INF 555 Geometric Modeling: Digital Representation and Analysis of Shapes Today •  Practical Information •  Introduction to the course •  Actual content: •  Transformations, Homogeneous Coordinates, Projective Geometry •  Curve design – Lagrange interpolation, Cubic Splines Practical Information •  Instructors: Maks Ovsjanikov Luca Castelli-Aleardi [email protected] [email protected] Bureau 2031 (2nd floor) Bâtiment Turing Bureau 2032 (2nd floor) Bâtiment Turing Practical Information Website: http://www.enseignement.polytechnique.fr/informatique/INF555 or http://goo.gl/k2kCT •  9 Lectures and Practical Sessions (TD) Lectures: Tuesdays 13:30 – 15:30 TD’s: Tuesdays 15:45 – 17:45 •  Final Exam: Project Presentations December 2nd – 5th Research Project: Implementation + Presentation + Short report (~4 – 6 pages) Practical Information Course Structure: •  9 Lectures and Practical Sessions (TD) Lectures: Tuesdays 13:30 – 15:00 TD’s: Tuesdays 15:15 – 17:15 •  Final Exam: Project Presentations December 2nd – 5th Evaluation: TD’s: 20% - Project: 50% - Quizzes: 30% Practical Information Late Policy: •  Each TD assignment is due 2 weeks after class. •  You can skip any 1 assignment. •  For every extra late day you lose 20 points (out of 100). •  You can collaborate but write your own code (changing variable names doesn’t count). •  No late days on quizzes and final project. Introduction to the course What is geometric modeling? •  Broad Goals: To create mathematical models and practical tools for digital representation and manipulation of 2D/3D shapes. Why Geometric Modeling? •  Modern manufacturing pipeline: e.g. Dassault Falcon 7X Computer model idea Why Geometric Modeling? •  Modern manufacturing pipeline: e.g. Dassault Falcon 7X Computer model idea 80% of the time Simulation Implementation What is Digitally Modeled? •  Everything! What is Digitally Modeled? •  And more! 3d Cinema and Animation Gaming What is Digitally Modeled? •  And more! Biological and Medical Data Geological Data Mathematical Surfaces Why Geometric Modeling? •  A digital model allows easy manipulation. •  Digital simulation is much cheaper. •  Model optimization and repair is possible. •  Comparison across models. •  Creation of new models from other ones is easy. Why Geometric Modeling Now? 3d printers are becoming widely available If you can model an object, you can create it at home. Why Geometric Modeling Now? 3d printers are becoming widely available If you can model an object, you can create it at home. Why Geometric Modeling Now? Our ability to digitally model directly affects the world we live in. What are we going to learn? We proceed by increasing dimension: •  0D: Points and their Transformations •  Projective Geometry and Homogeneous Coordinates – Today •  1D: Modeling Curves •  Parametric curves, polynomials, spline interpolation •  Implicit curves, subdivision methods What are we going to learn? We proceed by increasing dimension: •  2D / 3D: Surfaces •  Triangle Meshes and NURBS surfaces •  Subdivision surfaces What are we going to learn? We proceed by increasing dimension: •  2D / 3D: Point Clouds •  Analysis and cleanup – e.g. normal estimation •  Reconstruction What are we going to learn? We proceed by increasing dimension: •  2D / 3D: Shape Processing and Analysis •  Segmentation, Simplification •  Smoothing What are we going to learn? We proceed by increasing dimension: •  2D / 3D: Shape Matching •  Rigid vs. Non-Rigid What are we going to learn? We proceed by increasing dimension: •  2D / 3D: Shape Processing •  Deformation, Interpolation , Parametrization , Search Introduction? Questions?