Existing curved-layer-based process planning methods for multi-axis manufacturing address collisions only indirectly and generate toolpaths in a post-processing step, leaving toolpath geometry uncontrolled during optimization. We present an implicit neural field-based framework for multi-axis process planning that overcomes these limitations by embedding both layer generation and toolpath design within a single differentiable pipeline. Using sinusoidally activated neural networks to represent layers and toolpaths as implicit fields, our method enables direct evaluation of field values and derivatives at any spatial point, thereby allowing explicit collision avoidance and joint optimization of manufacturing layers and toolpaths. We further investigate how network hyperparameters and objective definitions influence singularity behavior and topology transitions, offering built-in mechanisms for regularization and stability control. The proposed approach is demonstrated on examples in both additive and subtractive manufacturing, validating its generality and effectiveness. • A universal implicit-field optimization framework for multi-axis manufacturing. • Explicit collision avoidance during field-based optimization. • Direct control of toolpath geometry by joint optimization.

To enable the design and manufacturing of optimized composite structures using fabric plies, we propose a field-driven optimization framework that jointly optimizes structural topology and manufacturable layers. A central challenge in this setting is the modeling and optimization of partial fabric layers with near-uniform thickness, which we formulate as a semi-continuous periodic scalar field parameterized by a continuous implicit neural vector field. Within this concurrent structure-layer optimization framework, we further derive a formulation of inter-layer anisotropic mechanical behavior that enables effective modeling of mechanical property transitions induced by partial-layer boundaries, together with additional objectives for manufacturability and field regularization. We validate the effectiveness of our approach through both numerical simulations and physical experiments, demonstrating that the optimized fabric-reinforced laminated composites achieve up to 43.8% higher stiffness compared to counterparts fabricated using planar fabric plies.

Flexible sensors are increasingly employed in soft robotics and wearable devices to provide proprioception of freeform deformations. Although supervised learning can train shape predictors from sensor signals, prediction accuracy strongly depends on sensor layout, which is typically determined heuristically or through trial-and-error. This work introduces a model-free, data-driven computational pipeline that jointly optimizes the number, length, and placement of flexible length-measurement sensors together with the parameters of a shape prediction network for large freeform deformations. Unlike model-based approaches, the proposed method relies solely on datasets of deformed shapes, without requiring physical simulation models, and is therefore broadly applicable to diverse robotic sensing tasks. The pipeline incorporates differentiable loss functions that account for both prediction accuracy and manufacturability constraints. By co-optimizing sensor layouts and network parameters, the method significantly improves deformation prediction accuracy over unoptimized layouts while ensuring practical feasibility. The effectiveness and generality of the approach are validated through numerical and physical experiments on multiple soft robotic and wearable systems.

This paper presents a correspondence-free, function-based sim-to-real learning method for controlling deformable freeform surfaces. Unlike traditional sim-to-real transfer methods that strongly rely on marker points with full correspondences, our approach simultaneously learns a deformation function space and a confidence map – both parameterized by a neural network – to map simulated shapes to their real-world counterparts. As a result, the sim-to-real learning can be conducted by input from either a 3D scanner as point clouds (without correspondences) or a motion capture system as marker points (tolerating missed markers). The resultant sim-to-real transfer can be seamlessly integrated into a neural network-based computational pipeline for inverse kinematics and shape control. We demonstrate the versatility and adaptability of our method on two vision devices and across four pneumatically actuated soft robots: a deformable membrane, a robotic mannequin, and two soft manipulators.

We propose a semantic-aware neural reconstruction method to generate 3D high-fidelity models from sparse images. To tackle the challenge of severe radiance ambiguity caused by mismatched features in sparse input, we enrich neural implicit representations by adding patch-based semantic logits that are optimized together with the signed distance field and the radiance field. A novel regularization based on the geometric primitive masks is introduced to mitigate shape ambiguity. The performance of our approach has been verified in experimental evaluation. The average chamfer distances of our reconstruction on the DTU dataset can be reduced by 44% for SparseNeuS and 20% for VolRecon. When working as a plugin for those dense reconstruction baselines such as NeuS and Neuralangelo, the average error on the DTU dataset can be reduced by 69% and 68% respectively.

In this paper, we present a concurrent and scalable trajectory optimization method to improve the quality of robot-assisted manufacturing. Our method simultaneously optimizes tool orientations, kinematic redundancy, and waypoint timing on input toolpaths with large numbers of waypoints to improve kinematic smoothness while incorporating manufacturing constraints. Differently, existing methods always determine them in a decoupled manner. To deal with the large number of waypoints on a toolpath, we propose a decomposition-based numerical scheme to optimize the trajectory in an out-of-core manner, which can also run in parallel to improve the efficiency. Simulations and physical experiments have been conducted to demonstrate the performance of our method in examples of robot-assisted additive manufacturing. Note to Practitioners—In robot-assisted manufacturing, how to determine the motion commands according to a sequence of waypoints is a typical problem to be solved where the waypoints represent the positions of a tool-tip. Factors in three aspects need to be planned at each waypoint, including the tool orientation, the tool speed and the redundant degrees-of-freedom on the robotic system. In the trajectory planning step, the objective is always defined as improving the kinematic performance of joint motion in terms of velocity, acceleration, and jerk. Taking the strategy of existing methods that consider these aspects separately will generate less optimal results. This paper presents a new formulation that optimizes all these together while assigning certain manufacturing constraints. Considering that a toolpath can consist of a large number of waypoints in practice, how to improve planning efficiency with limited computer memory is an important issue to be solved. A decomposition based numerical scheme is developed to tackle this problem. The aforementioned issues can be effectively solved by the method proposed in this paper, the performance of which has been demonstrated on a dual robotic system with 6+2 DoFs. The proposed method is general and can also be applied to other types of systems with single or multiple robots as well as other manufacturing methods (e.g. milling).

This paper presents a method for computing interleaved additive and subtractive manufacturing operations to fabricate models of arbitrary shapes. We solve the manufacturing planning problem by searching a sequence of inverse operations that progressively transform a target model into a null shape. Each inverse operation corresponds to either an additive or a subtractive step, ensuring both manufacturability and structural stability of intermediate shapes throughout the process. We theoretically prove that any model can be fabricated exactly using a sequence generated by our approach. To demonstrate the effectiveness of this method, we adopt a voxel-based implementation and develop a scalable algorithm that works on models represented by a large number of voxels. Our approach has been tested across a range of digital models and further validated through physical fabrication on a hybrid manufacturing system with automatic tool switching.

This paper introduces a novel curve-based slicing method for generating planar layers with dynamically varying orientations in digital light processing (DLP) 3D printing. Our approach effectively addresses key challenges in DLP printing, such as regions with large overhangs and staircase artifacts, while preserving its intrinsic advantages of high resolution and fast printing speeds. We formulate the slicing problem as an optimization task, in which parametric curves are computed to define both the slicing layers and the model partitioning through their tangent planes. These curves inherently define motion trajectories for the build platform and can be optimized to meet critical manufacturing objectives, including collision-free motion and floating-free deposition. We validate our method through physical experiments on a robotic multi-axis DLP printing setup, demonstrating that the optimized curves can robustly guide smooth, high-quality fabrication of complex geometries.

