# PhD Proposal : Implicit modeling for additive manufacturing

**Contact**

Sylvain Lefebvre (sylvain.lefebvre@inria.fr) and Cédric Zanni (cedric.zanni@loria.fr)

Team : Alice, LORIA

PDF Sujet : ThesisProposal

**Contexte**

Additive Manufacturing (AM) technology distinguishes itself from more traditional fabrication processes by several significant factors. It allows the creation of objects with complex geometry that would not be possible by subtractive manufacturing or molding. Additionally, 3d printers are of much simpler use than other tools. Finally, since the cost per objects does not change depending on the size of the production run, it allows for per object customization. These reasons, combined with the relatively low cost of some existing 3d printers, explain the interest taken in this technology by the general public. While fabrication of a given object is simplified by AM, it is not the case of the modeling of the geometric model that represents an object.

Existing geometric modelers tend to remain of complex use: the creation of 3d objects often requires as much technical skills as creativity. In the context of object personalization, this is accentuated by the fact that a potential user would need as much expertise as the original designer in order to simply modify the object, e.g. through deformations. Indeed, deformation techniques generally consider only the geometry and not the functionality of the objects. In the context of fabrication, this problem is accentuated by the most commonly used object representations: meshes and b-reps. In order to represent volumes, the latter should verify some properties: defining a 2-variety, being watertight and not presenting self-intersections. In addition, meshes do not intrinsically define smooth surfaces; their resolution should be adapted to the scale of the print, adding an additional parameter which the user should choose carefully.

On the other hand, implicit surfaces, due to their volume definition, do not face these problems [HWC13]. For instance, for a given slice of a model it is straightforward to extract an image representing the inside/outside property of each pixel by simply computing the sign of f for each pixels. One of their main advantages is the facility to create complex shapes by combination of simpler ones thanks to the combination of smooth blending [Blinn82] and sharp CSG [Ric73] operations. This property notably allows the representation of shapes of arbitrary topology. Recently, the two main drawbacks – cost of visualization [GPP*10,RLD*12] and precise control of blending [BBCW10,GBC*13,ZBC15] – limiting their use in practice have started to be overcome.

Existing geometric modelers tend to remain of complex use: the creation of 3d objects often requires as much technical skills as creativity. In the context of object personalization, this is accentuated by the fact that a potential user would need as much expertise as the original designer in order to simply modify the object, e.g. through deformations. Indeed, deformation techniques generally consider only the geometry and not the functionality of the objects. In the context of fabrication, this problem is accentuated by the most commonly used object representations: meshes and b-reps. In order to represent volumes, the latter should verify some properties: defining a 2-variety, being watertight and not presenting self-intersections. In addition, meshes do not intrinsically define smooth surfaces; their resolution should be adapted to the scale of the print, adding an additional parameter which the user should choose carefully.

On the other hand, implicit surfaces, due to their volume definition, do not face these problems [HWC13]. For instance, for a given slice of a model it is straightforward to extract an image representing the inside/outside property of each pixel by simply computing the sign of f for each pixels. One of their main advantages is the facility to create complex shapes by combination of simpler ones thanks to the combination of smooth blending [Blinn82] and sharp CSG [Ric73] operations. This property notably allows the representation of shapes of arbitrary topology. Recently, the two main drawbacks – cost of visualization [GPP*10,RLD*12] and precise control of blending [BBCW10,GBC*13,ZBC15] – limiting their use in practice have started to be overcome.

