Ergun Akleman

GUARANTEEING THE 2-MANIFOLD PROPERTY FOR MESHES WITH DOUBLY LINKED FACE LIST

Meshes, which generalize polyhedra by using non-planar faces, are the most commonly used objects in computer graphics. Modeling 2-dimensional manifold meshes with a simple user interface is an important problem in computer graphics and computer aided geometric design. In this paper, we propose a conceptual framework to model meshes. Our framework guarantees topologically correct 2-dimensional manifolds and provides a new user interface paradigm for mesh modeling systems.

A minimal and complete set of operators for the development of robust manifold mesh modelers

In this paper, we identify a minimal and complete set of fundamental operators, which is necessary and sufficient for performing all homeomorphic and topological operations on 2- manifold mesh structures. Efficient algorithms are developed for the implementation of these operators. We also developed a set of powerful, user-friendly, and effective operators at the level of user-interface. Using these operators, we have developed a prototype system for robust, interactive, and user-friendly modeling of orientable 2-manifold meshes. Users of our system can perform a large set of homeomorphic and topological changes with these user-interface level operators. Our system is topologically robust in the sense that users will never create invalid 2-manifold mesh structure with these operators. In our system, the homeomorphic and topological surgery operations can be applied alternatively on 2-manifold meshes. With our system, users can blend surfaces, construct rinds, and open holes on these rind shapes. With our system, the shapes that look like solid, non-manifold, or 2-manifold with boundary can be manipulated. The system also provides automatic texture mapping during topology changes.

Two methods for creating chinese painting

We present two methods to create realistic Chinese painting. The first method is to create 3D Chinese painting animation using existing software packages. The second method is an expressive paint tool which allows an artist to interactively create 2D Chinese painting.

Modeling expressive 3D caricatures

The concepts of abstraction, simplification and exaggeration, which are very common in traditional art and caricature, can directly be applied to the 3D modeling process. Therefore, the development of methods to teach these concepts is essential for 3D computer art and design education. In this work, we present an educational method to teach students these artistic concepts by modeling expressive 3D caricatures. This method has been successfully used in a geometric modeling course that combines artistic and scientific aspects of 3D modeling. Using the method, all the students, regardless of their artistic abilities, can create convincing 3D caricatures.

Generalized distance functions

We obtain a generalized version of the well-known distance function family L/sub p/ norm. We prove that the new functions satisfy distance function properties. By using these functions, convex symmetric shapes can be described as loci, the set of points which are in equal distance from a given point. We also show that these symmetric convex shapes can be easily parameterized. We also show these distance functions satisfy a Lipschitz-type condition. We provide a fast ray marching algorithm for rendering shapes described by these distance functions. These distance functions can be used as building blocks for some implicit modeling tools such as soft objects, constructive soft geometry, function representations (freps) or ray quadrics.

A new paradigm for changing topology during subdivision modeling

The authors present a paradigm that allows dynamic changing of the topology of 2-manifold polygonal meshes. Our paradigm always guarantees topological consistency of polygonal meshes. Based on our paradigm, by simply adding and deleting edges, handles can be created and deleted, holes can be opened or closed, polygonal meshes can be connected or disconnected. These edge insertion and edge deletion operations are highly consistent with subdivision algorithms. In particular, these operations can be easily included into a subdivision modeling system such that the topological changes and subdivision operations can be performed alternatively during model construction. We demonstrate practical examples of topology changes based on this new paradigm and show that the new paradigm is convenient, effective, efficient, and friendly to subdivision surfaces.

SMI 2013: Towards building smart self-folding structures

We report our initial progress on synthesizing complex structures from programmable self-folding active materials, which we call Smart Multi-Use Reconfigurable Forms. We have developed a method to unfold a given convex polygonal mesh into a one-piece planar surface. We analyze the behavior of this surface as if it were constructed from realistic active materials such as shape memory alloys (SMAs), in which sharp creases and folds are not feasible. These active materials can change their shapes when they are heated and have been applied to medical, aerospace, and automotive applications in the engineering realm. We demonstrate via material constitutive modeling and utilization of finite element analysis (FEA) that by appropriately heating the unfolded planar surface it is possible to recover the 3D shape of the original polygonal mesh. We have simulated the process and our finite element analysis simulations demonstrate that these active materials can be raised against gravity, formed, and reconfigured automatically in three dimensions with appropriate heating in a manner that extends previous work in the area of programmable matter. Based on our results, we believe that it is possible to use active materials to develop reprogrammable self-folding complex structures.

Cyclic plain-weaving on polygonal mesh surfaces with graph rotation systems

In this paper, we show how to create plain-weaving over an arbitrary surface. To create a plain-weaving on a surface, we need to create cycles that cross other cycles (or themselves) by alternatingly going over and under. We use the fact that it is possible to create such cycles, starting from any given manifold-mesh surface by simply twisting every edge of the manifold mesh. We have developed a new method that converts plain-weaving cycles to 3D thread structures. Using this method, it is possible to cover a surface without large gaps between threads by controlling the sizes of the gaps. We have developed a system that converts any manifold mesh to a plain-woven object, by interactively controlling the shapes of the threads with a set of parameters. We have demonstrated that by using this system, we can create a wide variety of plain-weaving patterns, some of which may not have been seen before.

Remeshing Schemes for semi-regular tilings

Most frequently used subdivision schemes such as Catmull-Clark create regular regions after several applications. This paper shows that all semi-regular regions can be created by subdivision schemes and each semi-regular region type can be created with one application of a particular subdivision scheme to a particular regular region. Using this property of subdivision schemes it is easy to cover any given surface with semi-regular tiles by applying one semi-regularity creating subdivision after several applications of a regularity creating subdivision.

Optimized fault location

A continuous and reliable electrical energy supply is the objective of any power system operation. However, faults inevitably occur in power system due to bad weather conditions, equipment damage, equipment failure, environment changes, human or animal interference and many other reasons. Since it is very important that correct information about fault location and its nature is provided as fast as possible, an automated system is proposed to track status of equipment and to calculate fault location. Calculated results are available to users through detailed graphical representation. This paper presents elements of proposed solution and describes the benefits.