We propose a specialized form of the curved-knot B-spline surface of Hayes [1982] that we call regular curved-knot spline surface . Unlike the original formulation where the knots of the first parametric coordinate can evolve arbitrarily with respect to the second coordinate, our formulation designs the knot functions as special curves that guarantee a monotonic blending of the knots corresponding to opposite surface boundaries. Furthermore, we demonstrate that local derivatives on the boundary can be described as an ordinary B-spline surface. The latter property allows for constructing smooth transitions between B-spline boundaries with different knot vectors.

Abstract Polar NURBS surface is a kind of periodic NURBS surface, one boundary of which shrinks to a degenerate polar point. The specific topology of its control‐point mesh offers the ability to represent a cap‐like surface, which is common in geometric modeling. However, there is a critical and challenging problem that hinders its application: curvature continuity at the extraordinary singular pole. We first propose a sufficient and necessary condition of curvature continuity at the pole. Then, we present constructive methods for the two key problems respectively: how to construct a polar NURBS surface with curvature continuity and how to reform an ordinary polar NURBS surface to curvature continuous. The algorithms only depend on the symbolic representation and operations of NURBS, and they introduce no restrictions on the degree or the knot vectors. Examples and comparisons demonstrate the applications of the curvature‐continuous polar NURBS surface in hole‐filling and free‐shape modeling.

Abstract This paper presents a novel content‐based method for transferring the colour patterns between images. Unlike previous methods that rely on image colour statistics, our method puts an emphasis on high‐level scene content analysis. We first automatically extract the foreground subject areas and background scene layout from the scene. The semantic correspondences of the regions between source and target images are established. In the second step, the source image is re‐coloured in a novel optimization framework, which incorporates the extracted content information and the spatial distributions of the target colour styles. A new progressive transfer scheme is proposed to integrate the advantages of both global and local transfer algorithms, as well as avoid the over‐segmentation artefact in the result. Experiments show that with a better understanding of the scene contents, our method well preserves the spatial layout, the colour distribution and the visual coherence in the transfer process. As an interesting extension, our method can also be used to re‐colour video clips with spatially‐varied colour effects.

BACKGROUND: Many molecules of interest are flexible and undergo significant shape deformation as part of their function, but most existing methods of molecular shape comparison treat them as rigid shapes, which may lead to incorrect measure of the shape similarity of flexible molecules. Currently, there still is a limited effort in retrieval and navigation for flexible molecular shape comparison, which would improve data retrieval by helping users locate the desirable molecule in a convenient way. RESULTS: To address this issue, we develop a web-based retrieval and navigation tool, named 3DMolNavi, for flexible molecular shape comparison. This tool is based on the histogram of Inner Distance Shape Signature (IDSS) for fast retrieving molecules that are similar to a query molecule, and uses dimensionality reduction to navigate the retrieved results in 2D and 3D spaces. We tested 3DMolNavi in the Database of Macromolecular Movements (MolMovDB) and CATH. Compared to other shape descriptors, it achieves good performance and retrieval results for different classes of flexible molecules. CONCLUSIONS: The advantages of 3DMolNavi, over other existing softwares, are to integrate retrieval for flexible molecular shape comparison and enhance navigation for user's interaction. 3DMolNavi can be accessed via https://engineering.purdue.edu/PRECISE/3dmolnavi/index.html.

Extraction and re-rendering of real materials give large contributions to various image-based applications. As one of the key properties of modeling the appearance of an object, materials mainly focus on the effects caused by light transportation. Therefore, understanding the characteristics of a complex material from a single photograph and transferring it to an object in another image becomes a very challenging problem.

Color transfer is a practical image editing technology which is useful in various applications. An ideal color transfer algorithm should keep the scene in the source image and apply the color styles of the reference image. All the dominant color styles of the reference image should be presented in the result especially when there are similar contents in the source and reference images.

Abstract We present a novel hierarchical grid based method for fast collision detection (CD) for deformable models on GPU architecture. A two‐level grid is employed to accommodate the non‐uniform distribution of practical scene geometry. A bottom‐to‐top method is implemented to assign the triangles into the hierarchical grid without any iteration while a deferred scheme is introduced to efficiently update the data structure. To address the issue of load balancing, which greatly influences the performance in SIMD parallelism, a propagation scheme which utilizes a parallel scan and a segmented scan is presented, distributing workloads evenly across all concurrent threads. The proposed method supports both discrete collision detection (DCD) and continuous collision detection (CCD) with self‐collision. Some typical benchmarks are tested to verify the effectiveness of our method. The results highlight our speedups over prior algorithms on different commodity GPUs.

Color transfer is an image editing technique which arises various applications, from daily photo appearance enhancement to movie post-processing. An ideal color transfer algorithm should keep the scene from the source image and apply the color style of the target image. All the dominant colors in the target image should be transferred to the source, while the colors in the source image which are apparently distinct from the target style should not appear in the result. The preservation of the scene details is also important for a good color transfer algorithm.

