Mark Pauly
Full Professor
EPFL IC IINFCOM GCM
BC 348 (Bâtiment BC)
Station 14
1015 Lausanne
+41 21 693 52 34
+41 21 693 75 21
Office:
BC 348
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Web site: Web site: https://ssc.epfl.ch
Fields of expertise
Geometric Computing, Geometry Processing, Digital Fabrication, Optimization, Computational Design, Architectural Geometry
Biography
Mark Pauly is a full professor at the School of Computer and Communication Sciences at EPFL. Prior to joining EPFL, he was assistant professor at the CS department of ETH Zurich since April 2005. From August 2003 to March 2005 he was a postdoctoral scholar at Stanford University, where he also held a position as visiting assistant professor during the summer of 2005. He received his Ph.D. degree (with distinction) in 2003 from ETH Zurich and his M.S. degree (with highest honors) in 1999 from TU Kaiserslautern. His research interests include computer graphics and animation, shape modeling and analysis, geometry processing, architectural geometry, and digital fabrication. He received the ETH medal for outstanding dissertation, was awarded the Eurographics Young Researcher Award in 2006 and the Eurographics Outstanding Technical Contributions Award in 2016.CURRENT WORK
Research at the EPFL Geometric Computing Laboratory focuses on efficient representations, scalable data structures, and robust algorithms for digital 3D models. Our goal is to understand fundamental principles of geometric computing and leverage these insights to develop new algorithms and tools for 3D shape analysis, simulation, design, and fabrication. Our research explores the interface of several scientific disciplines, such as mathematics, computer science, materials science, and architecture to facilitate innovative computational design solutions for advanced manufacturing and construction.Publications
Infoscience publications
Computational Design of Flexible Planar Microstructures
ACM Transactions on Graphics. 2023.
BamX: Rethinking Deployability in Architecture through Weaving
Advances in Architectural Geometry 2023; De Gruyter, 2023-10-04.
C-shells: Deployable Gridshells with Curved Beams
ACM Transactions on Graphics. 2023-12-15. DOI : 10.1145/3618366.
RUM: Reconfigurable Umbrella Mesh
Advances in Architectural Geometry 2023; De Gruyter, 2023. p. 474.
Computational Exploration of Multistable Elastic Knots
ACM Transactions on Graphics. 2023. DOI : 10.1145/3592399.
Umbrella Meshes: Elastic Mechanisms for Freeform Shape Deployment
ACM Transactions on Graphics. 2022. DOI : 10.1145/3528223.3530089.Human circadian rhythms and urban density: celebrating the natural day-night cycle
SBAU 2021 DATA Book; Seoul, South Korea: Seoul Metropolitan Government, 2021. p. 56-63.
CIRCA DIEM
2021.Computational Analysis and Design of Structurally Stable Assemblies with Rigid Parts
Lausanne, EPFL, 2021. DOI : 10.5075/epfl-thesis-8964.
Computational Inverse Design of Surface-based Inflatables
Acm Transactions On Graphics. 2021-08-01. DOI : 10.1145/3450626.3459789.
Bistable Auxetic Surface Structures
Acm Transactions On Graphics. 2021-08-01. DOI : 10.1145/3450626.3459940.
Computational Design of Weingarten Surfaces
Acm Transactions On Graphics. 2021-08-01. DOI : 10.1145/3450626.3459939.
3D Weaving with Curved Ribbons
Acm Transactions On Graphics. 2021-08-01. DOI : 10.1145/3450626.3459788.
MOCCA: Modeling and Optimizing Cone-joints for Complex Assemblies
Acm Transactions On Graphics. 2021-08-01. DOI : 10.1145/3450626.3459680.
State of the Art on Computational Design of Assemblies with Rigid Parts
2021-05-01. Eurographics 2021 (EG2021), Vienna, Austria, May 3–7, 2021. p. 633-657. DOI : 10.1111/cgf.142660.
A reprogrammable mechanical metamaterial with stable memory
Nature. 2021-01-21. DOI : 10.1038/s41586-020-03123-5.The Canopy Pavilion: A lightweight shading structure using a deployable auxetic linkage membrane
2020. Advances in Architectural Geometry 2020 (AAG 2020), Online, April 26-29, 2021.Method of encoding a 3d shape into a 2d surface
US2020151290 . 2020.
