Article
Computer Science, Software Engineering
Caigui Jiang, Hui Wang, Victor Ceballos Inza, Felix Dellinger, Florian Rist, Johannes Wallner, Helmut Pottmann
Summary: This study successfully represents free forms through precise isometric bending of surfaces made from a small number of molds, solving the paneling task with surfaces of constant Gaussian curvature. The research also explores interesting connections between the paneling problem and the geometry of Killing vector fields, designing and actuating isometries, curved folding in the case of double-curved surfaces, and quad meshes with rigid faces that remain flexible.
ACM TRANSACTIONS ON GRAPHICS
(2021)
Article
Computer Science, Software Engineering
Caigui Jiang, Cheng Wang, Xavier Tellier, Johannes Wallner, Helmut Pottmann
Summary: In this article, the geometric properties and modeling capabilities of quad meshes with planar faces are investigated, where the mesh polylines are contained in a single plane. This planarity is advantageous in architectural design and building construction. The design of meshes under the requirement that one half of the mesh polylines are planar (P meshes) is discussed, as well as the geometry and design of meshes where all polylines enjoy this property (PP meshes). Geometric insights, explicit constructions, and an approach to geometric modeling of both P meshes and PP meshes are provided.
ACM TRANSACTIONS ON GRAPHICS
(2023)
Article
Engineering, Manufacturing
Shrikant Shankarrao Pawar, Tufan Chandra Bera, Kuldip Singh Sangwan
Summary: The development of energy efficient machining is currently a priority for industries to reduce energy consumption and make manufacturing systems more sustainable. Fluctuations in force profiles during machining of variable curved components hinder stable machining and result in varying cutting power consumption. This research aims to develop an energy efficient machining strategy for milling variable curved components, achieving more uniform cutting force and power profiles by maintaining a constant chip load along the peripheral length of the curved geometry. The proposed strategy is compared with conventional cutting to validate its effectiveness. By regulating the entry angle of the milling cutter according to workpiece curvature, the proposed algorithm reduces cutting power fluctuations caused by variations in workpiece curvature, resulting in a 22% reduction in energy consumption during machining. This strategy not only enables energy efficient milling of variable curved geometries but also improves the stability of the machining process and prolongs tool life by reducing force fluctuations during metal removal.
JOURNAL OF MANUFACTURING PROCESSES
(2023)
Article
Architecture
Shizuo Kaji, Jingyao Zhang
Summary: This paper proposes an algorithmic approach for the conceptual design of architectural surfaces represented by triangulated meshes. The method optimizes the surface based on user-specified geometric properties, such as Gaussian curvature distribution and boundary location preference. It automates the time-consuming task of manually designing surfaces with specific Gaussian curvatures.
JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING
(2023)
Article
Computer Science, Software Engineering
Weidan Xiong, Chong Mo Cheung, Pedro Sander, Ajay Joneja
Summary: This paper introduces the problem of clustering vertices in a given 3D mesh to reduce fabrication cost in architectural projects. By establishing an equivalence between mesh vertices and physical joints, the unique number of joints in the facade mesh is significantly decreased, leading to cost reduction.
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
(2022)
Article
Computer Science, Software Engineering
Stefan Pillwein, Johanna Kubert, Florian Rista, Przemyslaw Musialski
Summary: Elastic geodesic grids (EGG) are lightweight structures that approximate designer provided free-form surfaces. Decomposing surfaces into smaller patches is an effective strategy to tackle limitations with more sophisticated design surfaces. This structure is suitable for various purposes like free-form sub-structures, panels, sun and rain protectors, etc.
COMPUTERS & GRAPHICS-UK
(2021)
Review
Biochemistry & Molecular Biology
Marina N. Iriondo, Asier Etxaniz, Zurine Anton, L. Ruth Montes, Alicia Alonso
Summary: Autophagy is a crucial process for cell self-repair and survival, involving the formation of autophagosomes that deliver cargo for degradation and re-use. The complex event of autophagosome formation requires specific proteins and membrane biogenesis, with curvature playing a key role in the process.
BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES
(2021)
Article
Computer Science, Software Engineering
Qie Yifan, Qiao Lihong, Nabil Anwer
Summary: An enhanced mesh partitioning method is proposed in this paper to enable more accurate feature decomposition by considering kinematic invariance classes. This two-step method involves partitioning based on sharp edge detection and enhanced partitioning based on non-sharp edge rectification. By utilizing conformal geometry to map 3D surfaces onto a 2D unit disk, the boundary points on non-sharp edges are refined, leading to effective partitioning of connecting regions at their natural boundaries.
COMPUTER-AIDED DESIGN
(2021)
Article
Automation & Control Systems
Shrikant Shankarrao Pawar, Tufan Chandra Bera, Kuldip Singh Sangwan
Summary: The study focuses on developing an energy consumption model for milling processes, specifically for variable curved surfaces. The developed model accurately estimates energy consumption and takes into account the influence of workpiece curvature. It provides a platform for understanding and characterizing energy consumption in machining curved geometries.
INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY
(2022)
Article
Computer Science, Artificial Intelligence
Lidija Comic, Gaelle Largeteau-Skapin, Rita Zrour, Ranita Biswas, Eric Andres
Summary: This article proposes a characterization of discrete analytical spheres, planes, and lines in the body-centered cubic (BCC) grid using both Cartesian and alternative compact coordinate systems. Spheres and planes are defined through double Diophantine inequalities, and their topological features, such as functionality, thickness, connectivity, and separation properties, are investigated. Lines are defined as the intersection of planes. The number of planes is equal to the number of pairs of faces of a BCC voxel parallel to the line.
PATTERN RECOGNITION
(2023)
Article
Physics, Mathematical
Muzaffer Adak, Tekin Dereli, Tomi S. Koivisto, Caglar Pala
Summary: In the conventional formulation of general relativity, gravity is described by metric curvature. However, there are alternative formulations in flat affine geometries using torsion and nonmetricity. These general teleparallel geometries have potential applications in material physics, such as the study of crystal defects. This work explores the general teleparallel geometry using differential forms, discusses different gauge fixings, and presents exact solutions for the quadratic theory in 2, 3, and 4 dimensions.
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
(2023)
Article
Engineering, Chemical
Joshua Benjamin, Samar Al Mashrafi, Andres Tejada-Martinez, Nancy Diaz-Elsayed, Mauricio E. Arias, Qiong Zhang
Summary: Existing desalination plants face challenges of high energy costs and environmental impacts. Pressure retarded osmosis (PRO) technology can mitigate these issues by capturing the potential energy in the salinity gradient. However, PRO faces the challenge of concentration polarization (CP), which can be reduced using membrane spacers but they also increase the pressure drop along the feed channel.
JOURNAL OF MEMBRANE SCIENCE
(2022)
Article
Energy & Fuels
Rohan Bhuiya, Niank Shah, Divanshu Arora, N. Vijay Krishna, S. Manikandan, C. Selvam, Ravita Lamba
Summary: This study proposes a technique to improve the energy efficiency of thermoelectric cooling systems by introducing phase change material in the heat sink. Computational studies show that the use of phase change material significantly reduces the hot side temperature of thermoelectric cooler, indicating the potential of phase change material for the thermal management of thermoelectric cooling systems.
JOURNAL OF ENERGY STORAGE
(2022)
Article
Mathematics
Karoly J. Boroczky, Apratim De
Summary: This study establishes the stability of the solution of the Logarithmic Minkowski problem on Sn-1 in the case of symmetries with respect to a Coxeter group G subset of O(n) acting without non-zero fixed points on R-n.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Computer Science, Software Engineering
Cheng Wang, Caigui Jiang, Hui Wang, Xavier Tellier, Helmut Pottmann
Summary: This paper focuses on the computational design of architectural structures based on a grid of intersecting beams aligned with parameter lines of a quad mesh. It addresses the planarity of long-range supporting beams along selected polylines in the underlying mesh, as well as other constraints such as planarity of faces, right node angles, and static equilibrium. The discrete counterparts of well-known surfaces in classical geometry are studied, and their knowledge is used to initialize the proposed optimization algorithms.
