Ahmad H. Nasri

Polyhedral subdivision methods for free-form surfaces

One of the central issues in computer-aided geometric design is the representation of free-form surfaces which are needed for many purposes in engineering and science. Several limitations are imposed on most available surface systems: the rectangularity of the network describing a surface and the manipulation of surfaces without regard to the volume enclosed are examples. Polyhedral subdivision methods suggest themselves as a solution to these problems. Their use, however, is not widespread for several reasons such as the lack of boundary control, and interpolation and interrogation capabilities. In this paper the original work on subdivision methods is extended to overcome these problems. Two methods are described, one for controlling the boundary curves of such surfaces, and another for interpolating points on irregular networks. A general surface/surface intersection algorithm is also provided: seven decisions need to be made in order to specify a particular implementation. The algorithm is also suitable for intersecting other classes of surfaces amongst which are the popular Bézier and B-spline surfaces.

Multicomponent Image Segmentation Using a Genetic Algorithm and Artificial Neural Network

Image segmentation is an essential process for image analysis. Several methods were developed to segment multicomponent images, and the success of these methods depends on several factors including (1) the characteristics of the acquired image and (2) the percentage of imperfections in the process of image acquisition. The majority of these methods require a priori knowledge, which is difficult to obtain. Furthermore, they assume the existence of models that can estimate its parameters and fit to the given data. However, such a parametric approach is not robust, and its performance is severely affected by the correctness of the utilized parametric model. In this letter, a new multicomponent image segmentation method is developed using a nonparametric unsupervised artificial neural network called Kohonens self-organizing map (SOM) and hybrid genetic algorithm (HGA). SOM is used to detect the main features that are present in the image; then, HGA is used to cluster the image into homogeneous regions without any a priori knowledge. Experiments that are performed on different satellite images confirm the efficiency and robustness of the SOM-HGA method compared to the Iterative Self-Organizing DATA analysis technique (ISODATA).

Surface interpolation on irregular networks with normal conditions

Abstract Interpolation is a well-known technique in free-form surface design and shape modelling contexts. Most of the previous interpolating schemes suffer from the reguarity requirement of the network describing a surface; a requirement which has long been considered as a source of irritation and limitation. Another problem is the inability to specify plane tangents or normal vectors at the points of a network; a property which is very attractive in local control. In this paper, a recursive division surface scheme is described that is capable of interpolating points on irregular networks as well as normal vectors given at these points, thus increasing local control by allowing the user to specify plane tangents at the interpolated points leading to more powerful surface systems. The devised algorithm is also presented.

Recursive subdivision of polygonal complexes and its applications in computer-aided geometric design

Abstract A method for subdividing polygonal complexes and identifying conditions to control their limit curves is presented. A polygonal complex is a sequence of panels where every two adjacent panels share one edge only. We formulate this problem and establish a general theory which has a number of applications in CAGD such as the generation of subdivision surfaces through predefined arbitrary network of curves. This is a further extension of the capability of these surfaces making them more attractive and more practical in surface modeling and computer graphics. One of the main advantages of the proposed scheme is that the regions of the surface between the interpolated curves do not have to be rectangular—a limitation of existing tensor-product based CAD systems.

Designing Catmull–Clark subdivision surfaces with curve interpolation constraints

Abstract Generating subdivision surfaces with curve interpolation constraints is needed in both computer graphics and geometric modeling applications. In the context of the Doo–Sabin subdivision scheme, this can be achieved through the use of polygonal complexes as suggested by Nasri (Presented at the Fifth Siam Conference on Geometric Design, Nashville, 1997; Comput. Aided Geom. Des. 17 (2000) 595). A polygonal complex is simply a polygonal mesh whose structure depends on the subdivision scheme used and whose limit of subdivision is a curve rather than a surface. The subdivision scheme applied to these complexes is basically the same applied to the mesh defining the surface but with possible modification of its subdivision rules. The advantage of that lies in the retention of the same subdivision coefficients, thus saving the need for any further analysis at the limit. In this paper, we propose a method for using polygonal complexes to generate Catmull–Clark subdivision surfaces with curve interpolation constraints. The polygonal complexes are embedded here in the given mesh, which can possibly interpolate intersecting curves.

Improving the sketch-based interface: Forming curves from many small strokes

Sketch-based interfaces are becoming a useful methodology for interaction with a wide range of applications. Drawing is a natural and simple paradigm for designers. One of the problems in most of the current generation of such interfaces is that designers are forced to use single strokes where they may prefer to use many strokes while drawing with traditional tools such as a pencil.In this work we have addressed this problem by analyzing multiple strokes and replacing them with a single stroke that makes a reasonable estimate of the designer’s intention. Our solution recursively subdivides space stopping where either there is only a single stroke, or several strokes that have a proper ordering using principal component analysis. The subspaces are then reconnected, and the orderings are joined to create the control points of a single B-spline curve. The resulting curve is very noisy due to the multitude of strokes. A multi-resolution technique that makes use of reverse subdivision has been used to fit a smooth B-spline curve.

Curve interpolation in recursively generated B-spline surfaces over arbitrary topology

Abstract Recursive subdivision is receiving a great deal of attention in the definition of B-spline surfaces over arbitrary topology. The technique has recently been extended to generate interpolating surfaces with given normal vectors at the interpolated vertices. This paper describes an algorithm to generate recursive subdivision surfaces that interpolate B-spline curves. The control polygon of each curve is defined by a path of vertices of the polyhedral network describing the surface. The method consists of applying a one-step subdivision of the initial network and modifying the topology in the neighborhood of the vertices generated from the control polygons. Subsequent subdivisions of the modified network generate sequences of polygons each of which converges to a curve interpolated by the limit surface. In the case of regular networks, the method can be reduced to a knot insertion process.

Taxonomy of interpolation constraints on recursive subdivision curves

This paper is the first of two, which together describe and classify the various situations that any complete study of interpolation constraints for a recursive subdivision surface needs to consider. They do so in the form of a systematic taxonomy of situations. Presented here are curve cases, which provide good illustrations of principles which will be used in both contexts; surfaces will be addressed in the second paper. Known results are classified and open questions identified.

Boundary-corner control in recursive-subdivision surfaces

Abstract The author of the paper previously addressed the problem of boundary control in recursive subdivision surfaces with some restriction on the boundary skirt of the polyhedron defining a surface. The paper aims to release the restriction imposed to allow more freedom on the boundary curves, i.e. more than one corner per face, and the ability to handle L-shaped regions.

Computing Volumes of Solids Enclosed by Recursive Subdivision Surfaces

The volume of a solid enclosed by a recursive subdivision surface can be approximated based on the closed‐form representation of regular parts of the subdivision surface and a tight estimate of the local convex hull near extraordinary points. The approach presented is efficient, i.e. non‐exponential, and robust in that it yields rapidly contracting error bounding boxes. An extension to measuring higher‐order moments is sketched.