Artistic Surface Rendering Using Layout of Text

An artistic rendering method of free-form surfaces with the aid of half-toned text that is laid-out on the given surface is presented. The layout of the text is computed using symbolic composition of the free-form parametric surface  S(u, v)  with cubic or linear Bézier curve segments  C(t) = {c_u (t), c_v (t)}  , comprising the outline of the text symbols. Once the layout is constructed on the surface, a shading process is applied to the text, affecting the width of the symbols as well as their color, according to some shader function. The shader function depends on the surface orientation and the view direction as well as the color and the direction or position of the light source.     

Isometric Texture Mapping for Free-form Surfaces

Texture mapping is a frequently exploited technique in computer graphics aimed at the emulation of high-resolution details in surfaces. In this paper we present a distance-ratios preservation method for bivariate raster texture mapping to free-form surfaces in an arbitrarily precise manner. The proposed method reduces the original general problem of computing the inverse of a three-dimensional parametric surface mapping into a problem of two-dimensional image warping. Several examples that demonstrate the proposed approach are also provided.     

Comparing offset curve approximation methods

Offset curves have diverse engineering applications, spurring extensive research on various offset techniques. In a paper on offset curve approximation (Lee et al., 1996), we suggested a new approach based on approximating the offset circle instead of the offset curve itself. To demonstrate the effectiveness of this approach, we compared it extensively with previous methods. To our surprise, Tiller and Hanson's (1984) simple method outperforms other methods for offsetting (piecewise) quadratic curves, even though its performance is not as good for high degree curves. The experimental results revealed other interesting facts, too. Had these details been reported several years ago, we believe offset approximation research might have developed somewhat differently. This article is intended to fill an important gap in the literature. We conducted qualitative as well as quantitative comparisons employing various contemporary offset approximation methods for freeform curves in the plane. We measured the efficiency of the offset approximation in terms of the number of control points generated while making the approximations within a prescribed tolerance     

Coupling the folding of homologous proteins

The empirical observation that homologous proteins fold to similar structures is used to enhance the capabilities of an ab initio algorithm to predict protein conformations. A penalty function that forces homologous proteins to look alike is added to the potential and is employed in the coupled energy optimization of several homologous proteins. Significant improvement in the quality of the computed structures (as compared with the computational folding of a single protein) is demonstrated and discussed.     

Interactive tree modeling and deformation with collision detection and avoidance

We present an interactive tree modeling and deformation system that supports an efficient collision detection and avoidance using a bounding volume hierarchy of sweep surfaces. Starting with conventional tree models (given as meshes), we convert them into sweep surfaces and deform their branches interactively while detecting and avoiding collisions with many other branches. Multiple tree models (sharing the same topology) can be generated with great ease using this sweep‐based approach, and they can serve as a basis for the generation of a multiparameter family of trees. We demonstrate the effectiveness of our approach in an automatic generation of similar trees, the colonization of trees to form a forest, and the tree growth, aging, and withering simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

Efficient Hausdorff Distance computation for freeform geometric models in close proximity

We present an interactive-speed algorithm for computing the Hausdorff Distance (HD) between two freeform geometric models represented with NURBS surfaces. The algorithm is based on an effective technique for matching a surface patch from one model to the corresponding nearby surface patch on the other model. To facilitate the matching procedure, we employ a bounding volume hierarchy (BVH) for freeform NURBS surfaces, which provides a hierarchy of Coons patches and bilinear surfaces approximating the NURBS surfaces (Kim et al., 2011 [1]). Comparing the local HD upper bound against a global HD lower bound, we can eliminate the majority of redundant surface patches from further consideration. The resulting algorithm and the associated data structures are considerably simpler than the previous BVH-based HD algorithms. As a result, we can compute the HD of two freeform geometric models efficiently and robustly even when the two models are in close proximity. We demonstrate the effectiveness of our approach using several experimental results.     

