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In this paper, we present a patch-based representation of surfaces, PolyFit, which is obtained by fitting jet functions locally on surface patches. Such a representation can be learned efficiently in a supervised fashion from both analytic…
Spline functions have long been used in numerical solution of differential equations. Recently it revives as isogeometric analysis, which offers integration of finite element analysis and NURBS based CAD into a single unified process.…
In pipeline inspection, traditional tethered inspection robots are severely constrained by cable length and weight, which greatly limit their travel range and accessibility. To address these issues, this paper proposes a self-propelled…
This paper studies the straight skeleton of polyhedra in three dimensions. We first address voxel-based polyhedra (polycubes), formed as the union of a collection of cubical (axis-aligned) voxels. We analyze the ways in which the skeleton…
Standard PolyCube-based hexahedral (hex) meshing methods aim to deform the input domain into an axis-aligned PolyCube volume with integer corners; if this deformation is bijective, then applying the inverse map to the voxelized PolyCube…
In this paper, modification of the classical PID controller and development of open-loop control mechanisms to improve stability and robustness of a differential wheeled robot are discussed. To deploy the algorithm, a test platform has been…
Robotic grinding is widely used for shaping workpieces in manufacturing, but it remains difficult to automate this process efficiently. In particular, efficiently grinding workpieces of different shapes and material hardness is challenging…
In this paper we develop a concrete way to construct bodies of constant width in dimension three. They are constructed from special embeddings of self-dual graphs.
In this exploration paper, we design algorithms for deforming and contracting a simply connected discrete closed manifold to a discrete sphere. Such a contraction is a kind of shrinking or reducing process. In our algorithms, we need to…
There exists a bijection between the configuration space of a linear pentapod and all points $(u,v,w,p_x,p_y,p_z)\in\mathbb{R}^{6}$ located on the singular quadric $\Gamma: u^2+v^2+w^2=1$, where $(u,v,w)$ determines the orientation of the…
We present two algorithms for unfolding the surface of any polyhedron, all of whose faces are triangles, to a nonoverlapping, connected planar layout. The surface is cut only along polyhedron edges. The layout is connected, but it may have…
We show the existence of families of periodic polyhedra in spaces of constant curvature whose fundamental domains can be obtained by attaching prisms and antiprisms to Archimedean solids. These polyhedra have constant discrete curvature and…
We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have 3-, 4-, or 6-fold rotational symmetry. The symmetry groups of…
Starting with the unsolved "D\"urer's problem" of edge-unfolding a convex polyhedron to a net, we specialize and generalize (a) the types of cuts permitted, and (b) the polyhedra shapes, to highlight both advances established and which…
A discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a…
The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This survey paper offers a scoping review, i.e., a literature…
Manipulating deformable objects in robotic cells is often costly and not widely accessible. However, the use of localized pneumatic gripping systems can enhance accessibility. Current methods that use pneumatic grippers to handle deformable…
Manipulation of deformable linear objects (DLOs) in constrained environments is a challenging task. This paper describes a two-layered approach for placing DLOs on a flat surface using a single robot hand. The high-level layer is a novel…
Curve and surface fairing is crucial in computer-aided geometric design, influencing product quality, physical performance, and aesthetics. Traditional methods often apply global modifications, lacking fine-grained control. This paper…
Modeling contact between deformable solids is a fundamental problem in computer animation, mechanical design, and robotics. Existing methods based on $C^0$-discretizations -- piece-wise linear or polynomial surfaces -- suffer from…