GEOGEBRA conference Linz JULY 2009 Teaching Computer Aided

GEOGEBRA conference, Linz. JULY 2009 Teaching Computer Aided Design with the use of Geogebra Francisco Pérez Universidad Politécnica de Madrid. Spain 1

GEOGEBRA conference, Linz. JULY 2009 Contents • Presentation Introduction The discipline of CAD Why Geo. Gebra? Examples Conclusions • Introduction • The discipline of CAD • Why Geogebra? • Examples • Conclusions 2

GEOGEBRA conference, Linz. JULY 2009 Presentation • Francisco Pérez Arribas Presentation • Naval Architecture School. Technical University Madrid Introduction The discipline of CAD • Technical Drawing: Euclidean Geometry (160 students) Why Geo. Gebra? Examples • http: //debin. etsin. upm. es/~geometria/ Conclusions • CAD (Computer Aided Design) (<10 students) Technical Drawing Basic CAD Descriptive Geometry CAD (Comp. Geometry) 3

GEOGEBRA conference, Linz. JULY 2009 Introduction (I) • CAD with commercial programs • + Business, - Teaching • Little knowledge on how CAD works Presentation Introduction • Consolidate theoretical concepts and acquire practice The discipline of CAD Why Geo. Gebra? Examples Conclusions 4

GEOGEBRA conference, Linz. JULY 2009 Introduction (II) • Bezier, B-Splines, NURBS curves: properties • Algorithms • Surfaces Presentation Introduction • Why? Geog. Geo. Gebra CAD programs Develop specific applications The discipline of CAD Why Geo. