1240 Research application Julius Rauscher, Raphael Buchmüller, Daniel A. Keim
and Matthias Miller are with University of Konstanz.
E-mail<EMAIL_ADDRESS>
# SkiVis: Visual Exploration and Route Planning in Ski Resorts

Julius Rauscher0000-0003-1318-9642  Raphael Buchmüller0000-0002-0612-8828
Daniel A. Keim0000-0001-7966-9740  and Matthias Miller0000-0002-6281-2173

###### Abstract

Optimal ski route selection is a challenge based on a multitude of factors,
such as the steepness, compass direction, or crowdedness. The personal
preferences of every skier towards these factors require individual
adaptations, which aggravate this task. Current approaches within this domain
do not combine automated routing capabilities with user preferences, missing
out on the possibility of integrating domain knowledge in the analysis
process. We introduce , a visual analytics application to interactively
explore ski slopes and provide routing recommendations based on user
preferences. In collaboration with ski guides and enthusiasts, we elicited
requirements and guidelines for such an application and propose different
workflows depending on the skiers’ familiarity with the resort. In a case
study on the resort of Ski Arlberg, we illustrate how to leverage volunteered
geographic information to enable a numerical comparison between slopes. We
evaluated our approach through a pair-analytics study and demonstrate how it
supports skiers in discovering relevant and preference-based ski routes.
Besides the tasks investigated in the study, we derive additional use cases
from the interviews that showcase the further potential of , and contribute
directions for further research opportunities.

###### keywords:

Geographic Visualization, Routing.

Our application interface visualizes the slopes and lifts of a ski resort on a
topographic map, allowing a detailed exploration through multiple linked and
brushed components tcbcolupperdlgA. By applying preferences tcbcolupperdlgB,
slope recommendations are provided tcbcolupperdlgC that can be integrated into
a route planning algorithm. The generated route can be investigated further
regarding its sequence and steepness profile in the route summary
tcbcolupperdlgD.

##  1 Introduction

Outdoor activities are prominent in many fields, including education [41],
entertainment [74], health [51], and team-building[56]. Especially mountain
regions are favored for outdoor activities due to scenic outlooks, fresh air,
and diverse flora and fauna [11]. There are various mountain outdoor
activities such as hiking, cycling, and skiing. Every year, approximately 400
million skiers find their way into ski resorts worldwide [81]. Larger ski
resorts tend to be more profitable [22], leading to an increased number of
linked lift constructions connecting neighboring resorts [21]. The resulting
joined areas become even more complex and hence are more difficult to
navigate, enhancing the need for routing support. Since the number of possible
slope route combinations is increasing, skiers and snowboarders face the
challenge of keeping a good overview. Similar outdoor activities to skiing,
such as hiking [80, 46] or bicycling [77, 88], provide solutions for
orientation and route planning. While some concepts are transferable, skiing
trip navigation poses specific challenges, such as high traffic on a
comparatively smaller route network, a frequent alteration between the use of
slopes and lifts, and the fact that slopes can only be traveled in one
direction. In addition, the demand for risk management, such as avoiding
causes for avalanches, is likewise increasing [73], especially for slopes that
invite to run off-piste with snow powder conditions. Weather events,
especially snow conditions and sun hours, can also have a considerable impact
on the number of visitors to ski resorts. On sunny days with plenty of snow,
the slopes and restaurants are typically crowded, resulting in disliked
waiting times at lift stations [35]. Conversely, bad weather negatively
influences customer demand [50] and ticket sales [68]. A lack of snow can
either be mitigated by using unfavorable artificial snow [58] or cause certain
slopes in lower altitudes to remain closed. Heavy winds or thunderstorms can
force the resort to shut down entirely. While ski resorts have been researched
concerning climate change [72], economic sustainability [53], demand
prediction [43], customer analysis [44], or pricing models [36, 1, 50], only a
few research projects focus on navigating along ski slopes.

The main resource for navigation in ski resorts is a ski slope map, as seen in
Figure 1, which is designed uniquely for every resort. Instead of depicting
the area in a topographically accurate manner, most ski resorts employ a more
aesthetically pleasing and panoramic style to artistically illustrate the
landscape [79]. While this partly marketing-focused design compactly depicts
the entire resort, it can compromise routing capabilities and thereby lead to
skiers’ misorientation [4]. From a graph theory viewpoint [62], ski resorts
can be modeled as a geospatial, partly directed network consisting of downhill
slopes and uphill lifts as edges and intersections as nodes. Occasionally,
some lifts bi-directionally link two otherwise separated ski resorts. There
are several types of lifts: t-bar , chair lift , gondola , and cable car ,
depending on the skiing resorts’ size and natural conditions. Slopes are
usually classified according to their difficulty and labeled by a color-coded
system, e.g., easy , intermediate , and advanced in Austria [3] or
Switzerland. Depending on the country where a ski resort is located, slopes
with similar characteristics are labeled using different difficulty
classification systems [8]. Such differences can lead to confusion among
visitors who are typically used to a single classification strategy. Due to
the simplicity of the color classification, hazards such as narrow slopes or
annoying uphill segments can not be identified with the current design.

The steepness serves as a general indication for difficulty [3], with steeper
slopes being ranked as more challenging. However, the difficulty label is
often imprecise since solely the steepest subsegment is typically responsible
for classifying the entire slope. Therefore, it is reasonable to consider
other, more detailed characteristics of slopes, such as the steepness or
compass direction of all its subsegments. The compass direction influences the
amount of solar radiation a slope is exposed to. In the northern hemisphere,
north-facing slopes experience more day hours of direct sun radiation, thus
exhibiting different snow conditions. At extremely low temperatures, northern
slopes are often frozen and more difficult to ski, especially for beginners.
In contrast, when temperatures rise at the end of a skiing season, southern
slopes become muddy and unattractive, especially for skiers with aging ski
gear. In such situations, it is advisable to use southern slopes in the
morning and switch to slopes that are not directly facing the sun later.

Skiing enthusiasts, ranging from intermediate or advanced skiers to ski
guides, can greatly benefit from domain-specific visual analytics solutions.
Offering customized visualizations can provide them with a novel viewpoint on
slopes within a ski resort, leading to insights they would not have otherwise.
Especially when traveling to previously unknown resorts, interactive route
planning capabilities can support skiers in identifying their preferred slopes
and suggest route recommendations according to their individual preferences.
Besides skiers, other ski resort visitors, such as snowboarders and sledgers,
exhibit different characteristics [47]. Addressing the needs of each visitor
group requires an adaptive, user-centered methodology. In some ski resorts,
downhill valley runs are shared by both sledgers and skiers, which requires
all slope users to pay extra attention. Otherwise, it could lead to severe
downhill slope accidents, which do not seldom occur [12].

The limitations of current approaches in the ski domain led us to investigate
the following research questions:

  * •

How can we visualize a ski resort as a geospatial network while effectively
incorporating individual slope properties?

  * •

How can we facilitate preference-based routing capabilities within a ski
resort?

Figure 1: Excerpt of the interactive Ski Arlberg slope map [69].

