Antonio J. Rueda

Parallel drainage network computation on CUDA

Abstract Drainage networks determination from digital elevation models (DEM) has been a widely studied problem in the last three decades. During this time, satellite technology has been improving and optimizing digitalized images, and computers have been increasing their capabilities to manage such a huge quantity of information. The rapid growth of CPU power and memory size has concentrated the discussion of DEM algorithms on the accuracy of their results more than their running times. However, obtaining improved running times remains crucial when DEM dimensions and their resolutions increase. Parallel computation provides an opportunity to reduce run times. Recently developed graphics processing units (GPUs) are computationally fast not only in Computer Graphics but in General Purpose Computation, the so-called GPGPU. In this paper we explore the parallel characteristics of these GPUs for drainage network determination, using the C-oriented language of CUDA developed by NVIDIA. The results are simple algorithms that run on low-cost technology with a high performance response, obtaining CPU improvements of up to 8 × .

A new algorithm for computing Boolean operations on polygons

This paper presents a new algorithm for computing Boolean operations on polygons. These kind of operations are frequently used in the geosciences in order to get spatial information from spatial data modeled as polygons. The presented algorithm is simple and easy to understand and implement. Let n be the total number of edges of all the polygons involved in a Boolean operation and k be the number of intersections of all the polygon edges. Our algorithm computes the Boolean operation in time O((n+k)log(n)). Finally, the proposed algorithm works with concave polygons with holes, and with regions composed of polygon sets. Furthermore, it can be easily adapted to work with self-intersecting polygons.

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.

A triangle-based representation for polygons and its applications☆

Abstract The layer representation (L-REP) is a triangle-based representation for polygons that presents interesting properties for several applications. It is simple and robust, and valid for any kind of polygons: convex or non-convex, manifold or non-manifold. This paper extends the introduction of the L-REP in previous works of the same authors, describing its implementation and several alternative algorithms for its construction. It also presents several applications of this representation, with a special emphasis on the point-in-polygon inclusion and shell location tests, which can be easily and efficiently solved using the L-REP.

A solution to the Path Planning problem using angle preprocessing

The Path Planning problem is a common topic for Robotics and Computational Geometry. Many important results have been found to this classic problem, some of them based on plane or space tessellation. The new approach we propose in this paper computes a partition of the plane called the Polar Diagram, using angle properties as criterion of construction. Compared to some other plane partitions as Voronoi Diagrams, this tessellation can be computed much more efficiently for different geometric objects. The polar diagram used as preprocessing can be applied to many geometric problems where the solution can be given by angle processing, such as Visibility or Path Planning problems.

A flooding algorithm for extracting drainage networks from unprocessed digital elevation models

A new method for extracting the drainage network from a digital elevation model (DEM) is presented. It is based on the well-known D8 approach that simulates the overland flow but uses a more elaborate water transfer model that is inspired by the natural behaviour of water. The proposed solution has several advantages: it works on unprocessed DEMs avoiding the problems caused by pits and flats, can generate watercourses with a width greater than one cell and detects fluvial landforms like lakes, marshes or river islands that are not directly handled by most previous solutions.

A simple algorithm for Boolean operations on polygons

In this paper a simple and efficient algorithm for computing Boolean operations on polygons is presented. The algorithm works with almost any kind of input polygons: concave polygons, polygons with holes, several contours and self-intersecting edges. Important topological information, as the holes of the result polygon, is computed.

Technical Section: The multi-L-REP decomposition and its application to a point-in-polygon inclusion test

This paper presents a scheme for decomposing polygons called multi-L-REP. The scheme can be considered as a generalization of the L-REP decomposition, which associates the edges of a polygon with a set of layered triangles. In the multi-L-REP these layered triangles are grouped into regions of a plane division. The paper also shows some alternative algorithms for its construction, and one of its applications: the point-in polygon inclusion test. Finally, a special case of multi-L-REP that has several interesting properties and shows a very fast point-in-polygon inclusion test is presented.

A comparison of native GPU computing versus OpenACC for implementing flow-routing algorithms in hydrological applications

In recent years GPU computing has gained wide acceptance as a simple low-cost solution for speeding up computationally expensive processing in many scientific and engineering applications. However, in most cases accelerating a traditional CPU implementation for a GPU is a non-trivial task that requires a thorough refactorization of the code and specific optimizations that depend on the architecture of the device. OpenACC is a promising technology that aims at reducing the effort required to accelerate C/C++/Fortran code on an attached multicore device. Virtually with this technology the CPU code only has to be augmented with a few compiler directives to identify the areas to be accelerated and the way in which data has to be moved between the CPU and GPU. Its potential benefits are multiple: better code readability, less development time, lower risk of errors and less dependency on the underlying architecture and future evolution of the GPU technology. Our aim with this work is to evaluate the pros and cons of using OpenACC against native GPU implementations in computationally expensive hydrological applications, using the classic D8 algorithm of OCallaghan and Mark for river network extraction as case-study. We implemented the flow accumulation step of this algorithm in CPU, using OpenACC and two different CUDA versions, comparing the length and complexity of the code and its performance with different datasets. We advance that although OpenACC can not match the performance of a CUDA optimized implementation (×3.5 slower in average), it provides a significant performance improvement against a CPU implementation (×2-6) with by far a simpler code and less implementation effort.

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.