The key issues such as vision sensor, sampling planning are studied for reverse engineering. For the developed sensor, the low sensitivity to the incident angle and the high linearity between the output and the input ...The key issues such as vision sensor, sampling planning are studied for reverse engineering. For the developed sensor, the low sensitivity to the incident angle and the high linearity between the output and the input are carried out. During digitizing, the adaptive sampling planning method based on the curvature of surface and the slope of tangent line of measured point is proposed. After integrating the vision sensor, CNC milling and relevant software, the reverse engineering system based on computer vision is developed. The experiment shows that this system is reliable and efficient.展开更多
A new method of extraction of blend surface feature is presented. It contains two steps: segmentation and recovery of parametric representation of the blend. The segmentation separates the points in the blend region f...A new method of extraction of blend surface feature is presented. It contains two steps: segmentation and recovery of parametric representation of the blend. The segmentation separates the points in the blend region from the rest of the input point cloud with the processes of sampling point data, estimation of local surface curvature properties and comparison of maximum curvature values. The recovery of parametric representation generates a set of profile curves by marching throughout the blend and fitting cylinders. Compared with the existing approaches of blend surface feature extraction, the proposed method reduces the requirement of user interaction and is capable of extracting blend surface with either constant radius or variable radius. Application examples are presented to verify the proposed method.展开更多
For reconstructing a freeform feature from point cloud, a deformation-based method is proposed in this paper. The freeform feature consists of a secondary surface and a blending surface. The secondary surface plays a ...For reconstructing a freeform feature from point cloud, a deformation-based method is proposed in this paper. The freeform feature consists of a secondary surface and a blending surface. The secondary surface plays a role in substituting a local region of a given primary surface. The blending surface acts as a bridge to smoothly connect the unchanged region of the primary surface with the secondary surface. The secondary surface is generated by surface deformation subjected to line constraints, i.e., character lines and limiting lines, not designed by conventional methods. The lines are used to represent the underlying informa-tion of the freeform feature in point cloud, where the character lines depict the feature’s shape, and the limiting lines determine its location and orientation. The configuration of the character lines and the extraction of the limiting lines are discussed in detail. The blending surface is designed by the traditional modeling method, whose intrinsic parameters are recovered from point cloud through a series of steps, namely, point cloud slicing, circle fitting and regression analysis. The proposed method is used not only to effectively and efficiently reconstruct the freeform feature, but also to modify it by manipulating the line constraints. Typical examples are given to verify our method.展开更多
This paper applied the neural network technology to surface reasoning in reverse engineering and established the neural network computation model. One of the main advantages of reasoning solid surface using neural net...This paper applied the neural network technology to surface reasoning in reverse engineering and established the neural network computation model. One of the main advantages of reasoning solid surface using neural network is that no knowledge about surface is needed, and the limited measured points on the surface will do sufficiently. This paper listed the related reasoning cases, including the elementary analytical surfaces and freeform surfaces, discussed the various issues occurring during reasoning process and proved the feasibility and efficiency of this approach from theory and practical computing cases. The results show that a neural network is an excellent aided analysis means for surface reasoning in reversing engineering and possesses practical use for the surface that is complex, incomplete and partially worn out or damaged.展开更多
the reconstruction of transition surface is one of time consuming activities during surface modeling in reverse engineering. Yet currently available software applications suffer from shortcoming in processing the conn...the reconstruction of transition surface is one of time consuming activities during surface modeling in reverse engineering. Yet currently available software applications suffer from shortcoming in processing the connection among free form surfaces. In this paper, a new method is put forward combining Surfacer with Unigraphics to resolve this problem: Curves and surfaces are first constructed in Surfacer, then, the finished data is imported into Unigraphics based on IGES fonnat. At last, the transition surface can be reconstructed in Unigraphics. The application of this method in transition surface reconstruction is illustrated by means of two case studies, showing the connection between free form surfaces; filleting and rounding among multiple surfaces: transition surface between two sets of surfaces.展开更多
