IGEL: A Virtual Heat Cutter for 3D Shape Modeling
Hitomi Imaizumi∗
Ochanomizu University

Takayuki Itoh†
Ochanomizu UniversityAbstract• We do not suppose to use high-spec input devices or graphicssystems.

Heat cutter is a tool for processing styrene forms. Since blades ofcutters are steal wires, user can freely bend them. We think this operation is intuitive for 3D shape modeling. IGEL virtually realizes
the operation of the heat cutters by a sketch input system. IGEL has
two different modes, 2D and 3D modes, and users can switch themfreely. In 2D mode, users can draw the shapes of cutters freely.
In 3D mode, users can cut the styrene forms using their own cutters. Our implementation represents the styrene forms as triangularmeshes, and cuts the meshes according to the user’s operation.

• We do not suppose highly accurate modeling such as designof industrial products. Instead, we aim to satisfy high-level
hobby users.

Keywords: 3D Modeling, Virtual Mockup, Heat Cutter.

1Introduction

3D Computer Graphics is a very important technology for variousentertainment fields, such as movie and video games. 3D shapemodeling is an important technical step for computer graphics.
Most of 3D computer graphics designers use professional shapemodeling software, but many of them feel that such software may
be difficult for novice users, because it is not very intuitive, andmay require special knowledge and training. Today we enjoy various consumer-generated contents on the Web, such as movies uploaded onto video-sharing Web sites. However, we do not have
many chances to enjoy consumer-generated 3D contents. We think
one of the reasons is the difficulty of 3D shape modeling environments.

Figure 1 shows a snapshot of a heat cutter, which features anelectrically-heated steal wire to process styrene forms. IGEL mimics the heat cutters to process 3D shapes. It supposes that users design both shapes of steal wires and its trajectory by using a sketch
interface. Users can freely cut and process the initial shapes of virtual styrene forms, by firstly designing the shape of the virtual steal
wire, and then moving it in a virtual 3D space. We think the process
is enjoyable since we can design the shapes of the cutter: we cangenerate wave-shaped cross-sections by designing wave-like cuttersor star-shaped holes by designing star-like cutters. IGEL enables
such kinds of enjoyable shape modeling intuitively, by only several
stroke inputs.

On the other hand, there have been many techniques for intuitively
enjoying 3D shape modeling processes. Some of famous techniques applied sketch interfaces [Igarashi et al. 1999] [Karpenkoand Hughes 2006] [Cherlin et al. 2005] [Ijiri et al. 2005], and someothers mimicked real manufacturing processes such as cutting andengraving [Mizuno et al. 1999] [Mitani and Suzuki 2004] [Owadaet al. 2004]. We think such kinds of enjoyable techniques may bringus motivation of 3D shape modeling for non-professional people.
Also, such technique may contribute to reduce design duration andcosts for professional users. The technique presented in this paper
is also categorized to such kind of techniques.
This paper proposes IGEL, a virtual heat cutter for 3D shape modeling applying a sketch interface. Our study supposes the following
conditions during the development of IGEL:• We attempt to implement all the functions by intuitive operations of pointing devices, without selection of menu or keyboard operations.
• We attempt to mimics real manufacturing operations such as
cutting or engraving.
∗ e-mail: hitomi@itolab.is.ocha.ac.jp† e-mail:itot@is.ocha.ac.jp

Figure 1: A heat cutter.
We implemented IGEL without supposing high-spec input devices:
we only used a mouse or a pen tablet to implement and test IGEL.
Also, we implemented virtual styrene forms as simple triangularmeshes, not volume or point models, because we did not suppose touse high-spec graphics system. We named this technique ”IGEL” asan abbreviation of ”Interactive Graphics Enabling Light-modeling”.
Remark that ”igel” means a hedgehog in German. We likened thecutters in our system to stings of a hedgehog.

