Algorithms for the Physical Fabrication of Shapes using 3...
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Algorithms for the Physical Fabrication of Shapes using 3-Axis Milling Machines Alessandro Muntoni, Marco Livesu, Riccardo Scateni, Alla Sheffer, Daniele Panozzo CG 3 Lab: Computer Graphics and Computational Geometry Cagliari Group – UniCA Computer Graphics Lab – New York University University of Cagliari Dept. of Mathematics and Computer Science Alessandro Muntoni – PhD Student at University of Cagliari (CG 3 Lab) – [email protected] Marco Livesu – Researcher at CNR-IMATI of Genoa – [email protected] Riccardo Scateni – Associate Professor at University of Cagliari (CG 3 Lab) – [email protected] Alla Sheffer – Full Professor at University of British Columbia - [email protected] Daniele Panozzo – Associate Professor at New York University - [email protected] ABSTRACT We propose two algorithms for the simplification and subdivision of three-dimensional free-form shapes that represent real objects, in order to allow their physical fabrication using 3-axis milling machines and to facilitate the construction of the final model. The first algorithm aims to simplify the model into a small set of large flat faces in a way that the folding process is as easy as possible. The goal of the second algorithm is to subdivide the entire shape of a digital model into a small set of pieces manufacturable using a milling machine, allowing the fabrication of free-form shapes on both a small and a large scale. The goal of this algorithm is to obtain a model composed of a small number of large planar faces, so that it is easy to cut all the faces of the unfolded model on a sheet of rigid material. We also want a model composed of a restricted set of angles between adjacent faces: in this way we can make furrows of certain angles on the face edges, making the folding process of the physical model easier and errorless. We developed a simplification algorithm based on Marching Cubes Reconstruction, that allows the user to choose the level of detail of the output model. After an automatic step, a user guided simplification tool is provided to remove spurious faces. 1. Lorensen W. E., Cline H. E.: Marching cubes: a high resolution 3d surface construction algorithm. ACM Computer Graphics 21, 4 (1987), 163–169. 2. Chen D., Sitthi-amorn P., Lan J.T., Matusik W.: Computing and Fabricating Multiplanar Models. EUROGRAPHICS Vol. 32 (2013), 305–315. 3. Herholz P., Matusik W., Alexa M.: Approximating Free-form Geometry with Height Fields for Manufacturing. EUROGRAPHICS Vol. 34 (2015). 4. Song P., Deng B., Wang Z., Dong Z., Li W., Fu C., Liu L.: CofiFab: Coarse-to-Fine Fabrication of Large 3D Objects. SIGGRAPH 2016, technical paper, 35 (2016). MILLING MACHINES Unlike 3D printers, milling machines can produce objects with a large set of materials, with limited energy costs. However they use subtractive techniques, and free-form is not allowed. FABRICATION USING SHEETS OF RIGID MATERIALS FABRICATION USING BLOCKS OF MILLABLE MATERIALS #Faces: 115 #Faces: 68 #Faces: 206 #Faces: 103 This approach has the goal to cover the entire surface of a digital model by using blocks that are height-fields, allowing the manufacturing of free form surfaces with milling machines. This type of fabrication can be applied on small scale objects, where we can produce completely filled objects built like 3D-puzzles or, on a large scale, objects such as statues or buildings, where the interior is empty. The main idea is to find a small set of axis-aligned boxes that cover a piece of surface that is an height-field relatively to the base of the box given a target normal. The intersection between the input surface and these boxes is an height-field piece by construction and it can be fabricated with a milling machine. The internal base complex will be empty space in case of large scale fabrication, and in this case we can use some metal L joints to join the pieces together. In case of small scale fabrication, the internal base complex can be trivially split into a small set of polycubes also fabricable using milling machines.
Transcript of Algorithms for the Physical Fabrication of Shapes using 3...
Algorithms for the Physical Fabrication of Shapes using 3-Axis Milling Machines
Alessandro Muntoni, Marco Livesu, Riccardo Scateni, Alla Sheffer, Daniele Panozzo CG3 Lab: Computer Graphics and Computational Geometry Cagliari Group – UniCA Computer Graphics Lab – New York University
University of Cagliari Dept. of Mathematics and Computer Science Alessandro Muntoni – PhD Student at University of Cagliari (CG3 Lab) – [email protected] Marco Livesu – Researcher at CNR-IMATI of Genoa – [email protected] Riccardo Scateni – Associate Professor at University of Cagliari (CG3 Lab) – [email protected] Alla Sheffer – Full Professor at University of British Columbia - [email protected] Daniele Panozzo – Associate Professor at New York University - [email protected]
ABSTRACT We propose two algorithms for the simplification and subdivision of three-dimensional free-form shapes that represent real objects, in order to allow their physical fabrication using 3-axis milling machines and to facilitate the construction of the final model. The first algorithm aims to simplify the model into a small set of large flat faces in a way that the folding process is as easy as possible. The goal of the second algorithm is to subdivide the entire shape of a digital model into a small set of pieces manufacturable using a milling machine, allowing the fabrication of free-form shapes on both a small and a large scale.
The goal of this algorithm is to obtain a model composed of a small number of large planar faces, so that it is easy to cut all the faces of the unfolded model on a sheet of rigid material. We also want a model composed of a restricted set of angles between adjacent faces: in this way we can make furrows of certain angles on the face edges, making the folding process of the physical model easier and errorless.
We developed a simplification algorithm based on Marching Cubes Reconstruction, that allows the user to choose the level of detail of the output model. After an automatic step, a user guided simplification tool is provided to remove spurious faces.
1. Lorensen W. E., Cline H. E.: Marching cubes: a high resolution 3d surface construction algorithm. ACM Computer Graphics 21, 4 (1987), 163–169.
2. Chen D., Sitthi-amorn P., Lan J.T., Matusik W.: Computing and Fabricating Multiplanar Models. EUROGRAPHICS Vol. 32 (2013), 305–315.
3. Herholz P., Matusik W., Alexa M.: Approximating Free-form Geometry with Height Fields for Manufacturing. EUROGRAPHICS Vol. 34 (2015).
4. Song P., Deng B., Wang Z., Dong Z., Li W., Fu C., Liu L.: CofiFab: Coarse-to-Fine Fabrication of Large 3D Objects. SIGGRAPH 2016, technical paper, 35 (2016).
MILLING MACHINES Unlike 3D printers, milling machines can produce objects with a large set of materials, with limited energy costs. However they use subtractive techniques, and free-form is not allowed.
FABRICATION USING SHEETS OF RIGID MATERIALS FABRICATION USING BLOCKS OF MILLABLE MATERIALS
#Faces:
115 #Faces:
68
#Faces:
206
#Faces:
103
This approach has the goal to cover the entire surface of a digital model by using blocks that are height-fields, allowing the manufacturing of free form surfaces with milling machines. This type of fabrication can be applied on small scale objects, where we can produce completely filled objects built like 3D-puzzles or, on a large scale, objects such as statues or buildings, where the interior is empty.
The main idea is to find a small set of axis-aligned boxes that cover a piece of surface that is an height-field relatively to the base of the box given a target normal. The intersection between the input surface and these boxes is an height-field piece by construction and it can be fabricated with a milling machine. The internal base complex will be empty space in case of large scale fabrication, and in this case we can use some metal L joints to join the pieces together. In case of small scale fabrication, the internal base complex can be trivially split into a small set of polycubes also fabricable using milling machines.