Contributions – This paper contributes a requirement and task analysis for
modeling a ski resort depending on the underlying properties of its lifts and
slopes. In collaboration with domain experts, we formalize the issues at hand
and provide a list of task characteristics. A major contribution is our user-
centered Visual Analysis prototype to explore a ski resort slope network. A
central part of the prototype enables the user to interactively receive route
recommendations tailored to slope preferences. Further, we conducted a
qualitative evaluation to assess the applicability of our approach and discuss
its benefits and shortcomings. Finally, we present open research opportunities
to encourage further research within the domain of visual analytics for ski
resorts.

##  2 Related Work

Since the research conducted in this paper covers the domains of ski
visualizations and routing in geospatial networks, we dedicate a section for
discussing related approaches to each of these topics.

Ski Visualizations – A survey on ski trail maps in North America [79]
determined a dominance of the painted panorama style (see Figure 1) (86%),
which distorts the underlying topography to emphasize certain memorable
features. According to Balzarini et al. [4], this so-called terrain invention
can introduce difficulties in interpretation, such as misunderstanding or
uncertainty. Field [27] investigated the effectiveness of a schematic metro
map in contrast to the dominating panorama-styled maps and proved its
usefulness for solving on-mountain navigation tasks. However, the absence of
geographical features relevant for orientation and the familiarity with
traditional panorama maps determined no clear advantage of the proposed
layout, especially for beginners. For additional information on schematic maps
in general, we refer to a survey of Wu et al. [86]. To enable preference-based
slope run selection, Dunlop et al. [19] conducted experiments with varying the
line width in slope maps according to a user’s preferences. Their evaluation
showed that the time required for route planning can be reduced when
implementing preference-based visualization techniques. Regarding slope
properties, Bortnyk et al. [8] investigated a Ukrainian ski resort based on
the slopes’ steepness. All of the above-mentioned approaches adhere to the
standard of visualizing slopes by a color-coded line according to their
difficulty. Thus, they fail to address the diversity of different slopes
regarding their geographical properties.

Web-based, interactive systems such as OpenSkiMap [59] or FATMAP [23] display
further information on individual slopes besides steepness, such as distance,
altitude, and compass direction, but do not comprise preference-based route
planning features. Other mobile applications within the ski domain offer
progress tracking [76, 9], or details on snow conditions [13, 54], but also
lack routing features and are limited regarding additional slope information.
Friedsam et al. [29] provide routing capabilities based on OpenStreetMap (OSM)
data, however, they do not take user preferences into account. Augmented
Reality systems provide the skier with visual and auditory signals at
junctions or safety-critical areas [65] or enable collaboration between skiers
to share personalized information on a digital trail map [25]. Aside from the
confined area of controlled ski resorts, the mitigation of avalanche risks has
received attention from researchers, using GPS tracking data to investigate
the behavior of out-of-bounds skiers [78] or explore the terrain preferences
of heli-ski guides [38].

In the closely related hiking domain, Bleisch and Dykes [7] conducted a study
to evaluate the usefulness of 3D visualizations, which concludes that 3D
layouts outperform 2D maps for general overview tasks but not for route
detection and planning. Human mobility patterns of hiking activities are
investigated by Lera et al. [46]. Tîrlă et al. [80] visually compared
elevation profiles of different hiking trails, and Korohoda et al. [45]
leveraged volunteered geographic information (VGI) and digital elevation model
(DEM) information to assess the difficulty classification of hiking routes and
to detect obstacles.

Routing in Geospatial Networks – The idea of routing in geospatial networks
has been investigated from several subfields of information science, such as
routing algorithms, decision-making, and route visualizations. Felício et al.
[26] describe how to leverage OSM data and integrate information into a multi-
criteria route planning approach. A similar approach by Guo et al. [32]
facilitates vehicle routing by adapting the edge costs of a network structure
according to a given context and preferences, providing personalized route
recommendations.

Various approaches to the shortest path problem, many of which factor in
multiple criteria, have been formulated in the domain of cycling. Storandt
[75] considers a hard constraint on the height difference to minimize energy
consumption along the path. Hrncir et al. [39] optimize concerning the travel
time, comfort, and minimum elevation gain, Song et al. [71] efficiently
compute full Pareto sets for these criteria. Zhu [88] further computes a
tourist satisfaction score as a criterion that influences the optimal route.
The reasoning and driving factors behind routing choices from trajectory data
of bike-sharing services have been studied by Scott et al. [67]. Molokac et
al. [52] used survey data to analyze the preferences regarding hiking trail
choices.

Regarding route visualizations, Haunert and Sering [37] propose the usage of
focus regions, where the area of interest is scaled up for better visibility.
Wu et al. [85] introduce the concept of travel-route-centered maps, a custom
metro map layout where the map is rotated and adapted to visualize the route
path in a straight line. In the context of tourism trip planning, Zhang et al.
[87] and Deng et al. [16] propose a visual analytics framework using multiple
linked views to facilitate interactive tour planning based on popular subtours
from crowdsourced data. Su et al.[77] provide a route planning interface for
cycling in Vancouver, incorporating user preferences regarding steepness, air
pollution, or vegetation. The domain of urban visual analytics [15],
particularly the optimization of bus routes [17, 48, 84], further relates to
this work.

Research Gap – While several approaches for route planning focus on other
outdoor activities such as cycling network analysis [75, 39, 67] or hiking
trails[80], only little research exists for the ski domain [29]. Despite its
discussed importance, current systems neglect user-specific preferences.
Moreover, established solutions for exploring ski resorts [59, 23] lack
customization and do not consider human-in-the-loop concepts for knowledge
generation [63]. To the best of our knowledge, for the domain of ski resorts,
no analysis approach exists that enables the visual exploration of the resort
and interactively provides routing recommendations based on user-defined
preferences.

##  3 Requirement Analysis

To precisely formulate the requirements for a workspace that addresses visual
exploration and route planning in ski resorts, we consulted with ski guides
and expert skiers about their opinions towards this initiative. In the context
of a pre-study, we had informal discussions with four experts (>15 years of
yearly skiing experience, two being certified ski guides) to learn about the
currently available tools, the limitations they encounter while using them,
and their expectations towards novel software. The most commonly utilized
tools [23, 69, 5] do not provide route planning functionalities and only
provide limited contextual information about individual slopes. Based on the
experts’ feedback, the following section frames the abstract model of the
workspace, with special regard to the utilized data and supported tasks. The
target audience of the system comprises ski guides as well as intermediate and
advanced skiers. While novice skiers are cognitively occupied with acquiring
various skiing techniques, routing is not their primary concern, and typically
they travel with a group where a more experienced skier is responsible for the
route planning. The system is designed to provide the best results when
guiding the user in unfamiliar resorts. However, gaining insights and optimal
route recommendations from resorts with which the user is already familiar
with is an equally important objective.

