RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES

A method to reconstruct symmetric B-spline curves and surfaces is presented. The symmetry property is realized by using symmetric knot vector and symmetric control points. Firstly, data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points. Then the divided data points are parameterized and a symmetric knot vector is selected in order to get symmetric B-spline basis functions. Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be symmetric with respect to the extracted symmetry axis or symmetry plane. Lastly, the constrained least squares fitting problem is solved with the Lagrange multiplier method. Two examples from industry are given to show that the proposed method is efficient, robust and able to meet the general engineering requirements.

MICRO-ROBOT FOR MEASUREMENT AND THREE-DIMENSION RECONSTRUCTION OF MICROPIPES

The presented system consists of field devices, a control system and a host computer system. The field devices, which are composed of an in-pipe micro-robot, a displacement sensor, a curvature sensor, and an inner surface measurement unit, can go into the pipe to get the data of displace- ment and axis curvature, and the shape data of the inner surface. With the conic-shape laser beam shot by the inner surface measurement unit, the intersectional curve between the laser beam and the inner-surface of the tested pipe can be calculated in the local coordination system （LCS） of the inner surface measurement unit. The relation between the LCS and the global coordination system （GCS） can be deduced, too. After the robot reaches the end of the pipe, all measured intersectional curves can be translated into the same coordination system to become a point cloud of the inner surface of the pipe according to the relations between LCS and GCS. Depending on this points cloud, the CAD model of the inner surface of the pipe can be reconstructed easily with reverse engineering tools, and the feature of flaw of the pipe can be obtained with flaw analysis tools.

An Approximating Algorithm on Reconstruction of Complicated Curved Surface

An approximating algorithm on handling 3-D points cloud data was discussed for reconstruction of complicated curved surface. In this algorithm, the coordinate information of nodes both in internal and external regions of partition interpolation was used to realize minimized least squares approximation error of surface fitting. The changes between internal and external interpolation regions are continuous and smooth. Meanwhile, surface shape has properties of local controllability, variation reduction, and convex hull. The practical example shows that this algorithm possesses a higher accuracy of curved surface reconstruction and also improves the distortion of curved surface reconstruction when typical approximating algorithms and unstable operation are used.

A New Algorithm for Feature Matching in Reverse Engineering

Feature recognition and surface reconstruction from point clouds are difficulties in reverse engineering. A new surface reconstruction algorithm for slicing point cloud was presented. The contours of slice were extracted. Then, the intersection of two adjacent curve segments in the contour was obtained and curves feature was extracted. Finally, adjacent section contours were matched directly with Fourier-Mellin curve matching method for feature extraction. An example of 3-D model reconstruction shows the reliability and application of the algorithm.