Interactive design exploration for constrained meshes

In architectural design, surface shapes are commonly subject to geometric constraints imposed by material, fabrication or assembly. Rationalization algorithms can convert a freeform design into a form feasible for production, but often require design modifications that might not comply with the design intent. In addition, they only offer limited support for exploring alternative feasible shapes, due to the high complexity of the optimization algorithm. We address these shortcomings and present a computational framework for interactive shape exploration of discrete geometric structures in the context of freeform architectural design. Our method is formulated as a mesh optimization subject to shape constraints. Our formulation can enforce soft constraints and hard constraints at the same time, and handles equality constraints and inequality constraints in a unified way. We propose a novel numerical solver that splits the optimization into a sequence of simple subproblems that can be solved efficiently and accurately. Based on this algorithm, we develop a system that allows the user to explore designs satisfying geometric constraints. Our system offers full control over the exploration process, by providing direct access to the specification of the design space. At the same time, the complexity of the underlying optimization is hidden from the user, who communicates with the system through intuitive interfaces

Dev2PQ: Planar Quadrilateral Strip Remeshing of Developable Surfaces

We introduce an algorithm to remesh triangle meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips that are aligned to principal curvature directions and closely approximate the curved parts of the input developable, and planar polygons representing the flat parts of the input. Developable PQ-strip meshes are useful in many areas of shape modeling, thanks to the simplicity of fabrication from flat sheet material. Unfortunately, they are difficult to model due to their restrictive combinatorics and locking issues. Other representations of developable surfaces, such as arbitrary triangle or quad meshes, are more suitable for interactive freeform modeling, but generally have non-planar faces or are not aligned to principal curvatures. Our method leverages the modeling flexibility of non-ruling based representations of developable surfaces, while still obtaining developable, curvature aligned PQ-strip meshes. Our algorithm optimizes for a scalar function on the input mesh, such that its level sets are extrinsically straight and align well to the locally estimated ruling directions. The condition that guarantees straight level sets is nonlinear of high order and numerically difficult to enforce in a straightforward manner. We devise an alternating optimization method that makes our problem tractable and practical to compute. Our method works automatically on any developable input, including multiple patches and curved folds, without explicit domain decomposition. We demonstrate the effectiveness of our approach on a variety of developable surfaces and show how our remeshing can be used alongside handle based interactive freeform modeling of developable shapes

Planar hexagonal meshing for architecture

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Differential Filtering and Detexturing

Extracting valuable information from 2D or 3D visual data plays an important role in image and geometry processing. Surfaces obtained through a scanning process or other reconstruction algorithms are inevitably noisy due to error in the scanning process and resampling of the data at various processing steps. These surfaces need to be denoised both for aesthetic reasons and for further geometry processing. Similarly, extracting or removing texture patterns from 2D or 3D data is challenging due to the complication of its statistical features. In this dissertation, I describe how to remove surface noise and image texture patterns. In particular, I focus on denoising triangulated models based on L0 minimization, in which a very important discrete differential operator for arbitrary triangle meshes has been developed. Compared to other anisotropic denoising algorithms, our method is more robust than other anisotropic denoising algorithms, and produces good results even in the presence of high noise. I also introduce how to use bilateral filter appropriately on image texture removal by modifying its range image. While current existing methods either fail to remove the textures completely or over blur main structures, our method delivers best-in-class image detexturing performance

Rethinking of timber joinery in 21st-century architecture The computation of a timber joinery through complex geometry

Master of ScienceDepartment of ArchitectureMajor Professor Not ListedIn recent years, there has been a renewed interest in timber joinery in contemporary architecture. With the introduction of digital fabrication technologies and computational design, it is now possible to create complex timber structures with more complex shapes and designs. One of the critical advantages of timber as a building material is its ability to be combined in various ways. Timber joinery can create solid and durable connections between structural members while providing an aesthetically pleasing finish. In the 21st century, architects and designers are exploring new ways to use timber joinery to create unique and innovative structures. Computational design tools allow designers to create complex geometries that can be fabricated precisely using computer numerical control (CNC) machines and other digital fabrication technologies. Designers who are well-versed in programs like Rhino, Grasshopper, or Revit have the ability to utilize parametric modeling software that can calculate timber joinery that is based on intricate geometry. These tools allow designers to create 3D models of the structure and conduct experiments with different joinery options and configurations. Once the joinery is designed, it can be fabricated using CNC machines or other digital fabrication tools. It allows for high precision and accuracy in the fabrication process, ensuring the joint perfectly fits together. The use of complex timber joinery in contemporary architecture provides functional benefits and a unique aesthetic that cannot be achieved with other materials. By rethinking traditional joinery techniques and embracing digital technologies, architects and designers can create structures that push the boundaries of what is possible through timber construction. This thesis will investigate and explore the timber joinery system and fabrication methods, one of the old wooden structure techniques used in the age of digital technologies that rejuvenate the usage of conventional construction processes in timber buildings. The main aim of this thesis was to study computational design in creating complex wooden segmental base structures that rely on interlocking timber joints as the primary form of connection. This involved analyzing the role of wooden joinery and exploring complex systems made using this technique. The second objective was to create a digital model of several types of parametric wood joineries, such as halve and lap joint, Tenon and mortise joint, and finger joints. A digital model of a complex segmental plate structure with three fundamental parametric joints was also developed. The three basic types include finger, halve and lap clip, and Mortise and Tenon joints. The third objective is a structural and shape optimization of the basic mesh for specified complex geometry, which will be a digital model to evaluate the applicability of the generated joints, and will be determined because of this investigation

Interactive design exploration for constrained meshes

In architectural design, surface shapes are commonly subject to geometric con- straints imposed by material, fabrication or assembly. Rationalization algo- rithms can convert a freeform design into a form feasible for production, but often require design modi�cations that might not comply with the design intent. In addition, they only o�er limited support for exploring alternative feasible shapes, due to the high complexity of the optimization algorithm. We address these shortcomings and present a computational framework for interactive shape exploration of discrete geometric structures in the context of freeform architectural design. Our method is formulated as a mesh optimiza- tion subject to shape constraints. Our formulation can enforce soft constraints and hard constraints at the same time, and handles equality constraints and inequality constraints in a uni�ed way. We propose a novel numerical solver that splits the optimization into a sequence of simple subproblems that can be solved e�ciently and accurately. Based on this algorithm, we develop a system that allows the user to explore designs satisfying geometric constraints. Our system o�ers full control over the exploration process, by providing direct access to the speci�cation of the design space. At the same time, the complexity of the underlying optimization is hidden from the user, who communicates with the system through intuitive interfaces