LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Shape Design and Optimization for 3D Printing

In recent years, the 3D printing technology has become increasingly popular, with wide-spread uses in rapid prototyping, design, art, education, medical applications, food and fashion industries. It enables distributed manufacturing, allowing users to easily produce customized 3D objects in office or at home. The investment in 3D printing technology continues to drive down the cost of 3D printers, making them more affordable to consumers. As 3D printing becomes more available, it also demands better computer algorithms to assist users in quickly and easily generating 3D content for printing. Creating 3D content often requires considerably more efforts and skills than creating 2D content. In this work, I will study several aspects of 3D shape design and optimization for 3D printing. I start by discussing my work in geometric puzzle design, which is a popular application of 3D printing in recreational math and art. Given user-provided input figures, the goal is to compute the minimum (or best) set of geometric shapes that can satisfy the given constraints (such as dissection constraints). The puzzle design also has to consider feasibility, such as avoiding interlocking pieces. I present two optimization-based algorithms to automatically generate customized 3D geometric puzzles, which can be directly printed for users to enjoy. They are also great tools for geometry education. Next, I discuss shape optimization for printing functional tools and parts. Although current 3D modeling software allows a novice user to easily design 3D shapes, the resulting shapes are not guaranteed to meet required physical strength. For example, a poorly designed stool may easily collapse when a person sits on the stool; a poorly designed wrench may easily break under force. I study new algorithms to help users strengthen functional shapes in order to meet specific physical properties. The algorithm uses an optimization-based framework — it performs geometric shape deformation and structural optimization iteratively to minimize mechanical stresses in the presence of forces assuming typical use scenarios. Physically-based simulation is performed at run-time to evaluate the functional properties of the shape (e.g., mechanical stresses based on finite element methods), and the optimizer makes use of this information to improve the shape. Experimental results show that my algorithm can successfully optimize various 3D shapes, such as chairs, tables, utility tools, to withstand higher forces, while preserving the original shape as much as possible. To improve the efficiency of physics simulation for general shapes, I also introduce a novel, SPH-based sampling algorithm, which can provide better tetrahedralization for use in the physics simulator. My new modeling algorithm can greatly reduce the design time, allowing users to quickly generate functional shapes that meet required physical standards

Geometristen muotojen reaaliaikainen tunnistus

Kynä- ja kosketuskäyttöliittymät vaativat toimiakseen tehokasta ja tarkkaa hahmontunnistusta. Tässä työssä esitellään reaaliaikaisen hahmontunnistuksen käsitteistöä, yleisiä menetelmiä ja aikaisempaa tutkimusta. Lyhyesti käsitellään eri tutkimusryhmien esittämiä hahmontunnistusjärjestelmiä. Lisäksi esitellään geometrisiin piirteisiin perustuva hahmontunnistusjärjestelmä. Työ antaa yksityiskohtaiset kuvaukset piirtoviivan esiprosessointi- ja piirteenirrotusalgoritmeista sekä hahmoluokittelumenetelmästä. Lisäksi kuvaillaan hahmontunnistusheuristiikka kahdelle yksinkertaiselle muodolle (nuoli ja tähti). Joukko koehenkilöitä käytti työssä toteutettua graa_sta käyttöliittymää, minkä tuloksena saatiin realistiset tulokset järjestelmän laskennallisesta suorituskyvystä ja tarkkuudesta: toteutettu järjestelmä on laskennallisesti nopea mutta tunnistustarkkuus monitulkintainen. Lopuksi pohditaan valitun lähestymistavan ongelmia ja rajoitteita.Effective sketch recognition is the basis for pen and touch-based human-computer interfaces. In this thesis the concepts, common methods and earlier work in the research area of online symbol recognition are presented. A set of shape recognition approaches proposed in the past by various research teams are briefly introduced. An online shape recognizer using global geometric features is described. The preprocessing and feature extraction algorithms as well as the shape classification method are described in detail. Recognition heuristics for two simple shapes (arrow and star) are suggested. A graphical user interface was implemented and a group of subjects employed to obtain realistic results of the computational performance and recognition accuracy of the system: the implemented system performs fast but the results on the recognition accuracy were ambiguous. Finally, the problems and restrictions of the approach are discussed

Large bichromatic point sets admit empty monochromatic 4-gons

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).Postprint (published version

Efficient From-Point Visibility for Global Illumination in Virtual Scenes with Participating Media

Sichtbarkeitsbestimmung ist einer der fundamentalen Bausteine fotorealistischer Bildsynthese. Da die Berechnung der Sichtbarkeit allerdings äußerst kostspielig zu berechnen ist, wird nahezu die gesamte Berechnungszeit darauf verwendet. In dieser Arbeit stellen wir neue Methoden zur Speicherung, Berechnung und Approximation von Sichtbarkeit in Szenen mit streuenden Medien vor, die die Berechnung erheblich beschleunigen, dabei trotzdem qualitativ hochwertige und artefaktfreie Ergebnisse liefern

Analyzing and controlling large nanosystems with physics-trained neural networks

In dieser Arbeit wird untersucht, wie Neuronale Netze genutzt werden können, um die Auswertung von Experimenten durch Minimierung des Simulationsaufwandes beschleunigen zu können. Für die Rekonstruktion von Silber-Nanoclustern aus Einzelschuss-Weitwinkel-Streubildern können diese bereits aus kleinen Datenätzen allgemeine Rekonstruktionsregeln ableiten und ermöglichen durch direktes Training auf der Streuphysik unerreichte Detailtiefen. Für Giant-Dipole-Zustände von Rydbergexzitonen in Kupferoxydul wird mittels Deep Reinforcement Learning ein Anregungsschema aus Simulationen hergeleitet.This thesis investigates the possible application of neural networks in accelerating the evaluation of physical experiments while minimizing the required simulation effort. Neural networks are capable of inferring universal reconstruction rules for reconstructing silver nanoclusters from single wide-angle scattering patterns from a small set of simulated data and when trained directly on scattering theory reaching unmatched accuracy. A dynamic excitation for giant dipole states of Rydberg excitons in cuprous oxide is derived through deep reinforcement learning interacting and simulation data