Interactive design exploration for constrained meshes

Computer Graphics Forum, 2013

Constraining 3D meshes to restricted classes is necessary in architectural and industrial design, but it can be very challenging to manipulate meshes while staying within these classes. Specifically, polyhedral meshes -those having planar faces -are very important, but also notoriously difficult to generate and manipulate efficiently. We describe an interactive method for computing, optimizing and editing polyhedral meshes. Efficiency is achieved thanks to a numerical procedure combining an alternating least-squares approach with the penalty method. This approach is generalized to manipulate other subsets of polyhedral meshes, as defined by a variety of other constraints.

2015

With the help of modern computer aided tools, complex architectural shapes are becoming increasingly popular and easy to model and design. As a consequence,questions are raised of how to realize and produce the design in a feasible and affordable way. This issue, in the building industry, is known as rationalization. Today, this process normally takes place at the end of the design process, while if it is considered at an early stage, the greatest gains can be made. In this study, rationalization in terms of different surface discretization methods has been a main focus. Historical and modern buildings combined with geometrical theory of how to divide a surface into smaller elements have been studied in order to understand what important factors exist. Site visits and interviews with practicing architects and engineers have been conducted in order to study different design approaches and rationalization of real projects. This study also explores multi-objective optimization, since m...

ACM Transactions on Graphics, 2016

We present a new approach to geometric modeling with developable surfaces and the design of curved-creased origami. We represent developables as splines and express the nonlinear conditions relating to developability and curved folds as quadratic equations. This allows us to utilize a constraint solver, which may be described as energy-guided projection onto the constraint manifold, and which is fast enough for interactive modeling. Further, a combined primal-dual surface representation enables us to robustly and quickly solve approximation problems.

Proceedings of the 1986 workshop on Interactive 3D graphics - SI3D '86, 1987

The success of solid modelling in industrial design depends on facilities for specifying and editing parameterized models of solids through user-friendly interaction with a graphical front-end. Systems based on a dual representation, which combines Constructive Solid Geometry (CSG) and Boundary representation (BRep), seem most suitable for modelling mechanical parts. Typically they accept a CSG-compatible input (Boolean combinations of solid primitives) and offer facilities for parameterizing and editing part definitions. The user need not specify the topology of the boundary, but often has to solve three-dimensional trigonometric problems to compute the parameters of rigid motions that specify the positions of primitive solids. A front-end that automatically converts graphical input into rigid motions may be easily combined with boundary-oriented input, but its integration in dual systems usually complicates the editing process and limits the possibilities of parameterizing solid definitions. This report proposes a solution based on three main ideas: (1) enhance the semantics of CSG representations with rigid motions that operate on arbitrary collections of sub-solids regardless of their position in the CSG tree, (2) store rigid motions in terms of unevaluated constraints on graphically selected boundary features, (3) evaluate constraints independently, one at a time, in user-specified order. The third idea offers an alternative to known approaches, which convert all constraints into a large system of simultaneous equations to be solved by iterative numerical methods. The resulting front-end is inadequate for solving problems where multiple constraints must be met simultaneously, but provides a powerful tool for specifying and interactively editing parameterized models of mechanical parts and mechanisms. The order in which constraints are evaluated may also be used as a language for specifying the sequence of assembly and setup operations. An implementation under way is based on the interpreter of a new object oriented programming language, enhanced with geometric classes. Constraint evaluation results in the activation of methods which compute rigid motions from surface information. The set of available methods may be extended by the users, and methods may be integrated in higher level functions whose algorithmic nature simplifies the treatment of degenerate cases. Graphic interaction is provided through a geometrical engine which lets the user manipulate shaded images produced efficiently from the CSG representation of solid models.

2020

Digital design and fabrication of complex geometries in architecture stimulated a significant amount of research most of which involves optimization. We present the main optimization methods with a focus on our preferred techniques. There, we discuss initialization, the formulation of constraints and their simplification through geometric considerations, and key concepts for regularization. This is illustrated at hand of a very recent type of discrete surfaces which are expressed via the pair of diagonal meshes in a quad mesh.

Springer tracts in mechanical engineering, 2018

Using a combination of surfaces and their transformations, one advantage of surface modelling is the ability to be able to create such CAD geometries that would not be possible only by combining the basic features of solid modelling. Using the example of a mass-market product-a hand blender-a number of procedures for working with surfaces are presented that can lead to a final target shape. Choosing a particular step depends on the functional and technical views, as well as the mathematical rules of CAD surface modelling. The choice of the model is not random, as modelling end products for mass-market products belongs to the most demanding design tasks, as it requires fulfilling a variety of working and design functions, many compromises, a great deal of experience and work, all at the same time. Here, it is important to understand the logical, mathematical properties of curves, surfaces and operations for working with them. Thus, this chapter brings the theory from the first chapter of this book into practice.

