# Investigating Input Modality and Task Geometry
on Precision–first 3D Drawing in Virtual Reality

Chen Chen1 Matin Yarmand1 Zhuoqun Xu1 Varun Singh1 Yang Zhang2 Nadir Weibel1
1Computer Science and Engineering, University of California San Diego, La
Jolla, CA, United States
2Electrical and Computer Engineering, University of California Los Angeles,
Los Angeles, CA, United States corresponding author, e-mail<EMAIL_ADDRESS>
###### Abstract

Accurately drawing non–planar 3D curves in immersive Virtual Reality (VR) is
indispensable for many precise 3D tasks. However, due to lack of physical
support, limited depth perception, and the non–planar nature of 3D curves, it
is challenging to adjust mid–air strokes to achieve high precision. Instead of
creating new interaction techniques, we investigated how task geometric shapes
and input modalities affect precision–first drawing performance in a
within–subject study (n = $12$) focusing on 3D target tracing in commercially
available VR headsets. We found that compared to using bare hands, VR
controllers and pens yield nearly $30$% of precision gain, and that the tasks
with large curvature, forward–backward or left–right orientations perform
best. We finally discuss opportunities for designing novel interaction
techniques for precise 3D drawing. We believe that our work will benefit
future research aiming to create usable toolboxes for precise 3D drawing.

###### keywords:

VR, Precise–First 3D Drawing, Usability Studies

Human-centered computingEmpirical studies in interaction design;

##  1 introduction

Interactions in 3D immersive Virtual Environment (VE) powered by today’s
Virtual Reality (VR) have unlocked numerous applications in general work
spaces [22] and healthcare [23, 24]. The ability to directly draw in mid–air
with physical tools and have traces appearing synchronously at the same
physical location, has been identified as a key primitive to enable many
drawing based applications in VR. With such capabilities, for example,
designers could efficiently externalize and communicate their ideas through 3D
sketches [38, 43]. It is also important in numerous healthcare applications,
where doctors need to precisely annotate on 3D medical structures [23, 24,
69]. However, it is challenging to enable precise drawing in unconstrained
mid-air environments with commercially available input modality (e.g., hands
and VR controllers). For example, while designers are usually very excited at
the prospect of using 3D sketching as a medium during the conceptualization
phase, they constantly reported how they found it frustrating to draw in VE
due to the lack of fine control over their strokes [40].

Although prior works have investigated the factors causing poor performance
while sketching 2D curves on 2D surfaces [37, 10, 51] and in 3D VE [16, 13,
20], understanding the performance of drawing non–planar 3D curves in
immersive VE has not yet been explored (see Fig. 1). Unlike 2D curves, where
all strokes are on the same virtual plane and can be described by a linear
combination of two orthonormal basis, 3D curves pass through the three-
dimensional spaces and can only be parameterized by three orthonormal basis.
This implies that while drawing on a particular surface, users need to adjust
their strokes in the additional dimension, causing challenges of maintaining
their drawing performance. Therefore, it is important to understand how
precise 3D drawing can be supported in VR, and how factors such as input
modality and task geometric shapes could affect such delineation performance.

In this work, we first investigate the performance of precision–first 3D
drawing, referring to the interaction when users prioritize drawing precision
over speed, while drawing 3D curves in VE. Instead of creating new interaction
techniques, we focus on understanding how the geometric shapes of 3D curves
(i.e., curvatures, slopes, and orientations) and four widely used input
methods (i.e., VR pen, VR controller, hand pointing, and pinching) can impact
drawing performance, as measured by drawing error and error correction
attempts (in the spatial domain), as well as speed (in the time domain).

We built proof-of-concept prototypes on HTC Vive [4] and Oculus Quest $2$ [7],
to assess performance in a within–subject study (n = $12$). Our experiments
focused on the analysis of $1,296$ trials and show that using a tool (i.e.,
the VR pen or controller) leads on average to $29.63$% higher precision
compared to hand gestures (i.e., pointing and pinching), and that using a VR
Pen yields $13.11$% higher precision than using a controller. We also found
that the large curvature, forward–backward or left–right orientation allow
participants to generate the most precise drawing. Finally, the qualitative
evaluations of the user experience unveiled the importance of tools and
occlusion during 3D precise drawing, and highlighted the demand of attention
generated across the different geometric configurations. In summary, our
contribution is two fold:

  1. (1)

We characterize how (a) 3D geometric characteristics and (b) input methods,
affect the performance of drawing 3D curves in unconstrained 3D immersive
environments (Sec. 4);

  2. (2)

We discuss how our findings can be used for designing techniques to optimize
drawing precision and experience in unconstrained VE without introducing
additional hardware (Sec. 5);

Figure 1: Prior works that evaluates drawn tasks in VR. We focus on
precision–first 3D drawing in VR. Demonstrative diagrams are revised from
[13]. Notably, “combined 2D” represents the curves that only consist of planar
2D curves and are not connected continuously, and “2.5D” represents the curves
that are 2D curves projected on a 3D surface.

##  2 Related Work

###  2.1 Input Methods for VR

Existing research has evaluated the usability of input devices for various VR
tasks. Pham et al. [58] discovered that a pen–based interface is better than a
controller for pointing tasks. Batmaz et al. [17] demonstrated that using
pen–like devices with precision grip could improve the performance for target
selections. Li et al. [48] found that a tripod grip at the rear–end of the pen
is the optimal posture for large ranges of motion.

Some prior research also investigated how to design novel stylus for VR (e.g.,
Flashpen [59] and OVR stylus [42]). Commercial VR styluses, e.g., Logictech VR
Ink [6] and Wacom VR Pen [8], also show the potential of using pens for
various VR input tasks. While the ergonomic designs of these VR pens are
usually considered as the vendor’s slogan for advertising performance merits
(e.g., “sketch in the air, just like they would with a real pen” [8] and
“offers control and precision” [6]), it is unclear in what contexts and how
much affordance these styluses can actually offer, particularly when it comes
to precise 3D drawing tasks.

With new advancements in vision and deep learning research, mainstream
headsets like the Oculus Quest $2$ [7] have enabled hand–based gesture
tracking, which can deliver a more natural and convenient way of interactions
[5, 36]. Prior works have demonstrated the effectiveness of using bare-hand,
either as a general input method for freehand sketching [54], as a surface
drawing system that uses hand gestures to create, and manipulate the 3D
sketches [60], or as a bi–manual interaction modality geared to enhance the
sketching precision by overcoming the lack of physical support [45]. Despite
these efforts, research outlining the differences between using bare–hand and
standard input devices in the context of 3D curves creation is heavily
under–explored.

We address the existing gap by comparing precise–first 3D drawing performance
with four input methods: VR controller, VR pen, hand–pointing, and
hand–pinching. Unlike prior efforts using self–fabricated VR styluses [58, 13,
48], we adopted Logitech VR Ink [6], a commercially available VR stylus,
throughout the study.

###  2.2 Evaluations of Drawing Performance in VR

Fig. 1 shows an inventory diagram, outlining the current research gap in
evaluating drawing performance in VR. For example, Arora et al. evaluated
sketching performance using pens and controllers, and found that the lack of
physical surface support and the limited depth perceptions can cause sketching
inaccuracies [13]. Cannavò [20] investigated the performance of drawing 2D
curves using the tasks designed by [13], but by using a consumer–grade
Logitech VR Ink pen and the HTC Vive controller. Bowers et al. [18] compared
line drawing performance with and without physical support on planar virtual
canvases, and found that while the addition of a physical surface increased
performance in terms of stroke speed and accuracy in some tasks, most
participants still preferred to use air–drawing. Kern et al. [47] and
Schneider et al. [61] focused on 2D interactions in 3D space with physical
surface support. While these works reported sketching performance when using a
2D surface in the 3D space, practical drawing in 3D often consists of 3D
curves, which can only be modelled by a linear combinations of three
orthonormal basis (i.e., passing through the 3D space). These are more
challenging and cannot be supported by a planar (or curved planar) virtual
surface. Although Arora et al. [13] included tasks with a few “2.5D” curves,
i.e., a circle projected on a curved surface (see Fig. 1), creating and
interacting with those curves is fundamentally different than engaging with
true 3D curves that could not be described by any planes (either curved or
non–curved) and could only be modelled by three orthonormal bases.
Additionally, this work [13] did not focus on the impact of various 3D curve
parameters (e.g., curvature).

Few existing works focused on volumetric shapes composed of “combined 2D”
curves, which include planar 2D curves that are not connected continuously
(e.g., the skeleton of a cube). For instance, Wise et al. [66] focused on
cognitive processes and found that sketching volumetric shapes consumes more
time, and it is more error prone when compared to sketching flat shapes. They
also suggested how this is due to the additional interaction dimension where
participants needed to make connections between several 2D sub–objects.
Barrera Machuca et al. [16] focused on the effects of spatial ability and
indicated that participants’ spatial ability affects the shapes of the line
drawn, yet the line precision is less affected. However, the “combined 2D”
volumetric shape is different than actual 3D curves. Using combined 2D curves
implicitly reduces the task difficulty, leaving many research questions
unanswered in terms of drawing in true 3D.

Figure 2: We consider four input methods. On the left (a – d) we show the
tool-based and hand-based gestures in real world; on the right (e – h) we show
the photo-realistic prefabs that participants saw in the VR scene (the blue
curves are drawn by the participants).

