Jiaye Wang

• Shandong University

Saving material and improving strength are two important but conflicting requirements in 3D printing. We propose a novel method for designing the internal supporting frame structures of 3D objects based on their medial axis such that the objects are fabricated with minimal amount of material but can still withstand specified external load. Our meth...

There are several prevailing methods for selecting knots for curve interpolation. A desirable criterion for knot selection is whether the knots can assist an interpolation scheme to achieve the reproduction of polynomial curves of certain degree if the data points to be interpolated are taken from such a curve. For example, if the data points are s...

Given two sets of points ℝ and B in the plane, we address the problem of finding a set of circles ℂ = {ci, i = 1, 2,... ,k}, satisfying the condition that every point in ℝ is covered by at least one circle in ℂ and each point in B is not covered by any circle in ℂ. We conjecture that to find such a set with the smallest k is NP-hard. In this paper,...

Path planning is one of important problems in virtual reality, computational geometry, robotic and GIS. This paper presents two methods of computing walkthrough paths in a polygon with h holes and a total of n vertices, for 3D virtual worlds such as virtual museums and games. For any two points s and t, one method is presented to compute the shorte...

Abstract Updating a Delaunay triangulation when data points are slightly moved is the bottleneck of computation time in variational methods for mesh generation and remeshing. Utilizing the connectivity coherence between two consecutive Delaunay triangulations for computation speedup is the key to solving this problem. Our contribution is an effecti...

There are several prevailing methods for selecting knots for curve interpolation. A desirable criterion for knot selection is whether the knots can assist an interpolation scheme to achieve the reproduction of polynomial curves of certain degree if the data points to be interpolated are taken from such a curve. For example, if the data points are s...

We present a method that uses signature sequences to classify the intersection curve of two quadrics (QSIC) or, equivalently, quadric pencils in PR3 (3D real projective space), in terms of the shape, topological properties, and algebraic properties of the QSIC. Specifically, for a QSIC we consider its singularity, reducibility, the number of its co...

A new fast two-dimension 8×8 discrete cosine transform (2D 8×8 DCT) algorithm based on the characteristics of the basic images of 2D DCT is presented. The new algorithm computes each DCT coefficient in turn more independently. Hence, the new algorithm is suitable for 2D DCT pruning algorithm of pruning away any number of high-frequency components o...

This paper proposes a new algorithm for querying the shortest path between two points s and t in a simple polygon P based on Voronoi diagram(VD). Based on the polygon's VD, we first find the Voronoi skeleton path S(s, t) from point s to t, and then along which we compute the shortest path SP(s, t) by visibility computing simultaneously. SP(s, t) ca...

We present an efficient method for classifying the morphology of the intersection curve of two quadrics (QSIC) in PR3, 3D real projective space; here, the term morphology is used in a broad sense to mean the shape, topological, and algebraic properties of a QSIC, including singularity, reducibility, the number of connected components, and the degre...

A new fast and easy to implement tracing algorithm is presented for querying the intersection points of two convex polygons. We trace two edges to find the intersection points always along the boundaries of the union and intersection of P and Q respectively, which is different from O'Rourke 's method that traces two edges always along P and Q respe...

In order to improve the precision of the boundary in 3D reconstruction, this paper analyzes the error brought by the Marching Cubes method and presents a new method. The new method distinguishes the pixels inside, across or outside of the boundary by a threshold, and determines the position of the boundary point according to the values of the three...

We present a simple, accurate and efficient algorithm for collision detection among moving ellipsoids. Its efficiency is attributed to two results: (i) a simple algebraic test for the separation of two ellipsoids, and (ii) an efficient method for constructing a separating plane between two disjoint ellipsoids. Inter-frame coherence is exploited by...

The construction of aGC 1 cubic interpolating curve that lies on the same side of a given straight line as the data points is studied. The main task is to choose appropriate approaches to modify tangent vectors at the data points for the desired curve. Three types of approaches for changing the magnitudes of the tangent vectors are presented. The f...

This paper discusses the problem of constructing C2 quartic spline surface interpolation. Decreasing the continuity of the quartic spline to C2 offers additional freedom degrees that can be used to adjust the precision and the shape of the interpolation surface. An approach to determining the freedom degrees is given, the continuity equations for c...

We present new results on classifying the morphology of the nonsingular intersection curve of two quadrics by studying the roots of the characteristic equation, or the discriminant, of the pencil spanned by the two quadrics. The morphology of a nonsingular algebraic curve means the structural (or topological) information about the curve, such as th...

This paper presents a simple, accurate, and efficient algorithm for collision detection among moving ellipsoids. The efficiency of this algorithm is based on two important results: (i) a simple algebraic test for the separation of two ellipsoids, and (ii) an efficient method for constructing a separating plane between two disjoint ellipsoids. Frame...

Generally speaking, it is impossible for a wire-frame to define a 3D object uniquely. But wire-frame as a graphics medium is still applied in some industrial areas. A sufficient condition is presented in this paper. If this condition is satisfied by a wire-frame, then the wire-frame can represent a 3D object uniquely. The result is applied to manuf...

Given two ellipsoids, we show that their characteristic equation has at least two negative roots and that the ellipsoids are separated by a plane if and only if their characteristic equation has two distinct positive roots. Furthermore, the ellipsoids touch each other externally if and only if the characteristic equation has a positive double root....

Parameter design is applied in different CAD/CAM systems. When the parametric design object is modified, the formulas attached to the geometric quantities are needed to be modified. The method of creating and modifying formulas is discussed in the paper. An efficient approach of combination of formulas is also presented.

A parallel implementation of Chebyshev method is presented for the B-spline surface interpolation problem. The algorithm finds the control points of a uniform bicubic B-spline surface that interpolates m × n data points on an m × n mesh-connected processor array in constant time. Hence it is optimal. Due to its numerical stability, the algorithm ca...

Using vectors between control points (ai=Pi+1-Pi), parameters λ and μ (such that ai + 1 = lai + mai + 2a_i + 1 = \lambda a_i + \mu a_i + 2 ) are used to study the shape classification of planar parametric cubicB-spline curves. The regiosn of λμ space corresponding to different geometric features on the curves are investigated. These results are use...

This paper presents a difference method for computing vertices of the polygon inscribed in a conic section. It can be applied to computer graphic package or to plotter to generate conic sections. This method is simpler and more efficient than traditional ones, and its form remains invariant under homogeneous affine transformations. The stability of...