X-Shell Pavilion: A Deployable Elastic Rod Structure
2019. IASS Annual Symposium, Barcelona, Spain.
chi-Shell, a new spatial deployable lattice compared to traditional reticulated shells
2019-01-01. 60th Anniversary Symposium of the International-Association-for-Shell-and-Spatial-Structures (IASS SYMPOSIUM) / 9th International Conference on Textile Composites and Inflatable Structures (STRUCTURAL MEMBRANES), Barcelona, SPAIN, Oct 07-10, 2019. p. 1932-1939.Combinations of single-top-quark production cross-section measurements and |f$_{LV}$V$_{tb}$| determinations at $ \sqrt{s} $ = 7 and 8 TeV with the ATLAS and CMS experiments
Journal of High Energy Physics. 2019-05-16. DOI : 10.1007/JHEP05(2019)088.
Design and Structural Optimization of Topological Interlocking Assemblies
Acm Transactions On Graphics. 2019-11-01. DOI : 10.1145/3355089.3356489.
X-Shells: A new class of deployable beam structures
Acm Transactions On Graphics. 2019-07-01. DOI : 10.1145/3306346.3323040.Computational Design of Auxetic Shells
Lausanne, EPFL, 2019. DOI : 10.5075/epfl-thesis-9662.Computational Design of Deployable Auxetic Shells
2018. Advances in Architectural Geometry 2018 (AAG 2018), Gothenburg, Sweden, September 22-25, 2018.Combination of inclusive and differential $ \mathrm{t}\overline{\mathrm{t}} $ charge asymmetry measurements using ATLAS and CMS data at $ \sqrt{s}=7 $ and 8 TeV
Journal of High Energy Physics. 2018-04-09. DOI : 10.1007/JHEP04(2018)033.
DESIA: A General Framework for Designing Interlocking Assemblies
Acm Transactions On Graphics. 2018-11-01. DOI : 10.1145/3272127.3275034.
Rapid Deployment of Curved Surfaces via Programmable Auxetics
Acm Transactions On Graphics. 2018-08-01. DOI : 10.1145/3197517.3201373.Real-Time Generative Hand Modeling and Tracking
Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8573.
Low-Dimensionality Calibration through Local Anisotropic Scaling for Robust Hand Model Personalization
2017 IEEE International Conference on Computer Vision (ICCV), Venice, Italy, Octobre 22-29, 2017.Double-layered timber plate shell. International Journal of Space Structures
International Journal of Space Structures. 2017-12-01. DOI : 10.1177/0266351117742853.
Online Generative Model Personalization for Hand Tracking
2017. 10th ACM SIGGRAPH Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia, Bangkok, THAILAND, NOV 27-30, 2017. p. 243. DOI : 10.1145/3130800.3130830.
Phace: Physics-based Face Modeling and Animation
Acm Transactions On Graphics. 2017. DOI : 10.1145/3072959.3073664.Physics-based Reconstruction and Animation of Humans
Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7880.
Design Transformations for Rule-based Procedural Modeling
Computer Graphics Forum. 2017. DOI : 10.1111/cgf.13105.Design of a refractive surface
US10732405 ; PL2963464 ; EP2963464 ; US2017139204 ; HK1220011 ; HK1219781 ; EP2963464 ; WO2016000926 ; EP2963464 ; EP2963463 . 2017.
Discovering Structured Variations Via Template Matching
Computer Graphics Forum. 2017. DOI : 10.1111/cgf.12788.Visualization, Adaptation, and Transformation of Procedural Grammars
Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7627.Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at $ \sqrt{s}=7 $ and 8 TeV
Journal of High Energy Physics. 2016-08-05. DOI : 10.1007/JHEP08(2016)045.Online modeling for real-time facial animation
US2023024768 ; US11348299 ; EP3518184 ; US2020160582 ; US10586372 ; AU2014277220 ; CN110310349 ; EP3518184 ; CN105900144 ; US2019156549 ; EP3005302 ; US10192343 ; US2017301125 ; US9734617 ; US2016350958 ; CN105900144 ; US9378576 ; AU2014277220 ; EP3005302 ; US2014362091 ; WO2014195018 . 2016.
