# RibbonSculpt: Voronoi Ball based 3D Sculpting from Sparse VR Ribbons

Anandhu Sureshkumar, Amal Dev Parakkat, Georges-Pierre Bonneau, Stefanie Hahmann, Marie-Paule Cani

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Anandhu Sureshkumar, Amal Dev Parakkat, Georges-Pierre Bonneau, Stefanie Hahmann, Marie-Paule Cani. RibbonSculpt: Voronoi Ball based 3D Sculpting from Sparse VR Ribbons. Siggraph Asia 2025 - 18th ACM SIGGRAPH Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia, Dec 2025, Hong-Kong, China. pp.1-11. hal-05330313

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# RibbonSculpt: Voronoi Ball based 3D Sculpting from Sparse VR Ribbons

ANANDHU SURESHKUMAR, LTCI-Telecom Paris, Institut Polytechnique de Paris, France

AMAL DEV PARAKKAT, LTCI-Telecom Paris, Institut Polytechnique de Paris, France

GEORGES-PIERRE BONNEAU, Univ. Grenoble Alpes, CNRS, INRIA, Grenoble INP, LJK, France

STEFANIE HAHMANN, Univ. Grenoble Alpes, CNRS, INRIA, Grenoble INP, LJK, France

MARIE-PAULE CANI, LIX-Ecole Polytechnique/CNRS, Institut Polytechnique de Paris, France

<figure><img src="image_2.png" /><figcaption>Fig. 1. An interactive modeling session with RibbonSculpt, where the user draws sparse oriented ribbons in VR to define the surface of a 3D shape, and gets immediate visual feedback (top). Key to our computations, but hidden from the user, the volume between the ribbons is identified in real-time by filtering the Voronoi balls defined from the ribbons (bottom). The final model (right) is watertight and can be 3D-printed.</figcaption></figure>

We introduce RibbonSculpt, the first method for interactive freeform shape design in VR through progressive sketching of sparse, oriented ribbons. Instead of reconstructing a surface from a fully drawn VR sketch, our method allows the real-time creation and progressive refinement of a closed surface of any topological genus, thanks to the continuous update of a volumetric proxy. The latter corresponds to a filtered subset of the Voronoi balls defined by the user-sketched ribbons. At each visualization step, a mesh extracted from the proxy is beautified through Laplacian-based energy minimization, yielding a smooth surface that interpolates the ribbons. Guided by this surface, users can easily refine their design by adding or removing ribbons, which sculpts, in return, the set of Voronoi balls forming the proxy. Our results, supported by user studies, show that RibbonSculpt allows VR users to easily and quickly draft the 3D shapes they have in mind.

Additional Key Words and Phrases: 3D sketching, Sketch-based modeling, Virtual reality, Surface modeling, Surface reconstruction

Authors' Contact Information: Anandhu Sureshkumar, anandhu.sureshkumar@telecom-paris.fr, LTCI-Telecom Paris, Institut Polytechnique de Paris, France; Amal Dev Parakkat, amal.parakkat@telecom-paris.fr, LTCI-Telecom Paris, Institut Polytechnique de Paris, France; Georges-Pierre Bonneau, georges-pierre.bonneau@inria.fr, Univ. Grenoble Alpes, CNRS, INRIA, Grenoble INP, LJK, France; Stefanie Hahmann, stefanie.hahmann@inria.fr, Univ. Grenoble Alpes, CNRS, INRIA, Grenoble INP, LJK, France; Marie-Paule Cani, marie-paule.cani@polytechnique.edu, LIX-Ecole Polytechnique/CNRS, Institut Polytechnique de Paris, France.

## 1 Introduction

With the democratization of immersive environments, virtual reality (VR) is currently revolutionizing the field of 3D modeling, as it allows for interactions of unprecedented intuitiveness. Indeed, while traditional 3D modeling techniques require the learning of complex 2D interfaces, which may limit creativity due to cognitive overload, virtual reality-based systems enable direct object creation and manipulation in their native 3D environment. By enabling gestural inputs, natural hand movements, and spatial awareness, VR provides an organic and intuitive modeling experience, as shown by the recent success of VR sketching systems [7, 62].

In contrast, VR-based interactive modeling remains largely underexplored when 3D shapes are concerned. Existing studies have introduced different modeling tools to create manifold surfaces in 3D, each tailored to specific objectives. For example, Surface-Brush [52], a state-of-the-art technique, creates 3D surfaces from VR ribbons but requires a dense arrangement of these ribbons to generate complex shapes. Subsequent research has explored alternatives: this includes control rod deformation [56], which limits the achievable geometries; proxy surface deformation towards a set of input ribbons, often resulting in slow performance and requiring an initial proxy; and methods to minimize the number of ribbons, often coming at the cost of increased computational complexity. No easy-to-use method has yet been proposed for the interactive
<figure><img src="image_3.png" /><figcaption>Fig. 2. Comparison of several VR modeling systems in terms of input (top, showing either ribbons or curves), results (second line) and surfacing time.</figcaption></figure>

modeling and progressive refinement in VR of arbitrary 3D shapes
of any topological genus.

Two critical aspects of 3D modeling are computational efficiency and minimal input requirements. First, a system that responds in real time enables users to correct and refine the resulting 3D surfaces, improving the quality and increasing user satisfaction. Second, minimizing the inputs, e.g. only requiring a few ribbons instead of entire surface patches, decreases the modeling effort - making it an enjoyable process rather than a time-consuming, complex task. As it accelerates the modeling process, minimal input also facilitates design exploration. However, to the best of our knowledge, no existing technique simultaneously addresses both efficiency and sparsity of the input (see Figure 2).

We introduce RibbonSculpt, an interactive framework that en-
ables users to effortlessly sculpt the 3D shapes they have in mind
by sketching a sparse set of oriented ribbons. Creating 3D surfaces
from sparse inputs is an extremely challenging problem in surface
reconstruction, in general, [8, 38]. To address this, RibbonSculpt
relies on a set of Voronoi balls extracted from the ribbons to define
a proxy volume, which, although transparent to the user, defines
an abstract volume enclosed by the ribbon strokes and serves as
a reference for generating a surface to be displayed. As the user
provides additional input by either adding or erasing ribbons, both
the proxy and the surface are progressively refined. Our choice
of a Voronoi-based proxy brings two key benefits: First, it can be
efficiently generated through a simple ball filtering process, which
only requires a single pass over the Voronoi structure formed by the
ribbons. Second, the Voronoi balls inherently capture volumetric
information, enabling them to represent a 3D shape despite the
sparsity of the input.