Feature Characteristics – The sport of Skiing is closely coupled to the
environment of mountain regions. Thus, it is apparent that geographic features
can be used to model the geospatial network of slopes and lifts. According to
domain experts, the steepness of a slope is the most significant feature and
serves as the main criteria for determining the difficulty of a slope in
Austria [3]. Another important feature is the compass direction. In the
northern hemisphere, north-facing slopes are less exposed to sunlight,
resulting in different snow conditions. Further slope features to note are the
length, altitude, width, or curvature. Very narrow or extremely curvy slopes
can impose a challenge, especially for novice skiers. Aside from geographical
features, further attributes can also be considered important for the analysis
of ski resorts. Especially in peak season, slopes and lifts can become
crowded, resulting in undesired waiting times. The majority of slopes in a
resort are groomed daily by means of a snowcat. However, some slopes remain
purposely ungroomed and require a different skiing technique. Dynamic
properties further contribute to the model, albeit being more complicated to
record and forecast. These include meteorologic conditions such as
temperature, wind, fog, snowfall, or snow conditions in general. Since
accurate readings for these properties are unobtainable on a slope-level
resolution, their impact on deciding which route to take is arguably limited.
Therefore, we decided to exclude these features in the development of our
initial prototype.

Task Requirements – As already outlined in the previous passage, the edges of
the geospatial network of a ski resort can be defined by a set of different
features. The exploration of these features (i.e., what is the steepness of a
certain segment of a given slope) constitutes a pivotal objective [T1]. Since
skiers have individual preferences regarding these features, a ranking of
slopes according to their given preferences should be incorporated to identify
favorite slopes [T2]. Concerning routing, the system should be able to provide
routing recommendations between any arbitrary points in the network, including
the possibility of a round trip, as skiers usually reside in a lodge or hotel
and finish their daily route at the exact same location where it started [T3].
Following [T2], the routing recommendations should be optimized to reflect the
personal user preferences along the entire route [T4]. To summarize, in
collaboration with domain experts, we elicit the following four tasks for our
further analysis:

[T1] Exploration of a ski resort according to the defined features
[T2] Provide a ranking based on preferences toward these features
[T3] Allow routing between two arbitrary network points
[T4] Integrate preferences into the routing algorithm

##  4 Application Design

This section introduces the developed workspace, the used data, the required
preprocessing steps, design choices regarding the individual components, and
recommended interaction workflows. can be accessed under the following domain:
https://skirouting.dbvis.de.

Ski Arlberg – Labeled as the cradle of alpine skiing, the area of Ski Arlberg
is the largest connected ski resort in Austria, consisting of 88 lifts and a
total slope length of 302 km [70]. It connects the three regions of St. Anton
- St. Christoph - Stuben, Lech - Oberlech - Zürs, and Warth-Schröcken with a
series of connecting lifts, resulting in a large, complex network structure.
According to [81], it is the resort with the second most annual skier visits
worldwide between 2016 and 2021. While the techniques applied in this paper
are applicable to virtually any other ski resort, we chose Ski Arlberg due to
its size and complexity as the most appropriate region to showcase the
potential.

###  4.1 Ski-Resort Related Data

In the subsequent section, we discuss the data sets used to model the feature
characteristics introduced in section 3, as well as preprocessing methods that
were implemented to enhance the data quality.

Data Sources – Detailed geographic and contextual information about individual
slopes and lifts is challenging to acquire. While most resorts provide an
interactive, online version of their slope map containing a list of the slopes
and lifts [69], no geographic information about the length, width, or actual
trajectory is present. We opted to obtain this information from OSM [55], a
community-owned, collaborative database for geographic data. Depending on the
ski resort, additional information such as the name of the slope, its
difficulty classification, the reference number, or grooming conditions is
available aside from the spatial line component. To attain details about
travel durations or the popularity of slopes, analyzing human mobility data
can be insightful. We opted for using VGI data from Strava [76], where users
can record and share their exercise data of different leisure activities, such
as skiing. We extracted trajectory data recorded on the slopes of the Ski
Arlberg resort between 2008 and 2022, resulting in more than 15.000
activities. These trajectories serve as the basis for our calculations to gain
insights on the crowdedness, as well as an estimate for the required skiing
time for each slope and lift alike.

Figure 2: Preprocessing pipeline.

Data Preprocessing – Since the OSM and the extracted trajectory data are
community-maintained data sources, a data preprocessing step is indispensable
to ensure satisfying data quality. To facilitate a comparison between slopes
and enable routing based on preferences, we need to construct a connected
network structure from our slope dataset and derive a value for every feature
on a fine-grained spatial resolution. By means of the pgRouting package [57],
a geospatial line-based dataset can be extended with routing functionalities.
In our initial exploration of the network topology created by pgRouting, we
noticed connectivity issues at some network nodes, where the slope endings
were not connected to the closest lift vertex. A total of 94 dead-end slopes
were detected in the topology. To improve the connectedness of the routing
network, all vertices with a degree of 1 (nodes with only one connection) were
checked for close, unconnected neighbor vertices within a spatial proximity of
30 meters. If such a close neighbor was found in the dataset, a helper slope
was inserted to connect these vertices. 80 such helper connections were
additionally inserted into the database, reducing the number of dead-end
slopes to 15.

For a more granular analysis of the slope network, each slope was divided into
smaller equidistant subsegments, where a value of 30 meters of length provided
the best results concerning the accuracy, visual clutter, and performance. The
DEM from the Copernicus earth observation programme [20] was utilized to
determine the altitude, steepness, and compass direction of every subsegment
independently to enable a more precise analysis.

Details regarding the popularity and travel duration were extracted from the
GPS trajectories according to the preprocessing pipeline in Figure 2. As GPS
tracking can provide infrequent temporal resolution results in mountain
regions, we filtered out 1874 activities where the median time between
subsequent timestamps was greater than one second. Since the activity data is
typically recorded over an entire day, the trajectory must be segmented into
sub-trajectories corresponding to the ski slopes and lifts. We followed
existing trajectory segmentation approaches [42, 33], which employ the concept
of map-matching when road network context is available. To introduce
additional robustness, we exploited the difference in altitude to segment the
activity into lift rides (increasing altitude) and ski rides (decreasing
altitude) prior to the map-matching procedure. Afterward, we split the
trajectories on intersection points into our desired sub-trajectories, each
corresponding to a slope or lift. We extracted a total of 1.8 million such
sub-trajectories, with 1088 entries on average per slope.

Due to privacy reasons, the obtained GPS trajectory data contains only
temporal information relative to the first datapoint of the series, concealing
the precise time of day when the activity commenced. This merely permits a
coarse estimation about popularity and average travel duration of each slope
and rules out a more detailed dynamic traffic analysis of the entire resort.
By counting the number of matched trajectories for every slope, we can
determine a popularity ranking, which we obtained by logarithmic normalization
to reduce skewness in the output value. In principle, the mean travel time can
be evaluated by calculating the median between the difference of the start and
end timestamp of the trajectories associated with each slope or lift. To prune
against outlier, we consider only the trajectories most similar to the initial
slope. For slopes with insufficient trajectory records (<10% of the average
per slope (1088) = 108) available, we had to interpolate the travel time from
subsegments with a similar steepness value.

(a)

(b)

(c)

(d)

(e)

Figure 3: Visual design of slopes. The outer line of slopes displays the
color-coded difficulty established by the resort. The inner line encodes the
actual steepness along the slope using our colorscale (a) and exposes patterns
such as steep passages on easy slopes (b), intermediate slopes with varying
steepness profile (c), uphill segments on advanced slopes (d), or ungroomed
(shown with a dotted line) freeride slopes (e).

