Lofted B-spline surface interpolation by linearly constrained energy minimization [CAD 2003, CAD 2008]
Given a sequence of contours each of whose point number varies from contour to contour, this work presents a method for generating a B-spline surface that passes through all the contour points with fewer control points. (a) Data points along serial contours whose point number varies from contour to contour (b) B-spline curves made compatible using linearly constrained energy minimization (c) Control net of a lofted B-spline surface (d) Wireframe of the B-spline surface You can refer to the work [IJAMT 2004a] which presents another interesting method using universal parameterization. |
3D shape reconstruction from 2D cross-sections [CAD 1996, JDM 1995, IJAMT 2005b, IJAMT 2000, IJAMT 1999]
 (a) Contours extracted from CT(Computerized Tomography) images of a human femur (b) Triangular mesh obtained via triangulation techniques such as tiling, branching, capping, and merging (c) Shaded display of the triangular mesh (d) Shaded display of the triangular mesh with normal smoothing  (a) Skinned surfaces represented with rectangular B-spline surfaces (b) Branced surface represented with triangular Bezier patches (c) Capped surfaces represented with triangular Bezier patches (d) Composite surface |
Smooth surface approximation to scattered 3D points [CAD 1995] |
This work describes an adaptive method for smooth surface approximation from scattered 3D points. The approximating surface is represented by a piecewise cubic triangular Bezier surface with C1 continuity. The method begins with a rough surface interpolating only boundary points and, in the successive steps, refines it by adding the maximum error point at a time among the remaining internal points until the desired approximation accuracy is reached. |
 (a) Scattered points with boundary polygons (b) Triangular mesh which is adaptively refined (c) C1 triangular Bezier surface defined over its domain mesh |