• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.1
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• pp.31-38
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• 2019

We present an explicit numerical algorithm for surface reconstruction from unorganized points using the Gaussian filter. We construct a surface from unorganized points and solve the modified heat equation coupled with a fidelity term which keeps the given points. We apply the operator splitting method. First, instead of solving the diffusion term, we use the Gaussian filter which has the effect of diffusion. Next, we solve the fidelity term by using the fully implicit scheme. To investigate the proposed algorithm, we perform computational experiments and observe good results.

• ETRI Journal
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• v.27 no.2
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• pp.235-238
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• 2005

A new mesh reconstruction scheme for approximating a surface from a set of unorganized 3D points is proposed. The proposed method, called a shrink-wrapped boundary face (SWBF) algorithm, produces the final surface by iteratively shrinking the initial mesh generated from the definition of the boundary faces. SWBF surmounts the genus-0 spherical topology restriction of previous shrink-wrapping-based mesh generation techniques and can be applied to any type of surface topology. Furthermore, SWBF is significantly faster than a related algorithm of Jeong and others, as SWBF requires only a local nearest-point-search in the shrinking process. Our experiments show that SWBF is very robust and efficient for surface reconstruction from an unorganized point cloud.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.10
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• pp.593-602
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• 2004

A new surface reconstruction scheme for approximating the surface from a set of unorganized 3D points is proposed. Our method, called shrink-wrapped boundary face (SWBF) algorithm, produces the final surface by iteratively shrinking the initial mesh generated from the definition of the boundary faces. Proposed method surmounts the genus-0 spherical topology restriction of previous shrink-wrapping based mesh generation technique, and can be applicable to any kind of surface topology. Furthermore, SWBF is much faster than the previous one since it requires only local nearest-point-search in the shrinking process. According to experiments, it is proved to be very robust and efficient for mesh generation from unorganized points cloud.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.9 s.186
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• pp.200-207
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• 2006

In this paper a new approach which combines implicit surface scheme and NURBS surface interpolation method is proposed in order to generate a complete surface model from unorganized point cloud data. In the method a base surface was generated by creating smooth implicit surface from the input point cloud data through which the actual surface would pass. The implicit surface was defined by a combination of shape functions including quadratic polynomial function, cubic polynomial functions and radial basis function using adaptive domain decomposition method. In this paper voxel data which can be extracted easily from the base implicit surface were used in order to generate rectangular net with good quality using the normal projection and smoothing scheme. After generating the interior points and tangential vectors in each rectangular region considering the required accuracy, the NURBS surface were constructed by interpolating the rectangular array of points using boundary tangential vectors which assure C$^1$ continuity between rectangular patches. The validity and effectiveness of this new approach was demonstrated by performing numerical experiments for the various types of point cloud data.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.11
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• pp.144-153
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• 2007

In order to generate the input data for rapid prototyping, a new approach which is based on the implicit surface interpolation method is presented. In the method a surface is reconstructed by creating smooth implicit surface from unorganized cloud of points through which the surface should pass. In the method an implicit surface is defined by the adaptive local shape functions including quadratic polynomial function, cubic polynomial function and RBF(Radial Basis Function). By the reconstruction of a surface, various types of error in raw STL file including degenerated triangles, undesirable holes with complex shapes and overlaps between triangles can be eliminated automatically. In order to get the slicing data for rapid prototyping an efficient intersection algorithm between implicit surface and plane is developed. For the direct usage for rapid prototyping, a robust transformation algorithm for the generation of complete STL data of solid type is also suggested.