Beyond Developable: Computational Design and Fabrication with Auxetic Materials
2016. ACM SIGGRAPH Conference. p. 89. DOI : 10.1145/2897824.2925944.
Sphere-Meshes for Real-Time Hand Modeling and Tracking
2016. ACM SIGGRAPH Asia Conference. p. 222. DOI : 10.1145/2980179.2980226.Exploratory Topology Modelling of Form-Active Hybrid Structures
2016. International Symposium on Novel Structural Skins - Improving Sustainability and Efficiency through New Structural Textile Materials and Designs', u'International Symposium on Novel Structural Skins - Improving Sustainability and Efficiency through New Structural Textile Materials and Designs. p. 71-80. DOI : 10.1016/j.proeng.2016.08.008.Advances in Architectural Geometry 2016
2016. Fifth edition of the AAG symposia.
A Double-Layered Timber Plate Shell - Computational Methods for Assembly, Prefabrication, and Structural Design
2016. Advances in Architectural Geometry 2016, Zürich, Switzerland, September 9-13, 2016. p. 104-122. DOI : 10.3218/3778-4.Analysis and Synthesis of Structured Variations in 3D Geometries
Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-6940.
Discovering Structured Variations via Coupled Template Matching
2016
ShapeOp - A Robust and Extensible Geometric Modelling Paradigm
2015. Design Modelling Symposium 2015, Copenhagen, Denmark, September 30 - October 2, 2015. p. 505–515. DOI : 10.1007/978-3-319-24208-8_42.Combined Measurement of the Higgs Boson Mass in $pp$ Collisions at $\sqrt{s}=7$ and 8 TeV with the ATLAS and CMS Experiments
Physical Review Letters. 2015-05-14. DOI : 10.1103/PhysRevLett.114.191803.
Interactive Design of Probability Density Functions for Shape Grammars
2015. ACM SIGGRAPH Asia Conference. p. 206. DOI : 10.1145/2816795.2818069.
Robust Articulated-ICP for Real-Time Hand Tracking
Computer Graphics Forum. 2015. DOI : 10.1111/cgf.12700.
Self Tuning Texture Optimization
Computer Graphics Forum. 2015. DOI : 10.1111/cgf.12565.Computational Methods for Fabrication-aware Modeling, Rationalization and Assembly of Architectural Structures
Lausanne, EPFL, 2015. DOI : 10.5075/epfl-thesis-6685.Realtime Face Tracking and Animation
Lausanne, EPFL, 2015. DOI : 10.5075/epfl-thesis-6666.
Dynamic 3D Avatar Creation from Hand-held Video Input
2015. SIGGRAPH 2015, Los Angeles, California, USA, August 9-13, 2015. DOI : 10.1145/2766974.Interactive Architectural Modeling from Point Clouds
2015Robust Articulated-ICP for Real-Time Hand Tracking
2015Fabrication-Aware Design with Performative Criteria
Lausanne, EPFL, 2015. DOI : 10.5075/epfl-thesis-6429.
Interactive design exploration for constrained meshes
Computer-Aided Design. 2015. DOI : 10.1016/j.cad.2014.01.004.
Dynamic 2D/3D Registration
2014. Eurographics 2014, Strasbourg, France, 7-11 april, 2014.Method of producing a reflective or refractive surface
EP2711745 ; US9576553 ; EP2711745 ; EP2711745 ; US2014071155 . 2014.
Projective Dynamics: Fusing Constraint Projections for Fast Simulation
Acm Transactions On Graphics. 2014. DOI : 10.1145/2601097.2601116.Semi-Supervised Facial Animation Retargeting
2014
Assembling Self-Supporting Structures
ACM Transactions on Graphics. 2014. DOI : 10.1145/2661229.2661266.
Wire Mesh Design
ACM Transactions on Graphics. 2014. DOI : 10.1145/2601097.2601106.Computational Shape Understanding for 3D Reconstruction and Modeling
Lausanne, EPFL, 2014. DOI : 10.5075/epfl-thesis-6259.
High-contrast Computational Caustic Design
2014. SIGGRAPH 2014, Vancouver, BC, Canada, August 10-14, 2014. p. 74:1-74:11. DOI : 10.1145/2601097.2601200.
Coupled Structure-from-Motion and 3D Symmetry Detection for Urban Facades
Acm Transactions On Graphics. 2014. DOI : 10.1145/2517348.