RibbonSculpt offers multiple advantages. First, we provide users
with continuous visual guidance through the displayed 3D shape,
as opposed to previous VR sketching tools, where only strokes are
interactively displayed. This enables users to progressively refine
their design, as in interactive sculpting systems, until the current
model corresponds to their mental image of the desired shape. Sec-
ond, the custom energy function we optimize ensures that while
interpolating the ribbons, the displayed surface is smooth and aes-
thetically pleasing, minimizing the impact of imperfections in the
input ribbons. In addition, the proxy, and therefore the displayed
surface, inherently captures the volume a viewer would imagine
from the sketch. Therefore, refining the design by adding a new

ribbon feels natural, as confirmed by our user study. Lastly, the good match between user intent and displayed shape also reduces the user's tendency to draw too many ribbons, which would not only increase modeling and computational times, but could also affect the shape's smoothness due to the lack of precision of VR input. Therefore, complex 3D models are easily modeled, using remarkably sparse input.

In summary, our core contribution is a novel framework for inter-
active 3D sculpting in VR, by progressively sketching a sparse set
of ribbons. We introduce a novel Voronoi ball filtering criterion for
computing and updating in real-time a proxy shape, and propose
a constrained surface fairing criterion to smooth it before display,
based on local curvature. As user studies show, our robust and re-
sponsive framework provides interactive visualizations that closely
match user expectations, despite the inherent ambiguity and irregu-
larity of the input, therefore significantly improving the VR-based
modeling experience.

2 Related Work

## 2.1 Surface Reconstruction from point clouds

Modeling a 3D shape from 3D user strokes, sketched in VR, can be in-
terpreted as the problem of generating a surface from the very sparse
point cloud defined by points sampled along the strokes, eventually
provided with normal vectors if the user sketched oriented ribbons.
Surface reconstruction from point clouds is a classical but ill-posed
problem in geometry processing, with techniques spanning from
early computational geometry approaches such as α-shapes [24], to
modern learning-based solutions [45] (we refer the reader to [33]
for a full, recent survey).

Geometry-based techniques relied on Delaunay triangulation [22, 23], implicit function fitting [17, 29, 37, 38], Voronoi structures [6, 47], or greedy/incremental strategies [9, 21] to infer the underlying unknown surface from a set of points, with [29] or without [5] normal information. In the spirit of PowerCrust [6], another line of research aims at estimating medial axis points directly from point clouds and uses them to reconstruct the desired surface [15, 31]. As medial axis computation itself is a challenging task, recent approaches rely on learning-based techniques [41] to efficiently and robustly estimate the medial axis. Although widely adopted for dense point-cloud reconstruction due to their theoretical foundations and practical effectiveness, these approaches struggle with noisy, sparse input and often require postprocessing to ensure surface smoothness or watertightness.

Recently, learning-based techniques introduced neural represen-
tations that implicitly encode the surface geometry [25], further
improved by rendering-driven techniques [40, 44]. Despite these
advances, surface reconstruction from sparse inputs remains a sig-
nificant challenge, with only very specifically designed techniques
– such as VIPSS [32] – being able to handle it, albeit at the cost of
high computational time, making them unsuitable as a real-time
visualisation tool during a sculpting process.

In this work, we take inspiration from the most recent, geometry-
based approaches by using Voronoi balls to define a coarse, proxy
volume within the user-sketched ribbons.
## 2.2 Surfacing VR strokes

With the recent spread of VR input devices [1-4], enabling to interactively draw sets of 3D curves forming a sketch (see [13] for a recent survey), several methods specifically tackled the challenging problem of generating free-form surfaces from such sketches. Finding the intended geometry and topology from a sparse set of 3D strokes being a difficult and ambiguous task, methods such as [2, 28, 34, 57] either relied on carefully drawn patch boundaries, arranged curve networks to fit non-overlapping surface patches, or performed an automatic snapping of free-drawn sketches [61] to get a tractable input. In contrast to ours, these techniques, however, require users to conceptualize the intended surface as a set of connected patches, increasing the cognitive and practical burden and making it challenging for novice users. Other solutions addressed the surface generation challenge by requesting the input of closely arranged ribbons [52, 53], making the design quite time-consuming and smoothness difficult to achieve due to the limited precision of VR input. A last category of methods made use of predefined proxy shapes fitted to the user's strokes, either limited to simple proxy geometries (planes, spheres) [12], or general but requesting a non-real-time computation of a proxy shape [60]. In addition, learning-based techniques showed promising results in generating 3D shapes from a sketch, but remain restricted to specific categories of objects due to training datasets [11, 19, 42, 49], and did not address the exact interpolation of user-sketched 3D strokes.

Closer to our goals, the VRSurf method [55] tackled the problem of generating a closed manifold surface surrounding a well-defined 3D volume while interpolating a sparse set of non-connected VR strokes. Although the balloon inflation metaphor looked promising, the authors report several minutes to several tenths of minutes to generate the 3D shape, which prevents its use to give interactive visual feedback during a modeling session.

Another closely related area of research is the surfacing of connected curve networks, where the objective is to construct surface patches bounded by closed curve cycles. Works in this direction employed different strategies such as flow-field alignment [46], energy minimization and interpolation [10], and often make use of cycles with [54] and without [63] explicit normals to do coherent surface reconstruction. While these methods can generate smooth and well-aligned surfaces from curve networks, they are generally limited to connected curve networks, which may restrict artistic flexibility and lack the ability to interpret loosely drawn 3D sketches, which is the specific focus of our work.

## 2.3 VR sculpting with Interactive visual feedback

Since the introduction of VR through pioneer immersive systems such as the cave, the idea of enabling interactive shape design through a series of sculpting gestures - with immediate visual feedback, was achieved in two different ways: Using volumetric painting tools to create a shape [26, 39], or using sketched strokes to deform an existing 3D mesh [48, 56]. Both were with real-time visual feedback for the user, which is key for enabling the progressive design and refinement of a 3D shape.

In this work, we assess the importance of providing immediate visual feedback to the user during an interactive modeling session.

Our work, however, differs from volumetric sculpting by interpreting the user's strokes as curves belonging to the intended surface, rather than some centerline evenly surrounded by volumetric material. Therefore, RibbonSculpt provides a design interface closer to 2D sketching and requires much fewer user strokes than volumetric sculpting to create a complex shape. Moreover, in contrast with stroke-based deformation tools, we don't require the input of any preexisting shape, but enable the user to interactively create from scratch any shape or arbitrary geometry and topological genus they have in mind.

## 3 Overview

In contrast to previous work, we address interactive 3D shape sculpting in VR based on user-sketched, oriented 3D strokes, displayed as ribbons. The main challenge we tackle is inferring a closed surface, computed at interactive rates, that matches the user's expectations given the current sparse set of ribbons. In the remainder of this section, we first outline the context in which our sculpting system, called RibbonSculpt, operates. We then justify the need for computing a proxy volume at each editing stage, and finally describe the algorithmic pipeline.

