Debiasi et al., 2014) is used for

the automatic generation of ﬂow maps where ﬂows

are aggregated together and the magnitude of each

ﬂow is represented by the thickness of the lines. Cui

et al. (Cui et al., 2008) describes a mesh-based edge

clustering method for graphs. Additional works on

edge bundling are described in the survey by Zhou et

al. (Zhou et al., 2013). The peculiarity of the edge

bundling is that it is used to understand the overall

patterns but not the single links of the graph because

the connections become harder to read.

Wong et al. (Wong et al., 2003) proposed Edge-

Lens; a technique that iteratively curves graph edges

away from the point of focus. This consents to dis-

ambiguate the relationship between nodes and edges

without losing information. Bearing this in mind,

Schmidt et al. (Schmidt et al., 2010) used a multi-

touch interaction in conjunction with some edge dis-

placement techniques. Tominski et al. proposed to

draw in a local focus region only the edges that con-

nect certain vertices within the lens scope (Tominski

et al., 2006).

Pietriga et al. (Pietriga and Appert, 2008) pre-

sented Sigma Lenses, a set of interactive lenses

that replaces standard optical distortions with dy-

namic translucence to transition between focus

and context areas. Another strategy presented to

reduce the clutter problem is to apply a unique

color to paths of interest that differentiates from

background clutters (Moscovich et al., 2009). Link

Sliding (Moscovich et al., 2009) allows users to slide

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a link-cursor along the edge towards the destination

node. To explore crowded areas (overlapping bun-

dles), semantic lenses can be used. MoleView (Hurter

et al., 2011) is a semantic lens that selects a set of

data elements falling within the lens position and

having an attribute value deﬁned by the user. In case

of graph layout the lens moves the control points that

compose the links around the lens.

Interactive Techniques for Clutter Reduction

in 3D Space. Different approaches were used to-

gether with extra interactions, such as panning and

tilting to reduce the visual clutter where the 3D vir-

tual environment is projected in a 2D display. View-

point dependent distortion of 3D data (Sheelagh et al.,

1996) highlights regions of interest by dedicating

more space to them. Viega et al. (Viega et al., 1996)

introduced the 3D Lens, which is a Magic Lens with a

volume, that affects objects contained within it. Bell

et al. (Bell et al., 2001) introduced Toolglass and

Magic Lenses as a see-through interface to modify

the visual appearance of application objects, enhance

data of interest or suppress distracting information.

McGufﬁn et al. (McGufﬁn et al., 2003) explored an

alternate strategy that uses deformations, where the

user can cut into and open up parts of the volume in

real time, making the interior visible while still re-

taining surrounding context. In contrast, the Balloon-

Probe (Elmqvist and Tudoreanu, 2007) provides an

inﬂatable force ﬁeld controlled by the user that can be

used in areas of locally high object congestion. Al-

though these techniques try to solve the clutter prob-

lem in the 3D space, none of them are speciﬁcally

designed for the arc congestion problem over geo-

graphic surface.

A recent trend in 3D virtual environments made

use of properties like transparency to expose hidden

content. Looser et al. (Looser et al., 2004) described

a 3D magic lens implementation for Augmented Real-

ity that supports information ﬁltering using the stencil

buffer, allowing the user to see through a house. Cof-

ﬁn and H

ollerer (Cofﬁn and Hollerer, 2006) presented

a similar technique with active interaction where the

user controls a volume that is dynamically subtracted

from the surrounding world geometry, again using the

stencil buffer. Elmqvist et al. (Elmqvist et al., 2007)

presented a technique that uses dynamic transparency

for managing occlusion of important target objects

in 3D visualization applications. In these techniques

the focus is clearly highlighted but due to the trans-

parency effect, part of the context is lost.

3 ARC CONGESTIONS OVER A

GEOGRAPHIC SURFACE

The problem addressed by this work falls into the cat-

egory of ”occlusion problems in 3D visualization”

where the camera view, the environment itself and

its geometrical properties cause occlusion of objects.