**Project description**

The proposed research is regrouped in three main axes with an additional transversal study. First, implicit surfaces representations,should be revisited. Contrary to previous works, we intend not only to improve blending behavior but also to design a mathematical model such that the processing of the resulting volume is simplified. Secondly, the development of visualization and processing algorithms that are both fast and robust will be targeted. We will notably investigate the use of direct rendering methods for slicing implicit surface as well as filtering for the case where the shape is too detailed for the printing resolution. Developed algorithms should use both the mathematical properties of the field function and be well adapted to the massive parallelism of the GPU. Then, the next goal is to develop dedicated modeling techniques that are well adapted to the creation of objects that can be parametrized. In order to do so, constraints between different elements that are not explicitly defined should be introduced: it is necessary to be able to apply position and contact constraints between points on implicit surfaces and relate those to the implicit surface parameters. Finally, those works should be extended to the control of gradient of properties. Indeed, the same problematics arise with multi-materials: guaranteeing the topology of each group of materials in presence of sharp transitions, efficient visualization and slicing.

**References**

[Bli82] J. F. Blinn : “A generalization of algebraic surface drawing”. ACM Trans. Graph. 1, 3 (July 1982), 235–256.

[BBCW10] A. Bernhardt, L. Barthe, M.-P. Cani, B. Wyvill : “Implicit blending revisited”. Proc of Eurographics, Computer Graphics Forum. 29, 2 (2010), 367 :76.

[GBC*13] O. Gourmel, L. Barthe, M.-P. Cani, B. Wyvill, A. Bernhardt, M. Paulin, H. Grasberger : “A gradient-based implicit blend”. ACM Trans. Graph. 32, 2 (Apr. 2013), 12 :1–12 :12.

[GPP*10] O. Gourmel, A. Pajot, M. Paulin, L. Barthe, P. Poulin : “Fitted BVH for Fast Raytracing of Metaballs”. Proc of Eurographics, Computer Graphics Forum. 29, 2 (2010), 281 :288.

[HWC13] P. Huang, C.L. Wang, Y. Chen : “Intersection-Free and Topologically Faithful Slicing of Implicit Solid”, ASME J. Comput. Inf. Sci. Eng, 13(2), (2013)

[JLW10] Z. Ji, L. Liu, Y. Wang : “B‐Mesh: A Modeling System for Base Meshes of 3D Articulated Shapes”. Computer Graphics Forum (2010), pp. 469–476.

[Ric73] A. Ricci : “A Constructive Geometry for Computer Graphics”. Computer Journal 16,2, (1973), 157–60.

[RLD*12] T. Reiner, S. Lefebvre, L. Diener, I. García, B. Jobard, C. Dachsbacher : “A Runtime Cache for Interactive Procedural Modeling”. Computer & Graphics 36,5, Proc of Shape Modeling International (2012).

[BBCW10] A. Bernhardt, L. Barthe, M.-P. Cani, B. Wyvill : “Implicit blending revisited”. Proc of Eurographics, Computer Graphics Forum. 29, 2 (2010), 367 :76.

[GBC*13] O. Gourmel, L. Barthe, M.-P. Cani, B. Wyvill, A. Bernhardt, M. Paulin, H. Grasberger : “A gradient-based implicit blend”. ACM Trans. Graph. 32, 2 (Apr. 2013), 12 :1–12 :12.

[GPP*10] O. Gourmel, A. Pajot, M. Paulin, L. Barthe, P. Poulin : “Fitted BVH for Fast Raytracing of Metaballs”. Proc of Eurographics, Computer Graphics Forum. 29, 2 (2010), 281 :288.

[HWC13] P. Huang, C.L. Wang, Y. Chen : “Intersection-Free and Topologically Faithful Slicing of Implicit Solid”, ASME J. Comput. Inf. Sci. Eng, 13(2), (2013)

[JLW10] Z. Ji, L. Liu, Y. Wang : “B‐Mesh: A Modeling System for Base Meshes of 3D Articulated Shapes”. Computer Graphics Forum (2010), pp. 469–476.

[Ric73] A. Ricci : “A Constructive Geometry for Computer Graphics”. Computer Journal 16,2, (1973), 157–60.

[RLD*12] T. Reiner, S. Lefebvre, L. Diener, I. García, B. Jobard, C. Dachsbacher : “A Runtime Cache for Interactive Procedural Modeling”. Computer & Graphics 36,5, Proc of Shape Modeling International (2012).