In this paper, a wild boar head was taken as the bionic research object for the development of new ridgers, a kind of plough. The reverse engineering technology was adopted to obtain the surface geometrical informatio...In this paper, a wild boar head was taken as the bionic research object for the development of new ridgers, a kind of plough. The reverse engineering technology was adopted to obtain the surface geometrical information of the head. Several three-dimensional (3D) point clouds of the head were captured first using a non-touch laser scanner, and an integrated point cloud was generated by aligning these point clouds using UG/Imageware. Then, the digital surface model of the head was rebuilt by means of CATIA. The characteristic curves of the surface model were analyzed. The results show that the average error between the rebuilt surface and the point cloud is -0.431 ram. The max curvature of the ridge on the neb of the head is 0.187 mm^-1, and the max and rain Gauss curvatures on the surface are 0.008 mm^-2 and -0.002 mm^-2. These geometrical information are the essential parameters for biomimetics study of the ridger.展开更多
This paper presents a principle and a method of col or 3D laser scanning measurement. Based on the fundamental monochrome 3D measureme nt study, color information capture, color texture mapping, coordinate computati o...This paper presents a principle and a method of col or 3D laser scanning measurement. Based on the fundamental monochrome 3D measureme nt study, color information capture, color texture mapping, coordinate computati on and other techniques are performed to achieve color 3D measurement. The syste m is designed and composed of a line laser light emitter, one color CCD camera, a motor-driven rotary filter, a circuit card and a computer. Two steps in captu ring object’s images in the measurement process: First, the color CCD camera ta kes the color picture of the object to be used for texture mapping in post proce ssing. Secondly, the monochrome data of the object is taken. The laser light emi tter is started; the light plane and the surface of the object intersect to form an undulate line, which forms an image on the CCD sensor. After the optic- electronics transformation, the electronic signals are captured and send to the computer. A new color 3D measurement model was derived, and a rapid calibra ting method to measure the system parameters was proposed--optical plane equat ion calibrating method. A calibrating drone was designed and built. 3D color sca nning system not only provides an object’s individual point information in the 3D coordinate, in the mean time, it provides the color information of each indiv idual point. This paper also advances a multi-frame auto-merging method, i.e. several frames of color 3D digital images measured are merged quickly according to their curvature characteristics and RGB information. Initial matching and fin e tune of the registration are completely performed by the computer; initial mat ching is via user interface in helping computer to find the transformation matri x. The transformation matrix is found according to the geometric characteristics chosen by hand. After the initial transformation matrix is found, fine tune of the registration is preformed to do the optimum adjustment to achieve a complete color textured 3D model. The system can be broadly used in the fields of produc t design, mold manufacture, multimedia, game development, animation, medical eng ineering, antique digitization, etc.展开更多
The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features becau...The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.展开更多
Acquisition of physical data with high precision is a key step in reverse engineering (RE). It is an important stimulative for the progress of reverse engineering with which various digitizing devices are invent ed,...Acquisition of physical data with high precision is a key step in reverse engineering (RE). It is an important stimulative for the progress of reverse engineering with which various digitizing devices are invent ed, developed and made applicable. This paper introduces a three dimensional opt ical measurement method based on digital fringe projection technique in RE to im prove the technique through its application. A practical example is presented an d the result demonstrates the applicability and feasibility of the measurement s ystem as well as the reliability and validity of relevant methods and algorithms .展开更多
Intersections and discontinuities commonly arise in surface modeling and cause problems in downstream operations. Local geometry repair, such as cover holes or replace bad surfaces by adding new surface patches for de...Intersections and discontinuities commonly arise in surface modeling and cause problems in downstream operations. Local geometry repair, such as cover holes or replace bad surfaces by adding new surface patches for dealing with inconsistencies among the confluent region, where multiple surfaces meet, is a common technique used in CAD model repair and reverse engineering. However, local geometry repair destroys the topology of original CAD model and increases the number of surface patches needed for freeform surface shape modeling. Consequently, a topology recovery technique dealing with complex freeform surface model after local geometry repair is proposed. Firstly, construct the curve network which freeform surface model; secondly, apply freeform surface fitting method determine the geometry and topology properties of recovery to create B-spline surface patches to recover the topology of trimmed ones. Corresponding to the two levels of enforcing boundary conditions on a B-spline surface, two solution schemes are presented respectively. In the first solution scheme, non-constrained B-spline surface fitting method is utilized to piecewise recover trimmed confluent surface patches and then employs global beautification technique to smoothly stitch the recovery surface patches. In the other solution scheme, constrained B-spline surface fitting technique based on discretization of boundary conditions is directly applied to recover topology of surface model after local geometry repair while achieving G~ continuity simultaneously. The presented two different schemes are applied to the consistent surface model, which consists of five trimmed confluent surface patches and a local consistent surface patch, and a machine cover model, respectively. The application results show that our topology recovery technique meets shape-preserving and Gt continuity requirements in reverse engineering. This research converts the problem of topology recovery for consistent surface model to the problem of constructing G1 patches from a given curve network, and provides a new idea to model repairing study.展开更多