We propose a neural network-based computational framework for the simultaneous optimization of structural topology, curved layers, and path orientations to achieve strong anisotropic strength in fiber-reinforced thermoplastic composites while ensuring manufacturability. Our framework employs three implicit neural fields to represent geometric shape, layer sequence, and fiber orientation. This enables the direct formulation of both design and manufacturability objectives - such as anisotropic strength, structural volume, machine motion control, layer curvature, and layer thickness - into an integrated and differentiable optimization process. By incorporating these objectives as loss functions, the framework ensures that the resultant composites exhibit optimized mechanical strength while remaining its manufacturability for filament-based multi-axis 3D printing across diverse hardware platforms. Physical experiments demonstrate that the composites generated by our co-optimization method can achieve an improvement of up to 33.1% in failure loads compared to composites with sequentially optimized structures and manufacturing sequences.

Joint injuries, and their long-term consequences, present a substantial global health burden. Wearable prophylactic braces are an attractive potential solution to reduce the incidence of joint injuries by limiting joint movements that are related to injury risk. Given human motion and ground reaction forces, we present a computational framework that enables the design of personalized braces by optimizing the distribution of microstructures and elasticity. As varied brace designs yield different reaction forces that influence kinematics and kinetics analysis outcomes, the optimization process is formulated as a differentiable end-to-end pipeline in which the design domain of microstructure distribution is parameterized onto a neural network. The optimized distribution of microstructures is obtained via a self-learning process to determine the network coefficients according to a carefully designed set of losses and the integrated biomechanical and physical analyses. Since knees and ankles are the most commonly injured joints, we demonstrate the effectiveness of our pipeline by designing, fabricating, and testing prophylactic braces for the knee and ankle to prevent potentially harmful joint movements.

This paper presents a learning based planner for computing optimized 3D printing toolpaths on prescribed graphs, the challenges of which include the varying graph structures on different models and the large scale of nodes & edges on a graph. We adopt an on-the-fly strategy to tackle these challenges, formulating the planner as a Deep Q-Network (DQN) based optimizer to decide the next 'best' node to visit. We construct the state spaces by the Local Search Graph (LSG) centered at different nodes on a graph, which is encoded by a carefully designed algorithm so that LSGs in similar configurations can be identified to re-use the earlier learned DQN priors for accelerating the computation of toolpath planning. Our method can cover different 3D printing applications by defining their corresponding reward functions. Toolpath planning problems in wire-frame printing, continuous fiber printing, and metallic printing are selected to demonstrate its generality. The performance of our planner has been verified by testing the resultant toolpaths in physical experiments. By using our planner, wire-frame models with up to 4.2k struts can be successfully printed, up to 93.3% of sharp turns on continuous fiber toolpaths can be avoided, and the thermal distortion in metallic printing can be reduced by 24.9%.

We introduce a novel neural network-based computational pipeline as a representation-agnostic slicer for multi-axis 3D printing. This advanced slicer can work on models with diverse representations and intricate topology. The approach involves employing neural networks to establish a deformation mapping, defining a scalar field in the space surrounding an input model. Isosurfaces are subsequently extracted from this field to generate curved layers for 3D printing. Creating a differentiable pipeline enables us to optimize the mapping through loss functions directly defined on the field gradients as the local printing directions. New loss functions have been introduced to meet the manufacturing objectives of support-free and strength reinforcement. Our new computation pipeline relies less on the initial values of the field and can generate slicing results with significantly improved performance.

Robot-assisted 3D printing has drawn a lot of attention by its capability to fabricate curved layers that are optimized according to different objectives. However, the support generation algorithm based on a fixed printing direction for planar layers cannot be directly applied for curved layers as the orientation of material accumulation is dynamically varied. In this paper, we propose a skeleton-based support generation method for robot-assisted 3D printing with curved layers. The support is represented as an implicit solid so that the problems of numerical robustness can be effectively avoided. The effectiveness of our algorithm is verified on a dual-material printing platform that consists of a robotic arm and a newly designed dual-material extruder. Experiments have been successfully conducted on our system to fabricate a variety of freeform models.

Soft robots can safely interact with environments because of their mechanical compliance. Self-collision is also employed in the modern design of soft robots to enhance their performance during different tasks. However, developing an efficient and reliable simulator that can handle the collision response well, is still a challenging task in the research of soft robotics. This paper presents a collision-aware simulator based on geometric optimization, in which we develop a highly efficient and realistic collision checking / response model incorporating a hyperelastic material property. Both actuated deformation and collision response for soft robots are formulated as geometry-based objectives. The collision-free body of a soft robot can be obtained by minimizing the geometry-based objective function. Unlike the FEA-based physical simulation, the proposed pipeline performs a much lower computational cost. Moreover, adaptive remeshing is applied to achieve the improvement of the convergence when dealing with soft robots that have large volume variations. Experimental tests are conducted on different soft robots to verify the performance of our approach.

In this paper, a deep learning framework combined with isogeometric analysis (IGA for short) called IGA-Reuse-Net is proposed for efficient reuse of numerical simulation on a set of topology-consistent models. Compared with previous data-driven numerical simulation methods only for simple computational domains, our method can predict high-accuracy PDE solutions over topology-consistent geometries with complex boundaries. UNet3+ architecture with interlaced sparse self-attention (ISSA) module is used to enhance the performance of the network. In addition, we propose a new loss function that combines a coefficients loss and a numerical solution loss. Several training datasets with topology-consistent models are constructed for the proposed framework. To verify the effectiveness of our approach, two different types of Poisson equations with different source functions are solved on three datasets with different topologies. Our framework can achieve a good trade-off between accuracy and efficiency. It outperforms the physics-informed neural network (PINN for short) model and yields promising results of prediction.

Reconstruction of high-fidelity 3D objects or scenes is a fundamental research problem. Recent advances in RGB-D fusion have demonstrated the potential of producing 3D models from consumer-level RGB-D cameras. However, due to the discrete nature and limited resolution of their surface representations (e.g., point or voxel based), existing approaches suffer from the accumulation of errors in camera tracking and distortion in the reconstruction, which leads to an unsatisfactory 3D reconstruction. In this article, we present a method using on-the-fly implicits of Hermite Radial Basis Functions (HRBFs) as a continuous surface representation for camera tracking in an existing RGB-D fusion framework. Furthermore, curvature estimation and confidence evaluation are coherently derived from the inherent surface properties of the on-the-fly HRBF implicits, which are devoted to a data fusion with better quality. We argue that our continuous but on-the-fly surface representation can effectively mitigate the impact of noise with its robustness and constrain the reconstruction with inherent surface smoothness when being compared with discrete representations. Experimental results on various real-world and synthetic datasets demonstrate that our HRBF-fusion outperforms the state-of-the-art approaches in terms of tracking robustness and reconstruction accuracy.

Multi-axis motion introduces more degrees of freedom into the process of 3D printing to enable different objectives of fabrication by accumulating materials layers upon curved layers. An existing challenge is how to effectively generate the curved layers satisfying multiple objectives simultaneously. This paper presents a general slicing framework for achieving multiple fabrication objectives including support free, strength reinforcement and surface quality. These objectives are formulated as local printing directions varied in the volume of a solid, which are achieved by computing the rotation-driven deformation for the input model. The height field of a deformed model is mapped into a scalar field on its original shape, the isosurfaces of which give the curved layers of multi-axis 3D printing. The deformation can be effectively optimized with the help of quaternion fields to achieve the fabrication objectives. The effectiveness of our method has been verified on a variety of models.