###  2.3 Techniques for Assisting Drawing in VR

Existing works also focused on assistive techniques to enhance 3D drawing
performance. The first thread of systems attempted to use haptic feedback to
enhance drawing performance. For example, Wacker et al. [65] focused on the
haptic feedback provided by actual physical interaction with a surface.
Elsayed et al. [29] used pneumatic force and vibrotactile haptic to simulate
the contact pressure of the stylus against sketching surface, and mimic the
textures, respectively. Keefe et al. [46] and Mohanty et al. [53] looked into
the effectiveness of incorporating a phantom haptic device. Others (e.g.,
Arora et al. [12]) integrated existing 2D sketching tools (e.g., tablet) into
VR, to provide haptic feeling and physical support. Although additional
support using 2D surfaces can help with sketching 2D curves, it does not help
3D drawing and increases hardware cost and complexity, ultimately impacting
the user experience. We attempt to understand the performance of different
commercially available and widely used input methods in 3D drawing tasks
contexts.

Another thread is to design assistive visual elements to overcome the
challenges introduced by the lack of depth perception. Early works from
Grossman et al. [35, 34] advocated the idea of leveraging virtual
cross–sectional planes for drawing 2D curves while constructing 3D non–planar
curves. Arora et al. [13] introduced visual feedback in terms of grids or
scaffolding curves, and showed that this approach increases accuracy by $17$%
and $57$% respectively. Smart3DGuides [50] looked at the effectiveness of
relying solely on visual guidance to increase the accuracy of the drawing
shape likeness. Multiplanes [49] demonstrated a 3D drawing system that
introduces virtual snapping planes and beautification triggers that are
automatically generated based on previous and current strokes, as well as
current controller poses. Commercially available 3D modelling applications
such as Gravity Sketch [2] also used the snapping techniques, where the
virtual snapping grids are used as the visual reference to help users better
sketch the 2D curves. While adding additional assistive visual components in
the VR scene could help increase drawing performance, the immersive experience
might be sacrificed [19]. In addition, the UI might become disorganized and
overwhelming due to the additional visual components [63].

Figure 3: The three types of orientations with respect to the participant: (a)
Up–Down; (b) Left–Right; (c) Forward–Backward.

##  3 Methods

###  3.1 Participants

We recruited $12$ participants ($3$ females and $9$ males, age: $\mu$ = $25$,
$\sigma$ = $2.73$). The average arm’s length of recruited participants was
$65.30cm$ ($\sigma$ = $2.90cm$). All participants were right–handed, and were
instructed to complete the tasks with their dominant hand. Our study was
approved by the Institutional Review Boards (IRB).

###  3.2 Task Design

We aim to measure performance when drawing continuous 3D curves in VE. We used
helical curve as the primitive building block for designing our
precision–first 3D drawing tasks for two reasons: First, the helical curve
mathematically represents one of the simplest continuous 3D curves with
constant curvature, which can be easily described by only two parameters
(i.e., curvature and slope). This effectively helped us better design the
controlled experiment. Second, the helical curve has been widely used in
popular CAD tools (e.g., Autodesk Inventor [15]) as the primitive building
block for designers to create 3D prototypes. With this rationale, we designed
a within–participant study protocol with four distinct variables and a total
of $108$ drawing combinations: orientation (with three parameters), curvature
(with three parameters), slope (with three parameters), and input method (with
four parameters). The mathematical modelling and derivations of the helical
curves are described in Appendix A.1.

Orientation – The drawing tasks followed three types of orientations with
respect to participants’ shoulders: Up–Down, Left–Right and Forward–Backward
(see Fig. 3). We positioned the center of each helical curve on the invisible
hemisphere, centered around the shoulder (the positioning of participants
shoulder is determined during the calibration phase, as described in Sec.
3.5). The Left–Right and Forward–Backward configurations can be generated by
rotating the helical curve $None$ with respect to the y and x axes
respectively.

Curvature and Slope – A 3D helical curve can be parameterized by its curvature
and slope. We devised three cases (i.e., Small, Medium, and Large) for each of
the variables, contributing to nine conditions: $4m^{-1}$, $8m^{-1}$, and
$12m^{-1}$ for curvature, as well as $0.05$, $0.25$, and $0.45$ for slope. The
parameters were determined by ensuring that each target stroke is within all
participants’ reach, without having to physically move from the standing
position.

Input Method – We base our evaluation on four input methods, including two 3D
sketching tools (i.e., VR Controller and VR Pen) and two air–drawing hand
gestures (i.e., Point and Pinch). Fig. 2 demonstrates these input methods,
along with the photo–realistic prefab shown in the VR scene.

$\bullet$ Tool Based Inputs – We selected two commercially available VR input
devices, the Logitech VR Ink [6] (hereafter referred as Pen) and the HTC Vive
Controller [3] (hereafter referred as Controller). Participants were
instructed to establish grip with the stylus using a _tripod front-end
gesture_ (see Fig. 2a). According to [48], the tripod front–end and rear–end
gripping postures are the easiest for distant target selections, but the
tripod rear–end would be impractical due to the bulky size of the tracking
rack. We demonstrated the gesture by showing how to use thumb and middle
finger to stabilize and control the stylus, and use the index finger to
trigger drawing by pressing the primary button. All participants were
comfortable with the grip before starting to work on their tasks. Similar to
the pen, we instructed participants to draw using the controller by pulling
the trigger button using their index finger and hold $+$ stabilize the
controller using the palm and rest of fingers (see Fig. 2b).

$\bullet$ Hand Based Inputs – We included two types of air–drawing hand
gestures: pointing and pinching. The drawing would be triggered by a foot
switch, aiming to prevent potential confounding factors associated with two
hands interactions. Typically the pointing gesture is preferred for fine
grained direct manipulations [11]. To ensure consistency, we asked all
participants to use their index finger for the hand pointing gesture. For
fine–grained control over the drawing stroke, we encouraged the participants
to incorporate different levels of finger dexterity (e.g., bent or stretched
index finger). We also included the pinch gesture due to its popularity in
mainstream AR/VR systems [5, 52]. We instructed participants to use the
thumb–index pinch (Fig. 2d). While the pinch gesture offers less flexibility
for finger dexterity, it provides a _self-haptic_ , tactile feedback during
the interaction, which has been used in existing AR/VR systems [5, 70].

###  3.3 Measures

We evaluate drawing performance using measures in spatial (MOD & NLM) and
temporal domains (MSP), in short:

Mean Overall Deviation (MOD) – We use MOD to measure the average error between
strokes and target curves [13]. After removing all extreme outliers using an
interquartile range (IQR) criterion [26], we compute the mean of stroke–target
distance (i.e., the Euclidean distance of each participant-drawn stroke to the
target traces) (see equation 1, where stroke and target traces are denoted by
$\boldsymbol{P}$ and $\boldsymbol{T}$, respectively; we used $d(p_{i},T)$ to
denote the $L2$ distance between stroke $p_{i}$ to target trace
$\boldsymbol{T}$).

$MOD=\frac{1}{N}\sum_{i=0}^{N-1}[d(\overrightarrow{p_{i}},\boldsymbol{T})]$
(1)

Number of Local Maxima of Stroke Deviations (NLM) – It is impractical for
participants to position every strokes precisely on the target trace. While
drawing, participants might try to correct the errors by re–adjusting the
stroke on top of the target trace. We computed NLM as the metric to evaluate
how frequently the participants attempted to correct the instantaneous drawing
errors [41] (see equation 2, where $\mathbb{I}(\cdot)$ denotes the indicator
function). A higher NLM theoretically indicates that the stroke is difficult
to be stabilized.

$NLM=\sum_{i=1}^{N-2}\mathbb{I}[d(\overrightarrow{p_{i}},\boldsymbol{T})>d(\overrightarrow{p_{i-1}},\boldsymbol{T})]\mathbb{I}[d(\overrightarrow{p_{i}},\boldsymbol{T})>d(\overrightarrow{p_{i+1}},\boldsymbol{T})]$
(2)

Mean Drawing SPeed (MSP) – We calculated the instantaneous speed at every
stroke, dividing the Euclidean distance (from the previous point) by the
elapsed time between two samples.

Figure 4: Study timeline. During long breaks ($10\sim 15$ min), participants
were asked to take off the headset. During short breaks, participants were
asked to rest their arms for $2\sim 3$ seconds. Figure 5: (a – i) Analysis of
main effects ($*=p<.05$, $**=p<.01$, $***=p<.001$), while the red colored
“$ns$” indicates no statistical significance. (j) FFT of instantaneous
stroke–target distance (a.k.a. error). We only show the frequency components
below $12$ Hz, as the frequency for one’s tremors is usually within $8$ –
$12$Hz, while higher frequency components could be caused by positional
tracking and is negligible in terms of human performance evaluations [21].
Indices of key takeaways are labelled at bottom left of each subplots.

