Additive manufacturing (AM) gives engineers unprecedented design and material freedom, providing the ability to 3D print polymer structures that can change shape. Many of these Shape Memory Polymer (SMP) structures require multi-material composites, and different programmed shapes can be achieved by designing and engineering these composites to fold and unfold at different rates. To enable SMP ...

Let a, b and c be positive integers, and consider a hexagon with side lengths a, b, c, a, b, c whose angles are 120◦ (see Figure 1.a). The subject of enumerating rhombus tilings of this hexagon (cf. Figure 1.b; here, and in the sequel, by a rhombus we always mean a rhombus with side lengths 1 and angles of 60◦ and 120◦) gained a lot of interest recently. This interest comes from two facts. Firs...

3D shape creation and modeling remains a challenging task especially for novice users. Many methods in the field of computer graphics have been proposed to automate the often repetitive and precise operations needed during the modeling of detailed shapes. This report surveys different approaches of shape modeling and correspondence especially for shapes exhibiting topological complexity. We foc...

Materials and devices with advanced functionalities often need to combine complex 3D shapes with functionality-inducing surface features. Precisely controlled bio-nanopatterns, printed electronic components, and sensors/actuators are all examples of such surface features. However, the vast majority of the refined technologies that are currently available for creating functional surface features...

Abstact Point/feature matching in 2D images has been well studied in the computer vision community. With the huge advancement in shape scanning and acquisition technology, feature matching has recently found usefulness in 3D shape matching and searching. We study the general problem of feature correspondence in 3D shapes represented by triangular meshes. This project is a survey and comparison ...

In the real world, we use our innate manual dexterity to create and manipulate 3D objects. Conventional virtual design tools largely neglect this skill by imposing non-intuitive 2D control mechanisms for interacting with 3D design models. Their usage is thus cumbersome, time consuming and requires training. We propose a novel design paradigm that combines users’ manual dexterity with the physic...

As the number of in-house and public-domain 3D shape models increase, importance of shape-similarity based search and retrieval for 3D shapes models has increased rapidly. In this paper, we describe our preliminary findings in applying a multiresolution analysis technique to the task of shape similarity comparison of polygon soup models. We used the 3D alpha shapes algorithm to create a multire...

We contribute a large scale database for 3D object recognition, named ObjectNet3D, that consists of 100 categories, 90,127 images, 201,888 objects in these images and 44,147 3D shapes. Objects in the 2D images in our database are aligned with the 3D shapes, and the alignment provides both accurate 3D pose annotation and the closest 3D shape annotation for each 2D object. Consequently, our datab...

Techniques for 3D model alignment and retrieval are proposed in this paper. Since the techniques of 3D modeling and digitizing tools are in great demand, the expectations of 3D models alignment and retrieval are increasingly. We propose an algorithm for 3D model alignment, which gets the affine transformation between two 3D models. The main idea of our 3D alignment algorithm in rotation is to s...

The interest in rhombus tilings has emerged from the enumeration of plane partitions in a given box (which was first carried out by MacMahon [5]). The connection comes from looking at the stacks of cubes of a plane partition from the right direction and projecting the picture to the plane. Then the box becomes a hexagon, where opposite sides are equal, and the cubes become a rhombus tiling of t...