Using the raw data from consumer-level RGB-D cameras as input, we propose a deep-learning-based approach to efficiently generate RGB-D images with completed information in high resolution. To process the input images in low resolution with missing regions, new operators for adaptive convolution are introduced in our deep-learning network that consists of three cascaded modules—the completion module, the refinement module, and the super-resolution module. The completion module is based on an architecture of encoder–decoder, where the features of input raw RGB-D will be automatically extracted by the encoding layers of a deep neural network. The decoding layers are applied to reconstruct the completed depth map, which is followed by a refinement module to sharpen the boundary of different regions. For the super-resolution module, we generate RGB-D images in high resolution by multiple layers for feature extraction and a layer for upsampling. Benefited from the adaptive convolution operators proposed in this article, our results outperform the existing deep-learning-based approaches for RGB-D image complete and super-resolution. As an end-to-end approach, high-fidelity RGB-D images can be generated efficiently at the rate of 22 frames/s.Note to Practitioners—With the development of consumer-level RGB-D cameras, industries have started to employ these low-cost sensors in many robotic and automation applications. However, images generated by consumer-level RGB-D cameras are generally in low resolution. Moreover, the depth images often have incomplete regions when the surface of an object is transparent, highly reflective, or beyond the distance of sensing. With the help of our method, engineers are able to “repair” the images captured by consumer-level RGB-D cameras in high efficiency. As the typical deep-learning networks are employed in this approach, the proposed approach fits well with the GPU-based hardware architecture of deep-learning computation—therefore, it potentially can be integrated into the hardware of RGB-D cameras.

In this paper, we present a new computational pipeline for designing and fabricating 4D garments as knitwear that considers comfort during body movement. This is achieved by careful control of elasticity distribution to reduce uncomfortable pressure and unwanted sliding caused by body motion. We exploit the ability to knit patterns in different elastic levels by single-jersey jacquard (SJJ) with two yarns. We design the distribution of elasticity for a garment by physics-based computation, the optimized elasticity on the garment is then converted into instructions for a digital knitting machine by two algorithms proposed in this paper. Specifically, a graph-based algorithm is proposed to generate knittable stitch meshes that can accurately capture the 3D shape of a garment, and a tiling algorithm is employed to assign SJJ patterns on the stitch mesh to realize the designed distribution of elasticity. The effectiveness of our approach is verified on simulation results and on specimens physically fabricated by knitting machines.

3D printing techniques such as Fused Deposition Modeling (FDM) have enabled the fabrication of complex geometry quickly and cheaply. Objects are produced by filling (a portion of) the 2D polygons of consecutive layers with contour-parallel extrusion toolpaths. Uniform width toolpaths consisting of inward offsets from the outline polygons produce over- and underfill regions in the center of the shape, which are especially detrimental to the mechanical performance of thin parts. In order to fill shapes with arbitrary diameter densely the toolpaths require adaptive width. Existing approaches for generating toolpaths with adaptive width result in a large variation in widths, which for some hardware systems is difficult to realize accurately. In this paper we present a framework which supports multiple schemes to generate toolpaths with adaptive width, by employing a function to decide the number of beads and their widths. Furthermore, we propose a novel scheme which reduces extreme bead widths, while limiting the number of altered toolpaths. We statistically validate the effectiveness of our framework and this novel scheme on a data set of representative 3D models, and physically validate it by developing a technique, called back pressure compensation, for off-the-shelf FDM systems to effectively realize adaptive width.

We present a method for effectively planning the motion trajectory of robots in manufacturing tasks, the tool paths of which are usually complex and have a large number of discrete time constraints as waypoints. Kinematic redundancy also exists in these robotic systems. The jerk of motion is optimized in our trajectory planning method at the meanwhile of fabrication process to improve the quality of fabrication. Our method is based on a sampling strategy and consists of two major parts. After determining an initial path by graph search, a greedy algorithm is adopted to optimize a path by locally applying adaptive filers in the regions with large jerks. The filtered result is obtained by numerical optimization. In order to achieve efficient computation, an adaptive sampling method is developed for learning a collision-indication function that is represented as a support-vector machine. Applications in robot-assisted 3-D printing are given in this article to demonstrate the functionality of our approach. Note to Practitioners-In robot-assisted manufacturing applications, robotic arms are employed to realize the motion of workpieces (or machining tools) specified as a sequence of waypoints with the positions of tool tip and the tool orientations constrained. The required degree of freedom (DOF) is often less than the robotic hardware system (e.g., a robotic arm has six-DOF). Specifically, rotations of the workpiece around the axis of a tool can be arbitrary (see Fig. 1 for an example). By using this redundancy, i.e., there are many possible poses of a robotic arm to realize a given waypoint, the trajectory of robots can be optimized to consider the performance of motion in velocity, acceleration, and jerk in the joint space. In addition, when fabricating complex models, each tool path can have a large amount of waypoints. It is crucial for a motion planning algorithm to compute a smooth and collision-free trajectory of robot to improve the fabrication quality. The time taken by the planning algorithm should not significantly lengthen the total manufacturing time; ideally, it would remain hidden as computing motions for a layer can be done while the previous layer is printing. The method presented in this article provides an efficient framework to tackle this problem. The framework has been well tested on our robot-assisted additive manufacturing system to demonstrate its effectiveness and can be generally applied to other robot-assisted manufacturing systems.

We present a method for fabricating general models with multi-directional 3-D printing systems by printing different model regions along with different directions. The core of our method is a support-effective volume decomposition algorithm that minimizes the area of the regions with large overhangs. A beam-guided searching algorithm with manufacturing constraints determines the optimal volume decomposition, which is represented by a sequence of clipping planes. While current approaches require manually assembling separate components into a final model, our algorithm allows for directly printing the final model in a single pass. It can also be applied to models with loops and handles. A supplementary algorithm generates special supporting structures for models where supporting structures for large overhangs cannot be eliminated. We verify the effectiveness of our method using two hardware systems: a Cartesian-motion-based system and an angular-motion-based system. A variety of 3-D models have been successfully fabricated on these systems.

The anisotropy of mechanical strength on a 3D printed model can be controlled in a multi-axis 3D printing system as materials can be accumulated along dynamically varied directions. In this paper, we present a new computational framework to generate specially designed layers and toolpaths of multi-axis 3D printing for strengthening a model by aligning filaments along the directions with large stresses. The major challenge comes from how to effectively decompose a solid into a sequence of strength-aware and collision-free working surfaces. We formulate it as a problem to compute an optimized governing field together with a selected orientation of fabrication setup. Iso-surfaces of the governing field are extracted as working surface layers for filament alignment. Supporting structures in curved layers are constructed by extrapolating the governing field to enable the fabrication of overhangs. Compared with planar-layer based Fused Deposition Modeling (FDM) technology, models fabricated by our method can withstand up to 6 . 35× loads in experimental tests.

Robots fabricated with soft materials can provide higher flexibility and, thus, better safety while interacting in unpredictable situations. However, the usage of soft material makes it challenging to predict the deformation of a continuum body under actuation and, therefore, brings difficulty to the kinematic control of its movement. In this article, we present a geometry-based framework for computing the deformation of soft robots within the range of linear material elasticity. After formulating both manipulators and actuators as geometry elements, deformation can be efficiently computed by solving a constrained optimization problem. Because of its efficiency, forward and inverse kinematics for soft manipulators can be solved by an iterative algorithm with a low computational cost. Meanwhile, components with multiple materials can also be geometrically modeled in our framework with the help of a simple calibration. Numerical and physical experimental tests are conducted on soft manipulators driven by different actuators with large deformation to demonstrate the performance of our approach.

