Inferring a globally consistent normal orientation for point clouds remains challenging, especially for noisy and non-watertight point clouds. To improve accuracy and robustness in orientation inference, a Boundary-Aware Consistent Normal Orientation (BACNO) method is proposed. Its main idea is to transform the normal orientation problem into a boundary-aware narrow band grid partitioning problem. This processing process is as follows: First, an unsigned distance field for an input point cloud is computed, which is defined on a regular grid. The field is then trimmed as a boundary-aware narrow band grid around the point cloud. Next, the narrow band grid is segmented into two parts, with each part located on one side of the input point cloud. Finally, a coarse-to-fine normal orientation strategy is presented to achieve the globally consistent orientation. Extensive experimental results demonstrate that the proposed method outperforms state-of-the-art methods, particularly for noisy and non-watertight point clouds.

Automatic single particle picking is a critical step in the data processing pipeline of cryo-electron microscopy structure reconstruction. In recent years, several deep learning-based algorithms have been developed, demonstrating their potential to solve this challenge. However, current methods highly depend on manually labeled training data, which is labor-intensive and prone to biases especially for high-noise and low-contrast micrographs, resulting in suboptimal precision and recall. To address these problems, we propose UPicker, a semi-supervised transformer-based particle-picking method with a two-stage training process: unsupervised pretraining and supervised fine-tuning. During the unsupervised pretraining, an Adaptive Laplacian of Gaussian region proposal generator is proposed to obtain pseudo-labels from unlabeled data for initial feature learning. For the supervised fine-tuning, UPicker only needs a small amount of labeled data to achieve high accuracy in particle picking. To further enhance model performance, UPicker employs a contrastive denoising training strategy to reduce redundant detections and accelerate convergence, along with a hybrid data augmentation strategy to deal with limited labeled data. Comprehensive experiments on both simulated and experimental datasets demonstrate that UPicker outperforms state-of-the-art particle-picking methods in terms of accuracy and robustness while requiring fewer labeled data than other transformer-based models. Furthermore, ablation studies demonstrate the effectiveness and necessity of each component of UPicker. The source code and data are available at https://github.com/JachyLikeCoding/UPicker.

Abstract Inverse rendering aims to infer scene parameters from observed images. In Solar Power Tower (SPT) systems, this corresponds to an aiming optimization problem—adjusting heliostats' orientations to shape the radiative flux density distribution (RFDD) on the receiver to conform to a desired distribution. The SPT system is widely favored in the field of renewable energy, where aiming optimization is crucial for ensuring its thermal efficiency and safety. However, traditional aiming optimization methods are inefficient and fail to meet online demands. In this paper, a novel optimization approach, DiffNEG, is proposed. DiffNEG introduces a differentiable rasterization method to model the reflected radiative flux of each heliostat as an elliptical Gaussian distribution. It leverages data‐driven techniques to enhance simulation accuracy and employs automatic differentiation combined with gradient descent to achieve online, gradient‐guided optimization in a continuous solution space. Experiments on a real large‐scale heliostat field with nearly 30,000 heliostats demonstrate that DiffNEG can optimize within 10 seconds, improving efficiency by one order of magnitude compared to the latest DiffMCRT method and by three orders of magnitude compared to traditional heuristic methods, while also exhibiting superior robustness under both steady and transient state.

Abstract B‐spline curve interpolation is a fundamental algorithm in computer‐aided geometric design. Determining suitable parameters based on data points distribution has always been an important issue for high‐quality interpolation curves generation. Various parameterization methods have been proposed. However, there is no universally satisfactory method that is applicable to data points with diverse distributions. In this work, a hybrid parametrization method is proposed to overcome the problem. For a given set of data points, a classifier via supervised learning identifies an optimal local parameterization method based on the local geometric distribution of four adjacent data points, and the optimal local parameters are computed using the selected optimal local parameterization method for the four adjacent data points. Then a merging method is employed to calculate global parameters which align closely with the local parameters. Experiments demonstrate that the proposed hybrid parameterization method well adapts the different distributions of data points statistically. The proposed method has a flexible and scalable framework, which can includes current and potential new parameterization methods as its components.

