An Integrated Processing Method for Multiple Large-scale Point-Clouds Captured from Different Viewpoints

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1 519 An Integrated Processing Method for Multiple Large-scale Point-Clouds Captured fro Different Viewpoints Yousuke Kawauchi 1, Shin Usuki, Kenjiro T. Miura 3, Hiroshi Masuda 4 and Ichiro Tanaka 5 1 Shizuoka University, f @ipc.shizuoka.ac.jp Shizuoka University, dsusuki@ipc.shizuoka.ac.jp 3 Shizuoka University, tkiur@ipc.shizuoka.ac.jp 4 University of Tokyo, asuda@sys.t.u-tokyo.ac.jp 5 Tokyo Denki University, tanaka@cck.dendai.ac.jp ABSTRACT 3D odels of industrial plants are useful for siulating aintenance and renovation. We ai to reconstruct 3D odels of coponents fro large-scale point-clouds captured for industrial plants. When an engineering facility is easured by a laser scanner, the location of the scanner is restricted in ost cases. We have such probles that the coponents of the engineering facility can be scanned only fro one side and they ight be partially occluded by other coponents. In order to solve the probles, we propose a new ethod which can process ultiple large-scale point data captured fro different viewpoints without erging the into a huge data which ight not be able to be handled on a coputer with a liited ain eory size. Keywords: large-scale point-clouds, laser scanner, data fro different viewpoints. DOI: 10.37/cadaps INTRODUCTION The recent progress on id/long-range laser scanners has ade it possible to capture large-scale point-clouds fro a broad range of scenes. These laser scanners can be used for acquiring 3D shapes of large-scale artifacts, such as factories, power plants, heavy goods, buildings, transportation infrastructure, etc. Large-scale artifacts require long-ter aintenance, and large cost is spent for aintenance in their long lifecycle. Model-based siulation is very useful for reducing tie and cost of aintenance tasks. It can effectively detect the interference of a new coponent with existing facilities during its setup process. However, old artifacts lack reliable drawings as well as 3D odels in ost cases, because they have been repeatedly renovated in their long lifecycles. In such cases, it is necessary to create new as-built solid odels for the aintenance siulation. Mid/long-range laser scanners are one of the ost proising solutions. Two types of laser scanners are coonly used for easuring large artifacts in the field of surveying. One type is the tie-of-flight scanner, which easures the round-trip travel tie of the laser pulses. This type of scanner can easure in the range of a few hundred eters, but it takes relatively long tie to easure any points that cover large artifacts. The other type is the phase-based laser scanner, which radiates Coputer-Aided Design & Applications, 8(4), 011, CAD Solutions, LLC,