COMPUTER-AIDED DESIGN
(2023)
Article
Computer Science, Software Engineering
Michael Barton, Michal Bizzarri, Florian Rist, Oleksii Sliusarenko, Helmut Pottmann
Summary: CNC machining is a leading subtractive manufacturing technology that still presents challenging problems. Researchers have demonstrated high-quality surface finishes through careful geometric analysis of five-axis machining on freeform surfaces, reducing the need for hard-to-control post-machining processes.
ACM TRANSACTIONS ON GRAPHICS
(2021)
Article
Computer Science, Software Engineering
Davide Pellis, Martin Kilian, Helmut Pottmann, Mark Pauly
Summary: This paper studies Weingarten surfaces and their potential in freeform architecture design. By leveraging the symmetries of Weingarten surfaces, surface paneling of double-curved architectural skins can be simplified. An optimization approach is presented to find a Weingarten surface close to a given input design.
ACM TRANSACTIONS ON GRAPHICS
(2021)
Article
Computer Science, Software Engineering
Caigui Jiang, Hui Wang, Victor Ceballos Inza, Felix Dellinger, Florian Rist, Johannes Wallner, Helmut Pottmann
Summary: This study successfully represents free forms through precise isometric bending of surfaces made from a small number of molds, solving the paneling task with surfaces of constant Gaussian curvature. The research also explores interesting connections between the paneling problem and the geometry of Killing vector fields, designing and actuating isometries, curved folding in the case of double-curved surfaces, and quad meshes with rigid faces that remain flexible.
ACM TRANSACTIONS ON GRAPHICS
(2021)
Article
Mathematics
Oleg Karpenkov, Christian Muller, Gaiane Panina, Brigitte Servatius, Herman Servatius, Dirk Siersma
Summary: We prove an equilibrium stressability criterion for trivalent multidimensional frameworks, which can be expressed in different ways.
EUROPEAN JOURNAL OF MATHEMATICS
(2022)
Article
Computer Science, Software Engineering
Hui Wang, Helmut Pottmann
Summary: Motivated by applications in architectural geometry, this study focuses on surfaces with a constant ratio of principal curvatures (CRPC surfaces), and explores their characteristic parameterizations. The research introduces characteristic parameterizations for rotational CRPC surfaces and discrete CRPC surfaces, and demonstrates efficient computation methods through numerical optimization. These surfaces have potential applications in computational design and mathematical studies of the CRPC surfaces.
COMPUTER AIDED GEOMETRIC DESIGN
(2022)
Article
Computer Science, Software Engineering
Yingying Ren, Uday Kusupati, Julian Panetta, Florin Isvoranu, Davide Pellis, Tian Chen, Mark Pauly
Summary: We propose a computational inverse design framework for a new type of volumetric deployable structures that can transform from compact rest states into bending-active 3D target surfaces. Umbrella meshes, consisting of elastic beams, rigid plates, and hinge joints, can be directly printed or assembled without using external energy. We develop a reduced physics-based simulation framework to accurately model the complex interaction between the deforming components. An inverse design optimization algorithm is proposed to determine the mesh topology and optimal shape parameters for approximating a given target surface. Physical models are fabricated to validate the effectiveness of our approach at various scales and using different manufacturing techniques.
ACM TRANSACTIONS ON GRAPHICS
(2022)
Article
Computer Science, Software Engineering
Eike Schling, Hui Wang, Sebastian Hoyer, Helmut Pottmann
Summary: This research focuses on simplifying the fabrication and assembly of freeform shells by controlling the curvature of structural elements during the design phase. It introduces a computational workflow for the design and modification of hybrid asymptotic geodesic webs, which are used to create robust and versatile triangulated grids. The feasibility of this approach is demonstrated through architectural applications such as timber roofs and steel facades.