Abstract Restoring the appearance of the model is a crucial step for achieving realistic 3D reconstruction. High‐fidelity textures can also conceal some geometric defects. Since the estimated camera parameters and reconstructed geometry usually contain errors, subsequent texture mapping often suffers from undesirable visual artifacts such as blurring, ghosting, and visual seams. In particular, significant misalignment between the reconstructed model and the registered images will lead to texturing the mesh with inconsistent image regions. However, eliminating various artifacts to generate high‐quality textures remains a challenge. In this paper, we address this issue by designing a texture optimization method to generate seamless and aligned textures for 3D reconstruction. The main idea is to detect misalignment regions between images and geometry and exclude them from texture mapping. To handle the texture holes caused by these excluded regions, a cross‐patch texture hole‐filling method is proposed, which can also synthesize plausible textures for invisible faces. Moreover, for better stitching of the textures from different views, an improved camera pose optimization is present by introducing color adjustment and boundary point sampling. Experimental results show that the proposed method can eliminate the artifacts caused by inaccurate input data robustly and produce high‐quality texture results compared with state‐of‐the‐art methods.

Structure-from-Motion (SfM) aims to recover 3D scene structures and camera poses based on the correspondences between input images, and thus the ambiguity caused by duplicate structures (i.e., different structures with strong visual resemblance) always results in incorrect camera poses and 3D structures. To deal with the ambiguity, most existing studies resort to additional constraint information or implicit inference by analyzing two-view geometries or feature points. In this paper, we propose to exploit high-level information in the scene, i.e., the spatial contextual information of local regions, to guide the reconstruction. Specifically, a novel structure is proposed, namely, track-community, in which each community consists of a group of tracks and represents a local segment in the scene. A community detection algorithm is performed on the track-graph to partition the scene into segments. Then, the potential ambiguous segments are detected by analyzing the neighborhood of tracks and corrected by checking the pose consistency. Finally, we perform partial reconstruction on each segment and align them with a novel bidirectional consistency cost function which considers both 3D-3D correspondences and pairwise relative camera poses. Experimental results demonstrate that our approach can robustly alleviate reconstruction failure resulting from visually indistinguishable structures and accurately merge the partial reconstructions.

Landmarks on human body models are of great significance for applications such as digital anthropometry and clothing design. The diversity of pose and shape of human body models and the semantic gap make landmarking a challenging problem. In this paper, a learning-based method is proposed to locate landmarks on human body models by analyzing the relationship between geometric descriptors and semantic labels of landmarks. A shape alignment algorithm is proposed to align human body models to break symmetric ambiguity. A symmetry-aware descriptor is proposed based on the structure of the human body models, which is robust to both pose and shape variations in human body models. An AdaBoost regression algorithm is adopted to establish the correspondence between several descriptors and semantic labels of the landmarks. Quantitative and qualitative analyses and comparisons show that the proposed method can obtain more accurate landmarks and distinguish symmetrical landmarks semantically. Additionally, a dataset of landmarked human body models is also provided, containing 271 human body models collected from current human body datasets; each model has 17 landmarks labeled manually.

The complementary virtues of active and passive depth sensors inspire the LIDAR-Stereo fusion for enhancing the accuracy of stereo matching. However, most of the fusion based stereo matching algorithms have exploited dense LIDAR priors with single fusion methodology. In this paper, we intend to break these fetters, utilizing sparse LIDAR priors with multi-step fusion strategy for obtaining accurate disparity estimation more efficiently. At first, random sparse sampling LIDAR depth measurements are provided in Naive Fusion for updating the matching cost ofSemi-Global Matching (SGM).Then Neighborhood Based Fusion is performed based on the former step for further updating the cost. Subsequently, Diffusion Based Fusion is utilized to update both the cost and disparities. At last, Tree Filtering is applied for removing speckle outliers and smoothing disparities. Performance evaluations on various stereo data sets demonstrate that the proposed algorithm outperforms other most challenging stereo matching algorithms significantly with approximately real-time implementation efficiency. Furthermore, it is worth pointing out that our proposal surprisingly possessesoneof the toptenperformances on Middleburyv.3online evaluation system even if it has not been adopted any learning-based techniques.

Single-particle cryo-electron microscopy (cryoEM) methods are powerful for solving high-resolution structures of biological macromolecules. Locating numerous particles from micrographs is essential for three-dimensional reconstruction but challenging due to the extremely low signal-to-noise ratio and various particle shapes in micrographs. In this study, we devise the TransPicker, a two-dimensional particle picking framework based on a novel end-to-end transformer-based detective method named crDETR (cryoEM DEtection TRansformer). crDETR applies an improved deformable Transformer to perform inference in parallel on particle relocation and global context, without hand-crafted components like anchors, non-maximum suppression procedure, or sliding windows. Also, it uses a combined loss function to guarantee fast convergence. It uses divide-and-conquer to overcome the limitations of the object query number. Moreover, we develop a series of optimizations, including denoising, enhancing, bad particle filtering, adding masks on carbon areas and ice contaminants to decrease the false-positive ratio and improve the accuracy of particle picking. Experimental results on various datasets demonstrate that TransPicker can select particles with more accuracy, especially in high noise compared with other methods. To our knowledge, TransPicker is the first application of the transformer technique in cryoEM particle picking.