###  4.2 Design Rationale

This section outlines design choices of the workspace, in particular the map
visualization, the routing algorithm, and the interaction workflows.

Map Visualization – The application interface consists of a topographical 2D
map as its core component. The visualization aims to encode as many features
as possible [T1] without overextending the cognitive load of the user. In
contrast to the vast majority of ski trail maps, we decided against a
panoramic layout in favor of accurate geographic distances. All slopes and
lifts are visualized as lines along their geographical location. Lifts are
easily distinguishable due to their dashed line stroke and gray coloring, with
an icon placed in the middle of the line indicating the lift type (, , , ).
Traditional ski trail maps indicate slopes by colored lines in accordance with
the local difficulty classification (see Figure 1), providing the user with a
high-level overview of the resort. To better assess the gradient along the
slope, we opted for a double-line visual approach consisting of an outer and
inner line. Similar to the slope marker poles which enclose the slopes on
their sides, the outer line encodes the declared difficulty. The Austrian
Standard [3] states that slopes where the steepness value does not exceed 25%
are labeled as easy , not exceeding 40% as intermediate , and slopes with even
higher steepness values as advanced . Backcountry, or freeride slopes, which
are typically ungroomed and tend to have a more extreme steepness profile, are
often not indicated on the ski trail maps available from the resorts. We
decided to include them in our design as they provide diverse alternatives for
more experienced skiers. Other mapping services [59, 23] color these slopes in
orange , a convention we adopted into our design. Since the steepness was
regarded as the most critical indicator regarding a slope’s difficulty, we
dedicated the inner line of our slope visualization to this feature. Every
slope subsegment is colored according to the color scale in 3(a), permitting a
direct comparison between the difficulty classification (outer line) and the
actual steepness (inner line). In addition, the introduction of the green
color for negative steepness values allows easy identification of undesired
uphill segments (3(d)). In the case of ungroomed slopes, the line is displayed
as pointed to mimic the appearance of a mogul slope (3(e)). Due to the
accurate representation of distances and angles in our map layout, the rough
compass direction of every slope can be read directly from the map, and the
contour lines provide information about altitude levels.

Tooltip – Additional information, such as the covered distance or the median
travel time of each lift or slope can be obtained from a tooltip (see Figure
4) accessible through a click on the respective line [T1]. For lifts, details
about the occupancy or seat heating are shown in a table-like enumeration.
Some Chairlifts provide seat heating or a bubble as protection from harsh
weather conditions (e.g., snow or wind). For slopes, the tooltip provides
details about the ascent and descent, mean and max steepness as well as the
type of grooming. For a more detailed steepness investigation of the
respective slope, an altitude plot was integrated into the tooltip, a
linechart where the x-axis encodes the length and the y-axis the altitude of
the slope. For a visual comparison of the difficulty classification and the
actual steepness, the line itself is colored according to the difficulty,
while the area beneath follows our steepness color scale. To leverage visual
concepts familiar within the domain, the compass direction distribution is
depicted using a compass rose metaphor and grouped into the cardinal (N, E, S,
W) and ordinal (NE, SE, SW, NW) directions. For each direction, a needle and
an arc are displayed on the rose, where the length of the needle and the
grayscaled fill of the arc encode the percentage of the slopes’ subsegments
pointing into the corresponding direction.

Figure 4: Tooltip displaying additional information about a slope. The
altitude plot displays a flat, uphill section at the beginning of the slope,
followed by a steeper section. The compass indicates the north-east, east
direction of the slope.  Figure 5: The user is interested in finding slopes
that face south, are groomed, and exhibit a steepness of 38%. The list of best
matches returns a set of slopes that best match the given preferences, where
indicates slopes that are part of the current recommended route.

Integration of Preferences – An essential characteristic and major
contribution of this work is the individualization of the workspace through
the integration of user preferences [T2], [T4]. A widget as seen in Figure 5
allows users to input their weighted preferences towards the properties of
steepness, altitude, compass direction, grooming, and crowdedness. Default
preference configurations for different difficulty categories (Easy,
Intermediate, Advanced, or Freeride) are available and are selectable by a
simple button press. According to these preferences, slope recommendations are
provided in a list in descending order of a computed score [T2]. The score
ranges between 0 and 1 and is derived from the routing cost, which will be
introduced in detail in the following paragraph. Since the total slope cost is
computed as the sum of its subsegments’ costs, the preference score $S_{pref}$
can be obtained using the following formula: $S_{pref}=(1-(cost_{s}/K))$,
where $K$ is the number of subsegments for a given slope. Similar to the
concept of Dunlop et al. [19], the slope visualization on the map is adapted
whenever preference scores are updated, rendering preferable slopes and
subsegments with greater width and higher opacity.

Figure 6: The recommended route can be highlighted on the map using opacity,
providing a spatial overview of all slopes. However, the correct sequence in
which the slopes have to be taken is unclear.  Figure 7: Route summary widget
providing general route information (a). The slope distribution donut chart
(b) compares the slope difficulty (outer ring) and steepness (inner ring)
distribution, revealing a dominance of easy steepness segments and only a
small number of advanced segments. The altitude plot (c) sequentially
visualizes the entire route and allows brushing to highlight the corresponding
slope on the map.

Routing – Given a routable network and two specific nodes, Dijkstra’s
algorithm [18] computes the shortest path connecting these nodes [T3]. The
shortness of the path is determined by costs which are assigned to each edge
in the network according to specific properties. In accordance with [32], we
can leverage Dijkstra’s algorithm to generate a route that is optimized
according to the user preferences [T4] by adopting the cost for each slope
with regard to the provided preferences of the user. Given a set of
preferences, each incorporating a weight and a value, the cost $cost_{s}$ for
any slope is computed using the following formula:

$cost_{s}=\sum_{k=1}^{K}\frac{1}{P}\cdot(\sum_{p=1}^{P}w_{p}\cdot
dist(v_{f},v_{p}))\\\ $ (1)

where $K$ is the number of 30-meter subsegments belonging to the slope, $P$ is
the number of preferences with a weight > 0, $w_{p}$ is the weight of a given
preference, $v_{p}$ is a given preference’s value, $v_{f}$ is a given
subsegment’s feature value, and $dist(v_{f},v_{p})$ is the distance of the
actual feature value to the preference value. We employ the concept of
attribute scoring functions (ASFs) [64] to compute the distance between the
actual and the preference value. ASFs generally transform the values of data
attributes into numerical scores between 0 and 1 according to a mathematical
function. We choose a multi-point, continuous transformation strategy for our
numerical attributes, where we model a bell curve (normal distribution) with
the mean as preference value $v_{p}$ and a standard deviation of 1. For
categorical attributes (compass direction and grooming), we apply a score
assignment approach, where desired values receive a score of $1$ and undesired
values $0.1$ otherwise.

Since slopes should generally be preferred over lifts, we assigned twice the
maximum cost ($2\cdot K$) to lift segments. This ensures that bidirectional
lifts that can be taken downhill are only taken when no other alternative is
available (e.g., for linking lifts between resorts).