### 3.1 The RibbonSculpt framework

Our sculpting method was specifically designed for immersive virtual reality environments. Our current setup makes use of an HTC Vive head-mounted display and two 6DoF handheld controllers for spatial interaction. The modeling system itself is a simple custom framework developed with Unity, inspired by [59]. Targeting novice users, it offers simple and intuitive controls allowing users to draw/erase ribbons, select colors and ribbon widths, hide/display ribbon and proxy surfaces, and flip ribbon normals as needed. To provide immediate visual feedback on the 3D shape at any stage of the modeling process, a smooth mesh extracted from a volumetric proxy shape is recomputed and displayed after each user edit.

Our interface uses ribbon-based strokes for 3D sketching, a technique commonly used in many VR-based drawing systems. Ribbons are particularly effective for helping users perceive the shape induced by a sparse set of unstructured strokes and also provide normal information that our system uses for computing proxy shapes. Each ribbon stroke is uniquely defined by a 3D path, ruling length and the normal direction at each point along the path. While the path can be directly captured by tracking the tip of the controller and the length is user-specified, computing normals is ambiguous [51]. The simplest approach is to use the controller's local coordinate frame, but requires users to rotate the controller to match the desired normal - often forcing them to perform uncomfortable, if not bio-mechanically impossible, wrist movements. A solution is to employ a flexible mapping constrained by optimality criteria for computing normals [51]. In our case, the user only uses short, disconnected ribbon strokes that resemble brushstrokes to sculpt the 3D shape. Their simplicity allows for the simple adaptive mapping to compute normals and rulings described next.

Ribbons are represented as quad strips where the transverse edges of prescribed length are the rulings centered at the path traced by the VR controller. From regularly sampled path positions, we first
<figure><img src="image_4.png" /><figcaption>Fig. 3. Computational pipeline at each user edit. Left to Right: Current ribbon set (a), filtered Voronoi balls forming a proxy volume (b), meshed proxy using the implicit blending of the balls (c), uniform remeshing (d), smooth surface fitting the input strokes, after Laplacian energy minimization (e), visual feedback for user guidance (f).</figcaption></figure>

compute, at each point $p \in R^3$, a unit trajectory tangent vector $\vec{T}$ by fitting a low-degree polynomial curve to the neighboring points. We then impose the ruling $\vec{R}$ to be orthogonal to the tangent $\vec{T}$ in the (tangent) plane spanned by $(\vec{R}_c, \vec{T})$ as follows:

$$ \vec{R} = (\vec{T} \times \vec{R}_c) \times \vec{T}, \quad \vec{N} = \vec{T} \times \vec{R}, $$

where $\vec{R}_c$ is the unit direction of the thin cylinder (in green) represented at the controller's tip (see inset). $\vec{N}$ is the unit normal vector of the ribbon forming the local orthogonal frame $[\vec{T}, \vec{R}, \vec{N}]$. The two sides of the ribbons are displayed in different colors, allowing the user to reverse the normal if necessary. It is worth noting that though we employed this simple solution, our system is agnostic to how the ribbons are derived. Also, automatically deriving normals [58] would have been a viable alternative if interactive feedback were not a priority.

## 3.2 Processing pipeline

The system is designed to operate in real time, generating and adapting surface geometry dynamically as the user sketches or removes ribbons. Surface construction and display begin as soon as the user has drawn the first two ribbons, and the surface is updated at interactive rates after each user edit until the end of the design session, see Fig. 1. At each design stage, the input data points $\mathcal{P} = \{p_1, p_2, ..., p_m\}$ and the associated normal vectors $n_{p_i}$ are processed in two main steps:

(1) Computing a proxy volume that roughly approximates the shape, see Fig. 3(b).

(2) Extracting from it a smooth surface to be displayed, see Fig. 3(e).

We address these challenges with the following key insights:

**Proxy volume:** Inspired by the successful use of Voronoi diagrams in surface reconstruction from point clouds [6, 8, 47], we note that 1) Voronoi diagrams lend themselves to efficient, simple and parallel calculation, and 2) as point density increases, a conveniently selected subset of the Voronoi balls may capture increasingly well the intended surface. Therefore, RibbonSculpt filters out a specific subset of the Voronoi balls to form a proxy volume, using a dedicated algorithm detailed in Section 4.

**Sculpted surface:** Observing that the filtered Voronoi balls form a blobby volume (Fig. 3(b)), we blend them into an implicit surface (Fig. 3(c)) from which a triangular mesh is extracted (Fig. 3(d)). To get rid of the undesirable bumps while forcing the mesh to interpolate the input ribbons, we apply a specific constrained fairing process to

the mesh, as described in Section 5, yielding the smooth surface to be displayed (Fig. 3(e,f)).

# 4 Proxy Shape Computation

## 4.1 Notion of proxy volume and design requirements

Since the 3D shapes to be modeled are volumetric, approximating them at each design stage by a volume roughly delimited by the ribbons is an intuitive, mandatory stage before computing a surface to be displayed. To achieve this, three crucial criteria must be maintained:

* The proxy volume's geometry should approximate the perceived space between ribbons;

* Its topological genus should match the intended one;

* Speed: the proxy must be both initialized and updated in real-time when ribbons are added or removed to support the interactive surface computation, giving visual feedback to the user.

Matching these three criteria at once is challenging. Indeed, as shown in Section 2, the existing algorithms for generating the perceptually expected 3D shape from a set of ribbons tend to involve complex calculations - even given priors of the topological genus - making them difficult to implement and slow to compute. In addition to efficiency and general applicability, our solution must also allow refining the proxy into the surface to be displayed, which is mandatory as a guide during the interactive modeling session.

We therefore introduce a new lightweight model for the proxy, imposing no restriction on the shape's topology and able to accommodate newly drawn ribbons at interactive rates. To solve this, we release the usual constraint on the proxy's smoothness, taking advantage of the fact that it is to remain transparent to the user.

## 4.2 Voronoi-ball-based solution

Our algorithm is built on Voronoi balls, inspired by their proven efficiency in surface reconstruction from point clouds. Formally, given a set of points $S \subset R^{d=3}$, a Voronoi ball $B(\text{center } c, \text{radius } r)$ is defined as a maximal closed ball satisfying two conditions:

* **Emptiness:** $B(c, r) \cap S = \emptyset$ - the ball contains no points from $S$

* **Maximality:** There exists no $B(c', r')$ such that $B(c', r') \cap S = \emptyset$ and $B(c, r) \subseteq B(c', r')$ - no larger empty ball contains $B(c, r)$.