Abstract This paper proposes a passive multi‐view system for human body shape reconstruction, namely RHF‐Human, to overcome several challenges including accurate calibration and stereo matching in self‐occluded and low‐texture skin regions. The reconstruction process includes four steps: capture, multi‐view camera calibration, dense reconstruction, and meshing. The capture system, which consists of 90 digital single‐lens reflex cameras, is single‐shot to avoid nonrigid deformation of the human body. Two technical contributions are made: (1) a two‐step robust multi‐view calibration approach that improves calibration accuracy and saves calibration time for each new human body acquired and (2) an accurate PatchMatch multi‐view stereo method for dense reconstruction to perform correct matching in self‐occluded and low‐texture skin regions and to reduce the noise caused by body hair. Experiments on models of various genders, poses, and skin with different amounts of body hair show the robustness of the proposed system. A high‐fidelity human body shape dataset with 227 models is constructed, and the average accuracy is within 1.5 mm. The system provides a new scheme for the accurate reconstruction of nonrigid human models based on passive vision and has good potential in fashion design and health care.

Shape segmentation is a fundamental problem in shape analysis. Previous research shows that prior knowledge helps to improve the segmentation accuracy and quality. However, completely labeling each 3D shape in a large training data set requires a heavy manual workload. In this paper, we propose a novel weakly-supervised algorithm for segmenting 3D shapes using deep learning. Our method jointly propagates information from scribbles to unlabeled faces and learns deep neural network parameters. Therefore, it does not rely on completely labeled training shapes and only needs a really simple and convenient scribble-based partially labeling process, instead of the extremely time-consuming and tedious fully labeling processes. Various experimental results demonstrate the proposed method's superior segmentation performance over the previous unsupervised approaches and comparable segmentation performance to the state-of-the-art fully supervised methods.

Abstract Morphing is an important technique for the generation of special effects in computer animation. However, an analogous technique has not yet been applied to the increasingly prevalent animation representation, i.e. 3D mesh sequences. In this paper, a technique for morphing between two mesh sequences is proposed to simultaneously blend motions and interpolate shapes. Based on all possible combinations of the motions and geometries, a universal framework is proposed to recreate various plausible mesh sequences. To enable a universal framework, we design a skeleton‐driven cage‐based deformation transfer scheme which can account for motion blending and geometry interpolation. To establish one‐to‐one correspondence for interpolating between two mesh sequences, a hybrid cross‐parameterization scheme that fully utilizes the skeleton‐driven cage control structure and adapts user‐specified joint‐like markers, is introduced. The experimental results demonstrate that the framework, not only accomplishes mesh sequence morphing, but also is suitable for a wide range of applications such as deformation transfer, motion blending or transition and dynamic shape interpolation.

Significant colour discrepancies between stereo images have severe impacts on stereo matching algorithms, which depend on colour similarity. To address this problem, a region‐wise colour correction method is proposed in this study. First, the source image, which is to be corrected, is segmented into a set of regions using the mean‐shift method. Scale invariant feature transform (SIFT) features are extracted from both the source image and the reference image, and then matched. The matched SIFT pairs are refined by exploiting epipolar geometry constraint. Based on the segmentation result and the refined SIFT matches, the regional correspondences between two stereo images are estimated. Then, each matched region pair is used to compute a local colour correction function. A set of colour weight maps is calculated for these functions. Finally, to alleviate the colour transformation discontinuities along the region boundaries and facilitate a smooth colour correction globally, the corrected colour is obtained by combining the colour correction functions using the colour weighting maps. The authors apply the proposed local colour correction method to stereoscopic images before conducting stereo matching. The results indicate that the proposed algorithm can effectively and robustly alleviate the colour discrepancies, and improve the accuracy of stereo matching.