2 Related Work
Sketch-based 3D shape modeling is an active research topic[Igarashi et al. 1999] [Karpenko and Hughes 2006] to realize easy
and friendly 3D shape modeling environments. These techniquesenable easy operations based on 3D shape generation from 2D
shape inputs. However, most of the techniques automatically decide the geometric features in the depth direction. This limitation
may sometimes make sophisticated 3D shape modeling more difficult using such techniques. We think it is a trade-off between
easiness and sophistication of 3D shape modeling.
Recent sketch-based 3D shape modeling techniques attempt tostrike a good balance between the easiness and sophistication.
Combination of parametric surface modeling and sketch interface isa good solution to balance them [Cherlin et al. 2005]. Also, several
excellent 3D shape modeling tools for specific objects (e.g. flowers[Ijiri et al. 2005] ) have been presented.
On the other hand, several intuitive 3D shape modeling techniques
mimic real manufacturing processes and construct virtual tools assoftware. Virtual sculpture [Mizuno et al. 1999] and paper crafts[Mitani and Suzuki 2004] are typical examples of such kind of theworks. These techniques are not only intuitive but also enjoyablebecause it realizes virtual experiences of real manufacturing processes. We think this is one of the values of virtual tool techniques.
IGEL is also a kind of virtual tools mimicking a heat cutter, featuring a sketch interface. Owada et al. presented a similar work
[Owada et al. 2004] which cuts virtual objects by one stroke using
a sketch interface, and maps natural-looking texture images onto
the cross-section. Against this work, IGEL realizes more flexible
shape modeling featuring two kinds of sketch interface: inputs ofshapes and trajectory of cutters.

3

Processing Flow of IGEL

As mentioned in Section 1, IGEL mimics a heat cutter. It is noteasy to freely deform the wires of real heat cutters due to thesestrengths. On the other hand, we implemented a sketch interface
to freely deform it in our virtual heat cutter, so that we can flexibly
and enjoyably realize 3D shape modeling.

3.1

Figure 2: (Upper) 2D mode for designing the shapes of cutters.
(Lower) 3D mode for inputing the trajectory of the cutters.

Technical Overview

IGEL provides the following two modes to enable 3D shape modeling, as shown in Figure 2:
2D mode: a sketch interface to input the shapes of cutters.
3D mode: another sketch interface to input the trajectory of thecutters.
We did not suppose high-spec input devices while the developmentof IGEL, and therefore we implemented the both modes only withdrag operations of popular pointing devices (mouse or pen tablet).

the cursor representing the shape of the virtual cutter, when a user
drags a pointing device.
IGEL interpolates the curved trajectory into a polygonal line, as
shown in Figure 3. This algorithm is similar to well-known vectorization algorithms of raster images. Our implementation firstgenerates a segment I1 connecting the start point v1 and end pointv2 of the trajectory. It then finds the point v3 where is on the trajectory and the distance to I1 is maximum, and divide I1 into I2
and I3, as shown in Figure 3(1)(2). Our implementation recursively
repeats the division of the segments Ij until the maximum distance
between the segments and trajectory gets smaller than the predefined threshold, as shown in Figure 3(3). Figure 3(4) shows anexample of the polygonal line interpolating the original shape ofthe virtual cutter. The algorithm drastically reduces the number ofvertices constructing the curve of the virtual cutter, so that we canreduce the computation time for cutting the virtual objects.
Here, we can cancel the shape by drawing again, if we do not preferalready drawn shape.

Also, we did not suppose high-spec graphics systems including
GPU while the development, and therefore we implemented IGEL
by only linking OpenGL and its extensions, without using GPUbased languages or video game development kits. Consequently,
we applied simple triangular polygon models, not volumetric orpoint models, as shape representation of the objects.
These assumptions are just based on our design policy. We do notopposite to implement IGEL-like techniques applying volumetricor point models, and using high-spec input devices or graphics systems.

3.2

2D modeIGEL provides a 2D sketch interface to design the shapes of virtualcutters, as shown in Figure 2 (Upper). It displays the trajectory ofFigure 3: Interpolation of shape of virtual wire into a polygonalline.

3.3

3D modeIGEL provides another sketch interface to input the trajectory ofvirtual cutters, as shown in Figure 2(Lower). IGEL enables it whena user finishes the input of the shape of the cutter and switches tothe 3D mode. It displays the cutter in the 3D space in a different
color when the user starts the dragging operation. It then calculates
the intersection between a virtual object and the trajectory of thecutter according to the dragging operation. When a user finishes
the dragging operation in the 3D mode, IGEL cuts the virtual object as mentioned below. Here, current our implementation only
supports translation on a projection plane to operate the cutter inthe 3D space.
3.3.1

Cross-Section Mesh

IGEL realizes the cutting operation by calculating the intersection
between a virtual object and the curved surface generated as thetrajectory of the virtual cutter. This paper defines a triangular meshthat interpolates the curved surface as ”cross-section mesh”. Our
implementation generates the cross-section mesh while a user inputs the stroke, and completes when the user finishes the input operation. Figure 4 illustrates the generation of the cross-section mesh.
It evenly generates a series of vertices on the trajectory, indicatedas ”sampling line 1” or ”sampling line 2” in Figure 4. It then completes the generation of the cross-section mesh by connecting thevertices.