In this particular scenario the problem is called ”arc

congestion over a geographic surface”, i.e. it de-

scribes the situation where a large numbers of three-

dimensional arcs occlude the nodes and their incident

arcs depicted over a geometric surface.

Formally, there is a 3D space U deﬁned by a

Cartesian space (x,y,z) ∈ R

. A geographic surface

S is the surface of a volume V within U (i.e., subset of

U). The volume V can be a virtual globe or a ﬂat plane

just to mention the more popular examples. Nodes in

the set N are points located over S. A 3D-arc a is

composed by a sequence of points p

, p

,..., p

∈ U

such that the ﬁrst and the last points represent nodes

(i.e. p

, p

∈ N). Let S

be the area of interest over

S (i.e. S

⊂ S), N

contains the nodes of interest such

that are inside S

. A line segment r is blocked by an

object o if it intersects o. An arc a occludes S

if exists

a line segment r between the viewpoint position v and

such that r is blocked by a.

The arcs are classiﬁed, as shown in Figure 2, in

the following way:

• the arcs of interest are the ones with one endpoint

in N

• the arcs of high interest are the ones with both

endpoints in N

• the undesired arcs are the arcs that occlude S

that

are not arcs of interest neither arcs of high inter-

est.

• the context arcs are the arcs in background (i.e.

the arcs in the context).

Figure 2: The arcs are classiﬁed accordingly with their re-

lations with the area of interest.

3DArcLens:InteractiveNetworkAnalysisonGeographicSurfaces

293

The area S

is deﬁned as:

• not visible if there exists at least one line segment

r between v and S

such that r is blocked by V .

• visible if there are no line segment r between v

and S

such that r is blocked by V .

• fully visible if it is visible and there are no unde-

sired arcs.

(a) (b)

Figure 3: Arc congestion over a geographic surface. (a)

fully visible area (S

), visible area (S

) that is partially hid-

den by undesired arcs and not visible area (S

) occluded by

the globe. (b) After moving the camera the area S

becomes

f ully visible.

Figure 3 shows examples of arc congestion over

a geographic surface. There are three area of inter-

ests S

, and S

identiﬁed by a colored circle. In

Figure 3(a), S

is fully visible, it is possible to see the

nodes inside the area and their connected arcs. S

visible, in fact some arcs occlude a part of its area,

thus also some nodes inside. Figure 3(b) shows the

same area S

but from a different camera view v, in

this case S

is fully visible. S

is placed in the hid-

den hemisphere so it is not visible, i.e. hidden by the

globe.

This paper proposes a solution to the following

question: How can we reduce the arc congestion in a

given area, revealing information about the nodes, the

arcs and the geographic surface independently from

the camera view?

This question is formalized by the deﬁnition of

the following requirements, which the desired solu-

tion has to satisfy:

1. No arc or node is removed from the scene to pre-

serve all the information related to the visible ele-

ments of the network.

2. Nodes are not moved due to the importance of

their geographical location.

3. The surface S must not be deformed due to the

importance of its geographical context.

4. The hidden information on the visible area S

must

be revealed, in particular about the following vi-

sual primitives, listed by importance in descend-

ing order: (a) The location of the nodes in N

. (b)

(a) (b)

Figure 4: (a) The lens is represented as a circle over the

globe, hence the lens’ shape is not distortion-free. (b) Our

adopted approach: the lens is a circle in 2D screen space.

The arcs of high interest. (c) The arcs of interest.

(d) The map layered on S

. (e) The undesired arcs,

although they cause the clutter, they may encode

useful information to the viewer. (f) The context

arcs.

5. A visible selected S

must be fully visible without

the need to change the viewpoint v.

6. After selecting an area of interest, the solution

must work also if the camera view is changed. Let

the visible selected area for a set of viewpoints

V , S

must be always fully visible.