Abstract Registration is a key step in the 3D reconstruction of real‐world objects. In this paper, we propose a hierarchical method for the rigid registration of multiple views. The multiview registration problem is solved via hierarchical optimization defined on an undirected graph. Each node or edge in this graph represents a single view or a connection between two overlapped views, respectively. The optimizations are performed hierarchically on the edges, the loops, and the entire graph. First, each overlapped pair of views is locally aligned. Then, a loop‐based incremental registration algorithm is introduced to refine the initial pairwise alignments. After a loop is registered, the views in the loop are merged into a metaview in the graph. Finally, global error diffusion is applied to the entire graph to evenly distribute the accumulated errors to all views. In addition, a new objective function is defined to describe the loop closure problem; it improves the accuracy and robustness of registration by simultaneously considering transformation and registration errors. The experimental results show that the proposed hierarchical approach is accurate, efficient and robust for initial view states that are not well posed.

Abstract Anti‐aliasing has recently been employed as a post‐processing step to adapt to the deferred shading technique in real‐time applications. Some of these existing algorithms store supersampling geometric information as geometric buffer (G‐buffer) to detect and alleviate sub‐pixel‐level aliasing artifacts. However, the anti‐aliasing filter based on sampled sub‐pixel geometries only may introduce unfaithful shading information to the sub‐pixel color in uniform‐geometry regions, and large G‐buffer will increase memory storage and fetch overheads. In this paper, we present a new Triangle‐based Geometry Anti‐Aliasing (TGAA) algorithm, to address these problems. The coverage triangle of each screen pixel is accessed, and then, the coverage information between the triangle and neighboring sub‐pixels is stored in a screen‐resolution bitmask, which allows the geometric information to be stored and accessed in an inexpensive manner. Using triangle‐based geometry, TGAA can exclude irrelevant neighboring shading samples and achieve faithful anti‐aliasing filtering. In addition, a morphological method of estimating the geometric edges in high‐frequency geometry is incorporated into the TGAA's anti‐aliasing filter to complement the algorithm. The implementation results demonstrate that the algorithm is efficient and scalable for generating high‐quality anti‐aliased images.

ABSTRACT The design of a compact and effective representation is a critical step in fully utilizing the abundant raw mesh‐based animation resources. In this paper, we present a high‐level control structure for animated mesh sequences referred to as an adaptive skeleton‐driven cage representation. This approach combines a skeleton and cage to express time‐varying shape details and offer flexible control for rigid limb motions. The initial skeleton is inferred by sketching on the rest pose mesh. The corresponding cage is constructed by using an adaptive cross‐section‐based method. Then, the initial skeleton and cage are propagated to the other meshes in the sequence. Additionally, the generated cage sequence can be automatically refined to improve the mesh reconstruction quality. Our results and comparisons demonstrate that the proposed approach is an intuitive, compact, and efficient representation. We demonstrate its potential through a variety of applications, such as animation compression, deformation transfer and pose editing. Copyright © 2014 John Wiley & Sons, Ltd.

Abstract In this paper we present an image‐based algorithm to render visually plausible anti‐aliased soft shadows in real time. Our technique employs a new shadow pre‐filtering method based on an extended exponential shadow mapping theory. The algorithm achieves faithful contact shadows by adopting an optimal approximation to exponential shadow reconstruction function. Benefiting from a novel overflow free summed area table tile grid data structure, numerical stability is guaranteed and error filtering response is avoided. By integrating an adaptive anisotropic filtering method, the proposed algorithm can produce high quality smooth shadows both in large penumbra areas and in high frequency sharp transitions, meanwhile guarantee cheap memory consumption and high performance.

Abstract This paper presents a method that generates natural and intuitive deformations via direct manipulation and smooth interpolation for multi‐element 2D shapes. Observing that the structural relationships between different parts of a multi‐element 2D shape are important for capturing its feature semantics, we introduce a simple structure called a feature frame to represent such relationships. A constrained optimization is solved for shape manipulation to find optimal deformed shapes under user‐specified handle constraints. Based on the feature frame, local feature preservation and structural relationship maintenance are directly encoded into the objective function. Beyond deforming a given multi‐element 2D shape into a new one at each key frame, our method can automatically generate a sequence of natural intermediate deformations by interpolating the shapes between the key frames. The method is computationally efficient, allowing real‐time manipulation and interpolation, as well as generating natural and visually plausible results.

