We consider the problem of 3D shape recovery from ultra-fast motion-blurred images. While 3D reconstruction from static images has been extensively studied, recovering geometry from extreme motion-blurred images remains challenging. Such scenarios frequently occur in both natural and industrial settings, such as fast-moving objects in sports (e.g., balls) or rotating machinery, where rapid motion distorts object appearance and makes traditional 3D reconstruction techniques like Multi-View Stereo (MVS) ineffective. In this paper, we propose a novel inverse rendering approach for shape recovery from ultra-fast motion-blurred images. While conventional rendering techniques typically synthesize blur by averaging across multiple frames, we identify a major computational bottleneck in the repeated computation of barycentric weights. To address this, we propose a fast barycentric coordinate solver, which significantly reduces computational overhead and achieves a speedup of up to$4.57 \times$, enabling efficient and photorealistic simulation of high-speed motion. Crucially, our method is fully differentiable, allowing gradients to propagate from rendered images to the underlying 3D shape, thereby facilitating shape recovery through inverse rendering. We validate our approach on two representative motion types: rapid translation and rotation. Experimental results demonstrate that our method enables efficient and realistic modeling of ultra-fast moving objects in the forward simulation. Moreover, it successfully recovers 3D shapes from 2D imagery of objects undergoing extreme translational and rotational motion, advancing the boundaries of vision-based 3D reconstruction.

Due to the limited attention given to geometric features of points in three-dimensional few-shot learning, the extracted and embedded features from point clouds lack sufficient distinction, resulting in significant intra-class variation and ambiguous inter-class differentiation of features. This hinders the development of few-shot semantic segmentation for point clouds. To address this issue, we propose a novel Feature-Rich Geometric Convolutional (FRGC) network. The FRGC executes edge and geometric convolution operations on point clouds through its feature extraction backbone network. This method models geometric relationships by capturing the distribution, magnitude, and direction of group deviations within feature vectors after extracting edge structure information. Furthermore, we introduce a cross-fusion module that employs a spatial cross-attention mechanism. This mechanism highlights regions with high spatial similarity between support and query features. By extracting discriminative features with the FRGC and facilitating targeted knowledge exchange and feature fusion between the support and query set via the cross-fusion module, we reduce intra-class variance while increasing inter-class differences, thereby significantly improving few-shot segmentation performance. Compared to state-of-the-art algorithms on the Stanford Large-Scale three-dimensional Indoor Spaces dataset and ScanNet dataset, our proposed method demonstrates performance improvements in mean Interaction over Union: 66.56% (＋3.79%) and 59.73% (＋3.22%) in 2-way 1-shot, 67.64% (−1.37%) and 60.78% (−1.32%) in 2-way 5-shot, 55.32% (＋2.54%) and 59.86% (＋4.42%) in 3-way 1-shot, 57.83% (−3.21%) and 63.61% (＋7.52%) in 3-way 5-shot.

k -nearest neighbor ( k -NN) search is a fundamental primitive in geometry processing and computer graphics. While spatial partitioning structures such as kd -trees are standard, they are often manifold-blind, failing to exploit the intrinsic low-dimensional structure of points sampled from 2-manifolds. Recent advances in dynamic programming-based nearest neighbor search (DP-NNS) leverage incrementally constructed Voronoi diagrams to accelerate queries, where each site p maintains a list of successors that progressively refine its Voronoi cell. However, DP-NNS is restricted to single nearest neighbor ( k = 1) searches, precluding their adoption in applications that require local neighborhood statistics. In this paper, we generalize the DP-NNS framework to support arbitrary k -NN queries for manifold-aligned data. Our approach is founded on the geometric observation that if p i is the nearest neighbor of a query q in P , then the second nearest neighbor of q must reside either within the prefix set P 1: i -1 = [ p 1 , ..., p i-1 } or within p i 's successor list. By recursively extending this principle, we introduce Manifold k -NN, a recursive algorithmic scheme that significantly outperforms conventional kd -trees for manifold-aligned data. Our method achieves a 1×-10× speedup in volume-to-surface query scenarios and inherently supports dynamic prefix queries—enabling k -NN searches within any subset P 1: m ( m ≤ n ) with zero overhead. Furthermore, we extend the framework to support point deletion via local Delaunay updates, providing a complete suite of dynamic operations for point set modification. Comprehensive experiments on diverse geometric datasets demonstrate the efficiency and broad applicability of our approach for modern graphics pipelines. Source code is available at https://github.com/sssomeone/manifold-knn.