4 PROPOSED APPROACH

As mentioned in Section 1, our goal is to facilitate the

exploration of both geographical network and layered

map with 3D view when arc congestion situations oc-

cur. Our proposed technique uses a lens metaphor that

is deﬁned by a given point of focus and a radius.

The lens can be represented as a circle that fol-

lows the terrain. Therefore, its shape is not distortion-

free. As shown in Figure 4(a), if the camera is tilted

the area of the lens becomes oval. For this reason we

opted to represent the lens as a circle in screen space

with the radius r in pixels. Hence, the camera move-

ment does not affect the lens’ shape (Figure 4(b)) and

the zoom interaction does not change the lens radius.

Up to now we refer to S

as the area of interest that is

covered by the lens.

As shown in Figure 5, the lens works in the fol-

lowing way: the undesired arcs are distorted in a way

that they do not pass though the surface of the globe

covered by the lens (i.e. S

). The distortion is applied

not only to the subsegments affected by the lens, but

also to the entire curve making arcs easier to trace.

In fact the arcs are depicted as splines composed by

a sequence of control points. The arc congestion can

be also affected by arcs of interest, thus their subseg-

ments inside the lens are ﬁltered out from the visual-

ization. This strategy permits to clearly identify the

nodes inside the lens and the arcs of high interest.

What is important to know about each arc is not its

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Figure 5: Each class of arcs is represented in a different

way. Context arcs are drawn with transparency, undesired

arcs are deformed, arcs of interest are colored differently

and parts of them are ﬁltered out, and arcs of high interest

are white colored.

shape but which are the incident nodes. Bearing this

in mind, each node of interest is represented as a col-

ored sphere and each arc of interest is colored with the

same color of its incident node inside the lens. Nodes

of interest are therefore easily identiﬁed together with

their incidents arcs. Moreover, the surrounding map

is also revealed (requirement 4). If the user navigate,

tilt or pan the camera (i.e v changes) the lens still re-

veal hidden information of S

previously covered by

the lens (i.e. S

remains fully visible thus the require-

ment 6 is satisﬁed). In fact its movement is snapped to

the terrain to improve the system usability; the camera

movement affects the lens position in screen coordi-

nates but not its geographical position, (Figure 6).

(a) (b)

Figure 6: Navigation and panning using the lens to highlight

the edges and the nodes over a given location. The latter is

always focused from different camera view.

Moreover, the effect of the lens is transient, i.e. the

deformed arcs return to their original shape when not

marked as undesired arcs. If the user detects an area

that requires further investigation and that is cluttered

by arcs (i.e., S

is visible but not fully visible), then

without moving the camera (i.e. v does not change),

he/she can drag the lens to that geo-location to reveal

the hidden information (i.e. S

becomes fully visible

thus the requirement 5 is satisﬁed).

It might happen that arcs might share a common

space from a given perspective, as depicted in Fig-

ure 7(a). Hence, that arcs are shifted to the border of

the lens and because of its intersection (yellow arrow

on Figure 7(b)) the two sides of the arcs can no longer

be traced. Although this drawback can be solved by

applying different color for each arc, we instead de-

cided to update the arcs’s distance to the lens circum-

ference based on its distance to the point of focus (see

Figure 7(c)).

(a) (b) (c)

Figure 7: (a) Arcs sharing a common area. (b) Arcs affected

by the lens sharing a common area. (c) Arcs affected by the

lens with shapes easier to trace. In these images green arcs

are arcs of interests and red arcs are undesired arcs.

This distortion can have negative implications in

(1) the context arcs that are near the lens area, (2) the

deformed undesired arcs, (3) the arcs of interest and

consequently their incident nodes. However, in the

ﬁrst case the arcs are the context thus for the analysis

of those visual elements the user can move the lens

over that location or increase the size of the lens. To

limit the second case all the context arcs are colored

with a medium level of transparency. Regarding the

last case, during the rendering phase the arcs of inter-

est are drawn on top of the other elements.