Abstract In this paper we present a novel image based algorithm to render visually plausible anti‐aliased soft shadows in a robust and efficient manner. To achieve both high visual quality and high performance, it employs an accurate shadow map filtering method which guarantees smooth penumbrae and high quality anisotropic anti‐aliasing of the sharp transitions. Unlike approaches based on pre‐filtering approximations, our approach does not suffer from light bleeding or losing contact shadows. Discretization artefacts are avoided by creating virtual shadow maps on the fly according to a novel shadow map resolution prediction model. This model takes into account the screen space frequency of the penumbrae via a perceptual metric which has been directly established from an appropriate user study. Consequently, our algorithm always generates shadow maps with minimal resolutions enabling high performance while guarantying high quality. Thanks to this perceptual model, our algorithm can sometimes be faster at rendering soft shadows than hard shadows. It can render game‐like scenes at very high frame rates, and extremely large and complex scenes such as CAD models at interactive rates. In addition, our algorithm is highly scalable, and the quality versus performance trade‐off can be easily tweaked.

Abstract We present variance soft shadow mapping (VSSM) for rendering plausible soft shadow in real‐time. VSSM is based on the theoretical framework of percentage‐closer soft shadows (PCSS) and exploits recent advances in variance shadow mapping (VSM). Our new formulation allows for the efficient computation of (average) blocker distances, a common bottleneck in PCSS‐based methods. Furthermore, we avoid incorrectly lit pixels commonly encountered in VSM‐based methods by appropriately subdividing the filter kernel. We demonstrate that VSSM renders high‐quality soft shadows efficiently (usually over 100 fps) for complex scene settings. Its speed is at least one order of magnitude faster than PCSS for large penumbra.

Shape simplification and re-sampling of underlying point-sampled surfaces under user-defined error bounds is an important and challenging issue. Based on the regular triangulation of the Gaussian sphere and the surface normals mapping onto the Gaussian sphere, a Gaussian sphere based re-sampling scheme is presented that generates a non-uniformly curvature-aware simplification of the given point-sampled model. Owing to the theoretical analysis of shape isophotic error metric for did that Gaussian sphere based sampling, the proposed simplification scheme provides a convenient way to control the re-sampling results under a user-specified error metric bound. The novel algorithm has been implemented and demonstrated on several examples.

Abstract Recent soft shadow mapping techniques based on back‐projection can render high quality soft shadows in real time. However, real time high quality rendering of large penumbrae is still challenging, especially when multilayer shadow maps are used to reduce single light sample silhouette artifact. In this paper, we present an efficient algorithm to attack this problem. We first present a GPU‐friendly packet‐based approach rendering a packet of neighboring pixels together to amortize the cost of computing visibility factors. Then, we propose a hierarchical technique to quickly locate the contour edges, further reducing the computation cost. At last, we suggest a multi‐view shadow map approach to reduce the single light sample artifact. We also demonstrate its higher image quality and higher efficiency compared to the existing depth peeling approaches.

Abstract This paper presents a new method which allows user to manipulate a two‐dimensional shape in an intuitive and flexible way. The shape is discretized as a regular grid. User places handles on the grid and manipulates the shape by moving the handles to the desired positions. To meet the constraints of the user's manipulation, the grid is then deformed in an as‐rigid‐as‐possible way. However, this straightforward approach tends to produce unnatural deformations when the grid resolution is not high enough to capture the topological structure of the shape. In the proposed method, the regular grid is trimmed and only the cells that are inside the fatty regions of the shape are preserved, namely “interior grid.” When user manipulates the shape, the interior grid and the shape boundary curve are deformed with minimum distortions. To make the deformations of the interior grid and the boundary curve consistent, a junction energy is introduced. In this way, the unnatural deformation effects could be effectively removed and the physically plausible results can be obtained. Meanwhile, the proposed approach provides user an intuitive and simple way to adjust the shape global and local stiffnesses. The deformation is formulated as an energy minimization problem. The energy function is non‐quadratic and could be efficiently solved using an iterative solver with the fast summation technique that exploits the interior grid and boundary curve regularities. In addition, the method could be easily extended to manipulate curves and stick figures. Experimental results demonstrate the capability and flexibility of the new method. Copyright © 2009 John Wiley & Sons, Ltd.

We present a new high quality tessellation method for implicit surfaces in this paper. The approach can handle arbitrary implicit functions and dynamic implicit surfaces based on skeletal primitives. We first samples the implicit surface uniformly using particle fission and floating, then reconstructs a triangular mesh from the sample points using ball pivoting algorithm (BPA). Finally, we subdivide the reconstructed surface using a 1 to 4 subdivision scheme to obtain the high quality implicit surface tessellation.