Intuitively, the centers of these Voronoi balls, called Voronoi vertices, are at equal distance from $(d = 3) + 1$ points in $S$, the ball's radius being equal to this distance. Thanks to efficient recent algorithms, the Voronoi diagram of a million points can be computed in seconds [16, 50]. In addition, this computation can be done incrementally
<figure><img src="image_5.png" /><figcaption>Fig. 4. 2D illustration of our algorithm. Left to Right: Progressively adding user-drawn strokes, corresponding retained (green) and removed (purple) Voronoi circles, and the final proxy shape as the union of all retained circles. Circles for which at least one input normal (black) point inward are removed.</figcaption></figure>

when new data points are added. For our use case of dynamically updated sparse ribbons, the typical number of sample points ranges in thousands. Their Voronoi diagram and its dynamic update can therefore be computed negligibly fast, satisfying already the third requirement of speed from Sect. 4.1.

The key of our method is to select a subset of the Voronoi balls and use their union as the proxy volume. As the union of all the Voronoi balls fills the entire 3D space, we are looking for a way to retain only those that contribute to the volume within the sparse set of ribbons. To achieve this, we start by making a rough cut, removing all balls whose centers are outside the convex hull of the input curves. In addition, we introduce a local filtering criterion based on the normals of the user-drawn ribbons so that the proxy matches the intended shape, thus satisfying our first requirement, see Sect. 4.1. As shown in the inset, let $n_p$ be the normal of the ribbon point $p$, and $n_c$ be the normal of the Voronoi ball $B$ touching $p$. We retain $B$ if $n_p \cdot n_c > 0$ for all samples associated with $B$. Thanks to this simple filtering condition, each Voronoi ball is visited only once, thereby enabling real-time computation. The key point allowing this real-time filtering is the availability of normals in the input data thanks to the VR controller (see Section 3.1). More complex approaches such as [6] are not needed here.

<figure><img src="image_6.png" /></figure>

Figure 4 shows a 2D illustration of our method using a user-oriented 2D sketch instead of 3D VR ribbons. As demonstrated, as we add more points, the filtered Voronoi circles (2D analogue of Voronoi balls), shown in green, progressively capture the desired shape. At the end of this filtering process, the proxy volume, formally defined as the union of retained Voronoi balls, is not yet materialized as a visual clue for the user. This proxy, however, constitutes an excellent support for computing a smooth, closed surface at interactive rates, as described next.

## 5 Sculpted Surface Extraction

The union of balls in the proxy shape computed in Section 4 resembles a rough sculpture of the intended surface, obtained by carving out all matter outside the filtered Voronoi balls. It assembles the ribbons into a volume of arbitrary topological genus, with protruding spherical regions of various diameters filling the gaps between strokes. While this solves the challenging problem of constructing a rough shape from the ribbons, the results are bumpy, especially

when the input strokes are very sparse - demanding additional fairing.

The first task is therefore to combine individual spheres in the proxy volume to create a single surface mesh. While a simple solution would be to use a smooth implicit formulation as a sum of Gaussian blobs, it involves multiple parameters and often ends up in undesired blending between shape parts that should remain disconnected. To avoid these drawbacks, we define an implicit surface directly as the union of balls, using a min of field functions:

$$ \{x | f(x) = 0\}, \quad \text{where } f(x) = \min_{\text{filtered } B(c_i, r_i)} ||x - c_i|| - r_i. \quad (1) $$

We then extract a mesh from this implicit function using the Marching Cube (MC) algorithm, followed by a uniform re-meshing procedure [14]. While we experimented using Dual Contouring [36], we found the combination of MC and re-meshing to give better results. Please note that the min function above could have been replaced by a softmin, and that although we used a default parameter value for the MC and re-meshing, these can be easily tuned to get the desired level of precision.

The next step is to smooth the resulting mesh $M = (V, E, F)$ to get rid of its bumpiness. Inspired by [12] we combine smoothing with soft-constraint interpolation of the ribbon points, as follows: First, we project the ribbon points $P$ onto $M$. For each ribbon point $p$ in $P$, we denote $v(p) = \alpha v_i + \beta v_j + \gamma v_k$ its closest point in $M$, where $v_i, v_j, v_k$ are the three vertices in $V$ of the face in $F$ containing $v(p)$ and $\alpha, \beta, \gamma$ are its barycentric coordinates, $\alpha + \beta + \gamma = 1$. We then minimize the following objective function:

$$ \arg\min_{V \in (R^3)^n} \sum_{i=1}^{n} ||\Delta_S v_i||^2 + \omega \sum_{l=1}^{m} ||p_l - v(p_l)||^2, \quad (2) $$

where $n$ is the number of mesh vertices, $\Delta_S v_i$ is the discrete Laplace-Beltrami operator for triangle meshes with cotangent weights [43], and $\omega$ is a scalar parameter that allows trading off smoothness (low value of $\omega$) against interpolation (high value of $\omega$). We use a default value of $\omega = 1$ in all our examples.

The Laplacian-based smoothing process polishes the protruding part of the filtered Voronoi balls while matching the intended surface, due to the soft interpolation constraints, as can be seen in Fig. 1.

## 6 3D Sculpting User Study

To evaluate the usability and performance of our VR-based sculpting tool, we conducted a user study with 10 participants. The study aimed at assessing how users interact with the system, how effectively they can model predefined shapes, and how creatively they can express their own ideas using the tool.
<figure><img src="image_7.png" /><figcaption>Fig. 5. Ribbons drawn by different users along with the outputs of RibbonSculpt. As can be seen, users followed their own imagination using arbitrary sketching styles, and our method could faithfully reconstruct the desired shape from all those variants. Note that most of these users were inexperienced in using VR or doing modeling itself.</figcaption></figure>

The participant group included both **expert users** with prior experience in 3D modeling tools such as Blender or Maya, and **novice users** with little to no experience in 3D content creation.

## 6.1 Procedure

The study began with a brief instructional video introducing the functionalities of the VR tool. The video explained the use of VR controllers, the drawing workflow involving ribbons, and the importance of ribbon orientation. After the video, participants were given approximately 1–2 minutes to familiarize themselves with the interface and test the basic functionalities.

Following this introduction, participants were then asked to model three familiar shapes: a Sphere, a Cube, and a Torus (or a doughnut, for those who did not know the term). These shapes were chosen due to their recognizability and varied geometric and topological characteristics (either smooth or sharp features, different topological genus). Each modeling task took around 3-5 minutes per shape for the first-time users despite the difficulties in mid-air drawings and inexperience in using a VR headset. And for an experienced user, it took only a few seconds to model these basic shapes. A few drawings and the models generated during the user study are shown in Figure 5 (note that the sparse sampling of the ribbons sometimes resulted in bumps on the surface). As can be noticed, each of them followed their own imagination and style to draw these simple shapes. RibbonSculpt, irrespective of these styles, could faithfully reconstruct the desired shape, allowing expressive freedom.