The recommended route can be visualized on the map (Figure 6), where the
slopes and lifts which are not part of the map are deemphasized with a lower
opacity. In the case of a round trip, or if the same slope is taken multiple
times, the traceability of the route can be compromised. To improve the
traceability regarding temporal ordering, we implemented a route summary
widget where the entire route is visualized in an altitude plot (Figure 7).
Hovering along the altitude plot with the mouse places a skier icon  on the
corresponding slope segment on the map, allowing the user to easily follow the
itinerary of the route. Slope sign symbols similar to the actual signs along
the slope are added above the altitude plot to support the navigation when
following the slope signs. A double donut chart provides distribution
information about both the difficulty classification (outer ring) and the
steepness of the segments (inner ring), allowing to visually compare these
attributes. General route details, namely the vertical descent, the total
length, and the estimated time, are shown on the left-hand side.

Workflows – In consultation with ski guides and enthusiasts, it became
apparent that, depending on the level of familiarity, different strategies
exist when manually planning routes in ski resorts. If skiers already have
prior knowledge of the resort, they might have already determined a particular
set of favorite slopes. In that case, they would like to receive precise
recommendations on how to visit all of these slopes. Otherwise, if skiers are
visiting the resort for the first time, they might be overwhelmed at first and
would like to effortlessly receive recommendations based on their preferences.
Similar to the end-to-end and step-by-step strategies introduced in [16], we
developed two workflows for route recommendation to meet both of these
approaches:

Automated workflow: For unfamiliar resorts, users input their preferences, a
start and end location, and the duration of the desired route. According to
their preferences, matching slopes in proximity will be selected and sequenced
using a traveling salesman approach. The route between these slopes will then
be calculated, resulting in the final route. The users receive the route and
the slopes selected as their favorites, allowing them to readjust the
initially recommended route.

Semi-automated workflow: If the users are already somewhat familiar with the
resort, they select matching slopes themselves by clicking the  symbol either
from the tooltip or the list of best matches (see Figure 5), effectively
performing the first part of the aforementioned workflow manually. The list of
best matches serves as a pool for recommended slopes, albeit users can also
take advantage of their resort knowledge and select their favorite slopes from
the map directly.

##  5 Evaluation

To evaluate the applicability of , we provide an exemplary usage scenario
leveraging both workflows, as well as a detailed user study.

###  5.1 Usage Scenario

Jamie is an experienced skier who annually partakes in skiing trips. This
year, she visits St. Christoph in the Ski Arlberg region for the first time
and uses to guide her through the resort. As a first step, she selects the
Advanced preference configuration to explore the resort [T1]. From the list of
best matching slopes, she can identify several slopes fitting her criteria
[T2]. Being unfamiliar with the resort, she initially opts for the automated
workflow and desires a route recommendation of two hours duration for a
morning run before returning to the hotel for lunch [T4]. Driven by her domain
knowledge, she sets her preferences on compass direction to southern-facing
slopes, as she prefers to ski on sunny slopes. Figure 5 shows the provided
preferences and the slopes considered as favorites by the routing algorithm
(indicated by ). The recommended route is seen in Figure 6. For the afternoon,
she decides on the semi-automated workflow to generate a trip of around two
hours duration [T3]. She enjoyed the 52 Kandahar-Galzig slope from her morning
run and marks it as one of her favorites as she wants to ski it again. She
also selects the 5 - Gampberg Direkte slope, a slope from the list of best
matching slopes that did not make it into the automated route suggestion she
followed in the morning. She is further looking for an ungroomed, north-facing
slope, knowing the snow conditions are better preserved with lesser sun
exposition. By adjusting her preferences accordingly, she identifies a number
of possible candidates, and finally decides on the Bachseite slope seen in
Figure 4, as it does not include any uphill segments and adheres to the time
restrictions. With an estimated duration of 130 minutes, she finalizes the
planning with the route visible in Figure 7.

###  5.2 User Study

For a quantitative, task-based evaluation of , we conducted online pair
analytics sessions [2] with six experts from the ski domain.

####  5.2.1 Study Design

Based on the task requirements established in section 3 and workflows
introduced in section 4, the participants had to carry out three analysis
challenges explained in the study methodology. The feedback from the
participants regarding their experience with the interface serves as the
foundation for identifying the benefits and drawbacks of our approach.

Participants – We defined the target audience of a visual exploration and
route planning interface in section 3. Hence, we selected our study
participants accordingly. In total, six participants with at least
intermediate (>ten years of experience) skiing expertise and varying knowledge
about the resort Ski Arlberg partook in the study. Three participants were
certified ski guides in the resort and are further referenced as
$\mathbf{G}_{\mathbf{1}}$ – $\mathbf{G}_{\mathbf{3}}$. Their extensive
knowledge of the slopes is valuable when evaluating the quality of the
recommended routes. The remaining participants were intermediate or advanced
skiers with little or no knowledge about the resort and are further referenced
as $\mathbf{P}_{\mathbf{1}}$ – $\mathbf{P}_{\mathbf{3}}$.

Methodology and Tasks – The study procedure comprised three sections through
which the participants were guided by a visual analytics expert (VAE) of our
team. The duration of each trial was scheduled for 60 minutes, with an average
duration of 68 minutes for all study trials.

The first part of the study marked a general introduction to the domain and
the tasks at hand. Each participant filled out a demographic questionnaire
recording their age, gender, profession, skiing proficiency, the average
number of skiing days per year, knowledge of the Ski Arlberg resort, and
whether they possessed a skiing instructor license. Several further questions
were asked to assess their knowledge on resources that facilitate visual
exploration or route planning in ski resorts and their frequency of use of
these resources. We further inquired about their main criteria when planning
routes, as well as their general expectations regarding an interactive
workspace for visual slope exploration and route planning in ski resorts.

In the second part, the participants were given a detailed explanation of all
components of the study prototype by the VAE. Afterward, the participants were
given the link to access the web-based prototype to acquaint themselves with
the application and interaction methods. Their first task was to explore the
resort independently [T1] and investigate the locations and characteristics of
the slopes that were recommended to them according to their applied
preferences [T2]. After the initial investigation, their next task was to
generate a route (~five hours duration) incorporating these preferred slopes
from a start and end location of choice [T3], following the semi-automated
workflow. As their last task, the participants were asked to plan a route
without favoring any specific pistes (based on the automated workflow), simply
by providing the same start and end locations, the duration of the route
(again ~five hours), and their applied preferences [T4].

The third and final part of the study consisted of an interview where the
participants were asked about their experiences, insights, and improvement
suggestions and to what extent met their initial expectations. We concluded
the study by assessing the participants’ conceptions regarding the mental,
physical, and temporal demand through the NASA Task Load Index (TLX) [34].

####  5.2.2 Evaluation Results

In the following section, we summarize the feedback received from the domain
experts during the study. We structured the section concerning the
participants’ initial expectations, their opinions on the exploration and
route generation tasks, and further possible use cases for that emerged during
the final discussion phase.