Figure 5: Generation of mesh-mesh intersection.

treats the segments constructing the mesh-mesh intersection as constraints, and applies the incremental constraint Delaunay triangulation algorithm [Sloan 1987] to adequately divide the triangles.
Our implementation of the mesh division consists of two steps. The
first step divides the triangles by adding the new vertices on themesh-mesh intersection. The second step modifies the triangles
based on the constraints of the segments on the mesh-mesh intersection.
Figure 6 illustrates the division of triangles in the first step. Thealgorithm adds new vertices on the mesh-mesh intersection to themesh, and divides the triangles so that the added vertices are adequately connected. A red point enclosed by a pink triangle, shownin Figure 6(1), is an example of the added triangle. The algorithm
firstly divides the triangle enclosing the added vertex, as shown inFigure 6(2). It then checks the geometry of the divided triangles
with its adjacent triangles, painted in yellow in Figure 6(3). It thenswaps some edges of the triangles, if the geometry of triangles isimproved by the swapping. Sky-blue triangles in Figure 6(4) are
examples of the triangles generated by the edge swapping. The
process adequately divides the triangles by recursively repeating
the above process.

Figure 4: Generation of cross-section mesh.
3.3.2

Mesh-Mesh Intersection

IGEL calculates intersection between the cross-section mesh andthe mesh of a virtual object. Figure 5 illustrates the process, wherepink triangles are parts of the virtual object, and sky-blue triangles are parts of the cross-section mesh. The process detects intersections between a triangle of a mesh and an edge of anothermesh. Traversing adjacent triangles one-by-one, and detecting theintersections of the traversed triangles, the process generates a setof segments connecting the intersections, shown as red arrows inFigure 5. This paper defines the intersection as ”mesh-mesh intersection”. Current our implementation completes the traverse oftriangles when it arrives at the first triangle and therefore the setof segments constructs a loop. The current implementation does
not support the generation of multiple loops yet. Also, it does notsupport the stop of cutting before constructing a closed loop, togenerate incisions.
3.3.3

Mesh Division

IGEL divides the triangles so that we can cut the virtual objects,
when the mesh-mesh intersection process is completed. IGEL

Figure 6: Division of triangles.
Figure 7 illustrates the swapping of triangles in the second step.
Here, a blue dotted segment in Figure 7(1) is an example of theconstraints. Our implementation extracts the four triangles intersected by the constraint segment, and swaps two of the triangles if
the number of intersected triangles is reduced by the swapping. In
this example, swapping of two triangles painted in Figure 7(2) does
not reduce the number of intersected triangles, but swapping of twotriangles painted in Figure 7(3) reduces it. Figure 7(4) shows afterswapping of triangles painted in Figure 7(3), where the number ofintersected triangles gets three. By swapping the painted triangles
in Figure 7(4), the number gets two, as shown in Figure 7(5). Finally, the number gets zero, by swapping the painted triangles inFigure 7(5). Figure 7(6) is the final result of the process.

3.4

User InterfaceCurrent our implementation uses GLUI, as an extension ofOpenGL, for implementation of graphical user interface of viewing
operations. The implementation provides gadgets for rotation andtranslation of virtual objects and viewpoints. The implementation
still needs some keyboard-based operations such as switch between
2D or 3D modes. However, we would like to improve the user interface so that we can operate IGEL only by pointing devices.

3.5

ExampleFigure 9 shows an example of shape modeling by cutting a virtualobject five times.

Figure 7: Division of triangles.
IGEL applies the process to both virtual object mesh and crosssection mesh. Here, a part of the cross-section mesh enclosed by
the mesh-mesh intersection can be reused as the cross-section of
the virtual object mesh.
3.3.4

Remaining Part Selection

When a mesh division process is completed, IGEL displays the twoparts of the virtual object mesh divided by the cross-section mesh in
two colors, as shown in Figure 8(Left). Users can click either of thetwo parts to specify the remaining part. When a user specifies theremaining part, IGEL maps the part of the cross-section mesh enclosed by the mesh-mesh intersection into the virtual object mesh.
As a result, IGEL generates the new shape of the virtual object, asshown in Figure 8(Right).
After completing the remaining part selection, users can cut thevirtual object by the same virtual cutter. Or, they can return to 2Dmode to design a different shape of cutter.