Efficient Minimum Distance Computation for Solids of Revolution

We present a highly efficient algorithm for computing the minimum distance between two solids of revolution, each of which is defined by a planar cross-section region and a rotation axis. The boundary profile curve for the cross-section is first approximated by a bounding volume hierarchy (BVH) of fat arcs. By rotating the fat arcs around the axis, we generate the BVH of fat tori that bounds the surface of revolution. The minimum distance between two solids of revolution is then computed very efficiently using the distance between fat tori, which can be boiled down to the minimum distance computation for circles in the three-dimensional space. Our circle-based approach to the solids of revolution has distinctive features of geometric simplification. The main advantage is in the effectiveness of our approach in handling the complex cases where the minimum distance is obtained in non-convex regions of the solids under consideration. Though we are dealing with a geometric problem for solids, the algorithm actually works in a computational style similar to that of handling planar curves. Compared with conventional BVH-based methods, our algorithm demonstrates outperformance in computing speed, often 10–100 times faster. Moreover, the minimum distance can be computed very efficiently for the solids of revolution under deformation, where the dynamic reconstruction of fat arcs dominates the overall computation time and takes a few milliseconds.     

Performing Efficient NURBS Modeling Operations on the GPU

We present algorithms for evaluating and performing modeling operations on NURBS surfaces using the programmable fragment processor on the Graphics Processing Unit (GPU). We extend our GPU-based NURBS evaluator that evaluates NURBS surfaces to compute exact normals for either standard or rational B-spline surfaces for use in rendering and geometric modeling. We build on these calculations in our new GPU algorithms to perform standard modeling operations such as inverse evaluations, ray intersections, and surface-surface intersections on the GPU. Our modeling algorithms run in real time, enabling the user to sketch on the actual surface to create new features. In addition, the designer can edit the surface by interactively trimming it without the need for retessellation. Our GPU-accelerated algorithm to perform surface-surface intersection operations with NURBS surfaces can output intersection curves in the model space as well as in the parametric spaces of both the intersecting surfaces at interactive rates. We also extend our surface-surface intersection algorithm to evaluate self-intersections in NURBS surfaces.     

Modeling (seemingly) impossible models

In recent years, there has been a growing interest in computer graphics and geometric modeling in the ability to create and manipulate seemingly impossible models (SIMs). Methods to create derivative work and modify drawings and paintings of SIMs made by artists were suggested. Similarly, 3D realization of SIMs of some of these drawings were also offered.In this work, we further explore the nature of SIMs and identify a class of SIMs that can be realized and modeled in 3D. As part of this analysis we show an invariance whose preservation allows one to model SIM artifacts that are completely realizable. We further present a mini-modeling package that allow end-users to realize whole new SIMs in two stages: modeling a regular 3D model and then converting it into a SIM using special deformations. We conclude with some examples, a discussion on the current limitations and a layout of possible future work.     

Real-time geometric deformation displacement maps using programmable hardware

Striving for photorealism, texture mapping, and its more advanced variations, bump and displacement mapping, have all become fundamental tools in computer graphics. Recently, the introduction of programmable graphics hardware has enabled the employment of displacement mapping in real-time applications. While displacement mapping facilitates the actual modification of the underlying geometry, it is constrained by being an injective mapping. Further, it is also limited because it usually maps the geometry of the (low-resolution) smooth base surfaces, typically by displacing their vertices. Drawing from recent work on deformation displacement mapping (DDM) [4], in this paper we offer real-time solutions to both these limitations. Our solutions make it possible to employ the DDM paradigm on programmable graphics hardware. By reversing the roles of the base surfaces and their geometric details, both the one-to-one constraint and the base surface resolution limitation are resolved. Furthermore, this role reversal also paves the way for other benefits such as a tremendous decrease in the memory consumption of geometric detail information in the DDM and the ability to animate the details over the base surface. We show that the presented scheme can be used effectively to generate highly complex renderings and animations, in real time, on modern graphics hardware. The capabilities of the proposed method are demonstrated for both rational parametric base surfaces and polygonal base surfaces.