Developing CNC measuring method on the base of coordinate machine can makethe best of the hardware resource of CNC system and realize the integration of CAD/CAM/CAT. Based onthe evenly spaced parallel planes scanning,...Developing CNC measuring method on the base of coordinate machine can makethe best of the hardware resource of CNC system and realize the integration of CAD/CAM/CAT. Based onthe evenly spaced parallel planes scanning, a new adaptive digitizing approach for freeform surfacenamely arc length extrapolation is put forward. By this way, the digitizing approach can be addedto the CNC system, while the system's hardware and software are not changed.展开更多
A new method is put forward combining computer vision with computer aidedgeometric design (CAGD) to resolve the problem of free-form surface reconstruction. The surface isfirst subdivided into N-sided Gregory patches,...A new method is put forward combining computer vision with computer aidedgeometric design (CAGD) to resolve the problem of free-form surface reconstruction. The surface isfirst subdivided into N-sided Gregory patches, and a stereo algorithm is used to reconstruct theboundary curves. Then, the cross boundary tangent vectors are computed through reflectance analysis.At last, the whole surface can be reconstructed jointing these patches with G^1 continuity(tangentcontinuity). Examples on synthetic images are given.展开更多
Visual method is now broadly used in reverse engineering for 3D reconstruction. The traditional computer vision methods are feature-based, i.e., they require that the objects must reveal features owing to geometry or ...Visual method is now broadly used in reverse engineering for 3D reconstruction. The traditional computer vision methods are feature-based, i.e., they require that the objects must reveal features owing to geometry or textures. For textureless free-form surfaces, dense feature points are added artificially. In this paper, a new method is put forward combining computer vision with CAGD. The surface is subdivided into N-side Gregory patches using marked curves, and a stereo algorithm is used to reconstruct the curves. Then, the cross boundary tangent vector is computed through reflectance analysis. At last, the whole surface can be reconstructed by jointing these patches with 1Gcontinuity.展开更多
Smoothly stitching multiple surfaces mainly represented by B-spline or NURBS together is an extremely important issue in complex surfaces modeling and reverse engineering. In recent years, a lot of progress has been m...Smoothly stitching multiple surfaces mainly represented by B-spline or NURBS together is an extremely important issue in complex surfaces modeling and reverse engineering. In recent years, a lot of progress has been made in smooth join of non-trimmed surface patches, while there has been seldom research on smoothly stitching trimmed surface patches together. This paper studies the problem of global continuity adjustment, damaged hole repair and local shape optimization for complex trimmed surface model, and presents a uniform scheme to deal with continuity adjustment of trimmed surfaces and geometric repair of local broken region. Constrained B-spline surface refitting technique and trim calculation are first utilized to achieve global G^1 continuity, and then local shape optimization functional is adopted to reduce fitting error and improve local quality of refitted surface patch. The proposed approach is applied to a discontinuity ship hull surface model with an irregular hole, and the result demonstrates the validation of our method. Furthermore, on the premise of global continuity, the proposed locally repairing damaged surface model provides a better foundation for following research work, such as topology recovery technique for complex surface model after geometric repair.展开更多
NC code or STL file can be generated directly from measuring data in a fastreverse-engineering mode. Compressing the massive data from laser scanner is the key of the newmode. An adaptive compression method based on t...NC code or STL file can be generated directly from measuring data in a fastreverse-engineering mode. Compressing the massive data from laser scanner is the key of the newmode. An adaptive compression method based on triangulated-surfaces model is put forward.Normal-vector angles between triangles are computed to find prime vertices for removal. Ring datastructure is adopted to save massive data effectively. It allows the efficient retrieval of allneighboring vertices and triangles of a given vertices. To avoid long and thin triangles, a newre-triangulation approach based on normalized minimum-vertex-distance is proposed, in which thevertex distance and interior angle of triangle are considered. Results indicate that the compressionmethod has high efficiency and can get reliable precision. The method can be applied in fastreverse engineering to acquire an optimal subset of the original massive data.展开更多
文摘The key issues such as vision sensor, sampling planning are studied for reverse engineering. For the developed sensor, the low sensitivity to the incident angle and the high linearity between the output and the input are carried out. During digitizing, the adaptive sampling planning method based on the curvature of surface and the slope of tangent line of measured point is proposed. After integrating the vision sensor, CNC milling and relevant software, the reverse engineering system based on computer vision is developed. The experiment shows that this system is reliable and efficient.