N-sided hole filling plays an important role in vertex blending. Piegl and Tiller presented an algorithm to interpolate the given boundary and cross-boundary derivatives in B-spline form. To deal with the incompatible cases that their algorithm cannot handle, we propose an extension method to manipulate the transition between sharp and rounded features. The algorithm first patches n crescent-shaped extended surfaces to the boundary with G2continuity to handle incompatibility problem in the corners. Then, we compute the inner curves and the corresponding cross-boundary derivatives fulfilling tangent and twist compatibilities. The generated B-spline Coons patches are G1-continuously connected exactly, and have ε-G1continuity with the extended surfaces. Our method improves the continuity-quality of the shape and reduces the count of the inserted knots. It can be applied to all G0-continuous boundary conditions without any restrictions imposed on the boundary or cross-boundary derivatives. It generates better shapes than some popular industrial modeling systems on these incompatible occasions. Some examples underline its feasibility.

Sectional views are widely used in engineering practice due to their clear and concise expression. However, it is difficult for computers to understand because of the large numbers of omitted entities and their diversified representations. This paper aims at reconstructing 3D models from 2D sectional views by improving the traditional volume based method. First, we present a two-stage loop searching algorithm to extract desired loops from sectional views. Then, sub-objects are identified by the hint-based feature identification algorithm with an intuitive loop-matching criterion. After that, a model-directed algorithm is proposed to guide the generation of sub-objects which are assembled together to form the final objects. The algorithm can handle full sections, partial sections and offset sections, as well as orthographic views. Multiple sectional views are supported in our algorithm. Moreover, the domain of objects is extended to inclined quadric surfaces and intersecting quadric surfaces with higher order curves. Experiment results show its practicability.

Abstract Image space photon mapping has the advantage of simple implementation on GPU without pre‐computation of complex acceleration structures. However, existing approaches use only a single image for tracing caustic photons, so they are limited to computing only a part of the global illumination effects for very simple scenes. In this paper we fully extend the image space approach by using multiple environment maps for photon mapping computation to achieve interactive global illumination of dynamic complex scenes. The two key problems due to the introduction of multiple images are 1) selecting the images to ensure adequate scene coverage; and 2) reliably computing ray‐geometry intersections with multiple images. We present effective solutions to these problems and show that, with multiple environment maps, the image‐space photon mapping approach can achieve interactive global illumination of dynamic complex scenes. The advantages of the method are demonstrated by comparison with other existing interactive global illumination methods.

Directional distance is commonly used in geographical information systems as a measure of openness. In previous works, the sweep line method and the interval tree method have been employed to evaluate the directional distances on vector maps. Both methods require rotating original maps and study points in every direction of interest. In this article, we propose a cell-based algorithm that pre-processes a map only once; that is, it subdivides the map into a group of uniform-sized cells and records each borderline of the map into the cells traversed by its corresponding line segment. Based on the pre-processing result, the neighbouring borderlines of a study point can be directly obtained through the neighbouring cells of the point, and the borderlines in a definite direction can be simply acquired through the cells traversed by the half line as well. As a result, the processing step does not need to enumerate all the borderlines of the map when determining whether a point is on a borderline or finding the nearest intersection between a half line and the borderlines. Furthermore, we implement the algorithm for determining fetch length in coastal environment. Once the pre-processing is done, the algorithm can work in a complex archipelago environment such as to calculate the fetch lengths in multiple directions, to determine the inclusion property of a point, and to deal with the singularity of a study point on a borderline.

Quadratic Bézier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic Bézier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing G1quadratic Bézier curves satisfying given endpoint (positions and arbitrary unit tangent vectors) conditions. Examples are given to illustrate the new solution and to perform comparison between the G1quadratic Bézier cures and other curve schemes such as the composite geometric Hermite curves and the biarcs.

We present a novel method for content-aware image resizing based on optimization of a well-defined image distance function, which preserves both the important regions and the global visual effect (the background or other decorative objects) of an image. The method operates by joint use of seam carving and image scaling. The principle behind our method is the use of a bidirectional similarity function of image Euclidean distance (IMED), while cooperating with a dominant color descriptor (DCD) similarity and seam energy variation. The function is suitable for the quantitative evaluation of the resizing result and the determination of the best seam carving number. Different from the previous simplex-mode approaches, our method takes the advantages of both discrete and continuous methods. The technique is useful in image resizing for both reduction/retargeting and enlarging. We also show that this approach can be extended to indirect image resizing.

This paper presents a new method on the intersection testing problem between an ellipsoid and an algebraic surface. In the new method, the testing problem is turned into a new testing problem whether a univariate polynomial has a positive or negative real root. Examples are shown to illustrate the robustness and efficiency of the new method.

