Tile-based modeling and its applications in computer graphics

• Main Author: Lai, Chi-Fu
• Other Authors: He Ying
• Format: Theses and Dissertations
• Language: English
• Published: 2016
• Subjects: DRNTU::Engineering::Computer science and engineering::Computing methodologies::Computer graphics; DRNTU::Visual arts and music::Visual arts; DRNTU::Visual arts and music::Animation::3D
• Online Access: https://hdl.handle.net/10356/69077
• Institution: Nanyang Technological University

Our ancient ancestors invented tiles predominantly for the purpose of decorating architectural interior and exterior structures varying from ceilings, floors to walls. Due to the beauty of tiles, mathematical analysis of 2D tilings has been well studied and classified, for example Wang and Corner Tiles, Periodic Tilings, and Non-Periodic Tilings. Graphics researchers, on the other hand, focused on the discovery of technique on applying tilings to various Computer Graphics classic applications like texture mapping, texture synthesis, and sampling. Applications on surface modeling were freshly proposed at the time this work began. Given the various properties of different types of tiles, say aperiodic, it is well concluded that tile-based techniques often offer a minimization of computational power and memory consumption, while keeping a high degree of freedom to provide wide range of flexible solutions to those classic applications. On the contrary, tiling in 3D space is a relatively new research area, and its applications have great potential in Computer Graphics and Computational Fabrication, which many of them have not yet been discovered until this work or similar works are established. Furthermore, there are many traditional art works hand-created by making use of 2D tiling concept, for example M. C. Escher’s artistic tessellation. Some of those art works present an optical illusion that confuses our visual system in reconstructing 3D geometry from the 2D drawing. There are very limited analysis and research on 3D visualization of such perceptual tiling art works. This thesis aims to study three various novel forms of tile-based models and their applications: Tile-based 3D Reconstruction and Navigation of Impossible World. In this work, we present a tile-based approach towards 3D gaming with impossible figures, delivering for the first time free view navigation in 3D mazes constructed from impossible figures. Such result cannot ii be achieved by previous research work in modeling and rendering impossible figures. To deliver seamless gaming navigation and interaction, we propose i) a tile-based 3D reconstruction method that converts the line-art impossible figure into 3D geometry representation, ii) a set of guiding principles for bringing out subtle perceptions and iii) a novel computational approach to construct 3D structures from impossible figure images and then to dynamically construct the impossible-figure maze subjected to user’s view. In the end, we demonstrate and discuss our method with a variety of generic maze types with extended applications. Tile-based Reconstruction of Surfaces. We introduce a method for optimizing the tiles of a quad-mesh. Given a quad-based surface, the goal is to generate a set of K quads whose instances can produce a tiled surface that approximates the input surface. A solution to the problem is a K-set tilable surface, which can lead to an effective cost reduction in the physical construction of the given surface. Rather than molding lots of different building blocks, a K-set tilable surface requires the construction of K prefabricated components only. To realize the K- set tilable surface, we use a cluster-optimize approach. First, we iteratively cluster and analyze the edge connectivity of the K quads. Then, we apply a non-linear optimization model with constraints that maintain the K quads connections and shapes.Our algorithm is demonstrated on various surfaces, including some that mimic the exteriors of certain renowned building landmarks. Tile-based Reconstruction of Interlocking Structure. A 3D burr puzzle is a 3D model that consists of interlocking pieces with a single-key property. The intriguing property of the assembled burr puzzle is that it is stable, perfectly interlocked, without glue or screws, etc, so that it is capable to be applied to solve the model partitioning problem of small volume fabrication like home-scale 3D printing. In this work, we generalize the 6-piece orthogonal burr puzzle (a knot) to design and model complex burr puzzles from 3D models. Given a 3D input model, we first interactively embed a tiled network of knots into the 3D shape. Our method automatically optimizes and arranges the orientation of each knot, and modifies pieces of adjacent knots with an appropriate connection type. Then, the entire 3D model is partitioned by splitting the solid while respecting the assembly motion of embedded pieces. Lastly, we also present an automated approach to generate the visualizations of the puzzle assembly process.