An algorithm for estimating surface normal from its boundary curves

Abstract

Recently, along with the improvements of geometry modeling methods using sketch-based interface, there have been a lot of developments in research about generating surface model from 3D curves. However, surfacing a 3D curve network remains an ambiguous problem due to the lack of geometric information. In this paper, we propose a new algorithm for estimating the normal vectors of the 3D curves which accord closely with user intent. Bending energy is defined by utilizing RMF(Rotation-Minimizing Frame) of 3D curve, and we estimated this minimal energy frame as the one that accords design intent. The proposed algorithm is demonstrated with surface model creation of various curve networks. The algorithm of estimating geometric information in 3D curves which is proposed in this paper can be utilized to extract new information in sketch-based modeling process. Also, a new framework of 3D modeling can be expected through the fusion between curve network and surface creating algorithm.

3D-look shading from contours and hatching strokes

“…Furthermore, for a future version of our implemented system, we are investigating an improved user interface that assists users to draw multiple hatching strokes quickly. Finally, we believe that there is much room for incorporating our detailed normal controls using hatching strokes into sketch-based modeling methods that have focused on rough 3D geometry and normal estimations [8,11,12,14,15,19,20,27]. (c) normal field generated without hatching stroke normals; (d) normal field generated by our hatching-based method; (e) rendering of (c); (f) rendering of (d).…”

Interactive PDE patch-based surface modeling from vertex-frames

“…In order to smooth arbitrary triangle meshes while satisfying G 1 boundary conditions, a new algorithm was presented in [17] to numerically solve a PDE with the discrete Laplace-Beltrami operator and 1-neighborhood based discretization of the mean curvature normal at a vertex. The discrete Laplace-Beltrami operator was also used to obtain variational minimization for surface deformations in [18], estimate surface normal in [14], and perform surface reconstruction in [15].…”

“…PDE-based geometric modeling has been intensively studied. Various numerical methods such as the finite element method [9,10,11], finite difference method [12,13], and direct discretization of polygonal models using a discrete Laplace operator [14,15] etc. have been proposed to solve PDEs for hybrid subdivision surface design [16], surface reconstruction [15], estimation of surface normal [14], smoothing arbitrary triangle meshes [17], surface deformations [18], defining geometric solid models [19], surface modeling [20,9], and direct shape manipulation [8] etc.…”

Construction Method for a Three-Dimensional Tunnel General Monomer Model Based on Parallel Pathfinding

“…Among the above, the first category of modeling methods can establish detailed roadway characteristics as required, but manual intervention is required to assist in the generation of 3D models, resulting in low modeling efficiency, high labor cost, low modeling accuracy, and unstable accuracy. This complex processing process poses great obstacles in terms of productivity and cannot be applied to largescale tunnel modeling [30]. In the second category of methods, tunnel modeling methods based on laser point cloud data, photogrammetry data, and other technologies can accurately express the spatial geometry of the tunnel, but the cost of the measurement equipment is high, the data redundancy of the constructed model is high, the number of triangular mesh sheets forming the surface of the model is large, the data processing and calculation burdens are heavy, and the costs associated with storage, rendering, transmission, and other resources are high.…”