Flowers are familiar in virtual scenes, however, the design of flower patterns is still mainly done by hand. To produce a number of flower color patterns required by a large scene can be very labor-consuming. In this paper, we present a biologically-motivated algorithm for modeling and visualization of flower color patterns. It is able to produce various flower color patterns with little user interaction. In our system, pigmentation is simulated by a modified reaction-diffusion system, and the simulation function is controlled by a few experiential parameters. Thus it can be adjusted to produce various flower color patterns widely observed in the real world. Furthermore, our algorithm can be easily embedded into other advanced shading models to improve the quality of their rendering results. We present an image-based texture generation method as an example.

One significant problem in tile-based texture synthesis is the presence of conspicuous seams in the tiles. The reason is that the sample patches employed as primary patterns of the tile set may not be well stitched if carelessly picked. In this paper, we introduce an optimized approach that can stably generate an ω-tile set of high pattern diversity and high quality. Firstly, an extendable rule is introduced to increase the number of sample patches to vary the patterns in an ω-tile set. Secondly, in contrast to the other concurrent techniques that randomly choose sample patches for tile construction, our technique uses Genetic Algorithm to select the feasible patches from the input example. This operation insures the quality of the whole tile set. Experimental results verify the high quality and efficiency of the proposed algorithm.

One significant problem in tile-based texture synthesis is the selection of sample patches. The reason is that the tiling process may produce results with poor quality when the sample patches used to fill the tiles can not find good cutting patches at the merging stage. In this paper, we use genetic algorithm to find the best group of sample patches from a considerable number of patch groups. Using tile set gene rated by these optimal sample patches can significantly improve the result quality of the tile-based texture synthesis.

A novel mesh parametrization method for an open connected surface is presented. The parametrization method is based on Hessian-based locally linear embedding (HLLE). Our method operates directly on the surface without using any partition technique and can preserve the local and global structure, while partition-based methods often produce high distortion and discontinuity nearby partition boundaries. In addition, some examples about texture mapping show the efficiency of our method.

We propose a new topological data structure for representing a set of polygonal curves embedded in a meshed surface. In this embedding, the vertices of the curve do not necessarily correspond to the vertices of the surface. The partition of the surface yielded by the intersecting curves is efficiently represented as a "cut-graph". The cut-graph stores combinatorial information of the network of curves. In our approach, the combinatorial form of information is systematically preferred to geometrical information since it improves both robustness and efficiency. Thanks to the topological data structure and algorithms, the cut-graph can be sketched through iterations of designing and erasing curves on the mesh surface in a "nondestructive" way, i.e. without modifying the mesh until the cutting operation is committed. We also demonstrate several prototype curve design tools inspired by 2D vector and bitmap graphics paradigms. We show how to sketch the cut-graph and how these tools can be mixedly used.

In this article, we introduce a general-purpose method for computing radiosity on scenes made of parametric surfaces with arbitrary trimming curves. In contrast with past approaches that require a tessellation of the input surfaces (be it made up of triangles or patches with simple trimming curves) or some form of geometric approximation, our method takes full advantage of the rich and compact mathematical representation of objects. At its core lies the virtual mesh , an abstraction of the input geometry that allows complex shapes to be illuminated as if they were simple primitives. The virtual mesh is a collection of normalized square domains to which the input surfaces are mapped while preserving their energy properties. Radiosity values are then computed on these supports before being lifted back to the original surfaces. To demonstrate the power of our method, we describe a high-order wavelet radiosity implementation that uses the virtual mesh. Examples of objects and environments, designed for interactive applications or virtual reality, are presented. They prove that, by exactly integrating curved surfaces in the resolution process, the virtual mesh allows complex scenes to be rendered more quickly, more accurately, and much more naturally than with previously known methods.

Having a better way to represent and to interact with large geological models are topics of high interest in geoscience, and especially for oil and gas companies. We present the design and implementation of a visualization program that involves two main features. It is based on the central data model, in order to display in real time the modifications caused by the modeler. Furthermore, it benefits from the different immersive environments which give the user a much more accurate insight of the model than a regular computer screen. Then, we focus on the difficulties that come in the way of performance.

Abstract This paper describes methods that can be used for modelling radiative properties of light sources and materials, in a radiosity computation algorithm. These methods have been designed in order to improve the photo‐realistic rendering of complex architectural scenes as well as to allow illumination engineering applications. They are based on the accurate modelling of the spatial and spectral emittance distributions of the light sources, and the surface reflectance/transmittance distributions from measurement, and allow the exact colorimetric properties of the light sources and the surfaces to be calculated. A method for changing radiosity inputs during the radiosity process, without recalculating the solution entirely is also proposed. This allows modifications in design or dynamic lighting effects to be simulated more interactively.

Abstract In computer graphics, image generation uses the RGB colorimetric system. However, this system does not produce an accurate simulation of the spectral characteristics of both light and material, due to the fact that it is device dependent. Indeed, to get realistic images, the image calculation process must deal with spectral characteristics of lights and materials and with the problem of sampling the wavelength domain. Methods have been shown that are a good way to solve the two problems mentioned above, however, these approaches do not take into account complex spectrums (discontinuous). In this paper, we propose a method which removes the constraints imposed by the current methods. Our method is based upon an algorithm of spectrum analysis.