Physical-based cloth modeling and animation is a hot topic in computer graphics. Recently the semi-implicit integration scheme has been widely employed in cloth animation because of its high stability. In this paper, we propose an efficient and simple iterative scheme to create realistic cloth animation. The linear system created in the semi-implicit scheme can be solved in approximately linear time complexity in one time-step. This greatly benefits real-time applications. We also improve the traditional mass-spring model by avoiding the shrink of the cloth model.

Abstract In this paper, we propose a novel mesh morphing approach based on polycubic cross‐parameterization. We compose parameterizations over the surfaces of the polycubes whose shape is similar to that of the given meshes. Because the polycubes capture the large‐scale features, we can easily preserve the shape of the models, mapping legs to legs, head to head, and so on. For the finer features that are not reflected by the shape of the polycubes, we split the polycubes into matching patches and optimize them to get a low‐distortion bijection that satisfies user‐prescribed constraints. Our approach works well for meshes with arbitrary genus as long as the polycubes capture this feature and transfers texture seamlessly. We can also build maps with singularities between models with different genus. Copyright © 2005 John Wiley & Sons, Ltd.

Abstract In this paper, we propose a novel practical method for blob‐based liquid 3D morphing. Firstly, blobby objects are employed to approximate a given polygonal surface. The primitives in the medial axis sphere‐tree of a polygonal model are utilized as initial blobs—this greatly improves the robustness and efficiency of the blob‐based approximation. Secondly, we establish the blob correspondences between two models by sphere cellular matching and hierarchical matching. Finally, we interpolate the parameters of the implicit representation to get the intermediate shapes. Experiments show our method can produce visually pleasing liquid morphing effects. Copyright © 2005 John Wiley & Sons, Ltd.

Developing intuitive and efficient methods for shape editing is one of the most important areas in computer graphics, and free-form deformation (FFD), which is one of such methods, allows the user to deform a model easily by moving a set of control points, collectively called the lattice. Although the FFD method can be used for both global and local deformations, the user must define a suitable lattice manually or use a simple shaped lattice such as a parallelepiped. Therefore, we propose a new FFD method that automatically generates the lattices with which both types of deformations can be achieved. Our method refines a bounding box of the model and generates a set of finer lattices, which hierarchically approximate the shape of the model. Through adjusting the control points of the generated lattices, both global and local deformations of the model can be achieved easily. Moreover, the method allows hierarchical deformation of the model by combining different levels of lattice.

Free-form deformation, abbreviated to FFD, plays an important role in both computer animation and geometric modeling. When polygonal objects are deformed by the traditional FFD scheme, however aliasing will appear since the deformation only acts on the sample points of the objects. To eliminate this problem, a new method of accurate B-spline FFD was proposed by authors previously, which is based on functional composition. Unfortunately it is a time consuming process because generalized de Casteljau algorithm is adopted to solve the functional composition. In this paper we propose a fast accurate B-spline FFD method. The proposed method makes use of the polynomial interpolation and symbolic computation to solve the functional composition. Both theoretical analysis and implementation results show that the proposed method runs faster than the original one.

In real life, some objects may deform along axial curves and the lengths of their skeletons usually remain constant during the axial deformation, such as a swimming fish, a swaying tree, etc. This paper presents a practical approach of arc-length-based axial deformation and axial-length-preserved animation. The space spanned by the arc-length parameter and the rotation-minimizing frame on the axis is taken as the embedding space. During animation, the keyframe axial curves are consistently approximated by polylines after sufficient subdivisions and both the edge lengths and the directional vertex angles of the keyframe polylines (or unit edge vectors) are then interpolated to generate the intermediate polylines which are regarded as the discrete expressions of the intermediate axes. Experiments show that our method is very useful, intuitive and easy to control.

Intuitive 30 sulfate control and deformation are czucial to CAD/CAM.To do this in a virtual environment, however, the tecZznique must be very efficient.A common method for shape deformation is the free-form deformation (FFD) method, in which the complete object is deformed by defozming a 30 grid of the object.In this paper, we propose an intuitive method for sulfate deformation based on deforming a hand s&ace, which is basically a bicubic B-spline sudace interpolating or approximating key data points of a sensor glove (i.e.finger joints and palm center of the user's hand).By setting up a corresponding mapping between the virtual object being deformed and the hand sugace, the object can be deformed with tlze control of the sensor glove.As the usersexes hislherfingers, the object changes its shape accordingly.Such control can be local or global.For local deformation, we introduce a region jilter function which imposes locality on the mapping/deformation.The new algorithm is made very efficient tlzrough incremental update.It is also intuitive as zfthe zzser were using his hand to deform the object directly.Experimental results show the potential of the new method.