Related papers: Snipperclips: Cutting Tools into Desired Polygons …
Triangulation algorithms that conform to a set of non-intersecting input segments typically proceed in an incremental fashion, by inserting points first, and then segments. Inserting a segment amounts to: (1) deleting all the triangles it…
Autonomous dual-arm manipulation is an essential skill to deploy robots in unstructured scenarios. However, this is a challenging undertaking, particularly in terms of perception and planning. Unstructured scenarios are full of objects with…
This paper tackles the challenging robotic task of generalizable paper cutting using scissors. In this task, scissors attached to a robot arm are driven to accurately cut curves drawn on the paper, which is hung with the top edge fixed. Due…
We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…
During the last decades, anatomy has become an interesting topic in education---even for laymen or schoolchildren. As medical imaging techniques become increasingly sophisticated, virtual anatomical education applications have emerged.…
We consider scheduling problems over scenarios where the goal is to find a single assignment of the jobs to the machines which performs well over all possible scenarios. Each scenario is a subset of jobs that must be executed in that…
In the Escherization problem, given a closed figure in a plane, the objective is to find a closed figure that is as close as possible to the input figure and tiles the plane. Koizumi and Sugihara's formulation reduces this problem to an…
Given two triangulations of a convex polygon, computing the minimum number of flips required to transform one to the other is a long-standing open problem. It is not known whether the problem is in P or NP-complete. We prove that two…
Partitioning and grouping of similar objects plays a fundamental role in image segmentation and in clustering problems. In such problems a typical goal is to group together similar objects, or pixels in the case of image processing. At the…
We prove that almost every triangle can be dissected only into $n^2$ triangles which have to be equal one another. Moreover, such a dissection is unique for every $n$. It turns out that to solve this "simple" problem it is convenient to use…
We study the problem of finding neck-like features on a surface. Applications for such cuts include robotics, mesh segmentation, and algorithmic applications. We provide a new definition for a surface bottleneck -- informally, it is the…
For grasp network algorithms, generating grasp datasets for a large number of 3D objects is a crucial task. However, generating grasp datasets for hundreds of objects can be very slow and consume a lot of storage resources, which hinders…
In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be NP-complete even when restricted to bipartite graphs. It has been…
We propose a new shape-based modeling technique for applications in imaging problems. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right dictionary elements and geometrically composing them…
We present a procedure to approximate a plane contour by piecewise polynomial functions, depending on various parameters, such as degree, number of local patches, selection of knots. This procedure aims to be adopted to study how…
Game maps are useful for human players, general-game-playing agents, and data-driven procedural content generation. These maps are generally made by hand-assembling manually-created screenshots of game levels. Besides being tedious and…
MacGyvering is defined as creating or repairing something in an inventive or improvised way by utilizing objects that are available at hand. In this paper, we explore a subset of Macgyvering problems involving tool construction, i.e.,…
Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…
We study the slices or sections of a convex polytope by affine hyperplanes. We present results on two key problems: First, we provide tight bounds on the maximum number of vertices attainable by a hyperplane slice of $d$-polytope (a sort of…
Implicit neural fields have made remarkable progress in reconstructing 3D surfaces from multiple images; however, they encounter challenges when it comes to separating individual objects within a scene. Previous work has attempted to tackle…