2 50 continuous odulated laser pulses and calculates distances using the phase difference between the eitted and received signals. The phase-based scanners can typically easure a range of 50~10 eters. In this paper, we call the forer long-range scanners, and the latter idrange. The reverse engineering of product shapes has been intensively studied in the CAD counity. Most of the previous studies are based on the points precisely easured by triangular-based laser scanners. However, point clouds of large artifacts captured by id/long-range scanners are quite different in the following aspects. The nuber of points is very large. In the case of the phase-based scanners, a single scan can capture 50M to 00M points. Naive algoriths easily exceed the liit of 3 bit PCs. Measuring precision is relatively low in coparison with point density. So generating surface esh fro the point cloud is not straight forward. Point data are very noisy and contain a lot of outliers. This is because the id/long-range scanners cannot avoid the ixed pixel, at which a laser bea is reflected fro ultiple surfaces. It is difficult to obtain coplete point sets of large artifacts, because it is very costly and tieconsuing to construct stages for easuring artifacts fro any directions. In addition, the intricate structure of engineering facilities restricts the locations for easureent. Large artifacts include a large nuber of coponents. Therefore, it is necessary to devide point-clouds into coponents. Many parts are overlapped, and they ay be partly occluded. Masuda and Tanaka proposed a ethod for creating sooth esh odels fro very noisy and large-scale point clouds [1]. This work has solved the first three probles described above. They introduced a robust soothing operator based on the Lorentzian estiate and applied the operator to point data captured by a phase-based scanner. In addition, they extracted surface priitives and showed their ethod could be used for creating 3D esh odels of large facilities. They also discussed the reaining probles and proposed a new odeling ethod for creating 3D solid odels based on iages and esh odels generated fro point-clouds []. Their contribution is to introduce iage-based techniques for the purpose of copensating for issing portions in esh odels. In their ethod, while the user interacts with iages, the coputer estiates geoetry using esh odels. This ethod is useful for generating solid odels based on incoplete point data, especially when points are easured only fro a liited nuber of viewpoints or any overlapping coponents are included. Figure 1(a) shows a sooth esh odel generated by the ethod proposed in [1]. When coponents are carefully easured fro appropriate positions, they can be converted to solid odels by conventional reverse engineering techniques. However, when the object is located behind other coponents, its point-cloud is partially occluded and ay be divided into fragents. In Fig. 1(b), cylindrical pipes are subdivided into fragents because of occlusions. In such cases, the user has to collect fragents and reconstruct the original shape to generate ideal shapes. However, it is often difficult for the user to recognize the original coponents fro fragents. It is also difficult to develop a general algorith that autoatically reconstructs the original shape fro fragents, although relatively sall gaps can be filled by esh processing [3,4]. The ethod in [] cobined iage-based techniques and esh processing techniques. Iages and esh odels can be generated fro a point-cloud, because id/long-range laser scanners output the reflectance value as well as the coordinate at each point. The reflectance value represents the strength of reflected laser bea at each point, and is strongly influenced by the aterial properties of objects. Generally, the reflectance value becoes large for white objects, and low for black ones. So they ake a black-and-white reflectance iage by noralizing the logariths of the reflectance value between 0 and 55. Figure (a) shows the reflectance iage generated by the point-cloud of Fig. 1(b). The eye position is placed at the origin of the laser beas in this figure. We can obviously identify each coponent in Fig. (a), unlike Fig. 1(b). In Fig. (b), esh odels in Fig. 1(b) are projected on the reflected iage. Fig. (b) shows that the iage and the esh odels can be siultaneously used for odeling 3D shapes. This hybrid representation allows not only the user to intuitively work on D iages, but also the coputer to deterine 3D geoetry using esh odels. Coputer-Aided Design & Applications, 8(4), 011, CAD Solutions, LLC,

3 51 Soe of the previous works discuss point-clouds and iages. Xu et al. [5] proposed a nonphotorealistic rendering technique based on point-clouds. They also proposed a segentation technique for a point-cloud using D iages[6]. However, they did not discuss 3D shape odeling based on iages and point-clouds. 3D reconstruction fro stereo iages is popular in coputer vision [6], but Masuda and Tanaka ethod is quite different fro those ethods. They use a single reflectance iage and a esh odel for generating solid odels. (a)mesh odel and a view volue. (b)close-up disconnected esh odels in the view volue Fig. 1: Disconnected esh odels generated fro point-cloud. (a) Reflectance iage. (b) Reflectance iage overlapped with esh odels. Fig. : Reflectance iage of point-cloud. The interface proposed in [1] and [] is excellent, but their syste could not handle ultiple point data captured fro different viewpoints. If we erge these ultiple point data after registration, we will have the following probles. We cannot use their interface anyore because it assues one to one correspondence between a pixel in the iage and a 3D easured point. If we erge two point data, this correspondence cannot be aintained. The other proble is that the data after erger ight becoe too large to be handled by a PC with a liited eory size. Therefore we develop a new ethod using their interface which can process ultiple large-scale point data captured fro different viewpoints without erging the into a huge point-cloud. In the following of this paper, we describe the fraework of the odeling syste proposed by Masuda and Tanaka [1,] in Section since our ethod is an extension of their ethodology. We discuss the syste overview and proble in Section 3, our proposed ethod in Section 4, and in Section 5. Finally, we conclude and ention future work in Section 6. Coputer-Aided Design & Applications, 8(4), 011, CAD Solutions, LLC,