###  3.4 System and Implementation

We implemented the testbed for controller and pen input using HTC Vive [4] and
hand based input using Oculus Quest $2$ [7]. We used Vive for implementing the
testbed of tool based input, because at the time of study the Oculus Quest $2$
did not support an SDK for the Logitech VR stylus that we wanted to use to
evaluate drawing precision. Additionally, using Vive for evaluating
precision–first bare hand drawing was impractical due to the low accuracy of
hand tracking. We therefore explored multiple tracking options and decided
against using optical motion capture (MoCap) system (e.g., OptiTrack) for
three reasons. First, MoCap systems usually requires wearing smart gloves with
Infrared (IR) markers, which introduces additional weight and haptic feelings,
and could cause non–negligible differences when compared to bare hand drawing.
Second, the tracking performance of certain hand poses might degrade due to
the occlusion of IR markers. Finally, we wanted to focus on participants’ 3D
drawing performance in readily accessible commercially available VR systems.
The high costs, complicated setups, potential issues caused by reflections
introduced by MoCap hinders the practical uses. With considerations of
commercial device availability, we eventually decided to prototype the hand-
based testbed on Quest $2$ using the Oculus Integration SDK.

###  3.5 Procedure

Our experimental procedure consist of three major steps (Fig. 4):

Pre–Study and Questionnaire –  Participants were first asked to complete a
pre–study questionnaire aiming to collect background information, and a
$6$–min Paper Folding Test (VZ-2) [27] to evaluate their spatial ability. All
participants exhibited above-average spatial abilities, with an average test
score of $92.92\%$ ($\sigma$ = $10.54\%$).

Evaluations –  We structured our evaluation around four sessions (see Fig. 4),
with each pertaining to one input methods, chosen based on balanced Latin
Square algorithm [26]. We chose to group trials by input method to minimize
the time and effort for switching tools. Participants completed $27$ trials in
each session with the order being randomized. Each session consists of three
phases:

$\bullet$Phase 1: Training –  Each session was preceded with a training phase.
First, the experimenter demonstrated the proper use of the equipment and the
drawing tasks. Second, the experimenter helped participants to wear the
headset and to try and draw until they felt comfortable with the environment
and input method. On average, this process lasted around $5\sim 10$ minutes.

$\bullet$Phase 2: Calibration –  Due to the diversity in participants’ heights
and arms’ lengths, we incorporated a calibration phase before the main drawing
tasks. We used the calibration process to adjust the positions and
orientations of the drawing tasks in the subsequent trials so that they appear
at relatively constant locations across all participants. Participants were
asked to hold the controller, stand at a fixed location, and keep their arm
straight and raised it to the forward, up, and right position, respectively.
While keeping the gesture constant for $5$ seconds, the system sampled and
computed the mean location of the controller. We finally used a hemisphere
centered around participants’ shoulder with a radius equal to the arm length
to denote the reachable region by participants. The calibration results were
then used to generate subsequent trials.

$\bullet$Phase 3: Drawing –  Participants were finally asked to trace over the
helical shapes that appeared in the VE using the associated input method. A
progress information panel was visible to help keep tracking the current state
of the trial and also improve engagement [56]. As we aim to evaluate the
precision of the drawing performance, we asked participants to prioritize
accuracy over speed (i.e., increase their speed only after participants
believed they reached the highest possible accuracy). Additionally, to avoid
motion sickness and fatigue, the study session contained multiple short breaks
(between trials) and long breaks (between sessions) (see Fig. 4). During the
short breaks, participants put their arms down momentarily to relieve any
fatigue. To avoid position inconsistency, we asked participants not to move
away from the standing position. After every session, participants took a
longer break during which the headset and input devices (if any) were removed.
On average, short breaks took approximately $2\sim 3$ seconds and long break
$10\sim 15$ minutes.

Post-Study User Experience (UX) Evaluations –  We finally evaluated
participants’ experience by asking them to fill out an experience evaluation
questionnaire and think–aloud while recording their responses. Our evaluation
questions were revised from [29]. As we focused on evaluating participants’
experience with respect to a particular input techniques instead of the entire
system experience, we excluded the questions of system engagement and system
convenience. We also added an additional assessment that focused on fatigue.
On a $5$–point Likert scale, participants indicated to what extent they agreed
or disagreed with the following two statements:

$\bullet$ Confidence: I am confident that I could draw the shape correctly.
$\bullet$ Fatigue: I do not feel increased fatigue using this device.

Figure 6: Analysis of two–way interaction effects ($*=p<.05$, $**=p<.01$,
$***=p<.001$). The purple colored “$ns$” indicates no statistical
significance. To enhance readability, we only annotate the contrast tests
within each group (i.e., when the independent variables of the horizontal axis
are identical). While visualizing the interaction effects involving input
methods, we only annotate the contrast test results by comparing within Tool
or Hand. Indices of key takeaways are labelled at bottom left of each
subplots.

##  4 Results

This section outlines the key results, with [MN-#] and [ITA-#] referring main
and interaction effects, [ITM-#] referring intermediate variables, and [SUB-#]
referring participants’ subjective comments.

###  4.1 Independent Variables

To examine the statistical significance of the effects of the four independent
variables over the three measures, we first perform the normality check, and
found that $39$, $9$, and $17$ (out of $108$) observations for MOD, NLM and
MSP did not comply to the normal distribution ($p<.05$). Therefore, we decided
to process all data using Aligned Rank Transform (ART) [67], followed by a
Repeated–Measure (RM) Analysis of Variance (ANOVA) ($\alpha=.05$). The ART
procedures for multifactor contrast test was used for post–hoc test, with
Bonferroni corrections [28]. As for confidence intervals, we first transformed
the data using Cousineau’s method [25] to minimize the impacts of
between–subject variations, and then computed the length of error bars using
$95\%$ confidence intervals.

Analysis of Main Effects
Main effect refers to the statistical relationship between the four input
methods and the three measures, averaging across the level of the other
independent variables. Fig. 5 visualizes the main effects that are considered
statistical significant ($p<.05$).

Figure 7: (a) Causal model of the three variables of interests. (b – d)
Correlations between (b) ASP vs. SSD, (c) Error vs. SSD, and (d) Error vs.
ASP. For stroke samples with the same independent variable, we only visualize
the average values of dependent variables.

Input Method – RM–ANOVA indicates a strong statistical significance of input
methods over MOD ($F_{3,33}=142.90$, $p<.001$, $\eta^{2}_{p}=0.267$), NLM
($F_{3,33}=2299.12$, $p<.001$, $\eta^{2}_{p}=0.854$) and MSP
($F_{3,33}=185.24$, $p<.001$, $\eta^{2}_{p}=0.321$). By examining Fig. 5(a –
c), we conclude three key findings:

$\bullet$ _[MN-1] MOD –_ Using a Tool (Pen and Controller) leads to $29.63$%
less MOD when compared to Hand input ($\mu_{tool}=5.7mm$ vs.
$\mu_{hand}=8.1mm$). Considering just Tool inputs, the MOD generated by the
Pen is $13.11$% less than the one of the Controller ($\mu_{controller}=6.1mm$
vs. $\mu_{pen}=5.3mm$). A similar behavior was observed for Hand input, where
Point gestures are $16.85$% more precise compared to Pinch gestures
($\mu_{pinch}=8.9mm$ vs. $\mu_{point}=7.4mm$).

$\bullet$ _[MN-2] NLM –_ Using a Tool generates a significant higher number of
NLM ($385.08$%), compared to using Hand gestures ($\mu_{tool}=143.1$ vs.
$\mu_{hand}=29.5$, see Fig. 5b). Recall that [MN-1] implied that when using a
Tool, users generate more accurate drawings than using Hand, which is possibly
caused by more frequent attempts to correct errors. To verify this, we
normalized the time series instantaneous stroke–target distance (a.k.a. error)
using $z$–score normalization, followed by a Fast Fourier Transform (FFT).
Magnitudes of each frequency bins (with $0.1$ Hz resolution) were aggregated
by averaging the values across all tasks and participants with the same input
methods. As evident in Fig. 5j, the FFT of instantaneous error generated by
Tool is significantly higher than that yielded by Hand, potentially causing
the traces to look more fluctuating. While Fig. 5b shows a slightly higher NLM
when comparing Pen vs. Controller, and Point vs. Pinch, the pairwise
difference between Pen and Controller does not show statistical significance.

$\bullet$ _[MN-3] MSP –_ When looking at MSP, drawing with Controller
($\mu_{controller}=11.89cm/s$) and Pinch ($\mu_{pinch}=12.54cm/s$) is
significantly faster than that using Point ($\mu_{point}=10.84cm/s$), followed
by Pen ($\mu_{pen}=8.48cm/s$) (see Fig. 5c). One possible reason is the
different use of finger dexterity across different devices. With Pen and
Point, participants were encouraged to use thumb and index finger, as well as
index finger only, respectively, to control and stabilize the strokes. While
these could enhance the precision, the average drawing speed would be
sacrificed. In contrast, with Controller and Pinch, participants were
encouraged to use the lower arms to control the stroke movement, which could
benefit drawing speed, yet sacrifice accuracy.