Expectations – The responses toward the initial expectations varied among the
participants. $\mathbf{G}_{\mathbf{3}}$ envisioned a Google Maps for ski
resorts, where he would receive detailed routing instructions for navigation
between locations within a resort. Aside from slope routing,
$\mathbf{G}_{\mathbf{1}}$ and $\mathbf{G}_{\mathbf{2}}$ expected ski huts and
restaurant information as part of the analysis process.
$\mathbf{P}_{\mathbf{2}}$ and $\mathbf{P}_{\mathbf{3}}$ anticipated
information regarding traffic on the slopes as well as waiting times at lifts.
Furthermore, $\mathbf{P}_{\mathbf{1}}$ expected a social network functionality
where the experiences of other skiers regarding lifts and slopes are shared.
Regarding preferences, $\mathbf{G}_{\mathbf{1}}$ and $\mathbf{P}_{\mathbf{1}}$
stated that they expect the route planning to incorporate constraints
regarding the difficulty classification (e.g., to only ski on blue slopes).

Exploration and Workflow Interaction – A finding that multiple participants
observed in the exploration task was that many of the slopes in the ski resort
exhibit segments where the steepness deviates from the difficulty
classification. The possibility of visually exposing uphill sections along the
slopes through the green color (see 3(d)) was also valued by multiple
participants. $\mathbf{G}_{\mathbf{1}}$ and $\mathbf{P}_{\mathbf{3}}$ were
interested in detecting north-facing slopes (since better snow conditions are
better preserved at later times of the day), and were able to identify regions
where these slopes were predominantly present.

All study participants mentioned that they prefer the automated workflow when
planning routes for a completely unknown resort. With increasing familiarity,
the benefit of selecting individual, known slopes and planning the route
around these favorites outweighs the shorter execution time, resulting in a
preference for semi-automated workflow. The functionality to receive different
route recommendations depending on the preference settings was appreciated by
$\mathbf{G}_{\mathbf{2}}$ and $\mathbf{G}_{\mathbf{3}}$, allowing them to
tailor the route planning to their customers’ needs. $\mathbf{P}_{\mathbf{1}}$
labeled the route summary (see Figure 7) as the _table of contents_ of the ski
day and emphasized the benefit of linking the visualization to the map on
hover. Regarding the recommended routes, $\mathbf{G}_{\mathbf{1}}$ and
$\mathbf{G}_{\mathbf{3}}$ concurred with the presented suggestions, agreeing
that they are appropriate choices for their selected preferences.
$\mathbf{G}_{\mathbf{2}}$ expressed skepticism about freeride
recommendations. Particular caution should be taken on these slopes, as
external factors such as avalanche dangers, wind, or visibility conditions can
complicate the downhill ride or even rule it out completely. Blindly following
the system’s recommendations could lead inexperienced skiers into hazardous
terrain.

$\mathbf{G}_{\mathbf{3}}$ suggested that the routing capabilities could be
extended to integrate bus routes. Since Ski Arlberg is the largest resort in
Austria, it is comprised of several towns which are also connected by buses.
Since the expectation of $\mathbf{G}_{\mathbf{1}}$ and
$\mathbf{G}_{\mathbf{2}}$ was to receive information about restaurants or
huts, they suggested integrating such information into the prototype.
Especially when planning routes for an entire day, the possibility of
including a stop for lunch was seen as an enrichment to the route planning
process. Although the routing capabilities were seen as a helpful feature to
plan a ski day, $\mathbf{G}_{\mathbf{2}}$ and $\mathbf{G}_{\mathbf{3}}$
critizised that finding the correct slope when actually skiing is a challenge
that is not addressed by the application.

Figure 8: Two visualization variants for a slope classified as intermediate,
containing segments that deviate significantly in steepness. The upper slope
is colored accordingly to the design introduced in section 4. The lower slope
emphasizes steepness deviations from the difficulty classification (25%–40%)
for intermediate.

Derived Use Cases – During the study, multiple participants mentioned further
application areas for , which we outline in the following section. Since these
feature requests surfaced during the study, they were implemented afterward
and thus not evaluated by our experts.

According to the finding that the steepness of the slope often deviates from
the difficulty classification, the feature to assess the entire resort
regarding this discrepancy was elicited as a further use-case scenario by
multiple study participants. To visually support this assessment, we designed
an alternative color scale that encodes the _difference_ between the actual
steepness of the segment and the value ranges used in the Austrian standard
for difficulty classification [3]. We propose a diverging scale from blue over
white to red, representing segments that are less steep than declared, as
steep as declared, and steeper than declared, respectively. Figure 8 compares
this novel coloring scheme to the one established in section 4. As blue and
red are established colors for indicating easy and intermediate slopes,
respectively, we are aware of the confusion this coloring introduces. However,
in this setting, we aim to showcase segments that deviate from their
difficulty classification. The novel coloring scheme leverages the association
of red with danger [60], accentuating slope segments that are steeper than
they are actually indicated on available trail maps.

(a) Freeride trajectories.

(b) Stop points along a slope.

(c) Estimation of slope width.

(d) Mismatch of OSM and trajectories.

Figure 9: Visualization of actual trajectories along the slopes, revealing
several findings.

Another requested feature that surfaced during the discussion phase was the
analysis of actual skier behavior, more precisely specific habits such as
stopping points or out-of-bounds skiing. It is not uncommon to take a short
break along parts of a slope. Especially when skiing in larger groups, such
breaks occur more often when faster group members have to wait for slower
members to catch up. Care must be taken to remain visible and not hinder any
traffic when selecting a location to stop (i.e., on the side of the slope on a
flat segment). Otherwise, other skiers might overlook a waiting party,
resulting in a crash and potential injuries. Identifying and analyzing common
stop points can be beneficial for resort planners, as they can shape the
slopes accordingly to minimize injury risk. Furthermore, more experienced
skiers often seek possibilities to leave the marked slopes and enjoy
untouched, deep powder snow. While ungroomed freeride slopes typically offer
powder conditions after a night of fresh snowfall, further options open up
when leaving the marked slopes and venturing out-of-bounds. Extensive
knowledge of the ski resort is required to locate such unmarked trails, assess
their safety, and ensure a return to the marked slopes without tedious uphill
walking is possible.

Such investigations can be conducted by visualizing the recorded GPS
trajectories, as selected examples presented in Figure 9 showcase. As
displaying individual raw trajectories would not scale, we calculated a
spatial kernel density estimation of the trajectory points and generated a
raster image representing each slope’s traffic intensity as a heatmap.
Recommendations for skiing out-of-bounds can be taken from single trajectory
paths, as observed in 9(a). Stop points can be identified as hotspots, visible
in 9(b). Aside from the above-elicited use-cases, this technique allows the
examination of other interesting causes. As 9(c) demonstrates, the
visualization enables an approximation of the width of individual slopes,
which is a property not included in the OSM data. The uncertain data quality
of the volunteered data from OSM can visually be assessed with the trajectory
heatmap. In 9(b), a shortcut taken by many skiers can be identified that is
not recorded. 9(d) reveals a vastly different path for a certain slope.

