Harlen Costa Batagelo
Centro de Matemática, Computação e Cognição (CMCC)
Universidade Federal do ABC (UFABC)
Email: harlen.batagelo at ufabc.edu.br
Sala 501-2, Torre 2, Bloco A
+55 11 4996 8297
Solving Tangram Puzzles Using Raster-Based Mathematical Morphology
The Tangram is a dissection puzzle composed of polygonal pieces which can be combined to form different patterns. Solving the Tangram is a two-dimensional irregular shape packing problem known to be NP-hard. Tangram patterns may be composed of multiple connected components, and assembling them may require the reflection transformation and unconstrained rotations of the pieces. In this work, we propose a novel approach for the automatic solution of the Tangram based on a raster representation of the puzzle. In order to adapt the geometrical techniques that are applied to the prevention of piece overlapping and the reduction of space between pieces, we use morphological operators and representations commonly used in the discrete domain such as the dilation operator, the distance transform and the morphological skeletonization. We investigate the effects of the raster representation in the puzzle assembly process and verify the effectiveness of the proposed method in solving different Tangram puzzles.
Contour-aware 3D reconstruction of side-view sketches
The 3D reconstruction from a single 2D side-view sketch faces challenges in capturing details of
the curves and inferring the hidden parts. Here, we introduce an approach that ensures the 2D contours
are interpolated to a suitable 3D reconstruction while capturing the small details of the sketch.
To this end, we propose a novel strategy that combines a proper 3D Hermitian data generation from the
vicinity of the sketches with an approach for identification and completion of sketch curves. Feasible
3D models are then generated using Hermitian Radial Basis Functions (HRBF) Implicit Surfaces. Results
indicate that our approach provides not only more detailed 3D reconstructed models but also more
perceptual agreement from the input sketches in comparison to previous work.
- Paper: Ramos, Saulo; Trevisan,
Diogo Fernando; Batagelo, Harlen Costa; Sousa, Mario Costa; Gois, João Paulo. Contour-aware 3D reconstruction of side-view sketches.
Computers & Graphics. 77:97--107. December 2018 (DOI 10.1016/j.cag.2018.09.009).
- Supplementary data (PDF, 7 MB).
Interactive Shading of 2.5D Models
Advances in computer-assisted methods for designing and animating 2D artistic models have incorporated
depth and orientation cues such as shading and lighting effects. These features improve the visual perception
of the models while increasing the artists' flexibility to achieve distinctive design styles. An advance that
has gained particular attention in the last years is the 2.5D modeling, which simulates 3D rotations from a
set of 2D vector arts. This creates not only the perception of animated 3D orientation, but also automates
the process of inbetweening. However, previous 2.5D modeling techniques do not allow the use of interactive
shading effects. In this work, we tackle the problem of providing interactive 3D shading effects to 2.5D
modeling. Our technique relies on the graphics pipeline to infer relief and to simulate the 3D rotation
of the shading effects inside the 2D models in real-time. We demonstrate the application on Phong, Gooch
and cel shadings, as well as environment mapping, fur simulation, animated texture mapping, and
(object-space and screen-space) texture hatchings.
- Paper: Gois, João Paulo; Marques, Bruno A. D.; Batagelo, Harlen Costa. Interactive Shading of 2.5D Models. In proceedings of Graphics Interface 2015. 89--96. June 2015.
GPU-based Sphere Tracing for Radial Basis Function Implicits
Ray tracing of implicit surfaces based on radial basis functions can demand high computational
cost in the presence of a large number of radial centers. Recently, it was presented
the Least Squares Hermite Radial Basis Functions (LS-HRBF) Implicits, a method for
implicit surface reconstruction from Hermitian data (points equipped with their normal
vectors) which makes use of iterative center selection in order to reduce the number of
centers. In the present work, we propose an antialiased Sphere Tracing algorithm fully
implemented in OpenGL Shader Language for ray tracing LS-HRBF Implicits, which
exploits a regular partition of unity for strong parallelization. We show that interactive
frame rates can be achieved for surfaces composed of thousands of centers even when
rendering effects such as cube mapping, soft shadows and ambient occlusion are used.
