# Driller: An Intuitive Interface for Designing Tangled and Nested Shapes

Tara Butler, Pascal Guehl, Amal Dev Parakkat, Marie-Paule Cani

► To cite this version:

Tara Butler, Pascal Guehl, Amal Dev Parakkat, Marie-Paule Cani. Driller: An Intuitive Interface for Designing Tangled and Nested Shapes. 45th Eurographics 2024 - Short Papers, CYENS Centre of Excellence in collaboration with the University of Cyprus and the Cyprus University of Technology, Apr 2024, Limassol, Cyprus. 10.2312/egs.20241025. hal-04824957

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Distributed under a Creative Commons Attribution 4.0 International License
# Driller: An intuitive interface for designing tangled and nested shapes

Tara Butler¹ ID, Pascal Guehl¹ ID, Amal Dev Parakkat² ID, Marie-Paule Cani¹ ID

¹ LIX - Ecole Polytechnique/CNRS, ² LTCI - Telecom Paris
Institut Polytechnique de Paris, France

<figure><img src="image_2.png" /><figcaption>**Figure 1:** Design steps for a tree model using sketch-based modeling extended with our Driller interface. All 3D shapes are initially created in the same drawing plane (left). Users can select a viewpoint (marked in black) and trigger the Driller interface (middle) to locally arrange elements, such as the depth ordering of branches and lianas (right - along with the modified arrangement in the Driller interface).</figcaption></figure>

## Abstract

The ability to represent not only isolated shapes but also shapes that interact is essential in various fields, from design to biology or anatomy. In this paper, we propose an intuitive interface to control and edit complex shape arrangements. Using a set of pre-defined shapes that may intersect, our "Driller" interface allows users to trigger their local deformation so that they rest on each other, become tangled, or even nest within each other. Driller provides an intuitive way to specify the relative depth of different shapes beneath user-selected points of interest by setting their local depth ordering perpendicularly to the camera's viewpoint. Deformations are then automatically generated by locally propagating these ordering constraints. In addition to being part of the final arrangement, some of the shapes can be used as deformers, which can be later deleted to help sculpt the target shapes. We implemented this solution within a sketch-based modeling system designed for novice users.

## CCS Concepts

* **Human-centered computing** → *Graphical user interfaces*; *Computing methodologies* → *Shape modeling*;

## 1. Introduction

While intuitive modeling systems have made significant progress in enabling novice users to create 3D shapes, modeling arrangements of closely related shapes remains challenging as geometric modeling systems typically concentrate on creating individual shapes. Despite organic shapes often exhibiting interferences through contact, as seen in natural phenomena such as plant growth, cellular arrangements, and vascular systems, modeling such intricate shapes proves particularly challenging. Motivated by applications such as the creation of 3D illustrations in biology and medicine, we introduce a solution to ease the creation, exploration, and manipulation of 3D shape arrangements. The user creates and positions a set of individual shapes, which may initially intersect. We then provide an interface called the "Driller," inspired by geology, which enables users to intuitively define the way shapes locally interact. This in-

terface is associated with a deformation mechanism that allows one shape to be deformed relative to another, seen as a support canvas, in order to meet the specified constraints. Our contributions are implemented within a sketch-based modeling system that relies on skeleton-based implicit surfaces [BPCB08, ZBQC13], enabling us to make use of isosurfaces of scalar fields to solve the problem. In addition to easing the creation of shape arrangements, the resulting system enables users to sculpt the targeted shapes, thanks to extra support canvases serving as shape deformers. In our investigation of organic shapes, we assume that the objects in question possess a natural smoothness, which is expected to be maintained throughout any editing process. While we can handle simple cases of tangled and nested shape arrangements intuitively, more complex and elaborated objects need to be further investigated in the future.

<footnote>© 2024 The Authors.
Proceedings published by Eurographics - The European Association for Computer Graphics.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.</footnote>
## 2. Related work

**Layering techniques in 2D and 3D shape design:** As-rigid-as-possible [IMH05] presents an approach that continuously updates depth values for deformable 2D objects to ensure proper stacking orders. In contrast, Local layering [MP09] offers a solution for handling complex 2D layering scenarios involving multiple objects and allowing users to change layer orders locally. These techniques have been extended to 3D modeling, as discussed in Apparent layer operations [IM10], where similar principles apply to the manipulation of 3D objects. Additionally, Soft stacking [MP12] introduces a continuous layer ordering approach, resembling volumes of fog, enabling layers to appear both in front of and behind others within the same pixel. Unlike prior methods limited to specific domains like 3D cloth and rope arrangements [IM10], we extend the layering operations to more generic organic 3D shapes.

**Deformers, canvases and nested shapes:** Inspired by anatomical drawing, Sketch-based modeling of vascular systems [PCP10] focuses on creating 3D models of branching vessels from a single sketch with future plans to explore sketching onto support surfaces. In OverCoat [SSGS11], an implicitly defined 3D scalar field representing the canvas concept is used, offering a unified painting and sculpting metaphor for canvas fine-tuning. In contrast, our method approaches this challenge differently by using the isosurface of another shape to deform and infer depth levels. In Skippy [KYC*17], 2D strokes align with a 3D object's surface to create a 3D model, but unlike our method, they require viewpoint adjustments to create complex 3D arrangements. Other papers focusing on creating nested structures are SecondSkin [DPS15], which automates the creation of layered 3D structures from sketches by interpreting stroke geometry, and Generalized Matryoshka [Jac17] that introduces a method to find the largest scale replica of an object that nests inside itself. However, these methods work directly in a 3D environment, making it difficult to create complex, tangled, and nested structures.

