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Abstract: This paper proposes a method to construct a B-spline surface that interpolates the specified four groups of boundary derivative curves in the B-spline form. The discontinuity can be bounded by an arbitrary geometric invariant as the tolerance. The method first handles the six types of the compatibility problems by continuity-preserving reparameterization, knot-insertion and local control-point tuning. The transformed boundary conditions are then parametrically compatible, so the Coons strategy can be applied to construct the final interpolant. Not only can it be used in the reliable geometric modeling, but the approach also can be applied to many other algorithms that require compatibility guarantee. [Copyright &y& Elsevier]

Abstract: An unstructured tetrahedral mesh generation algorithm for 3D model with constraints is presented. To automatically generate a tetrahedral mesh for model with constraints, an advancing front algorithm is presented based on conforming constrained Delaunay tetrahedralization (CCDT). To reduce the number of visibility tests between vertices with respect to model faces as well as the computation of constrained Delaunay tetrahedra, a sufficient condition for DT (constrained Delaunay tetrahedralization whose simplexes are all Delaunay) existence is presented and utilized coupled to uniform grid and advancing front techniques in our algorithm. The mesh generator is robust and exhibits a linear time complexity for mechanical models with uniform density distribution. [Copyright &y& Elsevier]

Abstract: This paper focuses on interpolating vertices and normal vectors of a closed quad-dominant mesh 1 [1] A mesh is quad-dominant if it contains quad facets as its majority. The quantity of quad facets is much more than the quantity of triangular and other multi-sided facets. -continuously using regular Coons B-spline surfaces, which are popular in industrial CAD/CAM systems. We first decompose all non-quadrangular facets into quadrilaterals. The tangential and second-order derivative vectors are then estimated on each vertex of the quads. A least-square adjustment algorithm based on the homogeneous form of continuity condition is applied to achieve curvature continuity. Afterwards, the boundary curves, the first- and the second-order cross-boundary derivative curves are constructed fulfilling continuity and compatibility conditions. Coons B-spline patches are finally generated using these curves as boundary conditions. In this paper, the upper bound of the rank of continuity condition matrices is also strictly proved to be , and the method of tangent-vector estimation is improved to avoid petal-shaped patches in interpolating solids of revolution. Several examples demonstrate its feasibility. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a second order geometric iteration algorithm for point projection and inversion on parametric surfaces. The iteration starts from an initial projection estimation. In each iteration, we construct a second order osculating torus patch to the parametric surface at the previous projection. Then we project the test point onto the torus patch to compute the next projection and its parameter. This iterative process is terminated when the parameter satisfies the required precision. Experiments demonstrate the convergence speed of our algorithm. [Copyright &y& Elsevier]

Abstract: A new algorithm for reducing control points in lofted surface interpolation to rows of data points is presented in this paper. The key step of surface lofting is to obtain a set of compatible B-spline curves interpolating each row. Given a set of points and their parameterization, a necessary and sufficient condition is proposed to determine the existence of interpolating B-spline curves defined on a given knot vector. Based on this condition, we first properly construct a common knot vector that guarantees the existence of interpolating B-spline curves to each row of points. Then we calculate a set of interpolating B-spline curves defined on the common knot vector by energy minimization. Using this method, fewer control points are employed while maintaining a visually pleasing shape of the lofted surface. Several experimental results demonstrate the usability and quality of the proposed method. [Copyright &y& Elsevier]

Abstract: By Bezout''s theorem, three quadric surfaces have at most eight isolated intersections although they may have infinitely many intersections. In this paper, we present an efficient and robust algorithm, to obtain the isolated and the connected components of, or to determine the number of isolated real intersections of, three quadric surfaces by reducing the problem to computing the real intersections of two planar curves obtained by Levin''s method. [Copyright &y& Elsevier]

Abstract: A new algorithm for Boolean operations on general planar polygons is presented. It is available for general planar polygons (manifold or non-manifold, with or without holes). Edges of the two general polygons are subdivided at the intersection points and touching points. Thus, the boundary of the Boolean operation resultant polygon is made of some whole edges of the polygons after the subdivision process. We use the simplex theory to build the basic mathematical model of the new algorithm. The subordination problem between an edge and a polygon is reduced to a problem of determining whether a point is on some edges of some simplices or inside the simplices, and the associated simplicial chain of the resultant polygon is just an assembly of some simplices and their coefficients of the two polygons after the subdivision process. Examples show that the running time required by the new algorithm is less than one-third of that by the Rivero and Feito algorithm. [Copyright &y& Elsevier]