Sketch-based modeling and adaptive meshes

Emilio Vital Brazil, Ronan Amorim, Mario Costa Sousa, Luiz Velho, Luiz Henrique de Figueiredo
2015 Computers & graphics  
We present two sketch-based modeling systems built using adaptive meshes and editing operators. The first one has the capability to control local and global changes to the model; the second one follows geological domain constraints. To build a system that provides the user with control of local modifications we developed a mathematical theory of vertex label and atlas structure for adaptive meshes based on stellar operators. We also take a more theoretical approach to the problem of
more » ... surface modeling (SBSM) and introduce a framework for SBSM systems based on adaptive meshes. The main advantage of this approach is a clear separation between the modeling operators and the final representation, thus enabling the creation of SBSM systems suited to specific domains with different demands. Sketches are the most direct way to communicate shapes: 2 humans are able to associate complex shapes with few curves. 3 However, sketches do not have complete shape information, 4 and the information sketches do provide is often inexact; thus, 5 ambiguities are natural. On the other hand, to create, edit, 6 and visualize shapes using computers, we need precise math-7 ematical information, such as a function formula or a triangle 8 mesh. The problem of how to model shapes using sketches can 9 be formulated as how to fill the missing information about the 10 model. In the last 15 years, sketch-based modeling (SBM) has 11 become a well established research area, encompassing work in 12 different domains, such as computer vision, human-computer 13 interaction, and artificial intelligence [1]. However, this body 14 of work lacks a more theoretical approach on how to build a 15 sketch-based modeling system for a given application. In con-16 trast, we present here two sketch-based modeling systems built 17 on top of the same framework. This framework is tailored 18 for sketch-based surface modeling (SBSM) taking advantage 19 of adaptive meshes. 20 We advocate that SBSM systems must be suited to each spe-21 cific application: the specificities of a certain field require suit-22 major differences. The first system is the Detail Aware Sketch-48 Based Surface Modeling (DASS, Section 5), which approaches 49 a common problem in many SBSM systems: the lack of good 50 control of global and local transformations. We created DASS 51 to allow us to validate our proposed framework, exploring the 52 limitations of a general system without a well defined task. To 53 achieve the required control we developed a method to cre-54 ate atlas structures for adaptive meshes based on stellar oper-55 ators [2]. The second system is the Geological Layer Modeler 56 (GLaM, Section 6), which is a sketch-based system specialized 57 for geology that aims to help geophysicists to create subsurface 58 models. This system is a good illustration of controlled free-59 dom, where the sketch operators should be restricted to follow 60 geological rules. 61 2. Related Work 62 In the past decades there has been a large body of work in 63 sketch-based surface modeling [3, 4, 5, 6, 7]. However, these 64 systems are more concerned with the final results and do not 65 consider the theoretical aspects of the mathematical surface rep-66 resentation used. We discuss below the main works on free-67 form sketch-based surface modeling that start from scratch un-68 der the light of its representations. 69 There are many ways to represent surfaces in R 3 . The most 70 common and general are parametric representations and im-71 plicit representations. However, in order to be used in com-72 puter graphics and modeling applications, these representations 73 must be more specific and possess practical qualities. As exam-74 ples we can cite the BlobTree [8], piecewise algebraic surface 75 patches [9], convolution surfaces [10], generalized cylinders, 76 polygonal meshes, subdivision surfaces, among others. 77 Teddy [3], Fibermesh [4], and Kara and Shimada [11] use 78 triangle meshes as a base representation for their modeling sys-79 tems. Teddy and Fibermesh start with a planar curve and create 80 an inflated mesh based on the curve's geometry. Teddy supports 81 extrusion and cutting operators that cut a mesh part, then create 82 a new mesh patch, which is merged with the model. Similarly, 83 Fibermesh creates a new mesh based on the input sketches and 84 places it using optimization on differential coordinates, thus en-85 abling the system to keep all previous strokes as constraints. 86 Kara and Shimada also keep a set of 3D curves to define the 87 final model. However, they use curve loops to define triangle 88 mesh patches that have minimum curvature, instead of optimiz-89 ing across the whole mesh. These patches can be modified us-90 ing physically-based deformation tools. These three systems 91 are based on the triangle mesh representation and use it to build 92 their modeling operators; as result, their advantages and limita-93 tions are directly related with that chosen representation. 94 Using triangle meshes for modeling purposes has several 95 advantages over other representations. First, triangle meshes 96 are largely used by both academia and industry, and most graph-97 ics pipelines are based on triangles, which means that what 98 you see is what you get. Moreover, there is much research 99 on triangle meshes and many techniques have been developed 100 for creating and editing meshes. On the other hand, applying 101 these techniques in sketch-based modeling is not a straightfor-102 ward task: techniques must be chosen based on the application 103 scope, and these choices will define the limitations of the sys-104 tem. These limitations are noticeable in Teddy and Fibermesh -105 the latter approaches some drawbacks of the former using opti-106 mization on differential representation. Compared with Teddy, 107 in Fibermesh the mesh quality is improved, the topology can 108 be changed, and the construction curves are maintained using 109 157 constraints. Amorim et al. [16] presented a sketch-based system 158 using Hermite-Birkhoff interpolation to create implicit mod-159 els applied to geology. Araujo and Jorge [17] provided a set 160 of sketch-based operators adapting the multi-level partition-of- 161
doi:10.1016/j.cag.2015.07.020 fatcat:57ctcjcg7vfaliyfnxyqoqmcdy