Figure 9: An example.

4 Conclusion and Future Work
The paper presented IGEL, a virtual heat cutter for 3D shape modeling. It provides two modes of the sketch interface. One of themodes enables to design the shapes of the virtual cutters, and theother enables to manipulate the cutters.
The following are our on-going and future works for the extension
and improvement of IGEL.

Figure 8: Selection of remaining part.

[Extension of cutting operations] As described in Section 3.3.2,
current our implementation does not support the situation thatmesh-mesh intersection forms multiple loops. However, it is natural that we generate multiple loops while cutting bumpy objects.
We would like to extend our implementation so that we can cut multiple parts in one stroke. Also, we would like to support the stop of

the virtual cutter before the mesh-mesh intersection constructs aloop, so that we can generate incisions in virtual objects.
[Hole generation] Current our implementation does not support
generation of holes. We need to extend our implementation so thatit can recognize two loops of mesh-mesh intersection are topologically connected and they form a hole. We would like to implement
it because generation of holes is an important operation for virtual
heat cutters.
[Non-cutting operations] Current our algorithm does not take theeffect of heat into account. Therefore, it does not support melt ofobjects. We would like to implement such effect to mimic more realheat cutters.
[Evaluation] We have not had any evaluation with IGEL. We plan
two kinds of evaluations at this moment. Firstly we would liketo compare IGEL with existing shape modeling tools or real heatcutters. Secondly we would like to user evaluation with examinees.
[Discussion on input devices] Current our algorithm does not support translation of cutters along depth direction, and rotation of cutters. It is hard to implement while we limit the input devices tomouse or pen tablet. We would like to discuss what kind of pointing
devices are preferable for IGEL. Also, we would like to test IGEL
with haptic pointing devices, because we think force feedback ofsuch devices are effective for users.
[Test with virtual reality technology] Display of objects and cutters is also an important point for intuitive shape modeling. We
would like to test IGEL with virtual reality technologies, such aslarge or stereoscopic displays.

References
C HERLIN , J. J., S AMAVATI , F., S OUSA , M. C., AND J ORGE , J. A.
2005. Sketch-based modeling with few strokes. In Proceedingsof the 21st Spring Conference on Computer Graphics, 137–145.
I GARASHI , T., M ATSUOKA , S., AND TANAKA , H. 1999. Teddy:
A sketching interface for 3d freedom design. In Proceedings ofACM SIGGRAPH 99, ACM Press / ACM SIGGRAPH, 409–416.
I JIRI , T., OWADA , S., O KABE , M., AND I GARASHI , T. 2005.
Floral diagrams and inflorescences: Interactive flower modelingusing botanical structural constraints. In Proceedings of ACMSIGGRAPH 2005, ACM Press / ACM SIGGRAPH, 720–726.
K ARPENKO , O. A., AND H UGHES , J. F. 2006. Smoothsketch:
3d free-form shapes from complex sketches. In Proceedings ofACM SIGGRAPH 2006, ACM Press / ACM SIGGRAPH, 589–598.
M ITANI , J., AND S UZUKI , H. 2004. Making papercraft toys frommeshes using strip-based approximate unfolding. In Proceedings of ACM SIGGRAPH 2004, ACM Press / ACM SIGGRAPH,259–263.
M IZUNO , S., O KADA , M., AND T ORIWAKI , J. 1999. An interactive designing system with virtual sculpting and virtual woodcut
printing. Computer Graphics Forum: Journal of the European
Association for Computer Graphics 18, 3, 183–193.
OWADA , S., N IELSEN , F., O KABE , M., AND I GARASHI , T. 2004.
Volumetric illustration: Designing 3d models with internal textures. In Proceedings of ACM SIGGRAPH 2004, ACM Press /ACM SIGGRAPH, 322–328.
S LOAN , S. W. 1987. A fast algorithm for constructing delaunay
triangulations in the plane. Advances in Engineering Software 9,1, 34–55.