• The KIPS Transactions:PartA
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• v.14A no.3 s.107
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• pp.133-140
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• 2007

The SWBF(shrink-wrapped boundary face) algorithm is a recent mesh reconstruction method for constructing a surface model from a set of unorganized 3D points. In this paper, we point out the surface duplication problem of SWBF and propose an improved mesh reconstruction scheme. Our method tries to classify the non-boundary cells as the inner cell or the outer cell, and makes an initial mesh without surface duplication by adopting the improved boundary face definition. To handle the directional unbalance of surface sampling density arise in typical 3D scanners, two dimensional connectivity in the cell image is introduced and utilized. According to experiments, our method is proved to be very useful to overcome the surface duplication problem of the SWBF algorithm.

• Korean Journal of Computational Design and Engineering
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• v.12 no.4
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• pp.274-282
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• 2007

In this paper, a method of constructing a rectangular net from unorganized point cloud data is presented. In the method an implicit surface that fits the given point data is generated by using principal component analysis(PCA) and adaptive domain decomposition method(ADDM). Then a complete and quality rectangular net can be obtained by extracting voxel data from the implicit surface and projecting exterior faces of extracted voxels onto the implicit surface. The main advantage of the proposed method is that a quality rectangular net can be extracted from randomly scattered 3D points only without any further information. Furthermore the results of this works can be used to obtain many useful information including a slicing data, a solid STL model and a NURBS surface model in many areas involved in treatment of large amount of point data by proper processing of implicit surface and rectangular net generated previously.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.6
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• pp.307-317
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• 2002

In this paper we propose a new mesh reconstruction scheme that produces a displaced subdivision surface directly from unorganized points. The displaced subdivision surface is a new mesh representation that defines a detailed mesh with a displacement map over a smooth domain surface, but original displaced subdivision surface algorithm needs an explicit polygonal mesh since it is not a mesh reconstruction algorithm but a mesh conversion (remeshing) algorithm. The main idea of our approach is that we sample surface detail from unorganized points without any topological information. For this, we predict a virtual triangular face from unorganized points for each sampling ray from a parameteric domain surface. Direct displaced subdivision surface reconstruction from unorganized points has much importance since the output of this algorithm has several important properties: It has compact mesh representation since most vertices can be represented by only a scalar value. Underlying structure of it is piecewise regular so it ran be easily transformed into a multiresolution mesh. Smoothness after mesh deformation is automatically preserved. We avoid time-consuming global energy optimization by employing the input data dependant mesh smoothing, so we can get a good quality displaced subdivision surface quickly.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.8 s.185
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• pp.89-99
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• 2006

In this paper a new shape reconstruction method that allows us to construct surface models from very large sets of points is presented. In this method the global domain of interest is divided into smaller domains where the problem can be solved locally. These local solutions of subdivided domains are blended together according to weighting coefficients to obtain a global solution using partition of unity function. The suggested approach gives us considerable flexibility in the choice of local shape functions which depend on the local shape complexity and desired accuracy. At each domain, a quadratic polynomial function is created that fits the points in the domain. If the approximation is not accurate enough, other higher order functions including cubic polynomial function and RBF(Radial Basis Function) are used. This adaptive selection of local shape functions offers robust and efficient solution to a great variety of shape reconstruction problems.

• International Journal of CAD/CAM
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• v.5 no.1
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• pp.19-27
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• 2005

As three-dimensional range scanners make large point clouds a more common initial representation of real world objects, a need arises for algorithms that can efficiently process point sets. In this paper, we present a method for extracting smooth surfaces from dense point clouds. Given an unorganized set of points in space as input, our algorithm first uses principal component analysis to estimate the surface variation at each point. After defining conditions for determining the geometric compatibility of a point and a surface, we examine the points in order of increasing surface variation to find points whose neighborhoods can be closely approximated by a single surface. These neighborhoods become seed regions for region growing. The region growing step clusters points that are geometrically compatible with the approximating surface and refines the surface as the region grows to obtain the best approximation of the largest number of points. When no more points can be added to a region, the algorithm stores the extracted surface. Our algorithm works quickly with little user interaction and requires a fraction of the memory needed for a standard mesh data structure. To demonstrate its usefulness, we show results on large point clouds acquired from real-world objects.