Curvatures & Slope – RM-ANOVA shows that curvature has a significant impact on
MOD ($F_{2,22}=88.80,p<.001,\eta^{2}_{p}=0.131$), NLM
($F_{2,22}=47.21,p<.001,\eta^{2}_{p}=0.074$), and MSP
($F_{2,22}=79.93,p<.001,\eta^{2}_{p}=0.120$). We also show that the slope
measure only statistically affects NLM ($F_{2,22}=6.80$, $p<.01$,
$\eta^{2}_{p}=0.011$). Fig. 5 (d – g) illustrate key takeaways:

$\bullet$_[MN-4] MOD & NLM & MSP – _ An increase in curvature generally
reduces the MOD ($\mu$, $8.0mm$, $6.6mm$ and $6.0mm$ for Small, Medium and
Large, respectively). While examining Fig. 5e, a lower NLM is visible when the
curvature is larger ($\mu$, $90.79$, $85.92$, and $82.25$ for Small, Medium
and Large respectively, see Fig. 5e). This possibly means that participants
tend to draw slower with increasing curvature, as evident in Fig. 5f ($\mu$,
$11.99cm/s$, $10.92cm/s$, and $9.92cm/s$ for Small, Medium and Large,
respectively).

$\bullet$ _[MN-5] NLM –_ While Fig. 5g shows that an increase in slope reduces
NLM, only pairwise comparisons of Small and Large trials show statistical
significance ($p<.01$), and therefore the contributions from the Slope are
overall quite weak.

Orientation – RM–ANOVA shows that orientation has statistically significant
impacts on MOD ($F_{2,22}=24.16$, $p<.001$, $\eta^{2}_{p}=0.039$) and NLM
($F_{2,22}=26.77$, $p<.001$, $\eta^{2}_{p}=0.044$).

$\bullet$_[MN-6] MOD & NLM – _ Participants generated lower MOD and higher NLM
for Forward–Backward and Left–Right orientations, compared to the Up–Down
trial ($\mu_{MOD}$ = $6.50mm$, $6.55mm$, $7.65mm$ and $\mu_{NLM}$ = $88.73$,
$88.65$, $81.42$ for Forward–Backward, Left–Right, and Up–Down, post-hoc
contrasts, with $p<.001$, see Fig. 5 (h – i)). This implies that orienting the
helix in Forward–Backward and Left–Right configurations helps enhancing 3D
drawing precision.

Analysis of Interaction Effects
Interaction effects refer to those when one factor on the measure depends on
the level of the other factor. Fig. 6 summarizes the two–way interaction
effects that are statistically significant ($p<.05$). For the post-hoc
contrast test, we used, e.g., $A_{i}B_{j}\sim A_{k}B_{l}$, to represent the
pairwise comparison between $A_{i}B_{j}$ and $A_{k}B_{l}$, where $A_{i}$,
$A_{k}$ and $B_{j}$, $B_{l}$ are possible levels of factor $A$ and $B$. When
$j=l$, we use the notation of $A_{i}\sim A_{k}\mid B_{j}$.

Input Method + Curvature – Interaction effects between curvature and input
methods on MOD ($F_{6,66}=2.70$, $p<.05$, $\eta^{2}_{p}=0.014$) and NLM
($F_{6,66}=27.34$, $p<.001$, $\eta^{2}_{p}=0.122$) are identified in Fig. 6(a
– b), and summarized below:

$\bullet$ _[ITA-1] MOD & NLM for Tools – _ Pen generates more precise drawings
than Controller, but only at at larger curvature tasks (Pen $\sim$ Controller
at Small, Medium, and Large conditions: $p>.05$, $p<.01$, and $p<.001$, see
Fig. 6a). While interactions with the Pen also introduce higher NLM compared
to using the Controller at larger curvature, the post-hoc contrast tests do
not show statistical significance (see Fig. 6b). This verifies our finding in
Fig. 5b.

$\bullet$ _[ITA-2] MOD & NLM for Hand – _ When using a Hand gesture while
drawing, we found that the Point gesture generates significantly less error
compared to the Pinch one, but only in Small curvature tasks ($p<.05$), while
no statistical significance is detected during Medium and Large curvature
trials. Additionally, the Point gesture generates significantly higher NLM in
Small and Medium curvature tasks compared to the Large trials (Pinch $\sim$
Point in Small, Medium, and Large curvatures: $p<.001$, $p<.05$, $p>.05$).

Input Method + Orientation – RM–ANOVA results in Fig. 6 (c – d) show the
interaction effects of input methods and orientations on MOD ($F_{6,66}=4.47$,
$p<.05$, $\eta^{2}_{p}=0.022$) and NLM ($F_{6,66}=4.80$, $p<.05$,
$\eta^{2}_{p}=0.024$). In short:

$\bullet$ _[ITA-3] MOD & NLM for Tools – _ Drawing with a Tool in general, and
the Pen specifically produced significantly higher precision during Left–Right
orientation ($p<.01$). The other two orientations, did not show any advantages
when using the Pen.

$\bullet$ _[ITA-4] MOD & NLM for Hands – _ When using a Hand gesture, we found
that participants had a tendency of being more precise while drawing using
Point than Pinch, but only in the Left–Right orientation. The difference
between the two Hand modalities however was not statistical significant
($.05<p<.1$).

Orientation + Curvature / Slope – Fig. 6e shows the RM–ANOVA results for the
interaction effects of curvature and orientation on MOD ($F_{4,44}=4.23$,
$p<.01$, $\eta^{2}_{p}=0.014$). And Fig. 6 (f–g) show the interaction effects
of orientation and slope on MOD ($F_{4,44}=3.54$, $p<.01$,
$\eta^{2}_{p}=0.012$) and NLM ($F_{4,44}=6.08$, $p<.05$,
$\eta^{2}_{p}=0.020$).

$\bullet$_[ITA-5] MOD & NLM – _ In the Small curvature condition, participants
generated more precise output when drawing in the Forward–Backward and
Left–Right orientation. As for slope, the Up–Down orientation produces the
least accurate trials in all slope conditions, and the Small slope generates
significantly lower NLM in the Up–Down ($p<.001$) orientation, compared to the
other two orientations (see Fig. 6f – g)

Curvature + Slope – Finally, Fig. 6 (h–i) show the interaction of curvature
and slope on MOD ($F_{4,44}=3.31$, $p<.05$, $\eta^{2}_{p}=0.011$) and NLM
($F_{4,44}=5.56$, $p<.001$, $\eta^{2}_{p}=0.019$).

$\bullet$ _[ITA-6] NLM – _ The Large curvature and Large slope yields lowest
NLM compared to the rest of cases.

###  4.2 Uncontrolled and Intermediate Variables

It is also worth to investigate the correlation with critical intermediate
variables that have been examined in prior works [30, 39, 9]. We base our
description of the impact of intermediate variables on a causal model (see
Fig. 7a) with three hypothesized Causal Links (CLs), considering two specific
intermediate variables:

($1$) Stroke–Shoulder Distance (SSD) – SSD is defined as the Euclidean
distance between shoulder and real-time stroke position. We assumed that SSD
can affect drawing performance (see Fig. 7a). Since the arm length varies
among participants, we considered the percentage of absolute SSD over
participants’ arm length.

($2$) Absolute Drawing SPeed (ASP) – While we instructed participants to
prioritize precision over speed, actual speeds could vary within each trials
and across the participants depending on multiple confounding factors, such as
the use of specific tools, and specific task geometric features [13].

Fig. 7 (b–d) show the correlations among SSD, ASP and stroke-target distance
(i.e., error). We used Spearman’s Rank-Order Correlation to examine the
monotonic relationship between two variables. We outline the key findings
below:

_[ITM–1, CL1] ASP vs. SSD –_ We found only a very weak monotonic correlation
between distance and speed for Hand gestures ($p>.1$). When using Hand
gestures, participants draw faster when the strokes are either far or very
close to their shoulder. In contrast, when using a Tool, the drawing speed
increases with higher values of SSD for both Pen and Controller
($r_{s}(7)=0.95$, $p<.005$).

Figure 8: Participants’ answers to post-study questionnaires. The Likert
scores corresponding to the level of agreement are $1$ – $5$. We use the green
line to mark the mid point with the label of median (MED).

_[ITM–2, CL2] Error vs. SSD –_ When looking at error rates and their
relationship with distance, we observed a strong monotonic correlation for
both Pen ($r_{s}(7)=0.93$, $p<.005$) and Controller ($r_{s}(7)=0.82$,
$p<.01$), while such correlation was very weak for Hand ($p>.1$). When using
Hand gestures, with SSD $\sim 60\%$ of the length of their arm, the error is
minimized. When interacting with a Tool, with SSD $30\%\sim 40\%$ of the
length of their arm, error is minimized.

_[ITM – 3, CL3] Error vs. ASP –_ We observed a strong monotonic correlation
between speed and error for all input modalities (Controller:
$r_{s}(14)=0.84$, Pen: $r_{s}(14)=0.96$, Pinch: $r_{s}(14)=0.79$, Point:
$r_{s}(14)=0.73$; $p<.005$ for all modalities). Fig. 7c also shows that the
optimal speed for achieving minimal stroke–target distance for Controller,
Pen, Pinch, and Point is around $6cm/s$, $2cm/s$, $5cm/s$ and $2cm/s$
respectively.

###  4.3 Post–Study UX Evaluations

We analyzed the Likert–scale results of the questionnaire, and participants’
comments. We used median (MED) for analysis due to the ordinal nature of
Liker–scale data [64, 44] (Fig. 8). Thematic analysis was used to identify key
takeaways from qualitative responses.

