The goal of human-robot motion retargeting is to let a robot follow the movements performed by a human subject. This is traditionally achieved by applying the estimated poses from a human pose tracking system to a robot via explicit joint mapping strategies. In this paper, we present a novel approach that combine the human pose estimation and the motion retarget procedure in a unified generative framework. A 3D parametric human-robot model is proposed that has the specific joint and stability configurations as a robot while its shape resembles a human subject. Using a single depth camera to monitor human pose, we use its raw depth map as input and drive the human-robot model to fit the input 3D point cloud. The calculated joint angles of the fitted model can be applied onto the robots for retargeting. The robot's joint angles, instead of fitted individually, are fitted globally so that the transformed surface shape is as consistent as possible to the input point cloud. The robot configurations including its skeleton proportion, joint limitation, and DoF are enforced implicitly in the formulation. No explicit and pre-defined joints mapping strategies are needed. This framework is tested with both simulations and real robots that have different skeleton proportion and DoFs compared with human to show its effectiveness for motion retargeting.

In this paper, a new subdivision scheme for Polar embedded Catmull-Clark mesh structure is presented. The ripple effect commonly found at high-valence extraordinary points of a CCS surface is improved by replacing high-valence CCS extraordinary faces with triangular Polar faces. The new scheme is valence independent and is stationary. By using the same subdivision mask on both the quadrilateral part and the triangular part, artifacts that have been noticed before (mismatching subdivision masks, exponentially increased Valence at Polar extraordinary points by the recursive subdivision process) are resolved. Test results show that with the new scheme, one can generate very high quality, curvature continuous subdivision surfaces on the triangular part. Combined with current CCS G2 schemes, one can generate high quality subdivision surfaces appropriate for most engineering applications on any Polar embedded Catmull-Clark control meshes.

Conventional polynomial interpolation methods produce images with blurred edges, while edge-directed interpolation methods make enlarged images with good quality edges but with detail distortion in the non-edge portion. A new method for constructing a fitting surface to image data is presented. Unlike existing methods which produce enlarged images using image data as interpolation data, the new method constructs the fitting surface using the image data as constraints to reverse the sampling process for improving the fitting precision. To remove the zigzagging artifact, for each pixel and its nearby region, the edge information is used to determine the quadratic polynomial which approximates the original scene with a quadratic polynomial precision. Comparison results of the new method with other methods are included.

Quadratic Bézier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic Bézier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing G1quadratic Bézier curves satisfying given endpoint (positions and arbitrary unit tangent vectors) conditions. Examples are given to illustrate the new solution and to perform comparison between the G1quadratic Bézier cures and other curve schemes such as the composite geometric Hermite curves and the biarcs.

An elegant and efficient mesh clustering algorithm is presented. The faces of a polygonal mesh are divided into different clusters for mesh coarsening purpose by approximating the Centroidal Voronoi Tessellation of the mesh. The mesh coarsening process after clustering can be done in an isotropic or anisotropic fashion. The presented algorithm improves previous techniques in local geometric operations and parallel updates. The new algorithm is very simple but is guaranteed to converge, and generates better approximating meshes with the same computation cost. Moreover, the new algorithm is suitable for the variational shape approximation problem with L2, 1 distortion error metric and the convergence is guaranteed. Examples demonstrating efficiency of the new algorithm are also included in the paper.

In this paper, we present a new adaptive rendering method for general Catmull-Clark subdivision surfaces. The new method is based on direct evaluation of the limit surface to generate an inscribed polyhedron of the limit surface. The method generates fewer polygons in the final rendering process because inscribed approximation usually provides faster convergent rate than circumscribed approximation. The new adaptive rendering method can precisely measure error for every point of the limit surface. Hence, it has complete control of the accuracy of the rendering result. Cracks are avoided by using a recursive marking process to ensure that adjacent patches or subpatches use the same limit surface points in the construction of the shared boundary. The new method performs limit surface evaluation only at points that are needed for the final rendering process. Therefore it is very fast and memory efficient.

The current cubic spline curve interpolation scheme is derived based on the implicit assumption that the magnitude of the first derivative of the curve is close to a constant. However, the assumption is not realized by the interpolation scheme. A knot choosing technique for parametric cubic spline interpolating curve construction that accommodates this assumption is presented. A comparison of the new method with several existing methods is performed and test results are included.

An automatic smooth surface connection method that has the capability of tension control is presented. Given two trimmed NURBS surfaces, the new method constructs a smooth connection surface to connect the trimming regions of the trimmed surfaces at the trimming curves. The connection satisfies pseudo-G/sup 1/ or pseudo-C/sup 1/ smoothness requirement. The construction process consists of four major steps: connection curves construction and alignment, initial blends construction, setting up continuity constraints, and internal and external boundary smoothing. The advantages of the new method include: (1) providing the users with more flexibility in adjusting the shape of the connection surface; (2) the representation of the connection surface is compatible with most of the current data-exchange standards; (3) including the classical blending as a special case but with more flexibility on the setting of the rail curves; and (4) smoother shape of the resulting connection surface through an energy optimization process. Test cases that cover typical CAD applications are included.

