PhD Proposal : Implicit modeling for additive manufacturing
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.
[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).