Using Tool yields high–confidence with the drawings, however using the Pen
might introduce higher fatigue than using the Controller [SUB-1]

Most participants felt more confidence while using a Tool compared to using
Hand gestures (see Fig. 8a). Two participants pointed out how they were more
confident to use the Controller for balancing the speed–accuracy trade-off,
while they preferred the Pen for accuracy only: “For the controller, […] I can
go faster while maintaining reasonable accuracy. But for the pen […] it has a
tip, so I can mentally project the lines, even if the tip is small.” [P8].

Two participants reported that using the Pen would result in increased
fatigue, while no participants specifically pointed to it for the Controller.
Possible reasons includes the Pen’s heavy weight (e.g., “It’s a little bit
heavy in the back. I felt that I struggled to hold it up-right.” [P2]), its
bulky size (e.g., “[…] so thick that I cannot have a good grip.” [P9]), its
non-ergonomic gripping gestures (e.g., “[…] the positioning is a little bit
odd…like if this was a normal pen, I would have hold it closer to the back.”
[P2] ), and its instability, caused by the stroke triggering actions (e.g.,
“[…] pressing down [the drawing button] influenced my accuracy […]. I assume
it is because I am tapping against the pivot point.” [P8]).

Using Hand Input decreases fatigue, but the reason varies among Pinch and
Point [SUB-2] – Participants reported how they felt that “the hand type of
gestures would have the lowest fatigue [compared to the tools], because [of]
not holding anything” [P2]. While the median fatigue rating of Pinch is
slightly higher than Point ($4$ vs. $3.5$), three participants gave a Negative
rating for Pinch, while only one rated Point negatively. Possible reasons for
feeling increased fatigue while using both hand gestures include the needs of
mental attention for Pinch ( “[the pinching gesture] requires me to mentally
force to pinch, so this might cause slightly higher fatigue than pointing.”
[P2]) and the additional stretching of fingers for the Point gesture (“The
reason of increased fatigue with hand pointing is that I have to keep my
finger stretched.” [P10]).

Occlusions and poor hand tracking hinder confidence [SUB-3]
Confidence greatly decreased when participants were asked to use
Forward–Backward orientation, Large or Small curvature (see Fig. 8b, c). Most
likely, the awkward positioning of the geometric shapes of these tasks, caused
participants to not see the target traces in their entirety (e.g., “sketching
the smallest slope cases, it was really hard to distinguish the traces to make
the next move.” [P8]).

Four and two participants gave Negative confidence rating for the Pinch and
Point respectively, but not for any of the two Tool (Fig. 8a). Participants
explained this mostly in terms of the Hand tracking performance, that felt
less precise as compared to the Tool, causing less confidence while
controlling strokes for precise drawing (e.g., “I think hand tracking is
generally a big problem since [sometimes] the hand tracking is going crazy.
Whereas for the controller and pen, they were always tracked perfectly.” [P8],
“the tracking failures causing the disappearing of [the] virtual hands
[hindered] keep going with the previous gesture.” [P10]).

Medium curvature & slope yield best delineation experiences [SUB-4] – Despite
Large curvature generates higher precision (see [MN-4]), we observed that the
Medium curvature and slope typically obtain the highest number of Positive and
lowest number of Negative qualitative ratings (Fig. 8c, d). Participants
reported how Large slope and curvature require more attention and fine grained
control, which might cause fatigue and reductions of both drawing speed and
precision: “When the slope is large, I am deviating a lot and need more effort
and attention to control the stroke” [P8], “when [curvature] is large, you
cannot really make your movement fast enough.” [P2], and “[large curvature]
was harder to get it more precise.” [P11]. On the other hand, Small curvature
could lead to fatigue: “requires a lot of your arm movement, and it could be
more tiring.” [P2]), and could cause more occlusion [P8].

Interactions between curvature and orientation could affect the delineation
experience [SUB-5]– While we only consider the main effects, we found that
some participants felt that the interactions of curvature and orientations
also had important effects on the drawing experience. For instance, P8
commented: “for the forward-backward configuration, when [the tasks] are large
[i.e., small curvature], it was super easy. When they are small [i.e., large
curvature], I am not so sure.”, and: ‘for the left-right configurations, when
they are large [i.e., small curvature], it is super hard, but when they are
small [i.e., large curvature], it was pretty easy”.

##  5 Discussion and Design Recommendations

###  5.1 Pre–Session Design Recommendations

Pre–session indicates the strategies that are considered before each drawing
session, which could be summarized into two aspects:

VR Stylus is recommended for precision–first 3D drawing. We showed that using
Tool, in particular Pen, yields better overall drawing precision compared to
other approaches with highest frequent attempts for error correction. Although
bare hand drawing means not having to hold any physical objects, participants
felt less confident when performing precise–first drawings. primary because of
poor hand tracking performance (see [SUB-3]). Unlike Tool–based approaches,
whose positional tracking is achieved by measuring the time–of–flight of IR
pulses emitted by lighthouses, hand tracking is realized using machine
learning solutions [1, 36]. This resulted in a few inherent issues where
certain hand poses could not be well tracked, yet users needed them to perform
precision–first 3D drawing. This is most likely due to limited sample
diversity of the original training dataset. Although using bare hand is widely
advertised by vendors (e.g., [54]) as a better modality for 3D interactions
(see Sec. 2.1), we showed that using Hand gestures to perform precise 3D
drawings in today’s VR headsets is not as accurate as using a Controller.
Therefore, designers can benefit from utilizing a VR Pen for precise 3D
drawing, and allocating coarse–grained tasks (e.g., target selections) to
Hand.

Addressing occlusion could result in increased drawing precision. The source
of occlusions includes the occlusions by the drawing tasks itself and the
photo–realistic prefab of drawing tools. While entirely removing the photo-
realistic hand or tool visual images in VE might solve this issue, it might
reduce users’ proprioception, and ultimately could reduce the overall sense of
immersion [32, 33]. Instead, we believe that new interaction techniques can
extend current work that focus on, for example, moving the physical hand
position away from the stroke position (e.g., [57]) or optimize the
transparency of photo-realistic prefab similar to [14].

###  5.2 In-Session Design Recommendations

In-session recommendations refer to the design opportunities during the
drawing session. While geometry is usually unknown prior to the practical
drawing experience and requires designers to continuously adapt to the stroke
characteristic—which in turns breaks their workflow—we believe that our in-
session design recommendations promote feedback that could potentially
intervene in real-time and help participants decide on whether and how to
adjust their behaviors and transform the drawing canvas to obtain better
results.

Fatigue, drawing speed, stroke–shoulder distance, and hand tracking precision
should be assessed in real-time. While using the Pen yields higher precision
overall, this does not mean that the Pen can be blindly used in all drawing
scenarios. Ergonomically, we indicated how using the Pen might introduce
higher fatigue compared to using a Controller [SUB-1]. While a Pen could
support more precise 3D drawing, the use of thumb, index and middle fingers
seemed to reduce the overall drawing speed and induce more fatigue. In
contrast, the use of a Controller seems to be more beneficial for fast and
large movement (e.g., while drawing the Small curvature), compared to fine-
grained movements (e.g., while drawing the Large curvature). Although “control
and precision” have been advertised as the highlights for some commercially
available VR stylus [6], we implied that this might not apply for Small
curvature and Forward–Backward or Up–Down orientations. Second, our results
also showed the impacts from SSD and ASP (see Sec. 4.2). Although participants
were prompted to prioritize drawing precision, they tended to increase the
drawing speed when they felt confident, they perceived the current drawing
modality to be more convenient, and they experienced less fatigue ([SUB-1]).
This, however, might led to less precise drawings, even though
“precision–first” was used as the prompt throughout the study. Although
parameters such as the geometry of the drawing tasks are hard to predict and
control, being aware of and capable of regulating the stroke speed (ASP) and
stroke distance (SSD) might be helpful to improve precision. Therefore, we
recommend to integrate real–time visual feedback to regulate participants ASP,
SSD, and the time for resting to minimize the impacts of fatigue. This is
different from prior research that tried to use different forms of feedback
(e.g., visual anchors [13, 50]) for assisting participants “feel” the spatial
characteristic (e.g., the sense of depth). Finally, when it comes to hand, we
showed that occasional poor hand tracking might be one main reason for causing
low confidence [SUB-3]. While this is limited by today’s tracking technology,
we recommend to also integrate the visual feedback for real-time hand tracking
precision. Such visual prompts could encourage participants to in–situ adjust
their gestures to maintain high drawing performance while conducting
precision–first 3D drawing.

Real–time visual feedback could assist to find optimal scale and orientation
of the workspace. We indicated that the uses of Pen and Point gestures achieve
more accurate drawings in Left–Right orientations. This could be possibly due
to participants’ mental model of drawing on a 2D surface (similar to using
pen-and-paper), in which a stylus is usually held perpendicular to the drawing
surface [31]. However, when presented with orientations different from
Left–Right, participants needed to find other ways to perform precise drawing:
they changed the directions of Pen or Point by rotating their wrists, which
resulted in breaking the drawing workflow and might have caused discomfort,
reduced drawings’ quality [31], and increased cognitive and sensorimotor load
[66]. Additionally, while Large curvature resulted in higher precision, it
demanded finer control and prevented participants to draw fast. This possibly
contributed to participants considering Medium curvature as the optimal option
in terms of convenience and confidence in their subjective evaluations. While
we only consider curvature and slope as categorical variables with three
possibilities, these variables are continuous in practical 3D modelling
systems. While the geometry of the tasks is unknown prior to the drawing,
future system could analyze the directions and the velocity of the previously
drawn strokes, and used them to “guess” the direction of future strokes. A
real–time visual feedback containing guidance for optimal workspace
orientations and scale, could lead to better curvature and slope.