## 6.2 Observations

During the task, we observed clear differences between novice and expert users:

* **Novice users** faced challenges in handling the VR controller, particularly due to the cross-product-based ribbon orientation,

<figure><img src="image_8.png" /><figcaption>Fig. 6. Free-form models created by our users during the study. Note that all these are made by users using VR for the first time.</figcaption></figure>

which requires spatial understanding and precise hand movements. They also required more time and added more ribbons in pursuit of shape refinement.

* **Expert users**, on the other hand, appreciated the real-time feedback and interactive nature of the system. However, they expressed a desire for more advanced features commonly available in traditional 3D modeling tools, such as:

- Independent transformation of ribbons,

- Ability to erase specific parts of a ribbon,

- Manual correction of ribbon normals.

All users were asked to save their model once they were satisfied with the result. Some participants spent extra time refining their shapes, highlighting the challenge and skill required for precise free-form drawing in VR.

## 6.3 Creative Exploration

As an optional final task, users were encouraged to create a shape of their own choosing. This was intended to evaluate the tool's support for open-ended creativity. Participants produced a variety of models, including a *duck*, *car*, *flower*, *hammer*, and an *Eiffel Tower*, see Fig. 6. These creative explorations demonstrated the expressive potential of the tool despite its current limitations.

## 6.4 Survey and Feedback

At the end of the session, participants completed a two-part survey:
* **Part 1:** A subset of questions from the *Creative Support Index (CSI)* questionnaire [20], focusing on five key dimensions: Enjoyment, Exploration, Expressiveness, Immersion, and Effort vs. Results.

* **Part 2:** Custom questions to evaluate specific aspects of our system, such as ease of modeling, clarity of ribbon feedback, performance, and usefulness of intermediate and final shape previews.

The survey results were used to generate a color-coded Likert-scale visualization for each question across dimensions, which provided valuable insights into user satisfaction and areas for future improvement, see Fig. 7.

<figure><img src="image_9.png" /><figcaption>Fig. 7. Results of our user study. CSI Survey (left), custom survey (right).</figcaption></figure>

# 7 Results & Discussion

Figure 8 shows various models using the RibbonSculpt interface in VR by an expert user in under 4 minutes, inspired by various publicly available models on SketchFab. RibbonSculpt easily creates diverse shapes with few strokes, thanks to interactive visual feedback that guides users to place ribbons only where needed. The complexity of the generated models spans from simple ones like the double torus to intricate ones like the gargoyle. Despite the simple interface, the user was able to draw intricate details such as the small holes on the monkey statue, delicate structures like the crown's arch, flat shapes like a dolphin's tail, and spiky forms like an elephant's tusks.

All these examples show that our system robustly handles very sparse, shaky and disordered input strokes. In addition, we generated results on publicly available 3D sketches featuring smooth, connected curve networks from FlowRep [27] and

densely drawn ribbons from SurfaceBrush [52], as shown in Figures 9 and 10, to demonstrate the generality of our method across common 3D sketch categories.

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 9. Results with FlowRep inputs. Each quadruple shows, respectively, the input sketch, the ground truth mesh, our reconstructed result, and the error.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 10. Results with SurfaceBrush inputs. Each triple shows, respectively, the input sketch, mesh created by SurfaceBrush, and our reconstructed result.</figcaption></figure>

Defining a proxy volume as a collection of loosely arranged spheres not only fills the space between strokes, but also adapts easily to topological changes, enabling high-genus modeling by glueing parts or shaping holes—as shown in the inset with just three strokes.

We also investigated how sparsifying the number of ribbon strokes affects our reconstruction. In this experiment, we arbitrarily selected subsets containing 90% to 10% of the total ribbon strokes required by SurfaceBrush and applied our reconstruction; the results are shown in Figure 11. As demonstrated by the error plot (third row), even with only 10% of the ribbons, RibbonSculpt consistently produced high-quality reconstructions.

**Influence of modeling parameters.** The performance of our method is mainly influenced by two parameters:

* **The voxel grid size:** Used in the marching cube algorithm for meshing the proxy volume, and plays an important role in deciding the topology of the reconstructed surface. As the BB of the model grows progressively during sculpting, we ensure a constant voxel size during sculpting by voxelizing a virtual maximal box transparent to the user.

* **The remeshing parameter:** The mesh extracted with Marching Cubes is uniformly remeshed using a target edge length as a parameter, which controls the mesh resolution and directly affects computation time since it determines the number of variables in the surface fitting step (Fig. 12).

In order to guarantee at the same time, the correct capture of all shape details (ears, legs, etc.), an interactive frame rate for visual feedback to the user, we choose by default a grid size of 128³ voxels and a surface edge length of 5% of the bounding box diagonal, these can be easily tuned.

**Implementation.** The system is running on Windows with an Intel Xeon E5-1650 v4 CPU and 64 GB RAM, handling computational geometry tasks The GPU, NVIDIA RTX 2080 Ti (11 GB) for real-time rendering in Unity. We used two CGAL routines [18], triangulation-3 and isotropic-remeshing, and libigl [35] for marching cubes. Equation (2) leads to a linear system that we solve efficiently with the Iterative least-squares conjugate gradient solver from the Eigen library [30]. The number of iterations can be significantly reduced with a good initial guess. In our case, a perfect initial guess is the implicit surface of the Voronoi balls, as it is close to the final smooth
<figure><img src="image_13.png" /><figcaption>Fig. 8. Various results generated using the RibbonSculpt interface. Each triple shows the input VR sketch, the resulting mesh, and the mesh superimposed with ribbons. Each model was drawn with 50 to 150 ribbon strokes, totalling 1K to 4K points.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 11. Experimentation on progressively sparsifying dense ribbons. First row (left to right): input sketches with ribbon density decreasing from 100% to 10% (done by randomly picking a subset of ribbons). The input data furthest to the left comes from [52]. The second row shows the reconstructed meshes, and the third row shows the reconstruction errors, using the reconstruction from 100% ribbons as the ground truth.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 12. Mesh size: edge-length 20%, 10%, 5%, 2% of bounding box diagonal based on 128 voxel grid size.</figcaption></figure>

progressively grow, calculation times increase with the number of ribbons drawn. Therefore, we show how runtimes evolve over an entire sketching session, offering more insight than focusing solely on the final, most expensive shape. We illustrate these graphs using two representative models: dolphin (65 strokes with 2566 points, 3503 final mesh vertices) and fox (69 strokes with 3075 points, 1224 final mesh vertices).

surface. Prior remeshing with well-shaped triangles makes it partic-
ularly appropriate.