SAFE: Structure-aware Facade Editing
2014. EUROGRAPHICS 2014, Strasbourg, France, April 7-11, 2014. DOI : 10.1111/cgf.12313.
Dynamic 2D/3D registration for the Kinect
2013. SIGGRAPH '13: Special Interest Group on Computer Graphics and Interactive Techniques Conference, Anaheim, California, US, July 21 - 25, 2013.
Designing and Fabricating Mechanical Automata from Mocap Sequences
Acm Transactions On Graphics. 2013. DOI : 10.1145/2508363.2508400.
Sparse Iterative Closest Point
Computer Graphics Forum. 2013. DOI : 10.1111/cgf.12178.
Automatic Generation of Constructable Brick Sculptures
2013. p. 81-84. DOI : 10.2312/conf/EG2013/short/081-084.
Online Modeling For Realtime Facial Animation
Acm Transactions On Graphics. 2013. DOI : 10.1145/2461912.2461976.
Realtime Performance-Based Facial Avatars for Immersive Gameplay
2013. ACM SIGGRAPH Conference on Motion in Games 2013, Dublin, Ireland, November 7-9, 2013. p. 23–28. DOI : 10.1145/2522628.2541252.
Exploring Local Modifications for Constrained Meshes
2013. p. 11-20. DOI : 10.1111/cgf.12021.
Fabrication-aware Design with Intersecting Planar Pieces
2013. Eurographics 2013, Girona, Spain, May 6-10, 2013. p. 317-326. DOI : 10.1111/cgf.12051.
Dynamic Geometry Processing
2012. The European Association for Computer Graphics 33rd Annual Conference Eurographics 2012 (EG12), Cagliari, Sardinia, Italy, May 13-18, 2022. DOI : 10.2312/conf/eg2012/tutorials/t3.
Multi-view hair capture using orientation fields
2012. The 25th Conference on Computer Vision and Pattern Recognition (CVPR 2012), Providence, RI, US, June 16-21, 2012. p. 1490-1497. DOI : 10.1109/CVPR.2012.6247838.
Design and Optimization of Orthogonally Intersecting Planar Surfaces
2012. Design Modelling Symposium Berlin 2011, Berlin, Germany, October 10-12, 2011. p. 191-199. DOI : 10.1007/978-3-642-23435-4_22.
Caustic Art
2012
Coupled Structure-from-Motion and 3D Symmetry Detection for Urban Facades
2012
Shape-Up: Shaping Discrete Geometry with Projections
2012. p. 1657-1667. DOI : 10.1111/j.1467-8659.2012.03171.x.
Factored Facade Acquisition using Symmetric Line Arrangements
Computer Graphics Forum. 2012. DOI : 10.1111/j.1467-8659.2012.03046.x.
Temporally Coherent Completion of Dynamic Shapes
Acm Transactions On Graphics. 2012. DOI : 10.1145/2077341.2077343.
FingerGlass: Efficient Multiscale Interaction on Multitouch Screens
2011. The ACM CHI Conference on Human Factors in Computing Systems 2011, Vancouver, BC, Canada, May 7-12, 2011. p. 1601–1610. DOI : 10.1145/1978942.1979175.
Realtime Performance-Based Facial Animation
Acm Transactions On Graphics. 2011. DOI : 10.1145/1964921.1964972.Photo-Realistic Real-time Face Rendering
2011
Geometric Registration for Deformable Shapes
2010. 31st Annual Conference of the European Association for Computer Graphics, Eurographics 2010, Norrköping, Sweden, May 3-7, 2010. DOI : 10.2312/egt.20101067.
Polygon Mesh Processing
A K Peters/CRC Press.
Advances in Architectural Geometry 2010
2010. Advances in Architectural Geometry 2010.
Animation reconstruction of deformable surfaces
ETH Zurich, 2010. DOI : 10.3929/ethz-a-006342883.
The Scale Axis Transform
ETH Zurich, 2010. DOI : 10.3929/ethz-a-006393331.
Constraint-based surface processing for geometric modeling and architecture
ETH Zurich, 2010. DOI : 10.3929/ethz-a-006699489.