A technique to improve the performance of the shadow-volume method is presented. This technique does not require (1) extensive edge/edge intersection tests and intersection angle computation in shadow polygon construction, or (2) any ray/shadow-polygon intersection tests during scan-conversion. The first task is achieved by constructing ridge edge (RE) loops, an inexact form of silhouette, instead of the silhouette. The RE loops give us the shadow volume without any expensive computation. The second task is achieved by discretizing the shadow volume into angular spans. The angular spans, which correspond to scan lines, are stored in a lookup table. This lookup table enables us to mark the pixels that are in shadow directly, without the need of performing any ray/shadow-polygon intersection tests. In addition, the shadow on an object is determined on a line-by-line basis instead of a pixel-by-pixel basis. The new technique is efficient enough to achieve real time performance, without any special hardware, while being scalable with scene size.

A deformation-based fine tuning technique for parametric curves and surfaces is presented. A curve or surface is deformed by scaling its derivative, instead of manipulating its control points. Since only the norm of the derivative is adjusted, the resulting curve or surface keeps the basic shape of the original profile and curvature distribution. Therefore, the new technique is especially suitable for last minute fine tuning of the design process. Other advantages include: (1) the fine tuning process is a real local method, it can be performed on any portion of a curve or a surface, not just on a set of segments or patches; (2) by allowing a user to drag a scalar function to directly adjust the curvature (and, consequently, fairness) of a curve or surface, the new technique makes the shape design process more intuitive and effective; (3) the new technique is suitable for precise shaping and deforming such as making the curvature of a specific portion twice as big. In many cases, it can achieve results that other methods such as FFD can not; (4) the fine tuning process can also be used for subdivision curves and surfaces. Related techniques and test results are included.

The construction of a C/sup 1/ piecewise bicubic Bezier surface that interpolates a set of data points and lies on the same side of a given plane as the data points is presented. The main tasks in this construction process are the adjustment of the tangent vectors and the determination of the twist vectors at the data points. The tangent vectors are modified by decreasing their magnitudes. The twist vectors are first set by an energy minimization process and then filtered through a modification process to ensure the constructed surface lies on one side of the given plane. The technique for determining the twist vectors has an interpolation precision of cubic polynomials.

A method to scale a multi-surface object while holding the shape and size of specific features (trimming curves) unchanged is presented. The new method includes an earlier version for a one-NURBS-surface object as a special case by considering more general objects and more general features. The constrained scaling process is attach-and-deform based. The new surface is constructed by attaching the original features to a scaled version of the given object. The attaching process requires several transformations and a deformation of the scaled object. The resulting object has the same features as the original object while reflecting the shape and curvature distribution of the scaled object. The presented approach maintains a NURBS representation for each component surface of the resulting object and hence, is compatible with most of the current data-exchange standards. Test results on several car body surfaces with trimming curves are included. The quality of the resulting surfaces is examined using the highlight line model.

Three methods for evaluating the surface coordinates, first derivatives, and normal vectors of a NURB surface are compared. These methods include forward differencing, knot insertion, and a tow-stage Cox-de Boor technique. The computational complexity of each of these techniques is analyzed and summarized. The use of Hermite functions is shown to yield a poor approximation for the shading functions of a NURB surface. An improved method for computing derivatives by knot insertion is presented. An efficient algorithm for computing the foward difference matrix and a method for using foward differencing to compute the first derivatives of a NURB surface are also presented.

An algorithm to estimate subdivision depths for rational curves and surfaces is presented. The subdivision depth is not estimated for the given curve/surface directly. The algorithm computes a subdivision depth for the polynomial curve/surface of which the given rational curve/surface is the image under the standard perspective projection. This subdivision depth, however, guarantees the required flatness of the given curve/surface after the subdivision. This work has applications in surface rendering, surface/surface intersection, and mesh generation.

A parallel fitting algorithm using uniform bicubic B-spline surfaces is presented. This algorithm is based on the observation that a tensor product spline surface fitting problem can be split into two spline curve fitting problems, and each of these problems can be carried out in parallel by cyclic reduction. Using this approach, the control points of a uniform bicubic B-spline surface that interpolates a grid of m x n points can be found in O (log m + log n ) time on mn processors. Furthermore, since smaller systems of equations are solved in the algorithm, the accumulated error resulting from this approach is smaller than that of the traditional algorithms.