Most additive manufacturing processes fabricate objects by stacking planar layers of solidified material. As a result, produced parts exhibit a so-called staircase effect, which results from sampling slanted surfaces with parallel planes. Using thinner slices reduces this effect, but it always remains visible where layers almost align with the input surfaces. In this research we exploit the ability of some additive manufacturing processes to deposit material slightly out of plane to dramatically reduce these artifacts. We focus in particular on the widespread Fused Filament Fabrication (FFF) technology, since most printers in this category can deposit along slightly curved paths, under deposition slope and thickness constraints. Our algorithm curves the layers, making them either follow the natural slope of the input surface or on the contrary, make them intersect the surfaces at a steeper angle thereby improving the sampling quality. Rather than directly computing curved layers, our algorithm optimizes for a deformation of the model which is then sliced with a standard planar approach. We demonstrate that this approach enables us to encode all fabrication constraints, including the guarantee of generating collision-free toolpaths, in a convex optimization that can be solved using a QP solver. We produce a variety of models and compare print quality between curved deposition and planar slicing.

In this article, we introduce a novel method that can generate a sequence of physical transformations between 3D models with different shape and topology. Feasible transformations are realized on a chain structure with connected components that are 3D printed. Collision-free motions are computed to transform between different configurations of the 3D printed chain structure. To realize the transformation between different 3D models, we first voxelize these input models into a similar number of voxels. The challenging part of our approach is to generate a simple path—as a chain configuration to connect most voxels. A layer-based algorithm is developed with theoretical guarantee of the existence and the path length. We find that collision-free motion sequence can always be generated when using a straight line as the intermediate configuration of transformation. The effectiveness of our method is demonstrated by both the simulation and the experimental tests taken on 3D printed chains.

We present an inverse design tool for fabric formwork - a process where flat panels are sewn together to form a fabric container for casting a plaster sculpture. Compared to 3D printing techniques, the benefit of fabric formwork is its properties of low-cost and easy transport. The process of fabric formwork is akin to molding and casting but having a soft boundary. Deformation of the fabric container is governed by force equilibrium between the pressure forces from liquid fill and tension in the stretched fabric. The final result of fabrication depends on the shapes of the flat panels, the fabrication orientation and the placement of external supports. Our computational framework generates optimized flat panels and fabrication orientation with reference to a target shape, and determines effective locations for external supports. We demonstrate the function of this design tool on a variety of models with different shapes and topology. Physical fabrication is also demonstrated to validate our approach.

Bas-relief is characterized by its unique presentation of intrinsic shape properties and/or detailed appearance using materials raised up in different degrees above a background. However, many bas-relief modeling methods could not manipulate scene details well. We propose a simple and effective solution for two kinds of bas-relief modeling (i.e., structure-preserving and detail-preserving) which is different from the prior tone mapping alike methods. Our idea originates from an observation on typical 3D models, which are decomposed into a piecewise smooth base layer and a detail layer in normal field. Proper manipulation of the two layers contributes to both structure-preserving and detail-preserving bas-relief modeling. We solve the modeling problem in a discrete geometry processing setup that uses normal-based mesh processing as a theoretical foundation. Specifically, using the two-step mesh smoothing mechanism as a bridge, we transfer the bas-relief modeling problem into a discrete space, and solve it in a least-squares manner. Experiments and comparisons to other methods show that (i) geometry details are better preserved in the scenario with high compression ratios, and (ii) structures are clearly preserved without shape distortion and interference from details.

Robots fabricated by soft materials can provide higher flexibility and thus better safety while interacting with natural objects with low stiffness such as food and human beings. However, as many more degrees of freedom are introduced, the motion simulation of a soft robot becomes cumbersome, especially when large deformations are presented. Moreover, when the actuation is defined by geometry variation, it is not easy to obtain the exact loads and material properties to be used in the conventional methods of deformation simulation. In this paper, we present a direct approach to take the geometric actuation as input and compute the deformed shape of soft robots by numerical optimization using a geometry-based algorithm. By a simple calibration, the properties of multiple materials can be modeled geometrically in the framework. Numerical and experimental tests have been conducted to demonstrate the performance of our approach on both cable-driven and pneumatic actuators in soft robotics.

This paper introduces a novel approach for sensing the bending deformation on soft robots by leveraging multicolor 3D printing. The measurement of deformation enables to complete the feedback loop of deformation control on soft actuators. The working principle of our approach is based on using compact color sensors to detect deformation that is visualized by the change of color ratios. Two novel designs are presented to generate color signals on 3D printed objects, which we call an external signal generator and an internal signal generator. Signal processing and calibration methods are developed to transform the raw RGB-data into a meaningful deformation metric. Our experimental tests taken on soft pneumatic actuators verify that color signals can be stably generated and captured to indicate the bending deformation. The results also demonstrate the usability of this sensing approach in deformation control.

This paper presents a 3-D printing system that uses a low-cost off-the-shelf consumer projector to fabricate large models. Compared with traditional digital light processing (DLP) 3-D printers using a single vertical carriage, the platform of our DLP 3-D printer using delta mechanism can also move horizontally in the plane. We show that this system can print 3-D models much larger than traditional DLP 3-D printers. The major challenge to realize 3-D printing of large models in our system comes from how to cover a planar polygonal domain by a minimum number of rectangles with fixed size, which is NP-hard. We propose a simple yet efficient approximation algorithm to solve this problem. The key idea is to segment a polygonal domain using its medial axis and afterward merge small parts in the segmentation. Given an arbitrary polygon Q with n generators (i.e., line segments and reflex vertices in Q), we show that the time complexity of our algorithm is O(n2log2n) and the number of output rectangles covering Q is O(Kn), where K is an input-polygon-dependent constant. A physical prototype system is built and several large 3-D models with complex geometric structures have been printed as examples to demonstrate the effectiveness of our approach.

This paper presents a new method to fabricate 3D models on a robotic printing system equipped with multi-axis motion. Materials are accumulated inside the volume along curved tool-paths so that the need of supporting structures can be tremendously reduced - if not completely abandoned - on all models. Our strategy to tackle the challenge of tool-path planning for multi-axis 3D printing is to perform two successive decompositions, first volume-to-surfaces and then surfaces-to-curves. The volume-to-surfaces decomposition is achieved by optimizing a scalar field within the volume that represents the fabrication sequence. The field is constrained such that its iso-values represent curved layers that are supported from below, and present a convex surface affording for collision-free navigation of the printer head. After extracting all curved layers, the surfaces-to-curves decomposition covers them with tool-paths while taking into account constraints from the robotic printing system. Our method successfully generates tool-paths for 3D printing models with large overhangs and high-genus topology. We fabricated several challenging cases on our robotic platform to verify and demonstrate its capabilities.

Offsetting-based hollowing is a solid modeling operation widely used in 3D printing, which can change the model's physical properties and reduce the weight by generating voids inside a model. However, a hollowing operation can lead to additional supporting structures for fabrication in interior voids, which cannot be removed. As a consequence, the result of a hollowing operation is affected by these additional supporting structures when applying the operation to optimize physical properties of different models. This paper proposes a support-free hollowing framework to overcome the difficulty of fabricating voids inside a solid. The challenge of computing a support-free hollowing is decomposed into a sequence of shape optimization steps, which are repeatedly applied to interior mesh surfaces. The optimization of physical properties in different applications can be easily integrated into our framework. Comparing to prior approaches that can generate support-free inner structures, our hollowing operation can reduce more volume of material and thus provide a larger solution space for physical optimization. Experimental tests are taken on a number of 3D models to demonstrate the effectiveness of this framework.

This paper presents a robotic system - RoboFDM that targets at printing 3D models without support-structures, which is considered as the major restriction to the flexibility of 3D printing. The hardware of RoboFDM consists of a robotic arm providing 6-DOF motion to the platform of material accumulation and an extruder forming molten filaments of polylactic acid (PLA). The fabrication of 3D models in this system follows the principle of fused decomposition modeling (FDM). Different from conventional FDM, an input model fabricated by RoboFDM is printed along different directions at different places. A new algorithm is developed to decompose models into support-free parts that can be printed one by one in a collision-free sequence. The printing directions of all parts are also determined during the computation of model decomposition. Experiments have been successfully taken on our RoboFDM system to print general freeform objects in a support-free manner.