Case Studies in Cost-Optimized Paneling of Architectural Freeform Surfaces
2010. Advances in Architectural Geometry 2010, Vienna, Austria. DOI : 10.1007/978-3-7091-0309-8_4.
Example-Based Facial Rigging
2010. p. 32. DOI : 10.1145/1833349.1778769.
Discrete Scale Axis Representations for 3D Geometry
2010. DOI : 10.1145/1778765.1778838.
Paneling architectural freeform surfaces
2010. ACM SIGGRAPH. p. 1. DOI : 10.1145/1778765.1778782.
Face/off: Live facial puppetry
2009. Computer Animation, Conference Proceedings, New Orleans, LA, United states. p. 7-16. DOI : 10.1145/1599470.1599472.
Shadow art
2009. ACM Transactions on Graphics, Yokohama, Japan. p. 156:1-156:7. DOI : 10.1145/1661412.1618502.
Robust single-view geometry and motion reconstruction
2009. ACM Transactions on Graphics, Yokohama, Japan. p. 175:1-175:10. DOI : 10.1145/1661412.1618521.
The scale axis transform
2009. Proceedings of the Annual Symposium on Computational Geometry, Aarhus, Denmark. p. 106-115. DOI : 10.1145/1542362.1542388.
The scale axis picture show
2009. Proceedings of the Annual Symposium on Computational Geometry, Aarhus, Denmark. p. 94-95. DOI : 10.1145/1542362.1542381.
Positional, metric, and curvature control for constraint-based surface deformation
Computer Graphics Forum. 2009. DOI : 10.1111/j.1467-8659.2009.01395.x.
Symmetry for Architectural Design
2008. First Symposium on Architectural Geometry (AAG 2008), Vienna, Austria, September 13-16, 2008. p. 13-16.
Discovering structural regularity in 3D geometry
ACM Transactions on Graphics. 2008. DOI : 10.1145/1360612.1360642.
Global correspondence optimization for non-rigid registration of depth scans
Computer Graphics Forum. 2008. DOI : 10.1111/j.1467-8659.2008.01282.x.
Automatic generation of tourist maps
ACM Transactions on Graphics. 2008. DOI : 10.1145/1360612.1360699.
Curvature-domain shape processing
2008. Computer Graphics Forum, 9600 Garsington Road, Oxford, OX4 2XG, United Kingdom. p. 241-250. DOI : 10.1111/j.1467-8659.2008.01121.x.
The medial axis of the union of inner Voronoi balls in the plane
2007. 19th Canadian Conference on Computational Geometry (CCCG), Ottawa, CANADA, Aug 20-22, 2007. p. 515-523. DOI : 10.1016/j.comgeo.2010.03.006.
Embedded deformation for shape manipulation
ACM Transactions on Graphics. 2007. DOI : 10.1145/1276377.1276478.
Symmetrization
ACM Transactions on Graphics. 2007. DOI : 10.1145/1276377.1276456.
Medial axis approximation from inner Voronoi balls: A demo of the Mesecina tool
2007. Proceedings of the Annual Symposium on Computational Geometry, Gyeongju, Korea, Republic of. p. 123-124. DOI : 10.1145/1247069.1247090.
Medial Axis Approximation of Planar Shapes from Union of Balls: A Simpler and more Robust Algorithm
2007. p. 105-108.
Surface reconstruction using local shape priors
2007. p. 253-262. DOI : 10.1145/1281991.1282025.
Adaptive space deformations based on rigid cells
Computer Graphics Forum. 2007. DOI : 10.1111/j.1467-8659.2007.01056.x.
Geometric modeling based on polygonal meshes
2007. ACM SIGGRAPH 2007 International Conference on Computer Graphics and Interactive Techniques, San Diego, CA, United states. DOI : 10.1145/1281500.1281640.
Adaptively sampled particle fluids
ACM Transactions on Graphics. 2007. DOI : 10.1145/1276377.1276437.Resolution-independent detail preservation for 3D shape editing
2006
Versatile Virtual Materials Using Implicit Connectivity
2006. Eurographics Symposium on Point-Based Graphics 2006, Massachusetts, USA, July 29-30, 2006. DOI : 10.2312/spbg/spbg06/137-144.