##  6 Discussion

The study revealed several benefits and drawbacks of our implemented approach.
This section discusses the major controversial issues, outlines limitations,
and provides an outlook on further research opportunities. provides a novel
perspective to view and interact with ski resort data. Many observations made
by the participants, such as detecting uphill segments or north-facing slopes,
are not supported by the current state of the art. The route planning
capabilities can aid skiing enthusiasts in centering their ski day around
their preferred slopes, even when navigating unfamiliar territory. A concern
raised by several study participants was that the dangers of avalanches were
neglected in , especially regarding off-piste ventures. Thus, we extended our
prototype to display a disclaimer when a freeride slope is contained in the
route recommendation to address this.

Color Coding – The color scale used to encode steepness values (3(a))
incorporates both red and green color hues. Research suggests that red-green
color blindness is the most common vision deficiency [6]. Furthermore, some
countries (e.g., France, Norway, or the United States) employ a different
color-coding system on their slopes, where green slopes are sometimes
classified as very easy. As we limit our case study to an Austrian ski resort,
we aligned the colors to the prevailing system. However, the coloring can, in
theory, be adapted to follow any local scheme.
$\mathbf{G}_{\mathbf{1}}$–$\mathbf{G}_{\mathbf{3}}$ did not voice any concerns
when confronted with this discrepancy and further expressed that the color
scale helped them to identify undesired flat segments, albeit
$\mathbf{G}_{\mathbf{3}}$ and $\mathbf{P}_{\mathbf{3}}$ noted that the visual
design appeared almost too colorful. We implemented the option to reduce the
design presented in Figure 3 to only the outer line, to reduce the cognitive
load of users who prefer a more simple design.

Weather Information – Multiple study participants addressed the absence of
information about weather conditions. Providing accurate weather predictions
is a vast research topic on its own [61], and the reliability of such
information decreases rapidly the further one attempts to forecast into the
future, especially in mountain regions. While a context-aware routing
algorithm as proposed by [32] is capable of incorporating such settings,
weather information is given for the entire resort and thus cannot be
subdivided on individual slopes to serve as decision-making criteria. However,
by using domain knowledge, accurate daily weather information from external
sources can be utilized to derive user preferences. In case of strong winds or
heavy snowfall, high altitudes should be avoided, which can be achieved by
setting the altitude preference to a lower value. Similarly, slopes that
receive high sun exposure tend to exhibit difficult snow conditions later in
the afternoon and are evaded by preferring north-facing slopes.

Map Design – In contrast to our 2D topographic map design, panorama maps are
the dominant style to render ski trail maps [79]. Aside from facilitating
navigation and orientation, visual aesthetics and marketing reasons heavily
influence their design process. While Field [27] proposed an alternative
representation based on a metro map layout, the evaluation concluded that the
panorama style is too established and familiar for alternative concepts to
succeed. However, a study by Balzarini et al. [4] revealed that skiers feel
uncertain and face problems in understanding when performing tasks such as
locating, wayfinding, or decision-making using a panorama map. The deformation
of the terrain makes it impossible to display distances and compass directions
at any given location accurately. These drawbacks cannot be reconciled with
our requirements, specifically the exploration of a ski resort according to
geographic features [T1]. Since metro maps apply abstractions to simplify the
underlying geography [86], they are also unsuitable for our purposes. While 3D
maps are advantageous for understanding elevation differences [66], their
shortcomings include perspective distortion and occlusion issues, depending on
the viewpoint [10]. A study evaluating a 3D environment for hiking trails
suggests that 2D map layouts are preferred for route detection and planning
tasks and that participants had trouble assessing distances and identifying
the steepest section in a 3D layout [7]. These findings motivated us to deploy
a 2D map layout, although the option to provide both options (as done by [29])
would be a holistic compromise. During the study interviews,
$\mathbf{G}_{\mathbf{3}}$ and $\mathbf{P}_{\mathbf{3}}$ appreciated the
contour lines as a help to assess the terrain steepness.
$\mathbf{G}_{\mathbf{2}}$ stated that a 2D layout is sufficient for piste
navigation, although 3D terrain visualizations would be helpful for off-piste
ventures. Aside from the contour line approach, we provide other tiling
layers, such as relief shading, that can be interactively selected.

Data Quality – The quality of VGI data is often evaluated by comparing it
against a verified dataset released from official sources [28], which is
problematic since no or little official information is publicly available. The
ISO 19157 standard [40] defines data quality for geographic information, on
which we base this assessment on.

Thematic accuracy evaluates the correctness of the OSM tags, namely the
difficulty and the grooming of each slope. The difficulty can be assessed by
comparing it against the official slope map [69], whereas clear indications
about the grooming status are not given. OSM tags comprise easy, intermediate,
advanced, and freeride values, whereas Ski Arlberg classifies their slopes
into easy , medium , challenging  , and skiroute , with the diamond shape
presumably indicating partly ungroomed slopes. We noticed that these slopes
were tagged by their respective color (  as intermediate and  as advanced) and
marked as ungroomed in OSM, with two exceptions (3.5%) which were tagged as
freeride slopes. Aside from these irregularities, no slope marked as freeride
in the OSM data is visible on the official slope map.

The positional accuracy of both OSM and extracted trajectories can be assessed
visually in our prototype by comparing them against each other, as Figure 9
illustrates. However, errors from GPS transmitters, which can occur in
mountain regions, cannot be ruled out completely.

In terms of completeness, details about the total length of slopes by
difficulty are available [5], which can be compared against our slope network.
Individual missing or excess slopes cannot be detected, thus only serving as a
broad indicator. Table 1 indicates slight discrepancies between the numbers,
which are to be expected given the above-mentioned disparities. The recorded
GPS trajectories undeniably do not fully cover the entire extent of ski resort
visitors. Yet, we argue that our sample is significantly large enough to draw
estimations about crowdedness and travel durations values. Nonetheless,
related research indicates that socioeconomic biases can be contained [82],
and we assume more experienced skiers record their rides more frequently,
although we are unable to prove this scientifically.

Source |  easy |  intermediate |  advanced | total
---|---|---|---|---
Bergfex | 130km | 122km | 51km | 302km
| 134km | 114km | 46km | 294km
Table 1: Total slope length by difficulty.

Transferability – To showcase the potential of our approach, we focused on the
region of Ski Arlberg, being the largest ski resort in Austria. However, our
methods are in principle resort agnostic and applicable if the requirements
introduced in the following paragraph are met. A graph data structure
consisting of the resorts’ slopes and lifts is a necessity to facilitate a
general routing algorithm. Spatial information of every edge of said graph is
required in combination with a DEM to derive geographic properties such as the
altitude, steepness, and compass direction. Additional properties (such as
difficulty or grooming) aside from the spatial component refine the
preference-based visualization and routing capabilities. We used OSM to obtain
the resorts’ graph network structure, which provides volunteered geographical
details for many other ski resorts worldwide. However, other officially
verified sources (if available) can be used as well to improve the data
quality. Aside from Copernicus [20], other DEMs can be employed to acquire
elevation details. At last, GPS trajectories from the resort are required to
estimate popularity and travel durations and perform skier behavior
explorations. While the proposed methods are not limited to a certain resort
size, larger resorts benefit more from the methods presented since a route
planning feature is not necessarily needed for smaller resorts with only three
lifts. With the mentioned data requirements available, our concepts can also
be transferred to related domains such as hiking or mountain biking.