4 5 FRAMEWORK OF MODELING SYSTEM PROPOSED BY MASUDA AND TANAKA Masuda and Tanaka proposed a new solid odeling ethodology based on a reflectance iage and esh odels. A lot of point-clouds are usually captured in surveying large artifacts, and each pointcloud contains 30~50 M points. Since the total nuber of points often reaches 109~1010 points, it is very tie-consuing to process all point-clouds. Therefore, we developed an off-line point-processing syste and an online 3D odeling syste separately. In the off-line process, the syste converts each point-cloud to a esh odel and a reflectance iage. This phase is done by batch process. Then the user interactively generates solid odels using the online odeling syste. In the off-line phase, noisy point data are soothed using non-linear robust estiates [1], and then a large-scale esh odel is generated by using streaing Delaunay triangulation [8], which generates a very large esh odel represented in the streaing forat [9]. However, the streaing esh forat is not suitable for interactively referring to the user-specified region in the large esh odel. Therefore, we introduce the grid esh forat to handle a large-scale esh odel in an out-ofcore anner. We will discuss the grid esh forat in Section 4. In the online process, the user interactively creates solid odels using the reflectance iage and the esh odel. Fig. 3 shows the user interface of our odeling syste. Fig. 3(a) is a reflectance iage. Fig. 3(b) shows a odeling view in which the user generates solid odels. In our odeling syste, the user interacts with the reflectance iages for 3D odeling. Solid odels can be displayed in different views. In Fig. 3(b), solid odels are drawn on the perspective iage. The user can interactively generate, odify, and ove 3D odels on this view. Fig. 3(c) displays solid odels with the reflectance iage. We call this view as a spherical view, because the reflectance iage is displayed as a texture on a sphere. Fig. 3(d) displays solid odels using a Cartesian coordinate syste. The user can switch these four views to confir and generate solid odels. Fig. 3: User interface of our odeling syste. Coputer-Aided Design & Applications, 8(4), 011, CAD Solutions, LLC,

5 53 3 GENERATION OF REFRECTANCE IMAGE 3.1 Generation of Mercator Iage The directions of laser beas of a id/long-range scanner are controlled by the aziuth angle θ and the zenith angle φ, as shown in Fig. 4. In principle, the coordinate of a point is deterined by the distance r and the direction (θ, φ). Therefore, (x,y,z) coordinates can be converted to spherical coordinates (r,θ,φ), when the origin of the coordinate syste is placed at the source of laser beas. This coordinate syste is called the scanner coordinate syste. Each scanned data set has its own scanner coordinate syste. After converting coordinates (x,y,z) to the scanner coordinate (r,θ,φ), the reflectance value of each point is apped on the (θ,φ) of a unit sphere. Fig. 5(a) shows a spherical iage. This spherical iage can be converted to a rectangular iage by the Mercator projection, as shown in Fig. 5(b). This rectangular iage is called a Mercator iage. A Mercator iage consists of pixels for 30M~50M points in our syste. When ultiple scanned datasets are erged by a registration tool, their transforation atrices are aintained. These translation atrices are used to calculate coordinates on the scanner coordinate syste. Then a Mercator iage can be generated for each scan by using the spherical coordinates. Two different views are provided according to coordinate systes. In Fig. 3(c), 3D objects and a textured sphere are displayed on the scanner coordinate syste. In Fig. 3(d), 3D objects fro ultiple scans are displayed using registered coordinates on the world coordinate syste. 3. Generation of Perspective Iage While the Mercator iage is suitable for representing the whole point data of a single scan, it distorts straight lines to curved ones, as shown in Fig. 6(a). This distortion prevents the user to recognize each coponent and draw straight lines on the iage. Therefore, we convert the Mercator iage to perspective iages, because the perspective projection always aps straight lines in 3D space to D straight lines, as shown in Fig. 6(b). However, a perspective iage can cover only a liited range of a Mercator iage. In our syste, when the user selects a region of interest on a Mercator iage, the selected region is projected onto the perspective screen. Fig. 7 shows the relationship between D coordinate (θ,φ) on the Mercator iage and D coordinate (i,j) on the perspective iage. This figure shows that (i,j) and (θ,φ) can be utually converted by calculating the intersection with the line fro the origin. As each point (θ,φ) on the Mercator iage is associated with the easured point in the sae direction, we can associate (i,j) on the perspective iage with 3D coordinate (x,y,z) on an object, because (r,θ,φ)and (x,y,z) can be utually converted as (x,y,z) = (r cosθsinφ,r sinθsinφ,r cosφ). (a) Principle of id/long-range scanners. (b) The aziuth angle and zenith angle Fig. 4: The aziuth angle and zenith angle of id/long-range laser scanners. Coputer-Aided Design & Applications, 8(4), 011, CAD Solutions, LLC,

