J. Ruiz de Miras

Technical Section: GPU-based rendering of curved polygons using simplicial coverings

In this work, we describe a new algorithm for rendering polygons defined by cubic Bezier curve segments in current GPUs. Unlike other approaches, our algorithm has a simple preprocessing that does not require computing tessellations, and can be implemented in GPU as a geometry shader. The polygon is decomposed into a set of simplices which are individually rasterized into the stencil buffer to recreate the shape that is finally rendered in the frame buffer. Each simplex is rasterized using a fragment shader that evaluates the implicit equation of the Bezier curve to discard the pixels that fall outside it. The proposed method is simple, fast, robust and general, as it can handle curved polygons with holes, several components or self-intersections.

Three-dimensional thinning algorithms on graphics processing units and multicore CPUs

Three‐dimensional curve skeletons are a very compact representation of three‐dimensional objects with many uses and applications in fields such as computer graphics, computer vision, and medical imaging. An important problem is that the calculation of the skeleton is a very time‐consuming process. Thinning is a widely used technique for calculating the curve skeleton because of the properties it ensures and the ease of implementation. In this paper, we present parallel versions of a thinning algorithm for efficient implementation in both graphics processing units and multicore CPUs. The parallel programming models used in our implementations are Compute Unified Device Architecture (CUDA) and Open Computing Language (OpenCL). The speedup achieved with the optimized parallel algorithms for the graphics processing unit achieves 106.24x against the CPU single‐process version and more than 19x over the CPU multithreaded version. Copyright

Inclusion test for curved-edge polygons

Abstract In this work we present a new algorithm to study the inclusion of points into polygons whose edges are curve segments. It is valid for closed planar polygons whose edges can be straight line segments, conic arcs or cubic Bezier curves. Also it is valid for manifold and non-manifold closed planar polygons with and without holes. Our algorithm is robust and simple, firstly because it avoids the use of equations systems in the inclusion test, and secondly because it solves special cases effectively and homogeneously.

A Web platform for the interactive visualization and analysis of the 3D fractal dimension of MRI data

This study presents a Web platform (http://3dfd.ujaen.es) for computing and analyzing the 3D fractal dimension (3DFD) from volumetric data in an efficient, visual and interactive way. The Web platform is specially designed for working with magnetic resonance images (MRIs) of the brain. The program estimates the 3DFD by calculating the 3D box-counting of the entire volume of the brain, and also of its 3D skeleton. All of this is done in a graphical, fast and optimized way by using novel technologies like CUDA and WebGL. The usefulness of the Web platform presented is demonstrated by its application in a case study where an analysis and characterization of groups of 3D MR images is performed for three neurodegenerative diseases: Multiple Sclerosis, Intrauterine Growth Restriction and Alzheimers disease. To the best of our knowledge, this is the first Web platform that allows the users to calculate, visualize, analyze and compare the 3DFD from MRI images in the cloud.

Fast box-counting algorithm on GPU

The box-counting algorithm is one of the most widely used methods for calculating the fractal dimension (FD). The FD has many image analysis applications in the biomedical field, where it has been used extensively to characterize a wide range of medical signals. However, computing the FD for large images, especially in 3D, is a time consuming process. In this paper we present a fast parallel version of the box-counting algorithm, which has been coded in CUDA for execution on the Graphic Processing Unit (GPU). The optimized GPU implementation achieved an average speedup of 28 times (28×) compared to a mono-threaded CPU implementation, and an average speedup of 7 times (7×) compared to a multi-threaded CPU implementation. The performance of our improved box-counting algorithm has been tested with 3D models with different complexity, features and sizes. The validity and accuracy of the algorithm has been confirmed using models with well-known FD values. As a case study, a 3D FD analysis of several brain tissues has been performed using our GPU box-counting algorithm.

UJA-3DFD: A program to compute the 3D fractal dimension from MRI data

This work presents a computer program for computing the 3D fractal dimension (3DFD) from magnetic-resonance images of the brain. The program is based on an algorithm that calculates the 3D box counting of the entire volume of the brain, and also of its 3D skeletonization. The validity and accuracy of the software has been confirmed using solids with well-known 3DFD values. The usefulness of the program developed is demonstrated by its successful characterization of several neurodegenerative diseases.

Free-form solid modelling based on extended simplicial chains using triangular Bézier patches

Abstract We present a mathematical model for geometric modelling based on the concept of extended simplicial chain (ESC) defined in previous works. With this model, a solid is defined by means of an algebraic sum of non-disjoint extended cells, applying the divide and conquer concept. This allows us to obtain the traditional Boolean operations in geometric modelling through the operations defined for ESCs. The model enables us to represent free-form solids whose boundaries are free-form surfaces represented by a set of low degree triangular Bezier patches (TBPs) and operate with them. In fact, this model allows us to solve basic problems in solid modelling, like the point-in-solid test. In this case we make use of the generality of the definition of ESC to particularize it to the use of TBPs in 3D.

Rasterizing complex polygons without tessellations

Rasterization of polygons is a basic operation in computer graphics systems, representing the last and most time-consuming step in the visualization process. Therefore, the development of simple, efficient, and general polygon rasterization techniques is of prime interest. In this paper, we describe a new algorithm for this purpose, inspired on the ideas of the geometric modeling based on simplicial chains [Computer and Graphics 5 (1998) 611]. This algorithm is valid for any kind of polygon, is robust and extremely simple, and can be easily implemented in hard-ware. A similar approach can be used for the problem of polihedra voxelization in 3D.

Inclusion test for free-form solids

Abstract In this paper, a new algorithm to study the fundamental inclusion test of points into free-form solids is presented. The test is performed exactly, efficiently and robustly because it does not require solving equation systems, it does not use trigonometric functions and it is not necessary to deal with complex special cases. The point inclusion algorithm is based on the decomposition of the solid into original tetrahedra and free form cells , and it reduces the test calculation to carrying out the test on these simple elements and merging the individual results by means of a simple sum. The solid boundary is defined as a set of low-degree algebraic patches.

An Efficient Point Classification Algorithm for Triangle Meshes

Triangle meshes have become a general representation used for modeling. Using such a representation for purposes other than rendering requires the implementation of robust and efficient geometric algorithms. This work presents a new algorithm in order to solve the classification of a point in a B-rep solid model defined by a triangle mesh. The algorithm proposed is simple and more robust than those previously proposed. Furthermore, it does not require any connectivity information among triangles. Sample source code is available online.