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Title
Abstract
Figures
Introduction
Related Work
Transformation Objective
Results
Comparison to Previous Work
Limitations
Conclusion and Future Work
References
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Computer Science

Computing and Fabricating Multiplanar Models

Profile image of Pitchaya Sitthi-amornPitchaya Sitthi-amorn

2013, Computer Graphics Forum

https://doi.org/10.1111/CGF.12050
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11 pages

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Abstract

Figure 1: Our method takes an input mesh of primitives (left) and deforms it to a small number of polygons (center). The reduced mesh can be fabricated using a laser cutter and textured to easily create large physical models (right).

Figures (11)
Figure 1: Our method takes an input mesh of primitives (left) and deforms it to a small number of polygons (center). The reduced mesh can be fabricated using a laser cutter and textured to easily create large physical models (right). Desai Chen, Pitchaya Sitthi-amorn, Justin T. Lan and Wojciech Matusik Abstract
Figure 1: Our method takes an input mesh of primitives (left) and deforms it to a small number of polygons (center). The reduced mesh can be fabricated using a laser cutter and textured to easily create large physical models (right). Desai Chen, Pitchaya Sitthi-amorn, Justin T. Lan and Wojciech Matusik Abstract
Figure 2: Overview of the algorithm. Our system first finds some initial cluster seeds, then alternatively iterates between seg- mentation and flattening (described in 3.1. The result is a flattened model that is further processed into fabricable components.
Figure 2: Overview of the algorithm. Our system first finds some initial cluster seeds, then alternatively iterates between seg- mentation and flattening (described in 3.1. The result is a flattened model that is further processed into fabricable components.
Figure 3: Side view of adjoined planes. Left: two planes meet at an obtuse angle. One of the plane needs t - sin® of material to be removed along the boundary, where t is the thickness. Right: two planes meet at an acute angle. Both planes need to be truncated. One needs to cut t -cot® and the other needs to cut t - cot Os
Figure 3: Side view of adjoined planes. Left: two planes meet at an obtuse angle. One of the plane needs t - sin® of material to be removed along the boundary, where t is the thickness. Right: two planes meet at an acute angle. Both planes need to be truncated. One needs to cut t -cot® and the other needs to cut t - cot Os
Figure 4: Types of connectors based on the angle between two planes. Figure (a), (b), and (c) show the connector for acute angles, obtuse angles and concave intersections. Fig- ure (d) shows a concave connector with an acute angle that cannot be assembled.
Figure 4: Types of connectors based on the angle between two planes. Figure (a), (b), and (c) show the connector for acute angles, obtuse angles and concave intersections. Fig- ure (d) shows a concave connector with an acute angle that cannot be assembled.
Figure 5: Toothed connector. In cases the connectors in Fig- ure 4 cannot be used, we generate teeth between two pieces. The algorithm for computing polygonal deformation takes as input the number of desired polygons k. We experiment with k ranging from 30 to 90. While it is possible to use val- ues larger than 100, it would take a long time to assemble the resulting models. On the other hand, it is difficult to repre- sent models with fewer than 30 planes. We analyze the per- formance of the algorithm as a function of desired polygons k. We show the results for two different models in Figure 7 (top). Our algorithm iterates between the mesh segmentation step and mesh deformation step. We have used 50 iterations for all our experiments. The mesh segmentation has one pa- rameter, wy, which controls how smooth the segmentation is. In our experiments we have set its value to around 0.05. In the mesh deformation step, we can set relative importance of four different constraints: the mesh similarity constraint, the
Figure 5: Toothed connector. In cases the connectors in Fig- ure 4 cannot be used, we generate teeth between two pieces. The algorithm for computing polygonal deformation takes as input the number of desired polygons k. We experiment with k ranging from 30 to 90. While it is possible to use val- ues larger than 100, it would take a long time to assemble the resulting models. On the other hand, it is difficult to repre- sent models with fewer than 30 planes. We analyze the per- formance of the algorithm as a function of desired polygons k. We show the results for two different models in Figure 7 (top). Our algorithm iterates between the mesh segmentation step and mesh deformation step. We have used 50 iterations for all our experiments. The mesh segmentation has one pa- rameter, wy, which controls how smooth the segmentation is. In our experiments we have set its value to around 0.05. In the mesh deformation step, we can set relative importance of four different constraints: the mesh similarity constraint, the
Figure 6: Examples of a hole, a fin and a self-intersection produced by VSA.
Figure 6: Examples of a hole, a fin and a self-intersection produced by VSA.
D. Chen & P. Sitthi-amorn & J. Lan & W. Matusik / Multiplanar Models Figure 7: Comparison of outputs with different number of polygons and methods. The top row shows the results from our method. The middle row compares the results from VSA. The bottom row shows the results from QEM.
D. Chen & P. Sitthi-amorn & J. Lan & W. Matusik / Multiplanar Models Figure 7: Comparison of outputs with different number of polygons and methods. The top row shows the results from our method. The middle row compares the results from VSA. The bottom row shows the results from QEM.
Table 1: Comparison of different methods with different number of planar polygons. Our results are computed with- out user guidance for a fair comparison. In case of QEM, all polygons are triangles. The results are Hausdorff dis- tances measured as a percentage of a diagonal of the bound- ing boxe for each model. In some cases, we were unable to obtain a result with VSA using code provided by the original authors.
Table 1: Comparison of different methods with different number of planar polygons. Our results are computed with- out user guidance for a fair comparison. In case of QEM, all polygons are triangles. The results are Hausdorff dis- tances measured as a percentage of a diagonal of the bound- ing boxe for each model. In some cases, we were unable to obtain a result with VSA using code provided by the original authors.
Figure 8: Comparison of clustering with and without user painted saliency given the same number of clusters. Left: Clustering results without user guidance. Right: User guided clustering. The user painted higher saliency around the head and neck area and lower saliency around the legs and feet. Our algorithm accordingly assigned more planes to the head and neck while sacrificing details around the feet and legs.
Figure 8: Comparison of clustering with and without user painted saliency given the same number of clusters. Left: Clustering results without user guidance. Right: User guided clustering. The user painted higher saliency around the head and neck area and lower saliency around the legs and feet. Our algorithm accordingly assigned more planes to the head and neck while sacrificing details around the feet and legs.
Figure 9: Manufactured parts and assembled model. Parts were manufactured using a laser cutter with 1/8 inch thick basswood material. The cutting time was about 5 minutes, and the assembling process took roughly an hour and a half.
Figure 9: Manufactured parts and assembled model. Parts were manufactured using a laser cutter with 1/8 inch thick basswood material. The cutting time was about 5 minutes, and the assembling process took roughly an hour and a half.
Figure 10: Results of our algorithm on different models. These models have different geometric complexity and topology. We also tested our method on different types of materials and number of polygons.
Figure 10: Results of our algorithm on different models. These models have different geometric complexity and topology. We also tested our method on different types of materials and number of polygons.

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