This paper introduces a novel method for designing personalized orthopedic casts which are aware of thermal-comfort while satisfying mechanical requirements. Our pipeline starts from thermal images taken by an infrared camera, by which the distribution of thermal-comfort sensitivity is generated on the surface of a 3D scanned model. We formulate a hollowed Voronoi tessellation pattern to represent the covered region for a web-like cast design. The pattern is further optimized according to the thermal-comfort sensitivity calculated from thermal images. Working together with a thickness variation method, we generate a solid model for a personalized cast maximizing both thermal comfort and mechanical stiffness. To demonstrate the effectiveness of our approach, 3D printed models of personalized casts are tested on body parts of different individuals.

We present a general solution for steering microrobotic swarm by dynamic actuating fields. In our approach, the motion of micro-robots is controlled by changing the actuating direction of a field applied to them. The time-series sequence of actuating field's directions can be computed automatically. Given a target position in the domain of swarm, a governing field is first constructed to provide optimal moving directions at every points. Following these directions, a robot can be driven to the target efficiently. However, when working with a crowd of micro-robots, the optimal moving directions on different agents can contradict with each other. To overcome this difficulty, we develop a novel steering algorithm to compute a statistically optimal actuating direction at each time frame. Following a sequence of these actuating directions, a crowd of micro-robots can be transported to the target region effectively. Our steering strategy of swarm has been verified on a platform that generates magnetic fields with unique actuating directions. Experimental tests taken on aggregated magnetic micro-particles are quite encouraging.

We present a novel method for caging grasps in this paper by stretching ropes on the surface of a 3D object. Both topology and shape of a model to be grasped has been considered in our approach. Our algorithm can guarantee generating local minimal rings on every topological branches of a given model with the help of a Reeb graph. Cages and grasps can then be computed from these rings, and physical experimental tests have been conducted to verify the robustness of our approach.

We present a delta DLP 3D printer with large size in this paper. Compared with traditional DLP 3D printers that use a low-cost off-the-shelf consumer projector and a single vertical carriage, the platform of our delta DLP 3D printer can also move horizontally in the plane. We show that this structure allows the printer to have a larger printing area than the projection area of a projector. Our system can print 3D models much larger than traditional DLP 3D printers. The major challenge to realize delta 3D printing with large size comes from how to partition an arbitrary planar polygonal shape (possibly with holes or multiple disjoint polygons) into a minimum number of rectangles with fixed size, which is NP-hard. We propose a simple yet efficient approximation algorithm to solve this problem. The time complexity of our algorithm is O(n3log n), where n is the number of edges in the polygonal shape. A physical prototype system is built and several large 3D models with complex geometric structures have been printed as examples to demonstrate the effectiveness of our approach.

Abstract We present a method to design the deformation behavior of 3D printed models by an interactive tool, where the variation of bending elasticity at different regions of a model is realized by a change in shell thickness. Given a soft material to be used in 3D printing, we propose an experimental setup to acquire the bending behavior of this material on tubes with different diameters and thicknesses. The relationship between shell thickness and bending elasticity is stored in an echo state network using the acquired dataset. With the help of the network, an interactive design tool is developed to generate non‐uniformly hollowed models to achieve desired bending behaviors. The effectiveness of this method is verified on models fabricated by different 3D printers by studying whether their physical deformation can match the designed target shape.

We present an evolution method for designing the styling curves of garments. The procedure of evolution is driven by aesthetics-inspired scores to evaluate the quality of styling designs, where the aesthetic considerations are represented in the form of streamlines on human bodies. A dual representation is introduced in our platform to process the styling curves of designs, based on which robust methods for realizing the operations of evolution are developed. Starting from a given set of styling designs on human bodies, we demonstrate the effectiveness of set evolution inspired by aesthetic factors. The evolution is adaptive to the change of aesthetic inspirations. By this adaptation, our platform can automatically generate new designs fulfilling the demands of variations in different human bodies and poses.

We tackle the problem of photometric stereo under near point lighting in this paper. Different from the conventional formulation of photometric stereo that assumes parallel lighting, photometric stereo under the near point lighting condition is a nonlinear problem as the local surface normals are coupled with its distance to the camera as well as the light sources. To solve this non-linear problem of PS with near point lighting, a local/global mesh deformation approach is developed in our work to determine the position and the orientation of a facet simultaneously, where each facet is corresponding to a pixel in the image captured by the camera. Unlike nonlinear optimization schemes, the mesh deformation in our approach is decoupled into an iteration of interlaced steps of local projection and global blending. Experimental results verify that our method can generate accurate estimation of surface shape under near point lighting in a few iterations. Besides, this approach is robust to errors on the positions of light sources and is easy to be implemented.

This paper presents a framework to compute stable contact interfaces for automatically designing customized jigs used in bone surgeries. Given the surface model of a bone represented by polygonal meshes, we find out a small region on the surface to be used as the interface of a customized jig so that it can be stably fixed on the bone under a directional clamping force. The variation of directions on the clamping force is allowed in our formulation. Moreover, the surface region serves as the interface of stable contact must also be disassemblable so that the jig and the bone can be separated after removing the clamping force. The analysis of stable contact is formulated on a Gaussian map by the common regions of half-spaces according to the motion restrictions. A flooding algorithm is proposed to determine those disassemblable and stable contact interfaces on the surface of a bone, where the contact surfaces are later converted into the solid model of a jig to be fabricated by additive manufacturing. Experimental tests are taken to verify the stable contact between a bone and the jig generated by our approach.

In this paper, we propose a simple-yet-effective method for isotropic meshing relying on Euclidean distance transformation based centroidal Voronoi tessellation (CVT). Our approach improves the performance and robustness of computing CVT on curved domains while simultaneously providing high-quality output meshes. While conventional extrinsic methods compute CVTs in the entire volume bounded by the input model, we restrict the computation to a 3D shell of user-controlled thickness. Taking voxels which contain surface samples as sites, we compute the exact Euclidean distance transform on the GPU. Our algorithm is parallel and memory-efficient, and can construct the shell space for resolutions up to 2048 3 at interactive speed. The 3D centroidal Voronoi tessellation and restricted Voronoi diagrams are also computed efficiently on the GPU. Since the shell space can bridge holes and gaps smaller than a certain tolerance, and tolerate non-manifold edges and degenerate triangles, our algorithm can handle models with such defects, which typically cause conventional remeshing methods to fail. Our method can process implicit surfaces, polyhedral surfaces, and point clouds in a unified framework. Computational results show that our GPU-based isotropic meshing algorithm produces results comparable to state-of- the-art techniques, but is significantly faster than conventional CPU-based implementations.

To solve the problem of generating segmentations of meaningful parts from scanned models with freeform surfaces, we explore a compact shape prior-based segmentation approach in this paper. Our approach is inspired by an observation that a variety of natural objects consist of meaningful components in the form of compact shape and these components with compact shape are usually separated with each other by salient features. The segmentation for multiregions is performed in two phases in our framework. First, the segmentation is taken in low-level with the help of discrete Morse complex enhanced by anisotropic filtering. Second, we extract components with compact shape by using agglomerative clustering to optimize the normalized cut metric, in which the affinities of boundary compatibility, 2D shape compactness and 3D shape compactness are incorporated. The practical functionality of our approach is proved by applying it to the application of customized dental treatment. Note to Practitioners-The research work presented in this paper is to support the procedure of customized design and manufacturing. As a very important preprocessing step for the industrial design of many applications, the 3D shape of real objects must be scanned and reconstructed in computer systems. To assign semantic information to the reconstructed mesh surface, the surface are segmented into meaningful components which, however, is not a well-defined problem. There is no general segmentation approach that has good performance for scanned models with freeform surfaces. According to the observation that models in many industrial applications (e.g., customized dental treatment) have meaningful components in the form of compact shape (e.g., teeth) separating from other regions (e.g., gum), a segmentation method is developed in this paper by using the compact shape prior. The techniques developed here can speedup the design and manufacturing of devices for customized dental treatment (e.g., orthodontic braces).