Abstract Simultaneous four‐axis machining involves a cutter that moves in all degrees of freedom during carving. This strategy provides higher‐quality surface finishing compared to positional machining. However, it has not been well‐studied in research. In this study, we propose the first end‐to‐end computational framework to optimize the toolpath for fabricating complex models using simultaneous four‐axis subtractive manufacturing. In our technique, we first slice the input 3D model into uniformly distributed 2D layers. For each slicing layer, we perform an accessibility analysis for each intersected contour within this layer. Then, we proceed with over‐segmentation and a bottom‐up connecting process to generate a minimal number of fabricable segments. Finally, we propose post‐processing techniques to further optimize the tool directionand the transfer path between segments. Physical experiments of nine models demonstrate our significant improvements in both fabrication quality and efficiency, compared to the positional strategy and two simultaneous tool paths generated by industry‐standard CAM systems.

Revolved 3D objects are widely used in industrial, manufacturing, and artistic fields, with subtractive manufacturing being a common production method. A key preprocessing step is to maximize raw material utilization by generating as many rough-machined inputs as possible from a single stock piece, which poses a packing problem constrained by tool accessibility. The main challenge is integrating tool accessibility into packing. This paper introduces the carvable packing problem for revolved objects, a critical but under-researched area in subtractive manufacturing. We propose a new carvable coarsening hull and a packing strategy that uses beam search and a bottom-up placement method to position these hulls in the stock material. Our method was tested on diverse sets of revolved objects with different geometries, and physical tests were conducted on a 5-axis machining platform, proving its ability to enhance material use and manufacturability.

Tightly cutting raw materials into a set of carvable objects, known as the stock cutting problem, is a necessary step in subtractive manufacturing. This problem can be framed as a 3D irregular object packing task, aiming to fit as many objects as possible within a predefined container. While previous packing algorithms can generate dense, non-overlapping, and even disassemblable configurations, they cannot satisfy carvable constraints. This paper introduces the carvable hull-and-pack problem, which integrates irregular object packing with subtractive manufacturing. This problem is more challenging than general 3D packing, as it requires ensuring the carvability of each object and generate the disassembly sequence. To address this, we first define a novel geometric hull, called carving hull , which accounts for both the object's shape and the cutter accessibility, constrained by the real-time distribution of surrounding objects. Then we present Chapper , an effective solution to co-optimize carving hull packing and the planning of disassembly sequence to maximize space utilization while preserving the carvable constraints. Given a raw material and a list of generic 3D objects, our algorithm starts with densely packing each object into the material with a pre-computed placement order, while simultaneously maintaining a valid disassembly sequence. We solve the complex object-to-object and cutter-to-object collisions by leveraging a discrete voxel representation. The carvability of each object is also guaranteed in the packing process, where we define a novel carvable metric to determine whether each object is carvable or not. Based on the packing result and the disassembly sequence, we propose a clipped Voronoi-based volume decomposition method to generate the actual carving hull for each object and finally create feasible cutting tool paths on the carving hulls. Our approach effectively packs CAD and freeform datasets, exhibiting a unique space utilization rate performance compared to the alternative baseline.