基金This project is supported by General Electric Corporate ResearchDevelopment and National Advanced Technology Project of China (No.863-511-942-018).
文摘A new method of extraction of blend surface feature is presented. It contains two steps: segmentation and recovery of parametric representation of the blend. The segmentation separates the points in the blend region from the rest of the input point cloud with the processes of sampling point data, estimation of local surface curvature properties and comparison of maximum curvature values. The recovery of parametric representation generates a set of profile curves by marching throughout the blend and fitting cylinders. Compared with the existing approaches of blend surface feature extraction, the proposed method reduces the requirement of user interaction and is capable of extracting blend surface with either constant radius or variable radius. Application examples are presented to verify the proposed method.
基金the National Natural Science Foundation of China (No. 50575098)China Postdoctoral Science Foundation
文摘For reconstructing a freeform feature from point cloud, a deformation-based method is proposed in this paper. The freeform feature consists of a secondary surface and a blending surface. The secondary surface plays a role in substituting a local region of a given primary surface. The blending surface acts as a bridge to smoothly connect the unchanged region of the primary surface with the secondary surface. The secondary surface is generated by surface deformation subjected to line constraints, i.e., character lines and limiting lines, not designed by conventional methods. The lines are used to represent the underlying informa-tion of the freeform feature in point cloud, where the character lines depict the feature’s shape, and the limiting lines determine its location and orientation. The configuration of the character lines and the extraction of the limiting lines are discussed in detail. The blending surface is designed by the traditional modeling method, whose intrinsic parameters are recovered from point cloud through a series of steps, namely, point cloud slicing, circle fitting and regression analysis. The proposed method is used not only to effectively and efficiently reconstruct the freeform feature, but also to modify it by manipulating the line constraints. Typical examples are given to verify our method.
文摘This paper applied the neural network technology to surface reasoning in reverse engineering and established the neural network computation model. One of the main advantages of reasoning solid surface using neural network is that no knowledge about surface is needed, and the limited measured points on the surface will do sufficiently. This paper listed the related reasoning cases, including the elementary analytical surfaces and freeform surfaces, discussed the various issues occurring during reasoning process and proved the feasibility and efficiency of this approach from theory and practical computing cases. The results show that a neural network is an excellent aided analysis means for surface reasoning in reversing engineering and possesses practical use for the surface that is complex, incomplete and partially worn out or damaged.
基金Supported by Youth Science Foundation of Guangxi(No.0339004)
文摘the reconstruction of transition surface is one of time consuming activities during surface modeling in reverse engineering. Yet currently available software applications suffer from shortcoming in processing the connection among free form surfaces. In this paper, a new method is put forward combining Surfacer with Unigraphics to resolve this problem: Curves and surfaces are first constructed in Surfacer, then, the finished data is imported into Unigraphics based on IGES fonnat. At last, the transition surface can be reconstructed in Unigraphics. The application of this method in transition surface reconstruction is illustrated by means of two case studies, showing the connection between free form surfaces; filleting and rounding among multiple surfaces: transition surface between two sets of surfaces.
