• 한국정밀공학회지
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• 제23권9호
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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.

• 한국정밀공학회지
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• 제24권11호
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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.

• 한국CDE학회논문집
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• 제12권4호
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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.

• International Journal of CAD/CAM
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• 제12권1호
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• pp.9-19
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• 2012

Generation of optimum planar B-spline curve in terms of minimum deviation and required fairness to approximate a target shape defined by a strip-shaped unorganized 2D point cloud is studied. It is proposed to use the location of control points as variables within the geometric optimization framework of point distance minimization. An adaptive simulated annealing heuristic optimization algorithm is developed to iteratively update an initial approximate curve towards the target shape. The new implementation comprises an adaptive cooling procedure in which the temperature change is adaptively dependent on the objective function evolution. It is shown that the proposed method results in an improved convergence speed when compared to the standard simulated annealing method. A couple of examples are included to show the applicability of the proposed method in the surface model reconstruction directly from point cloud data.

• 한국정보과학회논문지:시스템및이론
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• 제31권10호
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• pp.593-602
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• 2004

정렬되지 않은 3차원 측정점들로부터 이들을 근사하는 표면을 재구성하는 방법을 제안하였다. 제안된 방법은 경계면 축소포장 방식에 의한 표면 재구성 방법(shrink-wrapped boundary face： SWBF) 으로, 측정점으로부터 경계셀과 경계면을 구해 초기 메쉬를 생성하고 이를 연속적으로 축소하는 방식에 의해 표면을 재구성한다. 제안된 방법은 기존의 표면 축소포장 방식의 메쉬 생성 방법의 문제점인 물체의 토폴로지에 대한 제약이 없이 어떠한 형태의 표면 재구성에도 적용이 가능하며, 기존 방법이 축소 단계에서 각 메쉬 정점에 대한 최단거리 측정점을 찾는 전역 탐색을 해야 하는데 비해 지역 탐색만으로 최적의 측정점을 찾을 수 있으므로 처리 시간 측면에서도 우월하다. 실험을 통해 제안된 표면 재구성 알고리즘이 측정점들간의 관계를 알 수 없는 정렬되지 않은 3차원 점들에 대한 표면 재구성에 매우 안정적이고 효과적임을 확인할 수 있었다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권1호
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• pp.31-49
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• 2012

In this paper, we propose a very efficient method which reconstructs the high resolution surface from a set of unorganized points. Our method is based on the level set method using adaptive octree. We start with the surface reconstruction model proposed in [20]. In [20], they introduced a very fast and efficient method which is different from the previous methods using the level set method. Most existing methods[21, 22] employed the time evolving process from an initial surface to point cloud. But in [20], they considered the surface reconstruction process as an elliptic problem in the narrow band including point cloud. So they could obtain very speedy method because they didn't have to limit the time evolution step by the finite speed of propagation. However, they implemented that model just on the uniform grid. So they still have the weakness that it needs so much memories because of being fulfilled only on the uniform grid. Their algorithm basically solves a large linear system of which size is the same as the number of the grid in a narrow band. Besides, it is not easy to make the width of band narrow enough since the decision of band width depends on the distribution of point data. After all, as far as it is implemented on the uniform grid, it is almost impossible to generate the surface on the high resolution because the memory requirement increases geometrically. We resolve it by adapting octree data structure[12, 11] to our problem and by introducing a new redistancing algorithm which is different from the existing one[19].