Remanufacturing effectively extends component lifespans by restoring used or end-of-life parts to like-new or even superior conditions, with an emphasis on maximizing reutilized material, especially for high-cost materials. Hybrid manufacturing technology combines the capabilities of additive and subtractive manufacturing, with the ability to add and remove material, enabling it to remanufacture complex shapes and is increasingly being applied in remanufacturing. How to effectively plan the process of additive and subtractive hybrid remanufacturing (ASHRM) to maximize material reutilization has become a key focus of attention. However, current ASHRM process planning methods lack strict consideration of collision-free constraints, hindering practical application. This paper introduces a computational framework to tackle ASHRM process planning for general shapes with strictly considering these constraints. We separate global and local collision-free constraints, employing clipping planes and graph to tackle them respectively, ultimately maximizing the reutilized volume while ensuring these constraints are satisfied. Additionally, we also optimize the setup of the target model that is conducive to maximizing the reutilized volume. Extensive experiments and physical validations on a 5-axis hybrid manufacturing platform demonstrate the effectiveness of our method across various 3D shapes, achieving an average material reutilization of 69% across 12 cases. Code is publicly available at https://github.com/fanchao98/Waste-to-Value.

the input target wire with consecutive line segments and circular segments to ensure the bending manufacturing constraints for each segment, then generate tuned wire through a bilevel optimization.This involves selecting the bending points at the upper level with a beam search strategy and determining the specifically tuned angles at the lower level.We perform a thorough physical evaluation using a DIY wire-bending machine.The results show the effectiveness of our proposed approach in realizing a wide range of intricate and complex wire sculptures.

In this study, we propose a computational framework for optimizing the continuity of the toolpath in fabricating surface models on an extrusion-based 3D printer. Toolpath continuity is a critical issue that influences both the quality and the efficiency of extrusion-based fabrication. Transfer moves lead to rough and bumpy surfaces, where this phenomenon worsens for materials with large viscosity, like clay. The effects of continuity on the surface models are even more severe in terms of the quality of the surface and the stability of the model. We introduce a criterion called the one–path patch (OPP) to represent a patch on the surface of the shell that can be traversed along one path by considering the constraints on fabrication. We study the properties of the OPPs and their merging operations to propose a bottom-up OPP merging procedure to decompose the given shell surface into a minimal number of OPPs, and to generate the “as-continuous-as-possible” (ACAP) toolpath. Furthermore, we augment the path planning algorithm with a curved-layer printing scheme that reduces staircase defects and improves the continuity of the toolpath by connecting multiple segments. We evaluated the ACAP algorithm on ceramic and thermoplastic materials, and the results showed that it improves the fabrication of surface models in terms of both efficiency and surface quality.

Additive and subtractive hybrid manufacturing (ASHM) involves the alternating use of additive and subtractive manufacturing techniques, which provides unique advantages for fabricating complex geometries with otherwise inaccessible surfaces. However, a significant challenge lies in ensuring tool accessibility during both fabrication procedures, as the object shape may change dramatically, and different parts of the shape are interdependent. In this study, we propose a computational framework to optimize the planning of additive and subtractive sequences while ensuring tool accessibility. Our goal is to minimize the switching between additive and subtractive processes to achieve efficient fabrication while maintaining product quality. We approach the problem by formulating it as a Volume-And-Surface-CO-decomposition (VASCO) problem. First, we slice volumes into slabs and build a dynamic-directed graph to encode manufacturing constraints, with each node representing a slab and direction reflecting operation order. We introduce a novel geometry property called hybrid-fabricability for a pair of additive and subtractive procedures. Then, we propose a beam-guided top-down block decomposition algorithm to solve the VASCO problem. We apply our solution to a 5-axis hybrid manufacturing platform and evaluate various 3D shapes. Finally, we assess the performance of our approach through both physical and simulated manufacturing evaluations.