We present the first method to animate sheets of paper at interactive rates, while automatically generating a plausible set of sharp features when the sheet is crumpled. The key idea is to interleave standard physically based simulation steps with procedural generation of a piecewise continuous developable surface. The resulting hybrid surface model captures new singular points dynamically appearing during the crumpling process, mimicking the effect of paper fiber fracture. Although the model evolves over time to take these irreversible damages into account, the mesh used for simulation is kept coarse throughout the animation, leading to efficient computations. Meanwhile, the geometric layer ensures that the surface stays almost isometric to its original 2D pattern. We validate our model through measurements and visual comparison with real paper manipulation, and show results on a variety of crumpled paper configurations.

This paper introduces a perceptual model for determining 3D printing orientations. Additive manufacturing methods involving low-cost 3D printers often require robust branching support structures to prevent material collapse at overhangs. Although the designed shape can successfully be made by adding supports, residual material remains at the contact points after the supports have been removed, resulting in unsightly surface artifacts. Moreover, fine surface details on the fabricated model can easily be damaged while removing supports. To prevent the visual impact of these artifacts, we present a method to find printing directions that avoid placing supports in perceptually significant regions. Our model for preference in 3D printing direction is formulated as a combination of metrics including area of support, visual saliency, preferred viewpoint and smoothness preservation. We develop a training-and-learning methodology to obtain a closed-form solution for our perceptual model and perform a large-scale study. We demonstrate the performance of this perceptual model on both natural and man-made objects.

In this paper, we propose an efficient method to reconstruct surface-from-gradients (SfG). Our method is formulated under the framework of discrete geometry processing. Unlike the existing SfG approaches, we transfer the continuous reconstruction problem into a discrete space and efficiently solve the problem via a sequence of least-square optimization steps. Our discrete formulation brings three advantages: 1) the reconstruction preserves sharp-features, 2) sparse/incomplete set of gradients can be well handled, and 3) domains of computation can have irregular boundaries. Our formulation is direct and easy to implement, and the comparisons with state-of-the-arts show the effectiveness of our method.

In this paper, we present a low-cost IMU-based system, Pedalvatar, which can capture the full-body motion of users in real-time. Unlike the prior approaches using the hip-joint as the root of forward kinematic model, a foot-rooted kinematic model is developed in this work. A state change mechanism has also been investigated to allow dynamically switching the root of kinematic trees between the left and the right foot. Benefitted from this, full-body motions can be well captured in our system as long as there is at least one static foot in the movement. The `floating' artifact of hip-joint rooted methods has been eliminated in our approach, and more complicated motions such as climbing stairs can be successfully captured in real-time. Comparing to those vision-based systems, this IMU-based system provides more flexibility on capturing outdoor motions that are important for many robotic applications.

Abstract Techniques have been developed to deform a mesh with multiple types of constraints. One limitation of prior methods is that the accuracy of demanded metrics on the resultant model cannot be guaranteed. Adding metrics directly as hard constraints to an optimization functional often leads to unexpected distortion when target metrics differ significant from what are on the input model. In this paper, we present an effective framework to deform mesh models by enforcing demanded metrics on length area and volume. To approach target metrics stably and minimize distortion, an iterative scale‐driven deformation is investigated, and a global optimization functional is exploited to balance the scaling effect at different parts of a model. Examples demonstrate that our approach provides a user‐friendly tool for designers who are used to semantic input.

We present an efficient algorithm to extract the manifold surface that approximates the boundary of a solid represented by a Binary Space Partition (BSP) tree. Our polygonization algorithm repeatedly performs clipping operations on volumetric cells that correspond to a spatial convex partition and computes the boundary by traversing the connected cells. We use point-based representations along with finite-precision arithmetic to improve the efficiency and generate the B-rep approximation of a BSP solid. The core of our polygonization method is a novel clipping algorithm that uses a set of logical operations to make it resistant to degeneracies resulting from limited precision of floating-point arithmetic. The overall BSP to B-rep conversion algorithm can accurately generate boundaries with sharp and small features, and is faster than prior methods. At the end of this paper, we use this algorithm for a few geometric processing applications including Boolean operations, model repair, and mesh reconstruction.

Given a set of corresponding user-specified anchor points on a pair of models having similar features and topologies, the cross parameterization technique can establish a bijective mapping constrained by the anchor points. In this paper, we present an efficient algorithm to optimize the complexes and the shape of common base domains in cross parameterization for reducing the distortion of the bijective mapping. The optimization is also constrained by the anchor points. We investigate a new signature, Length-Preserved Base Domain (LPBD), for measuring the level of stretch between surface patches in cross parameterization. This new signature well balances the accuracy of measurement and the computational speed. Based on LPBD, a set of metrics are studied and compared. The best ones are employed in our domain optimization algorithm that consists of two major operators, boundary swapping and patch merging. Experimental results show that our optimization algorithm can reduce the distortion in cross parameterization efficiently.

In this paper, we present an automatic approach to match correspondences on 3-D human bodies in various postures so that feature points can be automatically extracted. The feature points are very important to the establishment of volumetric parameterization around human bodies for the human-centered customization of soft-products (Trans. Autom. Sci. Eng., vol. 4, issue no. 1, pp. 11-21, 2007). For a given template human model with a set of predefined feature points, we first down-sample the input model into a set of sample points. Then, the corresponding points of these samples on the human model are identified by minimizing the distortion with the help of a series of transformations regardless of their differences in postures, scales or positions. The basic idea of our algorithm is to transform the template human body to the shape of the input model iteratively. To generate a bending invariant mapping, the initial correspondence/transformation is computed in a multidimensional scaling (MDS) embedding domain of 3-D human models, where the Euclidean distance between two samples on a 3-D model in the MDS domain corresponds to the geodesic distance between them in ℜ3. As the posture change (i.e., the body bending) of a human model can be considered as approximately isometric in the intrinsic 3-D shape, the initial correspondences established in the MDS domain can greatly enhance the robustness of our approach in body bending. Once the correspondences between the surface samples on the template model and the input model are determined after iterative transformations, we have essentially found the corresponding feature points on the input model. Finally, the locations of the based local matching step.

A fast offset surface generation approach is presented in this paper to construct intersection-free offset surfaces, which preserve sharp features, from freeform triangular mesh surfaces. The basic spirit of our algorithm is to sample a narrowband signed distance-field from the input model on a uniform grid and then employ a contouring algorithm to build the resultant offset mesh surface from the signed distance-field. Four filters are conducted to generate the narrowband signed distance-field around the offset surface in a very efficient way by alleviating computation redundancies in the regions far from the offset surfaces. The resultant mesh surfaces are generated by a modified dual contouring algorithm which relies on accurate intersections between the grid edges and the isosurfaces. A hybrid method is developed to prevent the expensive bisection search in the configurations that the analytical solutions exist. Our modified intersection-free dual contouring algorithm is based on convex-concave analysis, which is more robust and efficient. The quality and performance of our approach are demonstrated with a number of experimental tests on various examples.

