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Ahmad Nasikun

Publications and source records attributed to Ahmad Nasikun.

5 recordsLinked to original sources
arXiv2023

A Fast Geometric Multigrid Method for Curved Surfaces

We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid hierarchy to achieve a fast hierarchy construction and to extend the applicability of the method from triangle meshes to other surface representations like point clouds, nonmanifold meshes, and polygonal meshes. To build the prolongation operators, we associate each point of the hierarchy to a triangle constructed from points in the next coarser level. We obtain well-shaped candidate triangles by computing graph Voronoi diagrams centered around the coarse points and determining neighboring Voronoi cells. Our selection of triangles ensures that the connections of each point to points at adjacent coarser and finer levels are balanced in the tangential directions. As a result, we obtain sparse prolongation matrices with three entries per row and fast convergence of the solver.

cs.CG↗
arXiv2022

DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds

Learning from 3D point-cloud data has rapidly gained momentum, motivated by the success of deep learning on images and the increased availability of 3D~data. In this paper, we aim to construct anisotropic convolution layers that work directly on the surface derived from a point cloud. This is challenging because of the lack of a global coordinate system for tangential directions on surfaces. We introduce DeltaConv, a convolution layer that combines geometric operators from vector calculus to enable the construction of anisotropic filters on point clouds. Because these operators are defined on scalar- and vector-fields, we separate the network into a scalar- and a vector-stream, which are connected by the operators. The vector stream enables the network to explicitly represent, evaluate, and process directional information. Our convolutions are robust and simple to implement and match or improve on state-of-the-art approaches on several benchmarks, while also speeding up training and inference.

cs.CV↗
arXiv2021

The Hierarchical Subspace Iteration Method for Laplace--Beltrami Eigenproblems

Sparse eigenproblems are important for various applications in computer graphics. The spectrum and eigenfunctions of the Laplace--Beltrami operator, for example, are fundamental for methods in shape analysis and mesh processing. The Subspace Iteration Method is a robust solver for these problems. In practice, however, Lanczos schemes are often faster. In this paper, we introduce the Hierarchical Subspace Iteration Method (HSIM), a novel solver for sparse eigenproblems that operates on a hierarchy of nested vector spaces. The hierarchy is constructed such that on the coarsest space all eigenpairs can be computed with a dense eigensolver. HSIM uses these eigenpairs as initialization and iterates from coarse to fine over the hierarchy. On each level, subspace iterations, initialized with the solution from the previous level, are used to approximate the eigenpairs. This approach substantially reduces the number of iterations needed on the finest grid compared to the non-hierarchical Subspace Iteration Method. Our experiments show that HSIM can solve Laplace--Beltrami eigenproblems on meshes faster than state-of-the-art methods based on Lanczos iterations, preconditioned conjugate gradients and subspace iterations.

math.NA↗
arXiv2016

Digitory, A Smart Way of Learning Islamic History in Digital Era

In this paper, we would like to propose our web-based application for Islamic history learning system, named Digitory-Digital History. There are two main navigations to browse historical stories on the web. One is location-based navigation using on-line map which gives users access to understand events during Islamic introduction to Indonesia based on the location. Alternatively, users can browse on time base using sliding navigation marked timely, so they can comprehend history in time sequence. Implementing semantic web, this web-app can suggest users related articles, either based on time series, location similarities, or time-domain similarities, and also suggest pictures related to the articles. AJAX strengthen the real-time access and interactivity as users navigate around the web. By the end of this research, we will have the web-app prototype completed with its fundamental location-based navigation, semantic relationship among articles and pictures, and time- based navigation system. As the web-app deployed, we have some volunteers to try our application so that we can evaluate its result, particularly its effectiveness.

cs.CY↗