We present an interactive design system for knitting that allows users to create template patterns that can be fabricated using an industrial knitting machine. Our interactive design tool is novel in that it allows direct control of key knitting design axes we have identified in our formative study and does so consistently across the variations of an input parametric template geometry. This is achieved with two key technical advances. First, we present an interactive meshing tool that lets users build a coarse quadrilateral mesh that adheres to their knit design guidelines. This solution ensures consistency across the parameter space for further customization over shape variations and avoids helices, promoting knittability. Second, we lift and formalize low-level machine knitting constraints to the level of this coarse quad mesh. This enables us to not only guarantee hand- and machine-knittability, but also provides automatic design assistance through auto-completion and suggestions. We show the capabilities through a set of fabricated examples that illustrate the effectiveness of our approach in creating a wide variety of objects and interactively exploring the space of design variations.

Past work on optimizing fabrication plans given a carpentry design can provide Pareto-optimal plans trading off between material waste, fabrication time, precision, and other considerations. However, when developing fabrication plans, experts rarely restrict to a single design , instead considering families of design variations , sometimes adjusting designs to simplify fabrication. Jointly exploring the design and fabrication plan spaces for each design is intractable using current techniques. We present a new approach to jointly optimize design and fabrication plans for carpentered objects. To make this bi-level optimization tractable, we adapt recent work from program synthesis based on equality graphs (e-graphs), which encode sets of equivalent programs. Our insight is that subproblems within our bi-level problem share significant substructures. By representing both designs and fabrication plans in a new bag of parts (BOP) e-graph, we amortize the cost of optimizing design components shared among multiple candidates. Even using BOP e-graphs, the optimization space grows quickly in practice. Hence, we also show how a feedback-guided search strategy dubbed Iterative Contraction and Expansion on E-graphs (ICEE) can keep the size of the e-graph manageable and direct the search towards promising candidates. We illustrate the advantages of our pipeline through examples from the carpentry domain.

Bladed tools such as jigsaws are common tools for wood workers on job-sites and in workshops, but do not currently have sufficient autonomous hardware or path planning algorithms to enable automation. Here we present a system of an autonomous robot and a path planning algorithm for automating jigsaw operations. The robot can drill holes, insert the jigsaw, and cut plywood. Our algorithm converts complex shapes into paths for the jigsaw, drill holes, and traversal movements for the robot. The algorithm decomposes input shapes into cuttable sections and determines possible locations for drilling entry holes for inserting the blade. We cast the drill hole problem as a set coverage problem with a trade-off between number of holes and cutting distance. We characterize the algorithm on a series of shapes and determined the algorithm found valid solutions. We executed an example on the robot to demonstrate the end-to-end system.

Abstract We propose a novel method to generate fabrication blueprints from images of carpentered items. While 3D reconstruction from images is a well‐studied problem, typical approaches produce representations that are ill‐suited for computer‐aided design and fabrication applications. Our key insight is that fabrication processes define and constrain the design space for carpentered objects, and can be leveraged to develop novel reconstruction methods. Our method makes use of domain‐specific constraints to recover not just valid geometry, but a semantically valid assembly of parts, using a combination of image‐based and geometric optimization techniques. We demonstrate our method on a variety of wooden objects and furniture, and show that we can automatically obtain designs that are both easy to edit and accurate recreations of the ground truth. We further illustrate how our method can be used to fabricate a physical replica of the captured object as well as a customized version, which can be produced by directly editing the reconstructed model in CAD software.