##  6 Limitations

We summarize our limitations into four main categories.

(1) Our participants showed above–average spatial abilities, which might
affect some results on overall abilities to make precise delineations. Future
studies can consider more participants with a more diverse spatial abilities
and VR experience.

(2) To minimize complexities, participants were only asked to report on main
interaction effect qualitatively during post–study evaluation. However, P8
found it difficult to provide rate on several questions, and mentioned the
needs for more dimensions. Future works might consider evaluating subjective
experience for interaction effects, and potentially include a post–study
workshop [68] that can facilitate sharing more thoughts and articulate
feelings more in–depth.

(3) While we intentionally included breaks into task design to mitigate
fatigue, and this has been acknowledged positively by some participants, other
participants extensively referred to fatigue during post–study UX evaluations.
It is not clear how much of the reported fatigue is due to the experiment
design and how much to the tasks themselves. Future studies might consider
objective and quantifiable measures of the level of fatigue throughout the
study [62].

(4) Our study used Oculus Quest $2$ [7] due to its affordability and
commercial availability, which leverage a deep learning based approach to
track hands. Besides human factors, the less accurate hand tracking
performance, compared to the tools, might also contribute to the low MOD
[MN-1]. While this is considered as part of our study, future work might also
consider the individual impacts of tracking accuracies caused by technology
imperfections.

(5) We considered the geometric characteristics in our study as categorical
variables with only three possibilities for each of the factors. However,
practical drawing characteristics are not categorical, but typically are
parameterized by numerical variables. Although we believe that the three
categories we chose are a good representation of the possible spectrum, future
works might decide to investigate and establish more precise mathematical
models between the specific numerical variables and the drawing performance
outcomes.

##  7 Conclusion

We demonstrated how geometric characteristics and input methods can affect
precision–first 3D drawing in VR. Through a within–subject study (n = $12$),
we found that using a VR Pen and Controller leads on average to $29.63$% more
precision compared to using Hand, and that the Pen yields $13.11$% higher
precision than the Controller. We showed how Large curvature, Forward–Backward
or Left–Right orientations allow participants to generate more precise
drawings. Together with participants’ user experience, we finally proposed
four recommendations for enhancing accuracy and experience of precision–first
3D drawing that could be integrated in future 3D immersive drawing tools.