基金The authors are grateful for the financial support by the National Natural Science Foundation of China(Grant No.50635030)the Scientific and Technological Development Project of Jilin Province(Grant No.20050539)the"985 Project"of Jilin University.
文摘In this paper, a wild boar head was taken as the bionic research object for the development of new ridgers, a kind of plough. The reverse engineering technology was adopted to obtain the surface geometrical information of the head. Several three-dimensional (3D) point clouds of the head were captured first using a non-touch laser scanner, and an integrated point cloud was generated by aligning these point clouds using UG/Imageware. Then, the digital surface model of the head was rebuilt by means of CATIA. The characteristic curves of the surface model were analyzed. The results show that the average error between the rebuilt surface and the point cloud is -0.431 ram. The max curvature of the ridge on the neb of the head is 0.187 mm^-1, and the max and rain Gauss curvatures on the surface are 0.008 mm^-2 and -0.002 mm^-2. These geometrical information are the essential parameters for biomimetics study of the ridger.
文摘This paper presents a principle and a method of col or 3D laser scanning measurement. Based on the fundamental monochrome 3D measureme nt study, color information capture, color texture mapping, coordinate computati on and other techniques are performed to achieve color 3D measurement. The syste m is designed and composed of a line laser light emitter, one color CCD camera, a motor-driven rotary filter, a circuit card and a computer. Two steps in captu ring object’s images in the measurement process: First, the color CCD camera ta kes the color picture of the object to be used for texture mapping in post proce ssing. Secondly, the monochrome data of the object is taken. The laser light emi tter is started; the light plane and the surface of the object intersect to form an undulate line, which forms an image on the CCD sensor. After the optic- electronics transformation, the electronic signals are captured and send to the computer. A new color 3D measurement model was derived, and a rapid calibra ting method to measure the system parameters was proposed--optical plane equat ion calibrating method. A calibrating drone was designed and built. 3D color sca nning system not only provides an object’s individual point information in the 3D coordinate, in the mean time, it provides the color information of each indiv idual point. This paper also advances a multi-frame auto-merging method, i.e. several frames of color 3D digital images measured are merged quickly according to their curvature characteristics and RGB information. Initial matching and fin e tune of the registration are completely performed by the computer; initial mat ching is via user interface in helping computer to find the transformation matri x. The transformation matrix is found according to the geometric characteristics chosen by hand. After the initial transformation matrix is found, fine tune of the registration is preformed to do the optimum adjustment to achieve a complete color textured 3D model. The system can be broadly used in the fields of produc t design, mold manufacture, multimedia, game development, animation, medical eng ineering, antique digitization, etc.
基金This project is supported by Research Foundation for Doctoral Program of Higher Education, China (No.98033532)
文摘The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.
基金Project supported by the Science Foundation of Shanghai Munici pal Commission of Science and Technology ( Grant No.011461059)
文摘Acquisition of physical data with high precision is a key step in reverse engineering (RE). It is an important stimulative for the progress of reverse engineering with which various digitizing devices are invent ed, developed and made applicable. This paper introduces a three dimensional opt ical measurement method based on digital fringe projection technique in RE to im prove the technique through its application. A practical example is presented an d the result demonstrates the applicability and feasibility of the measurement s ystem as well as the reliability and validity of relevant methods and algorithms .
基金supported by China Postdoctoral Science Foundation(Grant No. 20110490376)National Natural Science Foundation of China (Grant No. 50575098)
文摘Intersections and discontinuities commonly arise in surface modeling and cause problems in downstream operations. Local geometry repair, such as cover holes or replace bad surfaces by adding new surface patches for dealing with inconsistencies among the confluent region, where multiple surfaces meet, is a common technique used in CAD model repair and reverse engineering. However, local geometry repair destroys the topology of original CAD model and increases the number of surface patches needed for freeform surface shape modeling. Consequently, a topology recovery technique dealing with complex freeform surface model after local geometry repair is proposed. Firstly, construct the curve network which freeform surface model; secondly, apply freeform surface fitting method determine the geometry and topology properties of recovery to create B-spline surface patches to recover the topology of trimmed ones. Corresponding to the two levels of enforcing boundary conditions on a B-spline surface, two solution schemes are presented respectively. In the first solution scheme, non-constrained B-spline surface fitting method is utilized to piecewise recover trimmed confluent surface patches and then employs global beautification technique to smoothly stitch the recovery surface patches. In the other solution scheme, constrained B-spline surface fitting technique based on discretization of boundary conditions is directly applied to recover topology of surface model after local geometry repair while achieving G~ continuity simultaneously. The presented two different schemes are applied to the consistent surface model, which consists of five trimmed confluent surface patches and a local consistent surface patch, and a machine cover model, respectively. The application results show that our topology recovery technique meets shape-preserving and Gt continuity requirements in reverse engineering. This research converts the problem of topology recovery for consistent surface model to the problem of constructing G1 patches from a given curve network, and provides a new idea to model repairing study.