6 54 (a) Reflectance iage projected onto a sphere. (b) Mercator iage. Fig. 5: Spherical iage and Mercator iage. (a) Mercator iage. (b) Perspective iage. Fig. 6: Generation of a perspective iage fro a Mercator iage. Fig. 7: Relationships aong ( i, j ) and (θ,φ), and ( x, y, z ). 3.3 The Probles of the Syste Proposed by Masuda and Tanaka By use of the syste proposed by Masuda and Tanaka, the user can efficiently perfor geoetric odeling based on the iage. However, since the syste takes advantages of the property that a 3D point data can be apped onto an D iage data, if plural point-clouds captured fro different viewpoints are cobined, the points corresponding the 3D points are overlapped and one to one correspondence between a pixel in the iage and a 3D point are broken. The ethodology adopted by the syste does not work anyore because the user cannot select a pixel to uniquely specify a 3D point. The other proble is that the erged data ight becoe too large for, especially a lap-top pc with a liited size of the ain eory at outside fields. Coputer-Aided Design & Applications, 8(4), 011, CAD Solutions, LLC,

7 55 A point-cloud data captured fro a single viewpoint usually does not contain a whole data of a coponent because of the coplex alignent of the coponents and the data of a coponent are separated by the occlusions of the coponents. That akes very difficult to identify a single coponent which consists of several separated data and plural objects are independently recognized. Fig. 8 shows this type of is-recognition and the syste detects several cylinders which are parts of a single cylinder. It is desirable for a syste to identify a single coponent. There are cases where this type of the proble can be solved by use of ultiple data fro different viewpoints since fro a different viewpoint, the whole iage of a coponent ight be captured and the connectivity of other coponent can be recognized easily. Fig. 8: Type of is-recognition and the syste detects several cylinders which are parts of a single cylinder. In order to solve the proble entioned above, we would like to use ultiple point-clouds captured fro different viewpoints without their erger of these data which will destroy the effectiveness of the interface provided by the syste and haper the efficiency of geoetric odeling capability and propose a new ethod to handle these ultiple point-clouds. 4 PROPOSED METHOD Our ethod is introduced into the interface proposed by Masuda and Tanaka with no odification. For odeling a coponent with their syste, it is necessary to show a point-cloud easured fro a certain point on the interface and to select a surface type and a seed region for fitting a surface of the specified type to the point-cloud. To solve a iniization proble by the non-linear least square ethod is necessary for fitting a surface. The objective function of the iniization proble is the su of the distances between the surface of the coponent and the point-cloud. The seed region is an initial region including point data which coe fro the coponent in the point-cloud. Since the paraeters of the specific surface are obtained by an iterative ethod, adequate initial values for the paraeters are necessary. If the specified surface type is a cylinder, its axis vector, the coordinates of a point on the axis, and its radius are necessary. Masuda and Tanaka described a ethod of the initial guess of the paraeters [1]. Our proposed ethod autoatically deterines fro the seed region selected by the user in the ain point-cloud other seed regions in other point-clouds easured fro different viewpoints for the sae coponent. It allows us to ake a geoetric odel in an integrated anner fro the seed regions in the plural point-clouds. 4.1 Outline of the Proposed Method In this subsection, we explain the outline of our ethod. Here we call the ain point-cloud using for the interface to the user D A and another point data obtained fro a different viewpoint D B. We assue that these two point-cloud are registered each other and they are using the sae coordinate syste. In the explanation here, we use only one point-cloud as well as the ain data, but it is possible to perfor the sae operations for other data if we have ore that one. We call the seed region of the ain point-cloud D A selected by the user S A and the seed region of the other data D B, S B. The proposed ethod consists of the steps described below and autoatically Coputer-Aided Design & Applications, 8(4), 011, CAD Solutions, LLC,