*Statistics & runtimes.* Figure 14 gives an overview of the execution time of our method. Since the set of input points and model size
<figure><img src="image_16.png" /><figcaption>Fig. 13. Comparison of our results with related works. Left to right: Input ribbons, results of PowerCrust [6], BPA [9], RBF [17], ScreenedPoisson [38], ScreenedPoisson [38] after Laplacian smoothing, VIPSS [32] and RibbonSculpt (ours).</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Fig. 14. Runtimes. run times are plotted as a function of the number of ribbon strokes (voxel grid size 128, remesh parameter 5%).</figcaption></figure>

Following the legend in Fig. 14, the total computing time comprises five parts: *proxy* computes the Voronoi balls, *grid* the implicit function, *MC* marching cubes, *uniform remesh*, and *smoothing surface fitting*. While the implicit function computation and *MC* are almost constant over the course of a sculpting session, the proxy volume and remeshing times increase with time. Surface fitting, which consists of the iterative resolution of a linear system, increases at first and is then fairly constant. The curves are not smooth because all steps are based on the bumpy proxy volume or proxy mesh, even the linear system solving uses the remeshed bumpy surface as the

initial guess. Indeed, many big spheres imply more surface variations. We can see that the total execution time during the sketch varies for the dolphin from 0.20s to 0.35s, and for the fox from 0.07s to 0.23s. Although these runtimes are technically not considered interactive frame rates when working with a mouse on a computer, in our context, however, when working with a VR controller in a 3D space, they are perceived as interactive. Indeed, when the user stops drawing, she/he prepare to draw the next stroke elsewhere in 3D space by moving around the model or rotating it. These interactions with a human-sized model in VR are so time-consuming that displaying the calculated shape in less than 0.3 seconds is perceived as immediate, as also pointed out by the user study, see Fig. 7.

*Comparisons.* Figure 13 shows the comparison between the results generated by our method and five state-of-the-art algorithms - PowerCrust, BPA, RBF, ScreenedPoisson, VIPSS. We have not made a comparison with the recent work of [55] as the computation cost is very high, see Figure 2 and Section 2.1. We included comparisons with two surface reconstruction algorithms, PowerCrust [6] and BPA [9]. However, they are not particularly designed for sparse point clouds (see [52]) and as can be seen consistently gave suboptimal
results. In contrast, RBF [17] led to unexpected shrinkage or expansion of surfaces, and sometimes blended nearby features. Screened Poisson [38], thanks to the normal information provided along with the input points, could reconstruct the overall shape. However, it resulted in rough surface artefacts (capsicum and mushroom), unnecessary holes (front leg of the camel), and struggled if the input ribbons are too sparse (the doughnut shape), which is especially the case when users start drawing. Though applying a smoothing on the resulting mesh can improve the roughness of the surface, the other issues remain the same. VIPSS [32], on the other hand, struggled with its custom normal recomputation (capsicum and camel) and sparse inputs (front legs of the fox). Additionally, VIPSS involves highly complex and time-consuming computations. Fig. 13 also shows the reconstruction time taken by different algorithms. As can be seen, all the methods are slower than the RibbonSculpt, making them less suitable for interactive use (the focus of our paper). While PowerCrust shows a relatively comparable run time, the resulting surfaces are of lower quality. And although the results of Screened Poisson+smoothing are often visually comparable, RibbonSculpt is at least three times faster.

**Limitations & Future Work.** While RibbonSculpt offers a simple system with interactive feedback for quick 3D modeling in VR, there are a few areas that could benefit from further enhancements. First, RibbonSculpt relies on Marching Cubes to mesh the proxy volumes and hence depends on the voxel grid size. A grid that is too coarse can lead to numerical issues, whereas increasing the resolution makes it challenging to use in an interactive application like ours without GPU acceleration. The current system, designed for abstract modeling, could be improved to capture finer details by incorporating adaptive Marching Cubes. Although our interface provides an option to flip incorrectly oriented normals, the system expects the normals to be nearly orthogonal to the intended surface. Our current smoothing step is specifically designed for smooth and organic shapes, which means RibbonSculpt cannot be used for creating sharp features. Finally, RibbonSculpt cannot create a surface from a simple, single ribbon. However, in practice, users could immediately understand this issue during the sculpting process and naturally add more strokes near places where the expected surface is missing.

Furthermore, while the users can currently create and erase ribbons, being able to deform them could be investigated as a complementary way to adjust the model to the intended shape. To achieve this, we could envision interactions enabling users to select a local part to deform and pull it with a VR gesture, e.g. using a simple physically-based deformation. The visual response of our system would still be real-time.

## 8 Conclusion

Unlike the natural experience of drawing curves and oriented ribbons in VR, 3D shape design lacks an easy way to continuously compute and display a shape from gesture-based input. RibbonSculpt addresses this challenge through a two-stage process, continuously repeated at each stage of a design session. First, we rely on an easy-to-compute proxy volume that captures the inherent

volume embedded into the user-drawn ribbons. Second, we refine this coarse proxy to provide, at interactive rates, a smooth surface that still interpolates the user-designed ribbons. This enables the visual output to better match what the user had in mind, which greatly eases the VR design experience.

## Acknowledgments

The authors thank all anonymous reviewers for their constructive feedback. The work is partially funded by the ANR JCJC project SketchMAD (ANR-23-CE33-0009) and generous support from Adobe.

## References

[1] 2016. Tilt Brush by Google. https://www.tiltbrush.com.

[2] 2017. GravitySketch. https://www gravitysketch.com/.

[3] 2019. Oculus Medium. https://www.oculus.com/experiences/rift/1336762299669605/.

[4] 2019. SculptrVR. https://www.sculptrvr.com/.

[5] Pierre Alliez, David Cohen-Steiner, Yiying Tong, and Mathieu Desbrun. 2007. Voronoi-based variational reconstruction of unoriented point sets. In *Symposium on Geometry processing*, Vol. 7. 39–48.

[6] Nina Amenta, Sunghee Choi, and Ravi Krishna Kolluri. 2001. The power crust. In *Proceedings of the Sixth ACM Symposium on Solid Modeling and Applications (SMA '01)*. ACM, 249–266.

[7] Rahul Arora and Karan Singh. 2021. Mid-air drawing of curves on 3d surfaces in virtual reality. *ACM Transactions on Graphics* (TOG) 40, 3 (2021), 1–17.

[8] Matthew Berger, Andrea Tagliasacchi, Lee M. Seversky, Pierre Alliez, Gaël Guennebaud, Joshua A. Levine, Andrei Sharf, and Claudio T. Silva. 2017. A Survey of Surface Reconstruction from Point Clouds. *Computer Graphics Forum* 36, 1 (2017), 301–329.