4.1 Implementation Details

Each arc is designed as a relaxed cubic spline com-

posed by a sequence of points p

, p

,..., p

∈ R

that

are deﬁned by a sequence of equal-distance control

points cp

,cp

,...,cp

∈ R

where cp

is the source

node and cp

is the target node, see Figure 8(a). We

use this kind of curve because it is possible to design a

polynomial curve segments controlling their shape in

an easy way and that pass through given data points.

The altitude of the control points over the ge-

ographical surface follows the formula of similar

works (Cox et al., 1996; Munzner et al., 1996):

1 + H sin(xπ ) where H is the maximum height and

x varies between 0 and 1 along the arcs path. In order

to take into account the path length l, the H parameter

is equal to l/4.

To detect whether a point that composes the arc

or a node is contained inside the lens area we use the

two combined approaches: (1) in screen coordinates

3DArcLens:InteractiveNetworkAnalysisonGeographicSurfaces

295

(a) (b) (c)

Figure 8: The steps required to apply the effects of the lens

over the arcs are: (a) each arc is composed by m control

points, (b) one or more couples of consecutive intersecting

points are detected, (c) for each couple a new control point

is used to deform the arc.

the distance between the element and the lens center

must be less that the lens radius. (2) using a ray-cast

technique we check if the line that connects the view-

point with the element in the world space does not

intersect the surface.

Arcs Deformation. The main aspect of the de-

formation of undesired arcs is that the original con-

trol points are removed and then new control points

are created making curves more aesthetically pleas-

ing and easier to trace. For this class of arcs the al-

gorithm is deﬁned by two steps that are executed at

every frame, before the main rendering phase:

Step 1. In the ﬁrst step the undesired arcs are

found and the intersecting points between these arcs

and the circumference of the lens are detected. These

points are deﬁned as ip

,ip

,... ⊂ p

, p

,..., p

such

that, in screen coordinates, they are the nearest to

the real intersection points ∈ R

. Then, the algo-

rithm identiﬁes the couples of consecutive intersect-

ing points that will be used to create the new control

points of the cubic curve (see Figure 8(b)). This step

is based on a GPU-based implementation to achieve

an acceptable frame rate. The points that compose

the lines are passed to the GPU into a single buffer

and then a geometry shader computes the intersecting

points to be passed to the next step using the trans-

form feedback buffer.

Step 2. In this step, the sets of control points are

updated and the arcs are redrawn. As shown in Fig-

ure 8(c), for each undesired arc, the control points in-

side the lens are removed and a new control point cp

is created and placed over the lens’ circumference.

The formula to calculate the screen coordinates of

the new control point cp

starting from the couple of

points {ip

,ip

} is the following:

mp = (ip

+ ip

)/2;

= c + r ∗

(mp − c);

mp is the middle point between ip

and ip

, c is

the center of the lens and r is the radius of the lens.

The aforementioned formula is applied to the x and

y attribute of cp

, meanwhile the z dimension, that is

the screen depth-coordinate, is calculated taking the

middle value between the z of ip

and ip

. Finally the

deformed arc is drawn reconverting the cp

in world

coordinates and recomputing the points p

, p

,... , p

Control Points Relocation. A feature that im-

proves the scenario where the shifted arcs can no

longer be traced, (see Figure 9(a)), is described in the

following steps:

Step 1. The lens is divided in p sections of equal

area. For each new control point cp

, the distance in

screen coordinates between its associated mp and the

center lens is stored, (see Figure 9(b)). Therefore for

each section, a list of control points ordered accord-

ingly with their distance is computed.

Step 2. Each control point is moved from the lens

center, accordingly to the distance as depicted in Fig-

ure 9(c). A maximum distance is deﬁned to limit the

effect in a closed area around the lens.