## References

  * [1] Using Gestures with Hand Tracking on Oculus Quest 2 and Quest.  https://ai.facebook.com/blog/hand-tracking-deep-neural-networks, 2019.  Accessed on: 08-10-2022.
  * [2] Gravity Sketch.  https://www.gravitysketch.com, 2021.  Accessed on: 08-10-2022.
  * [3] HTC Vive Controller.  https://www.vive.com/us/accessory/controller/, 2021.  Accessed on 08-09-2022.
  * [4] HTC Vive Pro.  https://www.vive.com/us/product/vive-pro, 2021.  Accessed on: 08-09-2022.
  * [5] Introduing ‘Horizon Workrooms‘: Remote Collaboration Re-imagined.  https://www.oculus.com/blog/workrooms/, 2021.  Accessed on: 08-08-2022.
  * [6] Logitech VR Ink.  https://www.logitech.com/en-us/promo/vr-ink.html, 2021.  Accessed on: 08-09-2022.
  * [7] Oculus Quest 2.  https://www.oculus.com/quest-2, 2021.  Accessed on: 08-09-2022.
  * [8] Wacom VR Pen.  https://developer.wacom.com/en-us/wacomvrpen, 2021.  Accessed on: 08-09-2022.
  * [9] J. Accot and S. Zhai.  Beyond Fitts’ Law: Models for Trajectory-Based HCI Tasks.  In Proceedings of the ACM SIGCHI Conference on Human Factors in Computing Systems, CHI ’97, p. 295–302. Association for Computing Machinery, New York, NY, USA, 1997. doi: 10 . 1145/258549 . 258760
  * [10] J. Accot and S. Zhai.  Performance Evaluation of Input Devices in Trajectory-Based Tasks: An Application of the Steering Law.  In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, CHI ’99, p. 466–472. Association for Computing Machinery, New York, NY, USA, 1999. doi: 10 . 1145/302979 . 303133
  * [11] R. Aigner, D. Wigdor, H. Benko, M. Haller, D. Lindbauer, A. Ion, S. Zhao, and J. Koh.  Understanding Mid-Air Hand Gestures: A Study of Human Preferences in Usage of Gesture Types for HCI.  Microsoft Research TechReport MSR-TR-2012-111, 2:30, 2012.
  * [12] R. Arora, R. Habib Kazi, T. Grossman, G. Fitzmaurice, and K. Singh.  SymbiosisSketch: Combining 2D & 3D Sketching for Designing Detailed 3D Objects in Situ.  In Proceedings of the 2018 CHI Conference on Human Factors in Computing Systems, CHI ’18, p. 1–15. Association for Computing Machinery, New York, NY, USA, 2018. doi: 10 . 1145/3173574 . 3173759
  * [13] R. Arora, R. H. Kazi, F. Anderson, T. Grossman, K. Singh, and G. Fitzmaurice.  Experimental Evaluation of Sketching on Surfaces in VR.  In Proceedings of the 2017 CHI Conference on Human Factors in Computing Systems, CHI ’17, p. 5643–5654. Association for Computing Machinery, New York, NY, USA, 2017. doi: 10 . 1145/3025453 . 3025474
  * [14] J. Auda, R. Heger, U. Gruenefeld, and S. Schneegass.  VRSketch: Investigating 2D Sketching in Virtual Reality with Different Levels of Hand and Pen Transparency.  In IFIP Conference on Human-Computer Interaction, pp. 195–211. Springer, 2021.
  * [15] Autodesk.  Sketching a 3D Helical Coil, 2014.
  * [16] M. D. Barrera Machuca, W. Stuerzlinger, and P. Asente.  The Effect of Spatial Ability on Immersive 3D Drawing.  In Proceedings of the 2019 on Creativity and Cognition, C & C ’19, p. 173–186. Association for Computing Machinery, New York, NY, USA, 2019. doi: 10 . 1145/3325480 . 3325489
  * [17] A. U. Batmaz, A. K. Mutasim, and W. Stuerzlinger.  Precision vs. Power Grip: A Comparison of Pen Grip Styles for Selection in Virtual Reality.  In 2020 IEEE Conference on Virtual Reality and 3D User Interfaces Abstracts and Workshops (VRW), pp. 23–28, 2020. doi: 10 . 1109/vrw50115 . 2020 . 00012
  * [18] B. Bowers, A. Tuttle, A. Rukangu, A. Franzluebbers, C. Ball, and K. Johnsen.  Comparing Virtual Constraints and a Physical Stylus for Planar Writing and Drawing in Virtual Reality.  2021. doi: 10 . 1109/vrw52623 . 2021 . 00048
  * [19] D. A. Bowman and R. P. McMahan.  Virtual Reality: How Much Immersion is Enough? Computer, 40(7):36–43, 2007. doi: 10 . 1109/mc . 2007 . 257
  * [20] A. Cannavò, D. Calandra, A. Kehoe, and F. Lamberti.  Evaluating Consumer Interaction Interfaces for 3D Sketching in Virtual Reality.  In ArtsIT, pp. 291–306. Springer, 2021. doi: 10 . 1007/978-3-030-73426-8_17
  * [21] P. D. Charles, G. J. Esper, T. J. Davis, R. J. Maciunas, and D. Robertson.  Classification of Tremor and Update on Treatment.  American Family Physician, 59(6):1565, 1999.
  * [22] C. Chen, K. Sun, and X. Zhang.  ExGSense: Toward Facial Gesture Sensing with a Sparse Near-Eye Sensor Array.  In Proceedings of the 20th International Conference on Information Processing in Sensor Networks (Co-Located with CPS-IoT Week 2021), IPSN ’21, p. 222–237. Association for Computing Machinery, New York, NY, USA, 2021. doi: 10 . 1145/3412382 . 3458268
  * [23] C. Chen, M. Yarmand, V. Singh, M. V. Sherer, J. D. Murphy, Y. Zhang, and N. Weibel.  Exploring Needs and Design Opportunities for Virtual Reality-Based Contour Delineations of Medical Structures.  In Companion of the 2022 ACM SIGCHI Symposium on Engineering Interactive Computing Systems, EICS ’22 Companion, p. 19–25. Association for Computing Machinery, New York, NY, USA, 2022. doi: 10 . 1145/3531706 . 3536456
  * [24] C. Chen, M. Yarmand, V. Singh, M. V. Sherer, J. D. Murphy, Y. Zhang, and N. Weibel.  VRContour: Bringing Contour Delineations of Medical Structures Into Virtual Reality.  In 2022 IEEE International Symposium on Mixed and Augmented Reality (ISMAR), 2022.
  * [25] D. Cousineau.  Confidence Intervals in Within-subject Designs: A Simpler Solution to Loftus and Masson’s Method.  Tutorials in Quantitative Methods for Psychology, 1, 09 2005. doi: 10 . 20982/tqmp . 01 . 1 . p042
  * [26] F. M. Dekking, C. Kraaikamp, H. P. Lopuhaä, and L. E. Meester.  A Modern Introduction to Probability and Statistics: Understanding why and how.  Springer Science & Business Media, 2005.
  * [27] R. B. Ekstrom, J. W. French, H. H. Harman, and D. Dermen.  Kit of Factor-Referemced Cognitive Tests.  1976.
  * [28] L. A. Elkin, M. Kay, J. J. Higgins, and J. O. Wobbrock.  An aligned rank transform procedure for multifactor contrast tests, 2021.
  * [29] H. Elsayed, M. D. Barrera Machuca, C. Schaarschmidt, K. Marky, F. Müller, J. Riemann, A. Matviienko, M. Schmitz, M. Weigel, and M. Mühlhäuser.  VRSketchPen: Unconstrained Haptic Assistance for Sketching in Virtual 3D Environments.  In 26th ACM Symposium on Virtual Reality Software and Technology, VRST ’20. Association for Computing Machinery, New York, NY, USA, 2020. doi: 10 . 1145/3385956 . 3418953
  * [30] P. M. Fitts.  The Information Capacity of the Human Motor System in Controlling the Amplitude of Movement.  Journal of experimental psychology, 47(6):381, 1954.
  * [31] G. W. Fitzmaurice, R. Balakrishnan, G. Kurtenbach, and B. Buxton.  An Exploration into Supporting Artwork Orientation in the User Interface.  In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, CHI ’99, p. 167–174. Association for Computing Machinery, New York, NY, USA, 1999. doi: 10 . 1145/302979 . 303033
  * [32] S. Gallagher.  Philosophical Conceptions of the Self: Implications for Cognitive Science.  Trends in Cognitive Sciences, 4(1):14–21, 2000.
  * [33] M. Gonzalez-Franco and T. C. Peck.  Avatar Embodiment. Towards a Standardized Questionnaire.  Frontiers in Robotics and AI, 5:74, 2018.
  * [34] T. Grossman, R. Balakrishnan, G. Kurtenbach, G. Fitzmaurice, A. Khan, and B. Buxton.  Interaction Techniques for 3D Modeling on Large Displays.  In Proceedings of the 2001 Symposium on Interactive 3D Graphics, I3D ’01, p. 17–23. Association for Computing Machinery, New York, NY, USA, 2001. doi: 10 . 1145/364338 . 364341
  * [35] T. Grossman, R. Balakrishnan, G. Kurtenbach, G. Fitzmaurice, A. Khan, and B. Buxton.  Creating Principal 3D Curves with Digital Tape Drawing.  In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, CHI ’02, p. 121–128. Association for Computing Machinery, New York, NY, USA, 2002. doi: 10 . 1145/503376 . 503398
  * [36] S. Han, B. Liu, R. Cabezas, C. D. Twigg, P. Zhang, J. Petkau, T.-H. Yu, C.-J. Tai, M. Akbay, Z. Wang, A. Nitzan, G. Dong, Y. Ye, L. Tao, C. Wan, and R. Wang.  MEgATrack: Monochrome Egocentric Articulated Hand-Tracking for Virtual Reality.  ACM Trans. Graph., 39(4), jul 2020. doi: 10 . 1145/3386569 . 3392452
  * [37] R. Helps and C. Helps.  Measuring Stylus and Tablet Performance for Usability in Sketching.  In Proceedings of the 5th Annual Conference on Research in Information Technology, RIIT ’16, p. 19–24. Association for Computing Machinery, New York, NY, USA, 2016. doi: 10 . 1145/2978178 . 2978186
  * [38] E. L. Hutchins, J. D. Hollan, and D. A. Norman.  Direct Manipulation Interfaces.  Human–computer interaction, 1(4):311–338, 1985.
  * [39] P. Isokoski.  Model for Unistroke Writing Time.  In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, CHI ’01, p. 357–364. Association for Computing Machinery, New York, NY, USA, 2001. doi: 10 . 1145/365024 . 365299
  * [40] J. H. Israel, E. Wiese, M. Mateescu, C. Zöllner, and R. Stark.  Investigating Three-Dimensional Sketching for Early Conceptual Design—Results from Expert Discussions and User Studies.  Computers & Graphics, 33(4):462–473, 2009. doi: 10 . 1016/j . cag . 2009 . 05 . 005
  * [41] Y. Itaguchi and K. Fukuzawa.  Influence of Speed and Accuracy Constraints on Motor Learning for a Trajectory-Based Movement.  Journal of Motor Behavior, 50(6):653–663, 2018. doi: 10 . 1080/00222895 . 2017 . 1400946
  * [42] B. Jackson.  OVR Stylus: Designing Pen-Based 3D Input Devices for Virtual Reality.  In 2020 IEEE Conference on Virtual Reality and 3D User Interfaces Abstracts and Workshops (VRW), pp. 13–18, 2020. doi: 10 . 1109/vrw50115 . 2020 . 00287
  * [43] R. J. K. Jacob.  Human-Computer Interaction: Input Devices.  ACM Comput. Surv., 28(1):177–179, 3 1996. doi: 10 . 1145/234313 . 234387
  * [44] S. Jamieson.  Likert Scales: How to (ab)use them.  Medical Education, 38(12):1217–1218, 2004. doi: 10 . 1111/j . 1365-2929 . 2004 . 02012 . x
  * [45] Y. Jiang, C. Zhang, H. Fu, A. Cannavò, F. Lamberti, H. Y. K. Lau, and W. Wang.  HandPainter - 3D Sketching in VR with Hand-Based Physical Proxy.  In Proceedings of the 2021 CHI Conference on Human Factors in Computing Systems, CHI ’21. Association for Computing Machinery, New York, NY, USA, 2021. doi: 10 . 1145/3411764 . 3445302
  * [46] D. Keefe, R. Zeleznik, and D. Laidlaw.  Drawing on Air: Input Techniques for Controlled 3D Line Illustration.  IEEE Transactions on Visualization and Computer Graphics, 13(5):1067–1081, 2007. doi: 10 . 1109/TVCG . 2007 . 1060
  * [47] F. Kern, P. Kullmann, E. Ganal, K. Korwisi, R. Stingl, F. Niebling, and M. E. Latoschik.  Off-The-Shelf Stylus: Using XR Devices for Handwriting and Sketching on Physically Aligned Virtual Surfaces.  Frontiers in Virtual Reality, 2:69, 2021.
  * [48] N. Li, T. Han, F. Tian, J. Huang, M. Sun, P. Irani, and J. Alexander.  Get a Grip: Evaluating Grip Gestures for VR Input Using a Lightweight Pen.  In Proceedings of the 2020 CHI Conference on Human Factors in Computing Systems, CHI ’20, p. 1–13. Association for Computing Machinery, New York, NY, USA, 2020. doi: 10 . 1145/3313831 . 3376698
  * [49] M. D. B. Machuca, P. Asente, W. Stuerzlinger, J. Lu, and B. Kim.  Multiplanes: Assisted Freehand VR Sketching.  In Proceedings of the Symposium on Spatial User Interaction, SUI ’18, p. 36–47. Association for Computing Machinery, New York, NY, USA, 2018. doi: 10 . 1145/3267782 . 3267786
  * [50] M. D. B. Machuca, W. Stuerzlinger, and P. Asente.  Smart3DGuides: Making Unconstrained Immersive 3D Drawing More Accurate.  In 25th ACM Symposium on Virtual Reality Software and Technology, VRST ’19. Association for Computing Machinery, New York, NY, USA, 2019. doi: 10 . 1145/3359996 . 3364254
  * [51] S. Meyer, O. Cohen, and E. Nilsen.  Device Comparisons for Goal-Directed Drawing Tasks.  In Conference Companion on Human Factors in Computing Systems, CHI ’94, p. 251–252. Association for Computing Machinery, New York, NY, USA, 1994. doi: 10 . 1145/259963 . 260468
  * [52] Microsoft.  Hololens 2 Gestures for Authoring and Navigating in Dynamics 365 Guides, 2021.
  * [53] R. R. Mohanty, R. M. Castillo, E. D. Ragan, and V. R. Krishnamurthy.  Investigating Force-Feedback in Mid-Air Sketching of Multi-Planar Three-Dimensional Curve-Soups.  Journal of Computing and Information Science in Engineering, 20(1). doi: 10 . 1115/1 . 4045142
  * [54] Oculus.  Using Gestures with Hand Tracking on Oculus Quest 2 and Quest.  https://support.oculus.com/articles/headsets-and-accessories/controllers-and-hand-tracking/hand-tracking-gestures, 2019.  Accessed on: 08-10-2022.
  * [55] J. O’Rourke.  Center of Circle from 3 Edge Points.  https://www.ics.uci.edu/~eppstein/junkyard/circumcenter.html, 1993.
  * [56] N. Patel.  The Power of The Progress Bar, 2021.  Accessed on: 08-10-2022.
  * [57] K. Pfeuffer, J. Alexander, M. K. Chong, Y. Zhang, and H. Gellersen.  Gaze-Shifting: Direct-Indirect Input with Pen and Touch Modulated by Gaze.  In Proceedings of the 28th Annual ACM Symposium on User Interface Software & Technology, UIST ’15, p. 373–383. Association for Computing Machinery, New York, NY, USA, 2015. doi: 10 . 1145/2807442 . 2807460
  * [58] D.-M. Pham and W. Stuerzlinger.  Is the Pen Mightier than the Controller? A Comparison of Input Devices for Selection in Virtual and Augmented Reality.  In 25th ACM Symposium on Virtual Reality Software and Technology, VRST ’19. Association for Computing Machinery, New York, NY, USA, 2019. doi: 10 . 1145/3359996 . 3364264
  * [59] H. Romat, A. Fender, M. Meier, and C. Holz.  Flashpen: A High-Fidelity and High-Precision Multi-Surface Pen for Virtual Reality.  In 2021 IEEE Virtual Reality and 3D User Interfaces (VR), pp. 306–315, 2021. doi: 10 . 1109/VR50410 . 2021 . 00053
  * [60] S. Schkolne, M. Pruett, and P. Schröder.  Surface Drawing: Creating Organic 3D Shapes with the Hand and Tangible Tools.  In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, CHI ’01, p. 261–268. Association for Computing Machinery, New York, NY, USA, 2001. doi: 10 . 1145/365024 . 365114
  * [61] D. Schneider, V. Biener, A. Otte, T. Gesslein, P. Gagel, C. Campos, K. Č. Pucihar, M. Kljun, E. Ofek, M. Pahud, P. O. Kristensson, and J. Grubert.  Accuracy Evaluation of Touch Tasks in Commodity Virtual and Augmented Reality Head-Mounted Displays, 2021. doi: 10 . 48550/arxiv . 2109 . 10607
  * [62] P. Shamli Fathima, C. Sandhra, D. Jojo, A. V. Gayathri, N. Sidharth, and G. Venugopal.  Fatigue Analysis of Biceps Brachii Muscle Using sEMG Signal.  In S. K V and K. Rao, eds., Smart Sensors Measurements and Instrumentation, pp. 307–314. Springer Singapore, Singapore, 2021.
  * [63] B. Shneiderman, C. Plaisant, M. Cohen, S. Jacobs, N. Elmqvist, and N. Diakopoulos.  Designing the User Interface: Strategies for Effective Human-Computer Interaction.  Pearson, 6 ed., 2016.
  * [64] G. M. Sullivan and J. Artino, Anthony R. Analyzing and Interpreting Data From Likert-Type Scales.  5(4):541–542. doi: 10 . 4300/JGME-5-4-18
  * [65] P. Wacker, A. Wagner, S. Voelker, and J. Borchers.  Physical Guides: An Analysis of 3D Sketching Performance on Physical Objects in Augmented Reality.  In Proceedings of the Symposium on Spatial User Interaction, SUI ’18, p. 25–35. Association for Computing Machinery, New York, NY, USA, 2018. doi: 10 . 1145/3267782 . 3267788
  * [66] E. Wiese, J. H. Israel, A. Meyer, and S. Bongartz.  Investigating the Learnability of Immersive Free-Hand Sketching.  In Proceedings of the Seventh Sketch-Based Interfaces and Modeling Symposium, SBIM ’10, p. 135–142. Eurographics Association, Goslar, DEU, 2010.
  * [67] J. O. Wobbrock, L. Findlater, D. Gergle, and J. J. Higgins.  The Aligned Rank Transform for Nonparametric Factorial Analyses Using Only ANOVA Procedures.  In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, CHI ’11, p. 143–146. Association for Computing Machinery, New York, NY, USA, 2011. doi: 10 . 1145/1978942 . 1978963
  * [68] M. Yarmand, C. Chen, D. Gasques, J. D. Murphy, and N. Weibel.  Facilitating Remote Design Thinking Workshops in Healthcare: The Case of Contouring in Radiation Oncology.  In Extended Abstracts of the 2021 CHI Conference on Human Factors in Computing Systems, CHI EA ’21. Association for Computing Machinery, New York, NY, USA, 2021. doi: 10 . 1145/3411763 . 3443445
  * [69] M. Yarmand, M. Sherer, C. Chen, L. Hernandez, N. Weibel, and J. D. Murphy.  Evaluating Accuracy, Completion Time, and Usability of Everyday Touch Devices for Contouring.  International Journal of Radiation Oncology, Biology, Physics, 2022\.
  * [70] G. Young, H. Milne, D. Griffiths, E. Padfield, R. Blenkinsopp, and O. Georgiou.  Designing Mid-Air Haptic Gesture Controlled User Interfaces for Cars.  Proc. ACM Hum.-Comput. Interact., 4(EICS), jun 2020. doi: 10 . 1145/3397869