Surface flattening has numerous applications in sheet manufacturing industries, such as garment industry, shoe industry, toy industry, furniture industry, and ship industry. Motivated by the requirements of those industries, WireWarping approach presented by Wang, 2008 is exploited to generate 2-D patterns with invariant length of feature and boundary curves. However, strict length constraints on all feature curves sometimes cause large distortions on 2-D patterns, especially for those 3-D surfaces which are highly non-developable. In this paper, we present a flexible and robust extension of WireWarping by introducing a new type of feature curves named elastic feature, which brings flexibility to shape control of the resultant 2-D patterns. On these new feature curves, instead of strictly preserving the exact lengths, only the ranges of their lengths are controlled. To achieve this function, a multiloop shape control optimization framework is proposed to find the optimized 2-D shape among all possible flattening results with different length variations on those elastic feature curves, while the lengths of other feature curves are kept unchanged. Besides, we also present a topology processing algorithm on the network of feature curves to eliminate cases that lead to numerical singularity. Experimental results show that the WireWarping++ can successfully flatten surface patches into 2-D patterns with more flexible shape control and more robust numerical performance.

We present a new approach to compute the approximate Boolean operations of two freeform polygonal mesh solids efficiently with the help of Layered Depth Images (LDIs). After applying the LDI sampling-based membership classification, the most challenging part, a trimmed adaptive contouring algorithm, is developed to reconstruct the mesh surface from the LDI samples near the intersected regions and stitch it to the boundary of the retained surfaces. Our method of approximate Boolean operations holds the advantage of numerical robustness as the approach uses volumetric representation. However, unlike other methods based on volumetric representation, we do not damage the facets in nonintersected regions, thus preserving geometric details much better and speeding up the computation as well. We show that the proposed method can successfully compute the Boolean operations of free-form solids with a massive number of polygons in a few seconds.

We present a volume and complexity bounded solid simplification of models represented by Binary Space Partition (BSP). Depending on the compact and robust representation of a solid model in BSP-tree, the boundary surface of a simplified model is guaranteed to be watertight and self-intersection free. Two techniques are investigated in this paper. The volume bounded convex simplification can collapse parts with small volumes on the model into a simple convex volume enclosing the volumetric cells on the input model. The selection of which region to simplify is based on a volume-difference metric, with the help of which the volume difference between the given model and the simplified one is minimized. Another technique is a plane collapse method which reduces the depth of the BSP-tree. These two techniques are integrated into our solid simplification algorithm to give satisfactory results.

Abstract Piecewise linear polygonal model has onlyG0continuity, thus users can easily feel the edges when using haptic device to touch a solid represented by coarse polygonal meshes. To produce an appealing haptic sensation for smooth solids, a large number of polygons are needed in conventional approaches. This, however, slows down computation and consumes much more memory. In this paper, we present a method to generate smooth feedback force in haptic interaction with coarse polygonal meshes. Our method calculates the interaction force based on Gregory patches, which are locally constructed fromn‐sided polygons and ensureG1continuity across boundaries of patches. During the real time haptic interaction, the contact point is continuously tracked on the locally constructed Gregory patches and thus generates smooth haptic forces to be rendered. Our method is validated on various models with comparison to conventional force rendering techniques. Copyright © 2010 John Wiley & Sons, Ltd.

In this paper, we present a fast algorithm for filling unknown regions in an image using the strategy of exemplar-matching. Unlike the original exemplar-based method using exhaustive search, we decompose exemplars into the frequency coefficients and select fewer coefficients which are the most significant to evaluate the matching score. We have also developed a local gradient-based algorithm to fill the unknown pixels in a query image block. These two techniques bring the ability of input with varied dimensions to the fast query of similar image exemplars. The fast query is based upon a search-array data structure, and can be conducted very efficiently. Moreover, the evaluation of search-arrays runs in parallel maps well on the modern graphics hardware with graphics processing units (GPU). The functionality of the approach has been demonstrated by experimental results on real photographs.

This paper presents an algorithm to approximate a solid model by a hierarchical set of bounding ellipsoids having optimal shape and volume approximation errors. The ellipsoid-tree is constructed in a top-down splitting framework. Starting from the root of hierarchy the volume occupied by a given model is divided into k sub-volumes where each is approximated by a volume bounding ellipsoid and will be later subdivided into k ellipsoids for the next level in hierarchy. The difficulty for implementing this algorithm comes from how to evaluate the volume of an ellipsoid outside the given model effectively and efficiently (i.e., the outside-volume-error). A new method - analytical computation based - is presented in this paper to compute the outside-volume-error. One application of ellipsoid-tree approximation has also been given at the end of the paper.

We present a robust method to generate mesh surfaces from unoriented noisy points in this paper. The whole procedure consists of three steps. Firstly, the normal vectors at points are evaluated by a highly robust estimator which can fit surface corresponding to less than half of the data points and fit data with multi-structures. This benefits us with the ability to well reconstruct the normal vectors around sharp edges and corners. Meanwhile, clean point cloud equipped with piecewise normal is obtained by projecting points according to the robust fitting. Secondly, an error-minimized subsampling is applied to generate a well-sampled point cloud. Thirdly, a combinatorial approach is employed to reconstruct a triangular mesh connecting the down-sampled points, and a polygonal mesh which preserves sharp features is constructed by the dual-graph of triangular mesh. Parallelization method of the algorithm on a consumer PC using the architecture of GPU is also given.

Abstract This paper presents the fireworks controller, a novel real‐time shape‐constrained fireworks animation system. We depict the shape of a firework by a 3D mesh. In order to approximate the mesh using evenly distributed points, we propose a fast point sampling method by extending the dual depth peeling algorithm. The samples are then taken as input to shape‐constrained fireworks whose physically plausible animations are based on inverse dynamics. We present a highly parallel iterative clustering algorithm to support multi‐level fireworks explosion. In order to simulate natural fuzzy fireworks, we impose extra random particles with a parallel random number generator. Several novel intuitive user interfaces are introduced to improve the usability of the system. Experimental results demonstrate the prettiness and efficiency of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd.

This paper addresses the problem of computing planar patterns for compression garments. In the garment industry, the compression garment has been more and more widely used to retain a shape of human body, where certain strain (or normal pressure) is designed at some places on the compression garment. Variant values and distribution of strain can only be generated by sewing different 2D patterns and warping them onto the body. We present a physical/geometric approach to compute 2D meshes that, when folded onto the 3D body, can generate a user-defined strain distribution through proper distortion. This is opposite to the widely studied mesh parameterization problem, whose objective is to minimize the distortion between the 2D and 3D meshes in angle, area or length.

Following the definition of developable surface in differential geometry, the flattenable mesh surface, a special type of piecewise- linear surface, inherits the good property of developable surface about having an isometric map from its 3D shape to a corresponding planar region. Different from the developable surfaces, a flattenable mesh surface is more flexible to model objects with complex shapes (e.g., cramped paper or warped leather with wrinkles). Modelling a flattenable mesh from a given input mesh surface can be completed under a constrained nonlinear optimization framework. In this paper, we reformulate the problem in terms of estimation error. Therefore, the shape of a flattenable mesh can be computed by the least-norm solutions faster. Moreover, the method for adding shape constraints to the modelling of flattenable mesh surfaces has been exploited. We show that the proposed method can compute flattenable mesh surfaces from input piecewise linear surfaces successfully and efficiently.