(a) (b) (c)

Figure 9: (a) the basic solution: new control points are

placed around the lens. (b) the lens is subdivided in sec-

tions. Control points are ordered accordingly to the distance

factor relative to their sector. (c) control points are placed

at different distances from the lens center around the lens.

The sector-based approach is applied to separate

the control points that do not share the same loca-

tion in screen space. For example if there are two

deformed arcs respectively on the opposite sides of

the lens, due to the fact that are in different sections

no control point will be relocated.

Arc Segments Filtering. For the creation of the

arcs of interest the steps are the following:

Step 1. As preprocessing phase a different color is

assigned for each node. During the rendering phase,

if the node is inside the lens and it is visible, than a

sphere colored with the node’s color is generated.

Step 2. Every part of the arc inside the lens

is drawn completely transparent using the blending

function, and the rest of the arc is colored with the

same color of its incident node inside the lens.

In order to facilitate the interaction with the sys-

tem, we added two graphical components to the GUI:

a slider interface allowing the user to readjust the lens

radius and a button to place the lens at the center of

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the screen. This last feature is handy when the user

loses sight of the lens while navigating.

4.2 Input Parameters

The parameters required by the algorithm affect di-

rectly the quality of the result. The ﬁrst parameter

is the number of control points m. If the number of

control points is too high the deformation technique

affects only a small localized area and if m is too

low the edges are deformed along their entire length.

As depicted in Figure 10, the advantage of using low

number of control points appears evident, however, if

the geographical surface is over a globe and both inci-

dents nodes are placed in different hemisphere, there

are extreme cases where the curve may pass through

the geographical surface. For such reason, we set m

equal to 7, to avoid to overlapping with the globe. The

second parameter is the number of sections p, if p is

high, only the control points close with each other will

be placed with different distances from the lens cen-

ter. As opposite, if the value is too low, more layers

will be used. This decision is up to the user. In our

tests we used p = 4. Another parameter is the number

of points n that compose each arc. Higher the value

is and smoother will be the curve. We set n = 200

to have a good balance between the aesthetic result

and the performance. The last parameter is the radius

of the lens r. Since this value has a considerable im-

pact on the effectiveness of the proposed technique,

the user can modify the lens size during the explo-

ration of the network.

4.3 Performance

In order to measure the performance of our technique

we take as metric the frame rate. 3DArcLens was de-

veloped extending NASA WorldWind

, an open source

virtual globe, and was tested on a single proces-

sor Intel Xeon 2.26 GHz equipped with an NVIDIA

GeForce GTX 280 with 1024 MB dedicated video

memory. Table 1 shows the fps on WorldWind with

and without 3DArcLens taking into account datasets

with different number of arcs tot arcs.

Table 1: The fps are shown with and without the use of

3DArcLens on WorldWind.

tot arcs fps (WW) fps (WW + 3DArcLens)

600 55 - 56 20 - 22

3000 33 - 35 15 - 17

15000 8 - 10 6 - 7

The performance of 3DArcLens depends mainly

on the number of arcs that are distorted. The Table 2

http://worldwind.arc.nasa.gov/java/

(a) Short edges

Initial situation

Good case with low

number of control points

Bad case with high

number of control points

(b) Long edges

Initial situation

Bad case with low

number of control points

Good case with high

number of control points

Figure 10: Two situations, one with short length edges (a)

and one with long edges (b). Examples showing advantages

and drawbacks of using high and low number of control

points. In these images the red color is used to depict unde-

sired arcs.

shows the fps on WorldWind taking into account the

deformed arcs of the dataset with 3000 arcs.

Table 2: The fps and the number of deformed arcs are shown

on WorldWind.

def arcs fps (WW + 3DArcLens)

0 21

150 18

300 15

400 13

5 DISCUSSION

At the current stage of the research there are no inter-

action techniques that can effectively reveal the infor-

mation about arcs, nodes and geographical surfaces

hidden behind an area congested in a 3D virtual envi-

ronment.