##  Appendix A Additional Modeling and Data

###  A.1 Modelling of the Task Traces

Mathematically, a helical curve $\textbf{c}(t;r,a)$ can be described
parametrically by equation (3), where curvature ($k$) is independent to $t$
and decided by radius ($r$) (see equation 4) and slope ($s$) (see equation 5).

${\bf c}(t;r,a)=[rcos(t),rsin(t),at]$ (3)

$k=\frac{\left\|{\bf\hat{c}}^{\prime\prime}(t)\right\|}{\left\|{\bf
c}^{\prime}(t)\right\|}=\frac{r}{r^{2}+a^{2}}$ (4)

$s=\frac{a}{r}$ (5)

Figure A1: Illustrative diagram of mathematical modelling of the calibration
results.

By transforming (5), and putting into (4), we can generate (6) and (7).

$k=\frac{r}{r^{2}+s^{2}r^{2}}=\frac{1}{(1+s^{2})r}$ (6)

$r=\frac{1}{(1+s^{2})k}$ (7)

Finally, we can get (8) by considering (7) and (5).

$a=sr=\frac{s}{(1+s^{2})k}$ (8)

Plugging (7) and (8) into (3), we are able derive the mathematical modelling,
depending on $k$ and $s$ for generating task with predefined parameters.

${\bf
c}(t;k,s)=[\frac{cos(t)}{(1+s^{2})k},\frac{sin(t)}{(1+s^{2})k},\frac{st}{(1+s^{2})k}]$
(9)

After this, the generated sample points would then be transformed (i.e.,
shifted and rotated) based on the calibration results at the beginning of each
study session. The calibration process would compute and approximate the
shoulder positions from $3$ controller locations while being placed in the
position of forward, up and right. Assuming the sample points at the positions
of front, up and right are $A$, $B$, and $C$, we can compute the position of
the circumcenter ($K_{pos}$) and normal direction ($K_{dir}$) of the triangle
$\Delta ABC$ (see Fig. 12) [55].

$\begin{split}K_{pos}=A&+\frac{||C-A||^{2}[(B-A)\times(C-A)]\times(B-A)}{2||(B-A)\times(C-A)||^{2}}\\\
&+\frac{||B-A||^{2}[(C-A)\times(B-A)]\times(C-A)}{2||(B-A)\times(C-A)||^{2}}\end{split}$
(10)

$K_{dir}=\overrightarrow{BA}\times\overrightarrow{CA}~{}$ (11)

Assuming $P$ is the position of the headset in world coordinate, we can then
approximate the shoulder position ($S$) by finding the closest point on line
$K_{pos}+tK_{dir}$ ($t\in\mathbb{R}$) (see (12)).

$S=K_{pos}+\frac{K_{pos}+K_{dir}}{||K_{pos}+K_{dir}||}\frac{\overrightarrow{K_{pos}P}\cdot(K_{pos}+K_{dir})}{||K_{pos}+K_{dir}||}$
(12)

###  A.2 RM–ANOVA Significance Test Results for Main and Interaction Effects

The full results of RM-ANOVA computations can be seen in Fig. A2. In Sec. 4,
the post-hoc contrast tests were conducted only if the main or interaction
effects are statistical significance ($p<.05$).

Figure A2: Results of repeated measure ANOVA.

###  A.3 Results without aggregated analysis

In Sec. 4.1, we analyze the main and interaction effects of $4$ within–subject
factors. In this note, we listed out the $3$ measures of each of $108$ trials,
by averaging the results collected on each of $12$ participants. The results
are listed in Fig. A3.

Figure A3: MOD, NLM and MSP of each of $108$ trials, averaged across $12$
participants. The green leftright arrows at bottom legend indicate the target
performance preference.

###  A.4 Dataset

To encourage future research, we have made our dataset publicly available111An
interactive web–based visualizer of our dataset can be accessed here:
https://precision-first-vr.github.io.. Although the focus of this work lies on
the analysis of spatial and temporal features of the drawn traces, we also
record participants participant’s drawing behaviors. This unlocks future
investigations for analyzing precision–first 3D drawing from the perspective
of participants’ drawing behaviors. Example key research questions include:
how do participants explore and observe during precision–first 3D drawing? and
how do participants hold the tools? etc. This is one–step beyond the current
method of analysis that only focuses on the temporal and spatial features of
what participant drew. To realize this, besides timestamp and sample world
coordinates of participants’ drawn strokes, we also recorded the transform222A
transform in the world space is represented by the position vector and three
Euler angles indicating rotation. of tools (i.e., VR Pen and Controller) or
hand, as well as camera in the world space, which indicates how participants
looked at target of interest.