Supplementary Material for earning Shape Placements by Example

Computer Graphics Forum, 2012

École Polytechnique Fédérale de Lausanne, Switzerland point cloud quadrilateral mesh tetrahedral mesh polygon mesh conformal deformation isometric deformation square elements sphere constraint Figure 1: Constraint-based optimization and interactive shape exploration on different geometry representations. Blue dots denote handle positions, green areas are constrained to remain rigid and red spheres indicate that vertices should be arranged on a sphere.

Environment and Planning B: Planning and Design, 1986

A fundamental problem in editing shapes is the recognition of partial shapes in a drawing to which changes are to be made. In this paper the possibility of using shape rules as a mechanism for effecting such changes is explored. Shape rules represent spatial relationships between two shapes a and /? with the interpretation that any instance of a in a shape can be replaced by a 'similar' instance of /?. A shape generation system implemented in PROLOG is described.

In this paper we will present a state of the art of the descriptive and generative models for shape. We will present several different approaches for the manipulation of shape in computational systems: numerical models, graph models, descriptive models. This investigation will lead to a discussion regarding the use of these models for supporting the generation of shapes in the early phases of the design process

2000

2004

Arrangements of planar curves are fundamental structures in computational geometry. Algorithms for computing such arrangements consist of a topological part and a geometric part. For both parts different algorithmic approaches and implementations are possible. In ECG, we further developed and implemented these approaches. We followed modern software design and encapsulated our solutions into modules with well-defined and tight interfaces. In particular, we can combine different realizations of the topological part (we have two) with different realizations of the geometric part (we have three, which in turn are parametrized by different implementations of the underlying number types). The implementations of the geometric part follow quite different designs. In this report, we provide first comparisons of our different designs. In a later version of the report, we also plan to compare implementations outside the ECG-project.

2006

Shape computations are a formal representation that specify particular aspects of the design process with reference to form. They are defined according to shape grammars, where manipulations of pictorial representations of designs are formalised by shapes and rules applied to those shapes. They have frequently been applied in architecture in order to formalise the stylistic properties of a given corpus of designs, and also to generate new designs within those styles. However, applications in more general design fields have been limited. This is largely due to the initial definitions of the shape grammar formalism which are restricted to rectilinear shapes composed of lines, planes or solids. In architecture such shapes are common but in many design fields, for example industrial design, shapes of a more freeform nature are prevalent. Accordingly, the research described in this thesis is concerned with extending the applicability of the shape grammar formalism such that it enables computation with freeform shapes.

8th IFAC International Workshop on Intelligent Manufacturing Systems, 2007, 2007

This work deals with the problem of minimize the waste of space that occurs on a placement of a set of bi-dimensional items inside a bi-dimensional container with fixed dimensions. This problem is approached with an heuristic based on Simulated Annealing, which is inspired on the physic-chemical process that take place during the recrystallization of a metal. Traditional "external penalization" techniques are avoided through the application of no-fit polygons, that represents collision-free areas for each items before its placement. That gives to the proposed process a more universal character, as external penalization is based on empiric parameters of great influence on the optimization performance. The simulated annealing controls: the rotation and the placement. For each nonplaced items a limited depth binary search is performed to find a scale factor that when applied to the items, would allow it to be fitted on the container. The proposed process is suited for non-convex items and containers, and can be easily adapted for related problems, such as container size minimization. Some results are shown with irregular items, non-convex items and containers.

Natural Computing, 2012

Efficient tile sets for self assembling rectilinear shapes is of critical importance in algorithmic self assembly. A lower bound on the tile complexity of any deterministic self assembly system for an n 9 n square is Xð logðnÞ logðlogðnÞÞ Þ (inferred from the Kolmogrov complexity). Deterministic self assembly systems with an optimal tile complexity have been designed for squares and related shapes in the past. However designing Hð logðnÞ logðlogðnÞÞ Þ unique tiles specific to a shape is still an intensive task in the laboratory. On the other hand copies of a tile can be made rapidly using PCR (polymerase chain reaction) experiments. This led to the study of self assembly on tile concentration programming models. We present two major results in this paper on the concentration programming model. First we show how to self assemble rectangles with a fixed aspect ratio (a:b), with high probability, using Hða þ bÞ tiles. This result is much stronger than the existing results by Kao et al. (Randomized self-assembly for approximate shapes, LNCS, vol 5125. Springer, Heidelberg, 2008) and Doty (Randomized self-assembly for exact shapes. In: proceedings of the 50th annual IEEE symposium on foundations of computer science (FOCS), IEEE, Atlanta. pp 85-94, 2009)which can only self assembly squares and rely on tiles which perform binary arithmetic. On the other hand, our result is based on a technique called staircase sampling. This technique eliminates the need for sub-tiles which perform binary arithmetic, reduces the constant in the asymptotic bound, and eliminates the need for approximate frames (Kao et al. Randomized self-assembly for approximate shapes, LNCS, vol 5125. Springer, Heidelberg, 2008). Our second result applies staircase sampling on the equimolar concentration programming model (The tile complexity of linear assemblies. In: proceedings of the 36th international colloquium automata, languages and programming: Part I on ICALP '09, Springer-Verlag, pp 235-253, 2009), to self assemble rectangles (of fixed aspect ratio) with high probability. The tile complexity of our algorithm is HðlogðnÞÞ and is optimal on the probabilistic tile assembly model (PTAM)-n being an upper bound on the dimensions of a rectangle.

WEC'05: The Fourth …, 2005

Packing problems arise in a wide variety of application areas. The basic problem is that of determining an efficient arrangement of different objects in a region without any overlap and with minimal wasted gap between shapes. This paper presents a novel population based approach for optimizing arrangement of irregular shapes. In this approach, each shape is coded as an agent and the agents' reproductions and grouping policies results in arrangements of the objects in positions with least wasted area between them. The approach is implemented in an application for cutting sheets and test results on several problems from literature are presented.

Computational Geometry: Theory and Applications, 2007

Arrangements of planar curves are fundamental structures in computational geometry. Recently, the arrangement package of Cgal, the Computational Geometry Algorithms Library, has been redesigned and re-implemented exploiting several advanced programming techniques. The resulting software package, which constructs and maintains planar arrangements, is easier to use, to extend, and to adapt to a variety of applications, is more efficient space-and timewise, and is more robust. The implementation is complete in the sense that it handles degenerate input, and it produces exact results. In this paper we describe how various programming techniques were used to accomplish specific tasks within the context of Computational Geometry in general and Arrangements in particular. A large set of benchmarks assured the successful applications of the adverted programming techniques. The results of a small sample are reported at the end of this article.