COMPUTER-AIDED DESIGN
(2022)
Article
Computer Science, Software Engineering
Caigui Jiang, Cheng Wang, Xavier Tellier, Johannes Wallner, Helmut Pottmann
Summary: In this article, the geometric properties and modeling capabilities of quad meshes with planar faces are investigated, where the mesh polylines are contained in a single plane. This planarity is advantageous in architectural design and building construction. The design of meshes under the requirement that one half of the mesh polylines are planar (P meshes) is discussed, as well as the geometry and design of meshes where all polylines enjoy this property (PP meshes). Geometric insights, explicit constructions, and an approach to geometric modeling of both P meshes and PP meshes are provided.
ACM TRANSACTIONS ON GRAPHICS
(2023)
Article
Engineering, Civil
Michael Wimmer, Iva Kovacic, Peter Ferschin, Florian Rist, Michael Hensel, Kristina Schinegger, Stefan Rutzinger, Hannes Kaufmann, Martin Kilian, Christian Mueller, Ivan Izmestiev, Georg Nawratil, Josef Fussl, Milena Stavric, David Hahn, Georg Suter
Summary: The SFB Advanced Computational Design aims to enhance design quality and efficiency in architecture and construction through the development of advanced computational design tools. The research consists of three areas: design methodology, visual and haptic design interaction, and form finding. Various techniques and algorithms are explored to improve the design process.
Article
Mathematics
Yang Liu, Olimjoni Pirahmad, Hui Wang, Dominik L. L. Michels, Helmut Pottmann
Summary: We determine all helical surfaces with a constant ratio of principal curvatures in three-dimensional Euclidean space. Our approach involves the involution of conjugate surface tangents and the use of well chosen generating profiles. The resulting surfaces and their behavior at singularities are analyzed and an overview of the possible shapes is provided.
BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY
(2023)
Article
Computer Science, Software Engineering
Cheng Wang, Caigui Jiang, Hui Wang, Xavier Tellier, Helmut Pottmann
Summary: This paper focuses on the computational design of architectural structures based on a grid of intersecting beams aligned with parameter lines of a quad mesh. It addresses the planarity of long-range supporting beams along selected polylines in the underlying mesh, as well as other constraints such as planarity of faces, right node angles, and static equilibrium. The discrete counterparts of well-known surfaces in classical geometry are studied, and their knowledge is used to initialize the proposed optimization algorithms.
COMPUTER-AIDED DESIGN
(2023)
Article
Mathematics, Applied
Martin Kilian, Christian Mueller, Jonas Tervooren
Summary: Cone-nets are conjugate nets on a surface where each individual curve of a parameter curve family is in tangential contact with a cone. The corresponding conjugate curve network is projectively invariant and can be characterized by specific transformations. This study focuses on the properties of the transformation theory and demonstrates how different surface classes can be represented within this framework. Cone-nets are examined in both the smooth setting of differential geometry and in a consistent discretization with counterparts to relevant statements and notions of the smooth setting. Special attention is given to smooth and discrete tractrix surfaces, which are identified as principal cone-nets with constant geodesic curvature along one family of parameter curves.
RESULTS IN MATHEMATICS
(2023)
Article
Computer Science, Software Engineering
Daoming Liu, Davide Pellis, Yu-Chou Chiang, Florian Rist, Johannes Wallner, Helmut Pottmann
Summary: This paper introduces the concept of C-mesh to capture kinetic structures that can be deployed from a collapsed state. The Quadrilateral C-meshes have rich geometry properties and surprising relations with differential geometry. The paper also presents tools for exploring the shape space of C-meshes and an application for freeform architectural skins.
ACM TRANSACTIONS ON GRAPHICS
(2023)
Article
Computer Science, Software Engineering
C. Freude, D. Hahn, F. Rist, L. Lipp, M. Wimmer
Summary: This article introduces a method based on computer graphics and thermal radiation to predict the thermal impact in architectural design and urban planning. The method combines photon tracing and finite element discretization to solve heat transfer problems efficiently, and integrates solar irradiation data for different simulation scenarios.
COMPUTER GRAPHICS FORUM
(2023)