- Source code (5.3 MB).
- Paper (PDF, 10 MB): Batagelo, Harlen Costa; Gois, João Paulo. GPU-based Sphere Tracing for Radial Basis Function Implicits. International Journal of Image and Graphics, 14(1-2), 2014 (DOI 10.1142/S0219467814500041).
A low-cost-memory CUDA implementation of the conjugate gradient method applied to globally supported radial basis functions implicits
Hermitian radial basis functions implicits is a method capable of reconstructing implicit surfaces from first-order Hermitian data. When globally supported radial functions are used, a dense symmetric linear system must be solved. In this work, we aim at exploring and computing a matrix-free implementation of the Conjugate Gradients Method on the GPU in order to solve such linear system. The proposed method parallelly rebuilds the matrix on demand for each iteration. As a result, it is able to compute the Hermitian-based interpolant for datasets that otherwise could not be handled due to the high memory demanded by their linear systems.
- Paper (PDF, 1.9 MB): Trevisan, Diogo Fernando; Gois, João Paulo; Batagelo, Harlen Costa. A low-cost-memory CUDA implementation of the conjugate gradient method applied to globally supported radial basis functions implicits. Journal of Computational Science, 5(5):701--708, 2014 (DOI 10.1016/j.jocs.2014.06.007).
Generalized Hermitian Radial Basis Functions Implicits
from Polygonal Mesh Constraints
In this work we investigate a generalized interpolation approach using radial basis functions to reconstruct implicit surfaces from polygonal meshes. With this method, the user can define with great flexibility three sets of constraint interpolants: points, normals, and tangents; allowing to balance computational complexity, precision, and feature modeling. Furthermore, this flexibility makes possible to avoid untrustworthy information, such as normals estimated on triangles with bad aspect ratio. We present results of the method for applications related to the problem of modeling 2D curves from polygons and 3D surfaces from polygonal meshes. We also apply the method to problems involving subdivision surfaces and front-tracking of moving boundaries. Finally, as our technique generalizes the recently proposed HRBF Implicits technique, comparisons with this approach are also conducted.
- Paper (PDF, 14 MB): Gois, João Paulo; Trevisan, Diogo Fernando; Batagelo, Harlen Costa; Macêdo, Ives. Generalized Hermitian Radial Basis Functions Implicits from Polygonal Mesh Constraints. The Visual Computer, 29:651--661, 2013 (DOI 10.1007/s00371-013-0802-8).
Least-squares Hermite RBF with adaptive sampling
HRBF Implicits have been used for the implicit reconstruction of point clouds with normals. They yield superior results when compared to non-Hermitian RBFs for the same number of centers and do not require offset points in order to avoid the trivial solution. We propose a center selection criteria for HRBF Implicits based on an adaptive greedy algorithm that takes into account function value, gradient and distance between centers. Residuals are computed using a least-squares solution that takes into account all non-center points. As a result, the sampled centers are globally well distributed (as in a Leja sequence), but at the same time preserve local features. Because the method produces good reconstructions with few centers, it may be useful for applications in which the implicit surface evaluation time is critical (e.g. real-time visualization).
OpenGL with Qt
On August 22, 2012 João Paulo Gois and me presented the tutorial Interactive Graphics Applications with OpenGL Shading Language and Qt (DOI 10.1109/SIBGRAPI-T.2012.10) during the 25th edition of the Conference on Graphics, Patterns and Images (SIBGRAPI 2012) in Ouro Preto, Minas Gerais, Brazil. It was a full-day tutorial targeted to an audience with basic knowledge of OpenGL, GLSL and C++. The source codes of the projects used in the tutorial are available here.
Older publications: http://www.dca.fee.unicamp.br/~harlen/.
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