We introduce carvable volume decomposition for efficient 3-axis CNC machining of 3D freeform objects, where our goal is to develop a fully automatic method to jointly optimize setup and path planning. We formulate our joint optimization as a volume decomposition problem which prioritizes minimizing the number of setup directions while striving for a minimum number of continuously carvable volumes, where a 3D volume is continuously carvable, or simply carvable, if it can be carved with the machine cutter traversing a single continuous path. Geometrically, carvability combines visibility and monotonicity and presents a new shape property which had not been studied before. Given a target 3D shape and the initial material block, our algorithm first finds the minimum number of carving directions by solving a set cover problem. Specifically, we analyze cutter accessibility and select the carving directions based on an assessment of how likely they would lead to a small carvable volume decomposition. Next, to obtain a minimum decomposition based on the selected carving directions efficiently, we narrow down the solution search by focusing on a special kind of points in the residual volume, single access or SA points, which are points that can be accessed from one and only one of the selected carving directions. Candidate carvable volumes are grown starting from the SA points. Finally, we devise an energy term to evaluate the carvable volumes and their combinations, leading to the final decomposition. We demonstrate the performance of our decomposition algorithm on a variety of 2D and 3D examples and evaluate it against the ground truth, where possible, and solutions provided by human experts. Physically machined models are produced where each carvable volume is continuously carved following a connected Fermat spiral toolpath.

3D printed objects are rapidly becoming prevalent in science, technology and daily life. An important question is how to obtain strong and durable 3D models using standard printing techniques. This question is often translated to computing smartly designed interior structures that provide strong support and yield resistant 3D models. In this paper we suggest a combination between 3D printing and material injection to achieve strong 3D printed objects. We utilize triply periodic minimal surfaces (TPMS) to define novel interior support structures. TPMS are closed form and can be computed in a simple and straightforward manner. Since TPMS are smooth and connected, we utilize them to define channels that adequately distribute injected materials in the shape interior. To account for weak regions, TPMS channels are locally optimized according to the shape stress field. After the object is printed, we simply inject the TPMS channels with materials that solidify and yield a strong inner structure that supports the shape. Our method allows injecting a wide range of materials in an object interior in a fast and easy manner. Results demonstrate the efficiency of strong printing by combining 3D printing and injection together.

Traditional manufacturing workflows strongly decouple design and fabrication phases. As a result, fabrication-related objectives such as manufacturing time and precision are difficult to optimize in the design space, and vice versa. This paper presents HL-HELM, a high-level, domain-specific language for expressing abstract, parametric fabrication plans; it also introduces LL-HELM, a low-level language for expressing concrete fabrication plans that take into account the physical constraints of available manufacturing processes. We present a new compiler that supports the real-time, unoptimized translation of high-level, geometric fabrication operations into concrete, tool-specific fabrication instructions; this gives users immediate feedback on the physical feasibility of plans as they design them. HELM offers novel optimizations to improve accuracy and reduce fabrication time as well as material costs. Finally, optimized low-level plans can be interpreted as step-by-step instructions for users to actually fabricate a physical product. We provide a variety of example fabrication plans in the carpentry domain that are designed using our high-level language, show how the compiler translates and optimizes these plans to generate concrete low-level instructions, and present the final physical products fabricated in wood.

We present an automatic algorithm for subtractive manufacturing of freeform 3D objects using high-speed machining (HSM) via CNC. A CNC machine operates a cylindrical cutter to carve off material from a 3D shape stock, following a tool path, to "expose" the target object. Our method decomposes the input object's surface into a small number of patches each of which is fully accessible and machinable by the CNC machine, in continuous fashion, under a fixed cutter-object setup configuration. This is achieved by covering the input surface with a minimum number of accessible regions and then extracting a set of machinable patches from each accessible region. For each patch obtained, we compute a continuous, space-filling, and iso-scallop tool path which conforms to the patch boundary, enabling efficient carving with high-quality surface finishing. The tool path is generated in the form of connected Fermat spirals , which have been generalized from a 2D fill pattern for layered manufacturing to work for curved surfaces. Furthermore, we develop a novel method to control the spacing of Fermat spirals based on directional surface curvature and adapt the heat method to obtain iso-scallop carving. We demonstrate automatic generation of accessible and machinable surface decompositions and iso-scallop Fermat spiral carving paths for freeform 3D objects. Comparisons are made to tool paths generated by commercial software in terms of real machining time and surface quality.