8 56 deterines S B of D B using S A of D A. Fig.8 shows the flow of the processes fro selecting S A to deterining S B. At first, the user specify a seed region in the point-cloud D A (see Fig.9(a)). 1 ) As shown in Fig.9(b), by use of the seed region S A, we estiate initial value of the surface paraeters and construct a closed object B A ade of the surface calculated by the. Then we generate a bounding box B A of the surface. ). The following two substeps are repeated for each cell C i (i=1,,,n) generated by subdividing the point-cloud D B into grids in the θ-φ space (see Fig.9(c)). 1 ) Define a bounding box B Bi by obtaining the axiu and iniu values of the X, Y, and Z coordinates of the point data in C i. ) Perfor an intersection check between Ba and BBi and if the intersection occurs, we add the point data in B Bi to a point data set v, which is a candidate point data for the seed region S B. Fig.9(c) shows both of the two cases, one is with intersection and the other is with no intersection. 3 ) Perfor a test to check whether each points in v Bi is inside or outside the estiated closed object B A and v Bi and if the point in v Bi is outside, it is reoved fro v Bi. 4 ) Define v Bi as S B as shown in Fig.9(e). Fig. 9: Flow of the processes fro selecting S A to deterining S B. The seed region deterined by the above steps is enlarged by the region glowing ethod. In the region glowing, the point near the seed region is checked whether it lies or not on the surface generated by the initial estiated paraeters and if it does, it is erged into the seed region. The region glowing is independently perfored for each point-cloud and after glowing, the seed regions of all the point-clouds are erged and a surface is estiated by solving the non-linear least square ethod. 4. Exaple of Cylinder Modeling Here we explain an exaple of the cylindrical surface odeling in our ethod. We use an AABB (axisaligned bounding box) as the bounding box in Steps 1 and. For the intersection test, we adopt the intersection check between two AABBs. In Step 1, we assue that a point along the axis of the cylinder is given by P 0, the unit vector whose direction is parallel to the axis p = ( a, b, c ), and the radius r, a set of points inside the seed region v Ai. The lengths along the axis l + and l - are calculated by the following equations: l ax{( p v ) p} l in{( p Now we have obtained all the paraeters to deterine a closed object. Next we think about a rectangular parallelepiped circuscribing the closed object. Since we assue that the rectangular parallelepiped is aligned along the X, Y, and Z axes, to define the rectangular parallelepiped, it is enough to obtain the axiu and iniu values of the X, Y, and Z coordinates. To calculate these axiu and iniu values, the axis p is assued to be calculated by the following equation: 0 0 v A, i A, i ) p} Coputer-Aided Design & Applications, 8(4), 011, CAD Solutions, LLC,

9 57 Where atrix M is given by M p M cos β sin αsin β 0 cosα sin β sin α cos β cosαsin β sin α cosα cos β In the above equation, α and β are rotation angles about the X and Y axes, respectively. The axiu and iniu values are given by the following equations. x ax l l r r a a ( ( 0) 0) x in l l r r a a ( ( 0) 0) y ax l l 3 3 r r 1 1 b b ( ( 3 3 0) 0) y in l l 3 3 r r 1 1 b b ( ( 3 3 0) 0) z ax l l r r c c ( ( 0) 0) z in l l r r c c ( ( 0) 0) The bounding box B Bi in Step is defined by the axiu and iniu values of the coordinates of the points in each Cell C i obtained as a grid in the θ-φ space. The C i s are constructed such that the nuber of the points in each C i is about a few hundreds. The bounding boxes generated by the ethod entioned above are used for the intersection check. Even in the case where the intersection is detected, each cell ight include a set of points which should not be erged to the seed region. Hence we perfor another intersection check using the bounding box B A defined by the initial paraeters to detect points which should be erged to the seed region. In the cylinder case, we define the bounding box B A by p 0, p, v Ai, l + and l -. Each point in the v Bi is checked whether it is inside or outside of the B A and if it is classified to be inside, the point is regarded as a point of the seed region for the point-cloud D B. 5 EXPERIMENT We had experients by aking virtual easureent data to validate our proposed ethod. Fig. 9 shows a virtual environent which we used for the experients. Fig. 10 shows Mercator iages of the virtual point-clouds D A and D B fro the viewpoints A and B calculated by a coputer. The table 1 indicates paraeters of these data. Date D A D B Nuber of point 00M 00M Nuber of cell 0,000 0,000 Tab. 1: Paraeters of D A and D B. Coputer-Aided Design & Applications, 8(4), 011, CAD Solutions, LLC,

10 58 As shown in Fig. 9 there are 6 cylinders in the environent. Three cylinders aong the are not easured copletely because of the existence of occluded objects. On the other hand, D B easured fro the viewpoint B has coplete data of these cylinders. (a) Virtual environent fro A side. Fig. 9: Virtual environent. (b) Virtual environent fro B side. (a) Mercator iage of D A fro viewpoints A. (b) Mercator iage of D A fro viewpoints B. Fig. 10: Mercator iages of the virtual point-clouds D A and D B fro the viewpoints A and B. By the original ethod proposed by Masuda and Tanaka, the odels shown in Fig. 11(a) are obtained. Our ethod generates the odels shown in Fig. 11(b). The original ethod cannot recognize the whole cylinders, but our ethod can generate whole cylinders as one coponents. The point set included in the seed region after growing are shown in Fig. 11(c). Coputer-Aided Design & Applications, 8(4), 011, CAD Solutions, LLC,