[9] Fausto Bernardini, Joshua Mittleman, Holly Rushmeier, Cláudio Silva, and Gabriel Taubin. 1999. The ball-pivoting algorithm for surface reconstruction. *IEEE Transactions on visualization and computer graphics* 5, 4 (1999), 349–359.

[10] Mikhail Bessmeltsev, Caoyu Wang, Alla Sheffer, and Karan Singh. 2012. Design-driven quadrangulation of closed 3D curves. *ACM Trans. Graph.* 31, 6 (2012).

[11] Sukanya Bhattacharjee and Parag Chaudhuri. 2022. Deep Interactive Surface Creation from 3D Sketch Strokes. In *International Joint Conference on Artificial Intelligence*.

[12] Georges-Pierre Bonneau and Stefanie Hahmann. 2024. 3D sketching in immersive environments: Shape from disordered ribbon strokes. *Computers and Graphics* 123 (Oct. 2024).

[13] Alexandra Bonnici and Kenneth P. Camilleri (Eds.). 2023. *Interactive Sketch-based Interfaces and Modelling for Design*. River Publishers, Series in Document Engineering.

[14] Mario Botsch and Leif Kobbelt. 2004. A remeshing approach to multiresolution modeling. In *Symposium on Geometry Processing*, Roberto Scopigno and Denis Zorin (Eds.). The Eurographics Association.

[15] Junjie Cao, Andrea Tagliasacchi, Matt Olson, Hao Zhang, and Zhinxun Su. 2010. Point cloud skeletons via laplacian based contraction. In *2010 Shape Modeling International Conference*. IEEE, 187–197.

[16] Laurent Caraffa, Pooran Memari, Murat Yirci, and Mathieu Brédif. 2019. Tile & merge: Distributed delaunay triangulations for cloud computing. In *2019 IEEE International Conference on Big Data (Big Data)*. IEEE, 1613–1618.

[17] Jonathan C Carr, Richard K Beatson, Jon B Cherrie, Tim J Mitchell, W Richard Fright, Bruce C McCallum, and Tim R Evans. 2001. Reconstruction and representation of 3D objects with radial basis functions. In *Proceedings of the 28th annual conference on Computer graphics and interactive techniques*. 67–76.

[18] CGAL Library. 2025. *CGAL, Computational Geometry Algorithms Library*. CGAL Editorial Board. https://www.cgal.org.

[19] Tianrun Chen, Chaotao Ding, Shangzhan Zhang, Chunan Yu, Ying Zang, Zejian Li, Sida Peng, and Lingyun Sun. 2024. Rapid 3D Model Generation with Intuitive 3D Input. In *2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)*. 12554–12564.

[20] Erin Cherry and Celine Latulipe. 2014. Quantifying the creativity support of digital tools through the creativity support index. *ACM Transactions on Computer-Human Interaction (TOCHI)* 21, 4 (2014), 1–25.

[21] David Cohen-Steiner and Frank Da. 2004. A greedy Delaunay-based surface reconstruction algorithm. *The visual computer* 20, 1 (2004), 4–16.

[22] Tamal K Dey and Joachim Giesen. 2001. Detecting undersampling in surface reconstruction. In *Proceedings of the seventeenth annual symposium on Computational geometry*. 257–263.

[23] Tamal K. Dey and Samrat Goswami. 2003. Tight cocone: a water-tight surface reconstructor. In *Proceedings of the Eighth ACM Symposium on Solid Modeling and*
Applications (SMA'03). 127-134.

[24] Herbert Edelsbunner and Ernst P Mücke. 1994. Three-dimensional alpha shapes. *ACM Transactions On Graphics* (TOG) 13, 1 (1994), 43–72.

[25] Anis Farshian, Markus Götz, Gabriele Cavallaro, Charlotte Debus, Matthias Nießner, Jón Atli Benediktsson, and Achim Streit. 2023. Deep-learning-based 3d surface reconstruction—a survey. *Proc. IEEE* 111, 11 (2023), 1464–1501.

[26] Eric Ferley, Marie-Paule Cani, and Jean-Dominique Gascuel. 2002. Resolution Adaptive Volume Sculpting. *Graphical Models* 63 (March 2002). Special Issue on Volume Modelling.

[27] Giorgio Gori, Alla Sheffer, Nicholas Vining, Enrique Rosales, Nathan Carr, and Tao Ju. 2017. FlowRep: descriptive curve networks for free-form design shapes. *ACM Trans. Graph*. 36, 4, Article 59 (2017).

[28] Cindy Grimm and Pushkar Joshi. 2012. Just DrawIt: a 3D sketching system. In *Proceedings of the International Symposium on Sketch-Based Interfaces and Modeling* (Annecy, France) (SBIM '12). Eurographics Association, 121–130.

[29] Gaël Guennebaud and Markus Gross. 2007. Algebraic point set surfaces. In *ACM siggraph 2007 papers*.

[30] Gaël Guennebaud, Benoît Jacob, et al. 2010. Eigen v3. http://eigen.tuxfamily.org.

[31] Hui Huang, Shihao Wu, Daniel Cohen-Or, Minglun Gong, Hao Zhang, Guiqing Li, and Baoquan Chen. 2013. L1-medial skeleton of point cloud. *ACM Trans. Graph*. 32, 4 (2013).

[32] Zhiyang Huang, Nathan Carr, and Tao Ju. 2019. Variational implicit point set surfaces. *ACM Transactions on Graphics* (TOG) 38, 4 (2019), 1–13.

[33] Zhangjin Huang, Yuxin Wen, Zihao Wang, Jinjuan Ren, and Kui Jia. 2024. Surface reconstruction from point clouds: A survey and a benchmark. *IEEE transactions on pattern analysis and machine intelligence* (2024).

[34] Bret Jackson and Daniel F. Keefe. 2016. Lift-Off: Using Reference Imagery and Freehand Sketching to Create 3D Models in VR. *IEEE Transactions on Visualization and Computer Graphics* 22, 4 (2016), 1442–1451.

[35] Alec Jacobson, Daniele Panozzo, et al. 2023. libigl: A simple C++ geometry processing library. *ACM Transactions on Graphics* (TOG) 42, 4 (2023), 1–7.

[36] Tao Ju, Frank Losasso, Scott Schaefer, and Joe Warren. 2002. Dual contouring of hermite data. *ACM Trans. Graph*. 21, 3 (2002), 339–346.

[37] Michael Kazhdan, Matthew Bolitho, and Hugues Hoppe. 2006. Poisson surface reconstruction. In *Proceedings of the Fourth Eurographics Symposium on Geometry Processing* (SGP '06). Eurographics Association, 61–70.