###  6.1 Limitations

While the study manifested the capabilities of in regard to the elicited
tasks, some limitations became apparent. For example, the visualization and
analysis methods deployed in the application heavily emphasize the steepness
property, and lift preferences (e.g., to exclude t-bar lifts ) are not
integrated into the routing algorithm.

DEMs provide altitude information based on the underlying geographic topology.
In exceptional cases (such as bridges or tunnels), the slopes do not strictly
follow this topology, resulting in incorrect steepness calculations. Since the
recorded GPS trajectory data also includes an altitude property, a comparison
between the DEM and the altitude information of the matched trajectories could
possibly expose such discrepant cases and could prove to be a viable strategy
to mitigate this limitation.

The y-axis of the altitude plot is always scaled according to the minimum and
maximum altitude, meaning the visual slope of the individual segments is
dependent on the total vertical descent of the respective slope. Thus, the
steepness is perceived as more severe for slopes with little vertical descent.
This limitation becomes apparent when comparing two plots where the total
vertical descent largely deviates. However, the color-coding of the segments
below the line still indicates the actual steepness.

Although we dedicated a stage in the preprocessing to improve the
connectedness of the network and connect spatially close, unconnected nodes,
some slopes still remain unconnected and constitute a total of 15 dead ends in
the network topology. These slopes cannot be integrated into the routing, as a
return path to other slopes is not available. Most of these dead ends are
located along roads, and including bus routes (as suggested by
$\mathbf{G}_{\mathbf{3}}$) could further reduce the number of such impasses.

provides a time approximation for each recommended skiing route. The current
solution calculates the median travel time of recorded trajectories on a given
slope and assumes the sum of all slopes in the route to be the required
duration. This is a first approximation but arguably imprecise and generalized
since skiers with varying levels of expertise ski at different speeds. While
an exact number is very hard to obtain, sophisticated machine learning
techniques could be deployed to better and individually estimate a skier’s
speed and consequently improve the duration estimation of the routing
algorithm.

$\mathbf{G}_{\mathbf{2}}$ pointed out that the routing recommendations help to
find preferred slopes and plan out an entire day of skiing, yet are not
beneficial for actual orientation on the mountain. A mobile-optimized version
would allow users to use the prototype on their smartphone but not facilitate
the transfer of the visualized route to the real world. The development of
embedded systems is beyond the scope of this research. However, novel AR
techniques [65, 25, 30] or wearable technology could be the solution to guide
the skier along the recommended route and indicate the correct slope to take
when approaching a junction.

An entire day of skiing usually includes at least one break. Hence,
$\mathbf{G}_{\mathbf{1}}$, $\mathbf{G}_{\mathbf{2}}$, and
$\mathbf{P}_{\mathbf{2}}$ requested integrating ski huts and restaurants into
the routing algorithm. While the interactive procedure of planning a route by
selecting favorite slopes was appreciated by the study participants,
$\mathbf{P}_{\mathbf{1}}$ desired the possibility to blacklist certain
unwanted slopes. Providing alternative bypasses on demand could further
enhance the routing capabilities. Additional features, such as the curvature
or width of the slope, could refine the capturing of preferences and result in
a better-personalized route.

###  6.2 Future Work and Research Opportunities

As visual analytics methods in the ski domain are underexplored, we propose
this work as a starting point, urging further research.

Context-aware Routing – As desired by multiple study participants, integrating
dynamic properties such as weather or snow conditions would further benefit
the routing capabilities. The high uncertainty and volatility of such data
pose challenges and can question reliability. Nonetheless, promising insights
could be obtained, such as finding the weather-optimal time for a lunch break
or optimizing a route to ski on the best snow conditions for the entire day.

Temporal Resort Dynamics – Our approach to estimate the crowdedness of slopes
only permits a coarse insight into the travel activities within a ski resort.
With temporally more fine-grained trajectory data, a sophisticated model could
identify cyclic patterns about slope crowdedness and lift congestion (e.g.,
certain slopes exhibit high traffic only during morning hours). Broader
temporal trends such as (un)popular weekends could be explored to determine an
optimal time interval with empty lifts and slopes. Slope conditions also
undergo substantial changes throughout the day and the entire season. eHyd
[24] provides details on snow heights and new snow for various locations in
Austria and could serve as a starting point to investigate temporal changes.

Collaborative Route Planning – Recent research [14] validates the claim that
skiing in a group is more popular than skiing alone, thus further complicating
the route planning procedure as preferences from different users can
contradict each other. This constitutes the need for a collaborative route
planning environment in which multiple users can contribute interactively to
the exploration and route generation process. To accommodate the diversity in
preferences of the users, a comparison of different recommendations would
benefit the decision-making process. Guidelines for the task of visual
comparison [31, 49] exist and recommend the use of superposition [83] when the
spatial context is considered as significant.  A common meeting point, such as
a specific restaurant at lunch, could also be a sustainable compromise.

Community-Based Annotation Methods – A limitation of all ski trail maps so far
is that they cannot be enhanced with content from the users themselves. Fedsov
et al. [25] already experimented with sharing information on HMDs, revealing
that the participants appreciated the functionality to mark hazards or points
of interest. A larger-scale social network (as envisioned by
$\mathbf{P}_{\mathbf{1}}$) could establish a geographic information-sharing
platform in ski resorts. The potential use cases could range from general
suggestions, such as slope quality, vantage points, or restaurant
recommendations, to more temporal dependent information, such as snow
conditions, accidents, slope closings, or long lift queues.

Resort comparison – Our work is limited to the analysis of the Ski Arlberg
resort. However, our approach is transferable to any other ski resort. Austria
alone is home to 253 resorts with five or more lifts, 15 of which generate
more than 1 million skier visits per season [81], complicating the search of
finding the most suitable resort. Providing a detailed comparison between
resorts in regard to decisive attributes such as price, travel time, resort
size, altitude, and family-friendliness can support ski enthusiasts in
choosing a resort. The difficulty classification of slopes varies among
countries and resorts, and a comparison and assessment of which factors
contribute to which extent could expose discrepancies and pave the way for
uniform guidelines.

##  7 Conclusion

In this paper, we introduced , an interactive workspace for visual exploration
and route planning in ski resorts. We identified requirements and task
characteristics for such an application, and conducted pair analytics studies
with six experts from the ski domain to evaluate the applicability of our
solution. The qualitative study results demonstrate that skiers can benefit
from interactive visualizations. The visual slope exploration allowed the
experts to detect patterns such as uphill segments, and the preference-based
routing recommendations were highly appreciated when investigating unknown ski
resorts. While we discuss the benefits and limitations of our approach, we
furthermore present research opportunities and encourage fellow researchers to
engage in the rather unexplored field of visual analytics for ski resorts.

###### Acknowledgements.

This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation) under Germany’s Excellence Strategy - EXC 2117 -
422037984 and the priority programme "Volunteered Geographic Information:
Interpretation, Visualisation and SocialComputing” (VGIscience, priority
programme 1894).

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