ACM Transactions on Graphics, 2006

: Conical meshes are planar quad meshes which discretize principal curvature lines, possess offset meshes at a constant distance as well as planar connecting elements supporting the offset meshes (left). Therefore they are especially suited for architectural design with glass structures (right). This design of a railway station by B. Schneider was generated by a subdivision-type process (see also Fig. 14).

2005

The need for more intuitive, faster and more effective tools for freeform product design is still an outstanding research issue in shape modeling. We propose a new methodology in which the designer can define optimal shape modification tools for the situation at hand. The key to this method is a dialogue between the designer and the computer, in which the details of the requested shape modifier are settled. The proposed tool, called user-defined modifier (UDM), is based on recent techniques from freeform shape recognition and parameterized, template-controlled shape modification. The dialogue between user and the system is described, and the basic techniques for the UDM tool are presented as well.

CIRP Annals, 1997

Parametric design is very stable but requires a predefined dimensioning and ordering scheme, thus limiting flexibility and precluding sketch input. Variational geometry design, while general and flexible, necessitates intensive use of numerical solvers to solve many simultaneous nonlinear equations. Frequently the solvers cannot solve these equations. A new system, based on an original theory for automatic constraint analysis, has been developed for solving sets of two-dimensional geometric constraints in product design. The proposed system offers the flexibility of variational based design along with the stability of parametric design. The solution strategy is based upon breaking down the problem into a sequence of construction steps. When no sequential construction is found, auxiliary geometrical constructions are automatically generated based on rules for relocating constraints. Thus, an apparently simultaneous constraint set is converted into a set that can be constructed sequentially by decomposing strongly connected components of the original constraint graph. This new approach has been implemented in a system for designing sheet metal parts.

International Journal of Architectural Computing, 2012

The adoption of digital planning methods has given rise to an unprecedented formal freedom in architectural design. Free-form shapes enjoy considerable popularity in architectural production today. However, these shapes prove to be notoriously hard to fabricate. In the course of a funded research project we investigated the approximation of continuous double-curved surfaces by discrete meshes consisting solely of planar facets, which can be fabricated efficiently using standardised, mass-produced building materials. We introduce our geometrical approach, which is based on the intersection of tangent planes to the surface, and present the digital tools we conceived to integrate the processes of design rationalisation and form-finding.

2003

2004

This document serves the final report for the grant titled "Surface Generation and Cartesian Mesh Support". This completed work was in algorithmic research into automatically generating surface triangulations from CAD geometries. NASA's OVERFLOW and Cavt3D simulation packages use surface triangulations as an underlying geometry description and the ability to automatically generate these from CAD files (without translation) substantially reduces both the wall-clock time and expertise required to get geometry out of CAD and into mesh generation. This surface meshing was exercised greatly during the Shuttle investigation during the last year with success. The secondary efforts performed in this grant involve work on a visualization system cut-cell handling for Cartesian Meshes with embedded boundaries.

Buildings, 2023

Free-form architecture is a prominent trend in contemporary architecture where streamlined geometric buildings are constructed. The main problem in free-form architecture is rationalization, which involves realizing free-form surfaces at a reasonable cost while meeting design requirements. Balancing the design intents and construction costs simultaneously is essential for successful rationalization. This study proposes parametric and generative program flows to balance both requirements efficiently. The suggested parametric program flow, which is based on a mathematical algorithm, classifies a free-form surface into multiple areas, which are favorable to flat, single-curved, and double-curved panels. The proposed generative program flow optimizes the double-curved panels' area through the integration of Multi-Objective Optimization and Pareto optimality. Designers can select the best design option that fits their design objectives through trade-offs using the results of the program flows. Eventually, more efficient and mindful decisions can be made in the early design process by using the results of this study for successful free-form architecture.

Advances in Engineering Software, 2010

It is generally thought within the meshing tool community that object-orientation and other decoupling techniques penalize performance when they are used for building concrete meshing tools. In this paper we show that building a meshing tool with good object-oriented design metrics could not only improve maintainability and all other derived attributes such as portability and extensibility, but also its performance is comparable to a standard meshing tool that implements the same algorithms.

2017

The Rapid Manufacturing techniques that emerged from Rapid Prototyping techniques such as 3D printing or laser cutting allow to fabricate unique objects. However, the design of those objects with existing CAD software remain a difficult task: rapid prototyping processes impose constraints on the geometry of the model. This thesis presents a set of techniques that assist the user in the design of an object by taking into account the constraints of the fabrication process. To achieve this, the algorithm automatically performs part of the modelling process. The following problems have been tackled: First, I propose to improve the quality of 3D printed objects by minimizing defects that appear during the fabrication. The technique developed impacts only the algorithm that drives the printer. Then, I propose to help the user to take into account the fabrication constraints during the modelling process. My techniques rely on partial information about the shape that the user wants to fabri...