## 3. Inspiring from geology to specify shape arrangements

Our interactive sketch-based modeling system, based on Matisse [BPCB08] and SCALIS [ZBQC13], iteratively takes 2D painted regions as input sketches and generates 3D implicit surfaces. Each surface represents the 0.5 isosurface of a volumetric scalar field created

from a flat skeleton—a graph of polylines approximating the medial axis of the painted region. Initially, the input shapes have flat silhouettes and require deformation to become intertwined. Drawing inspiration from the way geologists study soil and rock layers by digging perpendicularly to the surface to generate core samples (as shown in the inset), we introduce the "Driller" interface to enable users to specify shape interaction constraints through intuitive 1D drag-and-drop operations. Our interface allows users to click on any point of the screen to display the equivalent of a "core sample," computed along a ray from the camera viewpoint, and edit the arrangement of shape layers at that point, thus avoiding

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 2:** Examples demonstrating Layering (Top) and Nesting (Bottom) along with corresponding Driller interfaces. User selects camera viewpoints (star mark) to locally arrange elements.</figcaption></figure>

the need for complex 3D navigation/manipulation. The screen widget representing the core sample is computed by casting a ray from the camera's viewpoint to display shape layers for each intersected shape (in the order of intersection). The local thickness and free space between layers are computed by identifying points at the 0.5 isovalue for each field function and colored accordingly to match the original drawing. Users can then reorder layers via simple 1D drag-and-drop along the selected ray, with different layer configurations managed internally by computing distances from shape centers.

At each arrangement-design stage, the user selects one shape as the "support canvas" and navigates to a viewpoint for arranging the depth of other shapes relative to this canvas. A click triggers the computation of a local driller interface, allowing manipulation of shapes relative to the canvas. A shape dragged onto the driller becomes the "active shape" and is automatically moved and/or deformed in 3D (see Figure 2). The support canvas can either be part of the final 3D model or only used for the actual deformation process and can be removed later (see Figure 5). Note that we need to pre-select a "support canvas" before deformation, since the constraints specified using the driller interface are constraints on isovalues, which should refer to some global volumetric field - namely the canvas's field.

## 4. Depth inference for the active shape

**Preprocessing the active shape:** Before processing the deformation, the active shape needs to be adequately sampled to have enough levels of detail to allow a perceptually natural, local deformation. In our framework, we consider that the thinner the shape is, the more flexible it should be, as if all the shapes were made of the same soft plastic material. Therefore, we associate our shapes with a manipulation skeleton of a sampling density proportional to the local radius of the shape computed during a traversal of the skeleton graph. The geometric primitives generating the implicit surface are resampled, if needed, by subdividing skeletal segments that are longer than the local diameter of the shape (see Figure 3).

**Identifying the target isosurface of the canvas:** Each time the user drops the slice representing the active shape to a new position on the Driller, it triggers the local 3D projection of the skeleton of the active shape to a well-chosen isosurface of the support canvas. We use the Driller interface to select the relevant isosurface: At
<figure><img src="image_5.png" /><figcaption>**Figure 5:** *Using a support canvas to ease the modeling of a complex cylinder anemone shape (the body is sketched separately).*</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 6:** *Various complex shapes created using our interface. Left to right: before and after using our interface.*</figcaption></figure>

interface takes only a few milliseconds, repolygonizing the shapes
due to our CPU implementation took around one second.

**Discussion and limitations:** While we succeeded in enabling the easy creation of simple tangled and nested elongated structures, more complicated objects with either more details (e.g. a basket of laundry) or a self-intersecting surface, such as a complex, elongated shape bending over itself and creating a knot (e.g. a bowl of spaghetti) need to be further investigated in the future. Indeed, the input shapes are created by painting 2D regions, so shape parts blend rather than self-intersecting. One workaround would be to incrementally paint these shapes, adjusting the depth appropriately and locally blending them at the end. Secondly, consistency in user input is crucial for maintaining the desired deformations due to the propagation of changes. Therefore, as in any depth ordering system, inconsistent user-specified depth ordering would lead to conflicting constraints. Our driller interface currently displays in the same way sandwiched shape layers and a shape nested within a larger one. Conducting a user study would be necessary to understand how to solve this visualization problem in the most natural way.

At the moment, our implementation supposes a uniform material
to deform our shapes. In the future, we plan to use a physically
based approach like a mass-spring system to manage different stiff-
ness, constrain bending, and simulate a more complex relaxation
scheme. As mentioned above, our deformation method takes a
smoothness hypothesis to extend the method to more rigid bodies

such as articulated characters. A different algorithm (e.g., inverse
kinematics) should be used for deforming the articulated skeletons,
while the use of the driller interface would remain unchanged.
Lastly, thick structures may not have enough degrees of freedom
to be able to interleave between thin ones - they will match the re-
quested isosurface locally, and then the deformation will be propa-
gated farther, which might destroy the effect of a previous position-
ing constraint, and cause interpenetrations.

Handling more detailed surfaces could be an interesting extension of our approach. In this case, local surface details could be associated with small skeletal segments, allowing us to apply deformation in a hierarchical order. In practice, the large skeletal structure could first be projected onto the support canvas before rigidly mapping the local details in the local frame of their parent skeletal structure.

## 6. Conclusion

We presented "Driller," an intuitive interface for crafting intricate 3D shape arrangements, from tangled to nested shapes. Using 1D drag-and-drop gestures, our interface enables simple interaction, triggering local or global shape deformations. In the future, we aim to explore enhancing control over deformation locality, currently determined automatically by the system based on shape thickness.

## Acknowledgements

This work was funded by Prof. Cani's fellowship from Hi!Paris.

## References

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