Multiresolution particle-based fluids
2006-06-15
Meshless Lagrangian methods for physics-based animations of solids and fluids
ETH Zurich, 2006. DOI : 10.3929/ethz-a-005330494.
Detail-preserving fluid control
2006. p. 7-12. DOI : 10.1145/1218064.1218066.
Point-based multiscale surface representation
ACM Transactions on Graphics. 2006. DOI : 10.1145/1138450.1138451.
Partial and approximate symmetry detection for 3D geometry
2006. ACM Transactions on Graphics, Boston, MA, United states. p. 560-568. DOI : 10.1145/1141911.1141924.
Probabilistic fingerprints for shapes
2006. p. 121-130. DOI : 10.1145/1281957.1281973.
The conformal alpha shape filtration
Visual Computer. 2006. DOI : 10.1007/s00371-006-0027-1.
PriMo: coupled prisms for intuitive surface modeling
2006. p. 11-20. DOI : 10.1145/1281957.1281959.
Example-Based 3D Scan Completion
2005. p. 23-32.
Meshless animation of fracturing solids
2005. ACM Transactions on Graphics, Los Angeles, CA, United states. p. 957-964. DOI : 10.1145/1073204.1073296.
Conformal alpha shapes
2005. Point-Based Graphics, 2005 - Eurographics/IEEE VGTC Symposium Proceedings, Stony Brook, NY, United states, June 21-22, 2005. p. 55-61. DOI : 10.1109/PBG.2005.194064.
Efficient raytracing of deforming point-sampled surfaces
Computer Graphics Forum. 2005. DOI : 10.1111/j.1467-8659.2005.00892.x.
Quasi-Rigid Objects in Contact
2004. Eurographics/ACM SIGGRAPH Symposium on Computer Animation 2004. p. 109-119. DOI : 10.2312/sca/sca04/109-119.
Perspective accurate splatting
2004. Proceedings - Graphics Interface, London, Ont, Canada. p. 247-254.
Point-based Computer graphics
Computers & Graphics. 2004. DOI : 10.1016/j.cag.2004.08.008.
Robust watermarking of point-sampled geometry
2004. Proceedings - Shape Modeling International SMI 2004, Genova, Italy. p. 233-242. DOI : 10.1109/SMI.2004.1314510.
Point primitives for interactive modeling and processing of 3D geometry
ETH Zurich, 2003. DOI : 10.3929/ethz-a-004612876.
Shape modeling with point-sampled geometry
2003. ACM Transactions on Graphics, San Diego, CA, United states. p. 641-650. DOI : 10.1145/882262.882319.
Multi-scale Feature Extraction on Point-Sampled Surfaces
2003. Computer Graphics Forum, Granada, Spain. p. 281-289. DOI : 10.1111/1467-8659.00675.
Multiresolution Modeling of Point-Sampled Geometry
2002
Pointshop 3D: An interactive system for point-based surface editing
2002. ACM Transactions on Graphics, United states. p. 322-329. DOI : 10.1145/566654.566584.
Efficient simplification of point-sampled surfaces
2002. Proceedings of the IEEE Visualization Conference, Boston, MA, United states. p. 163-170. DOI : 10.1109/VISUAL.2002.1183771.
Robust Monte Carlo Methods for Photorealistic Rendering of Volumetric Effects
University of Kaiserslautern, 1999.Teaching & PhD
Teaching
Computer Science
Communication Systems
PhD Students
Becker Quentin Christian, Kusupati Uday, Ren Yingying, Vidulis Michele,Past EPFL PhD Students
Bouaziz Sofien , Ceylan Duygu , Dang Ngoc Minh , Deuss Mario Moacir , Ichim Alexandru Eugen , Konakovic Lukovic Mina , Lienhard Stefan , Schwartzburg Yuliy , Tkach Anastasia , Wang Ziqi ,Courses
Computer graphics
The students study and apply fundamental concepts and algorithms of computer graphics for rendering, geometry
synthesis, and animation. They design and implement their own interactive graphics programs.
Geometric computing
This course will cover mathematical concepts and efficient numerical methods for geometric computing. We will explore the beauty of geometry and develop algorithms to simulate and optimize 2D and 3D geometric models with an emphasis towards computational design for digital fabrication.