[38] Michael Kazhdan and Hugues Hoppe. 2013. Screened poisson surface reconstruction. *ACM Transactions on Graphics* (ToG) 32, 3 (2013), 1–13.

[39] Daniel F. Keefe, Daniel Acevedo Feliz, Tomer Moscovich, David H. Laidlaw, and Joseph J. LaViola. 2001. CavePainting: a fully immersive 3D artistic medium and interactive experience. In *Symposium on Interactive 3D Graphics (13D'01)*. 85–93.

[40] Bernhard Kerbl, Georgios Kopanas, Thomas Leimkühler, and George Drettakis. 2023. 3d gaussian splatting for real-time radiance field rendering. *ACM Trans. Graph*. 42, 4 (2023).

[41] Cheng Lin, Changjian Li, Yuan Liu, Nenglun Chen, Yi-King Choi, and Wenping Wang. 2021. Point2skeleton: Learning skeletal representations from point clouds. In *Proceedings of the IEEE/CVF conference on computer vision and pattern recognition*. 4277–4286.

[42] Ling Luo, Pinaki Nath Chowdhury, Tao Xiang, Yi-Zhe Song, and Yulia Gryadskaya. 2023. 3d vr sketch guided 3d shape prototyping and exploration. In *Proceedings of the IEEE/CVF International Conference on Computer Vision*. 9267–9276.

[43] Mark Meyer, Mathieu Desbrun, Peter Schröder, and Alan H. Barr. 2003. Discrete Differential-Geometry Operators for Triangulated 2-Manifolds. In *Visualization and Mathematics III*, Hans-Christian Hege and Konrad Polthier (Eds.). Springer Berlin Heidelberg, 35–57.

[44] Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng. 2021. Nerf: Representing scenes as neural radiance fields for view synthesis. *Commun. ACM* 65, 1 (2021), 99–106.

[45] Amine Ouasfi and Adnane Boukhayma. 2024. Unsupervised Occupancy Learning from Sparse Point Cloud. In *Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)*. 21729–21739.

[46] Hao Pan, Yang Liu, Alla Sheffer, Nicholas Vining, Chang-Jian Li, and Wenping Wang. 2015. Flow aligned surfacing of curve networks. *ACM Transactions on Graphics* (TOG) 34, 4 (2015), 1–10.

[47] Amal Dev Parakkat, Stefan Ohrhallinger, Elmar Eisemann, and Pooran Memari. 2024. BallMerge: High-quality Fast Surface Reconstruction via Voronoi Balls. *Computer Graphics Forum* 43, 2 (2024).

[48] Helen Perkunder, Johann Habakuk Israel, and Marc Alexa. 2010. Shape modeling with sketched feature lines in immersive 3D environments. In *Proceedings of the Seventh Sketch-Based Interfaces and Modeling Symposium (SBIM '10)*. Eurographics Association, 127–134.

[49] S. Rasoulzadeh, M. Wimmer, P. Stauss, and I. Kovacic. 2024. Strokes2Surface: Recovering Curve Networks From 4D Architectural Design Sketches. *Computer Graphics Forum* 43, 2 (2024).

[50] Nicolas Ray, Dmitry Sokolov, Sylvain Lefebvre, and Bruno Lévy. 2018. Meshless Voronoi on the GPU. *ACM Transactions on Graphics* (TOG) 37, 6 (2018), 1–12.

[51] Enrique Rosales, Chrystiano Araújo, Jafet Rodriguez, Nicholas Vining, Dongwook Yoon, and Alla Sheffer. 2021. AdaptiBrush: adaptive general and predictable VR ribbon brush. *ACM Trans. Graph*. 40, 6, Article 247 (2021).

[52] Enrique Rosales, Jafet Rodriguez, and Alla Sheffer. 2019. SurfaceBrush: from virtual reality drawings to manifold surfaces. *ACM Trans. Graph*. 38, 4, Article 96 (2019).

[53] Steven Schkolne, Michael Pruett, and Peter Schröder. 2001. 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)*. ACM, 261–268.

[54] Tibor Stanko, Stefanie Hahmann, Georges-Pierre Bonneau, and Nathalie Saguin-Sprynski. 2016. Surfacing curve networks with normal control. *Computers & Graphics* 60 (2016), 1–8.

[55] Anandhu Sureshkumar, Amal Dev Parakkat, Georges-Pierre Bonneau, Stefanie Hahmann, and Marie-Paule Cani. 2025. VRSurf: Surface Creation from Sparse, Un-oriented 3D Strokes. In *Computer Graphics Forum*. Wiley Online Library, e70071.

[56] Floor Verhoeven and Olga Sorkine-Hornung. 2019. RodMesh: Two-handed 3D Surface Modeling in Virtual Reality. In *Vision, Modeling and Visualization*, Hans-Jörg Schulz, Matthias Teschner, and Michael Wimmer (Eds.). The Eurographics Association.

[57] Gerold Wesche and Hans-Peter Seidel. 2001. FreeDrawer: a free-form sketching system on the responsive workbench. In *Proceedings of the ACM Symposium on Virtual Reality Software and Technology (VRST '01)*. 167–174.

[58] Rui Xu, Zhiyang Dou, Ningna Wang, Shiqing Xin, Shuangmin Chen, Mingyan Jiang, Xiaohu Guo, Wenping Wang, and Changhe Tu. 2023. Globally consistent normal orientation for point clouds by regularizing the winding-number field. *ACM Transactions on Graphics* (TOG) 42, 4 (2023), 1–15.

[59] Emilie Yu. 2022. CASSIE sketching application code. https://gitlab.inria.fr/D3/cassie.

[60] Emilie Yu, Rahul Arora, J. Andreas Barentzen, Karan Singh, and Adrien Bousseau. 2022. Piecewise-smooth surface fitting onto unstructured 3D sketches. *ACM Trans. Graph*. 41, 4, Article 88 (Jul 2022).

[61] Emilie Yu, Rahul Arora, Tibor Stanko, J. Andreas Barentzen, Karan Singh, and Adrien Bousseau. 2021. CASSIE: Curve and Surface Sketching in Immersive Environments. In *Proceedings of the 2021 CHI Conference on Human Factors in Computing Systems (CHI'21)*. Article 190.

[62] Xue Yu, Stephen DiVerdi, Akshay Sharma, and Yotam Gingold. 2021. Scaffolds-ketch: Accurate industrial design drawing in vr. In *The 34th Annual ACM Symposium on User Interface Software and Technology*. 372–384.

[63] Yixin Zhuang, Ming Zou, Nathan Carr, and Tao Ju. 2013. A general and efficient method for finding cycles in 3D curve networks. *ACM Transactions on Graphics* (TOG) 32, 6 (2013), 1–10.