In order to improve the efficiency, we should know the loss characteristics of inverter-fed induction motors. We first have to accurately measure the total motor losses, and then obtain each loss component by reasonably separate the total motor losses. In this paper, the total losses of a 5.5 kW, a 22 kW, a 30 kW, a 37 kW, a 45 kW and a 55 kW induction motors under sinusoidal supply and PWM inverter supply conditions are measured. The total losses of those motor are divided into five parts based on the loss segregation procedure IEEE Std 112-B with some special considerations, such as using AC resistance to replace the dc resistance for taking skin and proximity effect into account. Finally, the characteristics of the stator I2R losses, rotor I2R losses, friction and windage losses (F&W losses), core losses as well as stray-load losses of those motor under sinusoidal supply and PWM inverter supply conditions are analyzed.

We develop a new kind of "space-filling" curves, connected Fermat spirals , and show their compelling properties as a tool path fill pattern for layered fabrication. Unlike classical space-filling curves such as the Peano or Hilbert curves, which constantly wind and bind to preserve locality, connected Fermat spirals are formed mostly by long, low-curvature paths. This geometric property, along with continuity, influences the quality and efficiency of layered fabrication. Given a connected 2D region, we first decompose it into a set of sub-regions, each of which can be filled with a single continuous Fermat spiral. We show that it is always possible to start and end a Fermat spiral fill at approximately the same location on the outer boundary of the filled region. This special property allows the Fermat spiral fills to be joined systematically along a graph traversal of the decomposed sub-regions. The result is a globally continuous curve. We demonstrate that printing 2D layers following tool paths as connected Fermat spirals leads to efficient and quality fabrication, compared to conventional fill patterns.

We present a technique for designing three-dimensional- (3D) printed perforated lampshades that project continuous grayscale images onto the surrounding walls. Given the geometry of the lampshade and a target grayscale image, our method computes a distribution of tiny holes over the shell, such that the combined footprints of the light emanating through the holes form the target image on a nearby diffuse surface. Our objective is to approximate the continuous tones and the spatial detail of the target image to the extent possible within the constraints of the fabrication process. To ensure structural integrity, there are lower bounds on the thickness of the shell, the radii of the holes, and the minimal distances between adjacent holes. Thus, the holes are realized as thin tubes distributed over the lampshade surface. The amount of light passing through a single tube may be controlled by the tube’s radius and by its orientation (tilt angle). The core of our technique thus consists of determining a suitable configuration of the tubes: their distribution across the relevant portion of the lampshade, as well as the parameters (radius, tilt angle) of each tube. This is achieved by computing a capacity-constrained Voronoi tessellation over a suitably defined density function and embedding a tube inside the maximal inscribed circle of each tessellation cell.

Visualization of hierarchical data is of great importance in information visualization. We present variational circular treemaps with a novel layout algorithm by solving disk packing as a continuous optimization problem. Our variational circular treemaps achieve higher space utilization ratio compared with the traditional circular treemaps and support natural interactions as focus+context distortions and drill-down and roll-up operations for data navigation. Experimental results show the effectiveness of our method for visualization and interaction.

The emergence of low-cost 3D printers steers the investigation of new geometric problems that control the quality of the fabricated object. In this paper, we present a method to reduce the material cost and weight of a given object while providing a durable printed model that is resistant to impact and external forces. We introduce a hollowing optimization algorithm based on the concept of honeycomb-cells structure. Honeycombs structures are known to be of minimal material cost while providing strength in tension. We utilize the Voronoi diagram to compute irregular honeycomb-like volume tessellations which define the inner structure. We formulate our problem as a strength--to--weight optimization and cast it as mutually finding an optimal interior tessellation and its maximal hollowing subject to relieve the interior stress. Thus, our system allows to build-to-last 3D printed objects with large control over their strength-to-weight ratio and easily model various interior structures. We demonstrate our method on a collection of 3D objects from different categories. Furthermore, we evaluate our method by printing our hollowed models and measure their stress and weights.