EdgeLens (Wong et al., 2003) is a technique that

iteratively curves graph edges, that are represented by

2D straight lines, away from the point of focus in a 2D

plane. Although it helps to disambiguate the relation-

ship between nodes and edges without losing infor-

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297

mation, it can not solve the arc’ congestion problem

due to the following:

Arcs’ Shape. In a 2D space, a straight line is de-

formed by taking into consideration the start and end

points (together with the lens focus and radius). With

3D arcs, the distortion and selection of these objects

is more complex.

The View Camera Information. The behavior of

the lens depends also on the position of the view cam-

era; if the view camera changes, the arcs affected can

differ in both number and shape.

The Occlusion Problem. In 3D virtual environ-

ments the effect of occlusion has to be considered;

arcs that intersect the lens having their extremities be-

hind a geographical surface can generate undesirable

behaviors.

The coordinate systems. In 3D virtual environ-

ments, the distortion process must take into account

the screen coordinates and the world coordinates.

MoleView (Hurter et al., 2011) is another inter-

active technique to reveal what is hidden behind a

congested area. The control points of the edges are

moved around the lens meanwhile the edges which

are selected in the lens stay unmoved, making them

easy to spot. Although this technique gives satisfac-

tory results it differs from 3DArcLens in the follow-

ing:

Information About Arcs. 3DArcLens puts more

effort on the traceability of arcs. In particular, the

control points affected by the lens are replaced with

others that are placed in different ”orbits” around the

lens. Additionally, the arcs that are contained inside

the lens are clutter free.

Geographical Context. Our technique allows not

only the graph elements to be visualized but also the

map inside the lens to be depicted without visual clut-

ters.

Interactive Navigation. In our technique the cam-

era view is also taken into account. This implies that

if the lens highlights a geographical area and the cam-

era view moves, then the lens remains still but the way

it reveals what is hidden in that area maybe differ.

Although choosing suitable colors is fundamental

for an effective utilization of 3DArcLens the deﬁnition

of a proper color pattern is not the aim of this work.

Moreover, the effectiveness of the colors assigned to

nodes depends on the task that has to be accomplish.

For example one task might involve information about

node attributes that can be encoded in a color pattern

deﬁned at priori.

A potential shortcoming may arises if the dataset

presents a large number of connected nodes in a small

location that is totally covered by the lens. In such

case the visual clutter is caused by the arcs of high

interest. However, if the area of interest is reduced,

changing the lens radius or zooming in, can consider-

ably alleviate this issue.

6 CONCLUSION

In this paper we describe 3DArcLens, an interactive

technique for exploring both geographical networks

and geographic surfaces.

Our aim is to enrich tools that can depict geo-

graphical networks, e.g. the virtual globes imple-

mented by Cox et al. (Cox et al., 1996), Munzner et

al. (Munzner et al., 1996), Buschmann (Buschmann

et al., ), Google Earth

and NASA WorldWind, as

well as the ArcMap technique, see Figure 11.

(a) (b)

Figure 11: 3DArcLens applied on an ArcMap.

In our informal test cases, we observed certain ad-

vantages in applying our technique to the exploration

of geographical networks. Overall our technique can

increase the effectiveness on low-level tasks for graph

analysis. Since it is locally applied to a speciﬁc area,

higher-level tasks such as ﬁnding connectivity pat-

terns remain difﬁcult. Also, for datasets with ∼3000

edges the frame rate was acceptable. Yet, it might

drop for much larger datasets. Future improvements

include shifting the generation of the splines to the

GPU side and the deﬁnition of an evaluation strategy.

ACKNOWLEDGEMENTS

This research has been supported by the European

Commission (EC) under the project LIFE+IMAGINE

(Grant Agreement N. 325232). The authors are solely

responsible this work which does not represent the

opinion of the EC. The EC is not responsible for any

use that might be made of information contained in

this paper.

http://www.google.com/earth/

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