11 59 (a) Original ethod generates. (b) Our ethod generates. (c) Seed region after growing. Fig. 11: Coparison of original ethod and our ethod. The points painted in red color are fro the point-cloud D A and those in blue are fro the pointcloud D B. In our ethod, although it takes 17 seconds to perfor the intersection tests for the pointcloud of illions of points and 0,000 grids, if we generate bounding boxes and stored the in the look-up table as a pre-process, it takes only 0.7 seconds. We have also applied our ethod to an actual easureent data and confired validity of our ethod. Fig. 1 shows the data which we have used for the experients. Fig. 1 shows point-clouds of a teple easured fro two different viewpoints and their Mercator iages. We used the point-cloud shown in Fig. 1(a) as D A and that shown in Fig. 1(b) as D B. Fig. shows the odeling result of a cylinder. It takes about 1 second to generate the cylindrical surface including the intersection tests. (a) Mercator iage of D A fro viewpoints A. (b) Mercator iage of D A fro viewpoints B. Fig. 1: Mercator iages of the virtual point-clouds D A and D B fro the viewpoints A and B. Fig. : Modeling result of a cylinder. Coputer-Aided Design & Applications, 8(4), 011, CAD Solutions, LLC,

12 530 6 CONCLUTION AND FUTURE WORK Our ethod proposed in the paper takes advantages of the previous ethod and with no odification of its interface we can reconstruct coplete shapes of the coponents, which ight not be obtained by use of one point-cloud easured fro a specific viewpoint, by using plural point-clouds easured fro several viewpoints without erging the. The processing tie is coparable with the previous ethod because the calculation of the bounding boxes can be pre-processed. We have validated our ethod by generating virtual easureent data and applying it to the and also we have applied it to an actual easureent data successfully. We are planning to apply our ethod to other ore coplicated actual easureent data, to validate it, and to iprove it for practical use. In this paper we have dealt with only two set of the point-clouds. We think it is straightforward to use ore than two point-clouds and we would like to apply our ethod for three or ore point-clouds, that akes our ethod effectively. REFERENCESERE [1] Masuda, H.; Tanaka, I.: Extraction of Surface Priitives fro Noisy Large-Scale Point-Clouds, Coputer-Aided Design & Applications, 6(3), 009, DOI:10.37/cadaps [] Masuda, H.; Tanaka, I.: As-Built 3D Modeling of Large Facilities Based on Interactive Feature Editing, Coputer-Aided Design & Applications, 7(3), 010, DOI:10.37/cadaps [3] Sharf, A.; Alexa, M.; Cohen-Or, D.: Context-based Surface Copletion, ACM Transaction of Graphics, 3(3), 004, DOI: / [4] Ju, T.: Robust Repair of Polygonal Models, ACM Transaction of Graphics, 3(3), 004, DOI: / [5] Xu, H.; Gossett, N.; Chen, B.: PointWorks: Abstraction and Rendering of Sparsely Scanned Outdoor Environents, Proc. of the 004 Eurographics Syposiu on Rendering, 004, [6] Yuan, X.; Xu, H. ; Nguyen, M.; Shesh, A.; Chen, B.: Sketch-Based Segentation of Scanned Outdoor Environent Models, Proc. of the nd Eurographics Workshop on Sketch-Based Interfaces and Modeling, 005, 19-6.Debra, N. L.: Principles of Mechanical Design, Oxford University Press, New York, NY, [7] Debevec, P.; Taylor, C.; Malik, J.: Modeling and Rendering Architecture fro Photographs: A Hybrid Geoetry- and Iage-Based Approach, SIGGRAPH 96, 1996, DOI: / [8] Isenburg, M.; Liu, Y.; Shewchuk, J.; Snoeyink, J.: Streaing Coputation of Delaunay Triangulations, ACM Transactions on Graphics, 5(3), 006, DOI: / [9] Isenburg, M.; Lindstro, P.: Streaing Meshes, Proc. of IEEE Visualization, 005, DOI: /VIS [10] Levin, D.: Mesh-Independent Surface Interpolation, Geoetric Modeling for Scientific Visualization, 003, Coputer-Aided Design & Applications, 8(4), 011, CAD Solutions, LLC,