Ahmad Nasikun

Former PhD Student at the Computer Graphics and Visualization group at TU Delft
Room E6.420, Building 28
Office Phone: +31 (0)15 278 4698
E-mail: <A.Nasikun_AT_tudelft.nl>

About Me

I am a third-year PhD student supervised by Dr. Klaus Hildebrandt. My researches are generously funded by Indonesia Endowment Fund for Education (LPDP) Scholarship. My research interest lies in the area of geometry processing, particularly in reduced methods for various applications in geometry processing and computer graphics.

I did my undergraduate at Department of Electrical Engineering, Faculty of Engineering, Universitas Gadjah Mada, Yogyakarta, Indonesia. I then continued my master at 3D Modeling and Processing laboratory of the Department of Electrical Engineering and Computer Science, Seoul National University (SNU), South Korea, under the supervision of Prof. Myung-Soo Kim. My master thesis was about the 3D printing of deformable objects. This master program was supported and funded by the Korean Government Scholarship Program (KGSP).

Linkedin: ahmad nasikun


The Hierarchical Subspace Iteration Method for Laplace–Beltrami Eigenproblems
Ahmad Nasikun and Klaus Hildebrandt
ACM Transactions on Graphics (to appear)

Abstract: 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.

Downloads: [preprint][supplementary material]

Locally supported tangential vector, n-vector, and tensor fields
Ahmad Nasikun, Christopher Brandt, Klaus Hildebrandt
Computer Graphics Forum 39(2) (Eurographics 2020)

Abstract: We introduce a construction of subspaces of the spaces of tangential vector, n-vector, and tensor fields on surfaces. The resulting subspaces can be used as the basis of fast approximation algorithms for design and processing problems that involve tangential fields. Important features of our construction are that it is based on a general principle, from which constructions for different types of tangential fields can be derived, and that it is scalable, making it possible to efficiently compute and store large subspace bases for large meshes. Moreover, the construction is adaptive, which allows for controlling the distribution of the degrees of freedom of the subspaces over the surface. We evaluate our construction in several experiments addressing approximation quality, scalability, adaptivity, computation times and memory requirements. Our design choices are justified by comparing our construction to possible alternatives. Finally, we discuss examples of how subspace methods can be used to build interactive tools for tangential field design and processing tasks.

Downloads: [preprint]

Fast Approximation of Laplace–Beltrami Eigenproblems
Ahmad Nasikun, Christopher Brandt, Klaus Hildebrandt
Computer Graphics Forum 37(5) (Presented at Symposium on Geometry Processing 2018)

Abstract: The spectrum and eigenfunctions of the Laplace-Beltrami operator are at the heart of effective schemes for a variety of problems in geometry processing. A burden attached to these spectral methods is that they need to numerically solve a large-scale eigenvalue problem, which results in costly precomputation. In this paper, we address this problem by proposing a fast approximation algorithm for the lowest part of the spectrum of the Laplace–Beltrami operator. Our experiments indicate that the resulting spectra well-approximate reference spectra, which are computed with state-of-the-art eigensolvers. Moreover, we demonstrate that for different applications that comparable results are produced with the approximate and the reference spectra and eigenfunctions. The benefits of the proposed algorithm are that the cost for computing the approximate spectra is just a fraction of the cost required for numerically solving the eigenvalue problems, the storage requirements are reduced and evaluation times are lower. Our approach can help to substantially reduce the computational burden attached to spectral methods for geometry processing.

Downloads: [preprint] [supp. document] [video 1] [video 2][code]