Abstract This paper addresses the problem of simulating the mechanical behavior of cloth in computer animation, which is very important and challenging. The micro‐structure of woven fabrics leads to significantly different shear reaction from other sheet materials, which has been neglected in previous approaches of cloth simulation. Therefore, it is beneficial for cloth simulation to model the shear buckling and structural bending separately. We analyze the shear buckling yielded by the micro‐structure of woven and the dynamic bending based on the thin‐shell theory, and develop a compact implementation of the new model on mass‐spring systems. Experimental results show that the animations generated using this technique are with wrinkles and folds appearing and vanishing in a more natural way than other approaches. Copyright © 2008 John Wiley & Sons, Ltd.

This paper presents a new approach for the mesh composition on models with arbitrary boundary topology. After cutting the needed parts from existing mesh models and putting them into the right pose, an implicit surface is adopted to smoothly interpolate the boundaries of models under composition. An interface is developed to control the shape of the implicit transient surface by using sketches to specify the expected silhouettes. After that, a localized Marching Cubes algorithm is investigated to tessellate the implicit transient surface so that the mesh surface of composed model is generated. Different from existing approaches in which the models under composition are required to have pairwise merging boundaries, the framework developed based on our techniques have the new function to fuse models with arbitrary boundary topology.

Stretch-free surface flattening has been requested by a variety of applications. At present, the most difficult problem is how to segment a given model into nearly developable atlases so that a nearly stretch-free flattening can be computed. The criterion for segmentation is needed to evaluate the possibility of flattening a given surface patch, which should be fast computed. In this paper, we present a method to compute the length-preserved free boundary (LPFB) of a mesh patch which speeds up the mesh parameterization. The distortion on parameterization can then be employed as the criterion in a trial-and-error algorithm for segmenting a given model into nearly developable atlases. The computation of LPFB is formulated as a numerical optimization problem in the angle space, where we are trying to optimize the angle excesses on the boundary while preserving the constraints derived from the closed-path theorem and the length preservation.

As ellipsoids have been employed in the collision handling of many applications in physical simulation and robotics systems, we present a novel algorithm for generating a bounding volume hierarchy (BVH) from a given model with ellipsoids as primitives. Our algorithm approximates the given model by a hierarchical set of optimized bounding ellipsoids. The ellipsoid-tree is constructed by a top-down splitting. Starting from the root of hierarchy, the volume occupied by a given model is divided into k sub-volumes where each is approximated by a volume bounding ellipsoid. Recursively, each sub-volume is then subdivided into ellipsoids for the next level in the hierarchy. The k ellipsoids at each hierarchy level for a sub-volume bounding is generated by a bottom-up algorithm - simply, the sub-volume is initially approximated by m spheres (m » k), which will be iteratively merged into k volume bounding ellipsoids and globally optimized to minimize the approximation error. Benefited from the anisotropic shape of primitives, the ellipsoid-tree constructed in our approach gives tighter volume bound and higher shape fidelity than another widely used BVH, sphere-tree.

Interactive control is one of the key issues when simulating crowd navigation in virtual environment. In this paper, we propose a simple but practical method for authoring crowd scenes in an effective and intuitive way. Radial Basis Functions (RBF) based vector field is employed as the governing tool to drive the motion flow. With this basic mathematical tool, users can easily control the motions of crowd by simply sketching velocities on a few points in the scene. Our approach is fast enough to allow on-the-fly modification of the vector field. Besides, the behavior of an individual in a crowd can be interactively adjusted by changing the ratio between its autonomous and governed movements.

This paper addresses the problem of volume parameterization that serves as the geometric kernel for design automation of customized free-form products. The purpose of volume parameterization is to establish a mapping between the spaces that are near to two reference free-form models, so that the shape of a product presented in free-form surfaces can be transferred from the space around one reference model to another reference model. The mapping is expected to keep the spatial relationship between the product model and reference models as much as possible. We separate the mapping into rigid body transformation and elastic warping. The rigid body transformation is determined by anchor points defined on the reference models using a least-squares fitting approach. The elastic warping function is more difficult to obtain, especially when the meshes of the reference objects are inconsistent. A three-stage approach is conducted. First, a coarse-level warping function is computed based on the anchor points. In the second phase, the topology consistency is maintained through a surface fitting process. Finally, the mapping of volume parameterization is established on the surface fitting result. Compared to previous methods, the approach presented here is more efficient. Also, benefitting from the separation of rigid body transformation and elastic warping, the transient shape of a transferred product does not give unexpected distortion. At the end of this paper, various industry applications of our approach in design automation are demonstrated. Note to Practitioners-The motivation of this research is to develop a geometric solution for the design automation of customized free-form objects, which can greatly improve the efficiency of design processes in various industries involving customized products (e.g., garment design, toy design, jewel design, shoe design, and glasses design, etc.). The products in the above industries are usually composed of a very complex geometry shape (represented by free-form surfaces), and is not driven by a parameter table but a reference object with free-form shapes (e.g., mannequin, toy, wrist, foot, and head models). After carefully designing a product around one particular reference model, it is desirable to have an automated tool for "grading" this product to other shape-changed reference objects while retaining the original spatial relationship between the product and reference models. This is called the design automation of a customized free-form object. Current commercial 3-D/2-D computer-aided design (CAD) systems, developed for the design automation of models with regular shape, cannot support the design automation in this manner. The approach in this paper develops efficient techniques for constraining and reconstructing a product represented by free-form surfaces around reference objects with different shapes, so that this design automation problem can be fundamentally solved. Although the approach has not been integrated into commercial CAD systems, the results based on our preliminary implementation are encouraging-the spatial relationship between reference models and the customized products is well preserved

As compatible meshes play important roles in many computer-aided design applications, we present a new approach for modelling compatible meshes. Our compatible mesh modelling method is derived from the skin algorithm [Markosian et al. 1999] which conducts an active particle-based mesh surface to approximate the given models serving as skeletons. To construct compatible meshes, we developed a duplicate-skins algorithm to simultaneously grow two skins with identical connectivity over two skeleton models; therefore, the resultant skin meshes are compatible. Our duplicate-skins algorithm has less topological constraints on the input models: multiple polygonal models, models with ill-topology meshes, or even point clouds could all be employed as skeletons to model compatible meshes. Based on the results of our duplicate-skins algorithm, the modelling method of n-Ary compatible meshes is also developed in this paper.

A variety of computer graphics applications sample surfaces of 3D shapes in a regular grid without making the sampling rate adaptive to the surface curvature or sharp features. Triangular meshes that interpolate or approximate these samples usually exhibit relatively big error around the insensitive sampled sharp features. This paper presents a robust general approach conducting bilateral filters to recover sharp edges on such insensitive sampled triangular meshes. Motivated by the impressive results of bilateral filtering for mesh smoothing and denoising, we adopt it to govern the sharpening of triangular meshes. After recognizing the regions that embed sharp features, we recover the sharpness geometry through bilateral filtering, followed by iteratively modifying the given mesh's connectivity to form singlewide sharp edges that can be easily detected by their dihedral angles. We show that the proposed method can robustly reconstruct sharp edges on feature-insensitive sampled meshes.

This paper proposes a fast approach to generate length-preserved natural boundary for intrinsic parameterization. Given a triangular mesh with disklike topology, we compute an optimal boundary for its parameterization. An optimal boundary is expected to be length-preserved with the length of every triangular edge on the boundary is invariant before and after parameterization; also, the boundary is requested to be natural where the inner angle is close to the angle excess at every boundary vertex on the given mesh. Computation of a length-preserved natural boundary is formulated as a constrained non-linear optimization problem, the procedure of solving which is in general very time-consuming. Here, we speed up the optimization by adopting the scheme of sequential linearly constrained programming. It is shown at the end of this paper that our length-preserved natural boundary could greatly improve the speed and quality of the original intrinsic parameterization.

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.