基金This project is supported by Provincial Key Science and Technology Planning of Zhejiang(No.971111198).
文摘Developing CNC measuring method on the base of coordinate machine can makethe best of the hardware resource of CNC system and realize the integration of CAD/CAM/CAT. Based onthe evenly spaced parallel planes scanning, a new adaptive digitizing approach for freeform surfacenamely arc length extrapolation is put forward. By this way, the digitizing approach can be addedto the CNC system, while the system's hardware and software are not changed.
基金National Natural Science Foundation of China(No.59975057).
文摘A new method is put forward combining computer vision with computer aidedgeometric design (CAGD) to resolve the problem of free-form surface reconstruction. The surface isfirst subdivided into N-sided Gregory patches, and a stereo algorithm is used to reconstruct theboundary curves. Then, the cross boundary tangent vectors are computed through reflectance analysis.At last, the whole surface can be reconstructed jointing these patches with G^1 continuity(tangentcontinuity). Examples on synthetic images are given.
文摘Visual method is now broadly used in reverse engineering for 3D reconstruction. The traditional computer vision methods are feature-based, i.e., they require that the objects must reveal features owing to geometry or textures. For textureless free-form surfaces, dense feature points are added artificially. In this paper, a new method is put forward combining computer vision with CAGD. The surface is subdivided into N-side Gregory patches using marked curves, and a stereo algorithm is used to reconstruct the curves. Then, the cross boundary tangent vector is computed through reflectance analysis. At last, the whole surface can be reconstructed by jointing these patches with 1Gcontinuity.
基金supported by National Natural Science Foundation of China (Grant No.50575098)
文摘Smoothly stitching multiple surfaces mainly represented by B-spline or NURBS together is an extremely important issue in complex surfaces modeling and reverse engineering. In recent years, a lot of progress has been made in smooth join of non-trimmed surface patches, while there has been seldom research on smoothly stitching trimmed surface patches together. This paper studies the problem of global continuity adjustment, damaged hole repair and local shape optimization for complex trimmed surface model, and presents a uniform scheme to deal with continuity adjustment of trimmed surfaces and geometric repair of local broken region. Constrained B-spline surface refitting technique and trim calculation are first utilized to achieve global G^1 continuity, and then local shape optimization functional is adopted to reduce fitting error and improve local quality of refitted surface patch. The proposed approach is applied to a discontinuity ship hull surface model with an irregular hole, and the result demonstrates the validation of our method. Furthermore, on the premise of global continuity, the proposed locally repairing damaged surface model provides a better foundation for following research work, such as topology recovery technique for complex surface model after geometric repair.
基金This project is supported by Provincial Key Project of Science and Technology of Zhejiang(No.2003C21031).
文摘NC code or STL file can be generated directly from measuring data in a fastreverse-engineering mode. Compressing the massive data from laser scanner is the key of the newmode. An adaptive compression method based on triangulated-surfaces model is put forward.Normal-vector angles between triangles are computed to find prime vertices for removal. Ring datastructure is adopted to save massive data effectively. It allows the efficient retrieval of allneighboring vertices and triangles of a given vertices. To avoid long and thin triangles, a newre-triangulation approach based on normalized minimum-vertex-distance is proposed, in which thevertex distance and interior angle of triangle are considered. Results indicate that the compressionmethod has high efficiency and can get reliable precision. The method can be applied in fastreverse engineering to acquire an optimal subset of the original massive data.