INTRODUCTION TO CAD/CAM SYSTEMS IM LECTURE HOURS PER WEEK PRESENTIAL

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1 COURSE CODE INTENSITY MODALITY CHARACTERISTIC PRE-REQUISITE CO-REQUISITE CREDITS ACTUALIZATION DATE INTRODUCTION TO CAD/CAM SYSTEMS IM LECTURE HOURS PER WEEK 48 HOURS CLASSROOM ON 16 WEEKS, 96 HOURS OF INDEPENDENT WORK PRESENTIAL NOT SUFICIENTABLE COMPUTER PROGRAMMING - ST0240; CÁLCULO III (Calculus of Several Variables) - CB0232; LINEAR ALGEBRA - CB0234; (FIRST CONTROL IN A SECOND LANGUAGE) NONE JUSTIFICATION This course equips the undergraduate student with conceptual principles and practical programming skills which complement and solidify his / her usage of Computer Aided Design (CAD), Manufacturing (CAM) and Engineering software. The course explains the mathematical elements underlying CAD CAM CAE, to enable the engineer to extend the capabilities of such software tools in a given case. It also gives the student a formal understanding of the common challenges in CAD, along with the different manners to avoid and correct them, to facilitate the transit of geometric modeling data to other engineering calculations software. INTRODUCTION Nowadays CAD-CAM-CAE systems are used to increase the productivity in several areas of engineering, improving the quality of designs and integrating the communication between all the areas involved in the production of artifacts. CAD-CAM-CAE systems are widely used in the design of tools and machinery and in the drafting and design of all types of products. It s used throughout the engineering process from conceptual design and layout of products, through strength and dynamic analysis of assemblies to definition of manufacturing methods of 1

2 components. It has become an especially important technology, with benefits such as lower product development costs and a greatly shortened design cycle. AIMS OF THE COURSE Make simplified and approximate operations more commonly used in Computer Aided Geometric Design and performed by popular commercial geometric modelers. Apply basic engineering math concepts with physical insight into the effects they represent in the practice of Computer Aided Geometric Design. Develop and implement algorithms prototypes used to solve common problems in industrial practice of Computer Aided Geometric Design. Give the student a theoretical foundation to understand the technical choices and practices of commercial Computer Aided Engineering (CAE) software. GENERAL CONTENTS 1. Mathematical Background 1.1. Relations vs. Functions 1.2. Bijections 1.3. Groups 1.4. Affine Aff(n) 1.5. General Linear GL(n) 1.6. Orthogonal O(n) 1.7. Special Orthogonal SO(n) 2. Geometric Transformations 2.1. Property Preservation: Volume, Orientation, Angle, Distance, Origin, Colinearity 2.2. Coordinates and Coordinate Systems 2.3. Rigid Transformations 2.4. Non rigid Transformations 3. Curves and Surfaces 3.1. Curves 3.2. Surfaces 4. Geometric Modeling 4.1. Theoretical Background. 2-manifold and 1-manifolds in R Boundary Representation 4.3. Enumerations 2

3 4.4. Quadtrees & Octrees 4.5. Constructive Solid Geometry (CSG) EVALUATION EXAM / TEST / GRADE WEIGHT Math Review 5 % Rigid Transformations 10 % Non-Rigid Transformations 15 % Parametric Curves and Surfaces 20 % Geometric Modeling 10 % Class Homeworks and Participation 20 % Workshop 20 % TOTAL 100 % Note: grading schedule and percentages will vary as per particular needs of the student group. 3

4 REFERENCES Books Geometric Functions in Computer Aided Geometric Design. Oscar E. Ruiz, Carlos A. Cadavid.. Editorial: Fondo Editorial EAFIT, Medellin: 2008, v.1, p.134. ISBN: Understanding CAD / CAM / CG. Oscar E. Ruiz. Americal Society of Mechanical Engineers ASME. Continuing Education Institute. Global Training. ASME Code GT An introduction to solid modeling, Martti Mantyla, 1987, isbn , Computer Science Press, Inc. New York, NY, USA. Geometric modeling, Michael E. Mortenson, 1985, isbn , John Wiley and Sons, Inc., New York, NY, USA. Geometric and solid modeling: an introduction, Christoph M. Hoffmann, 1989, isbn , Morgan Kaufmann Publishers Inc., San Francisco, CA, USA. Computer graphics & geometric modeling, Max K. Agoston ISBN Springer-Verlag. Computer Graphics and Geometric Modeling(1st Edition). David Salomon ISBN-13: , ISBN: Springer Verlag. Web Pages Quaternion: Eigenvectors and Eigenvalues Matlab 4

5 WEEKLY SYLLABUS AND STUDENT WORK Week Topic Student Work 1 Math Review. Relations, Functions, Jacobian, Groups 2 Preservation of Colinearity, Volume, Angle, Distance, Orientation Linear GL(n) and Affine Af(n) groups EXAM MATH REVIEW Programming Review Non affine preservations. 3 Space Basis. Coordinates and Coordinate Systems. Homogeneous / Cartesian Coordinates 4 Orthogonal O(n) and Special Orthogonal SO(n) groups. Rigid Transformations 5 Eigen-pairs of SO(n) transformations Quaternions vs. Eigen-pairs of SO(n) matrices. EXAM RIGID TRANSFORMATIONS 6 Parallel Projections Pseudo-Affine functions 7 Perspective Projections Counting of Vanishing Points Scaling and Shear Transformations EXAM NON RIGID TRANSFORMATIONS 8 Convex Hulls and Linear combinations. Basis for Parametric Curves. 9 Student Proposal for Parametric Curves. Bezier Curves 10 Spline Curves Catmull Clark Interpolations and violation of Convex Hulls. Non affine preservations and coordinate systems Application of Transformations Instantaneous Quaternion Applications. Tool Trajectories Object Reconstruction from Parallel Projections. Object Reconstruction from Perspective Projections Own 3 pt curve fitting. Own 4 pt curve fitting. Bernstein Polynomials Matrix Representations of Bernstein Polynomials Spline curves and multi identity History of Coefficients. 5

6 11 Weight History Matrix Parametric Surfaces 12 Closed Parametric Surfaces Stage Construction for Parametric Surfaces 13 Closed Parametric Surfaces Stage Construction for Parametric Surfaces EXAM PARAMETRIC CURVES AND SURFACES 14 Open and Closed Sets. Boundaries of Sets. Balls in Rn. 2- and 1-manifolds 15 Boundary Representations. Constructive Solid Geometry 16 Enumeration Quadtrees / Octrees. Boolean Quadtree Operations EXAM GEOMETRIC MODELING Multiple Hybrid patch sets. Multiple Hybrid patch sets. Multiple Hybrid patch sets. Topology and Geometry of Triangular Mesh Boundary Representation Examples. Programming Refresh Quadtree Representation 6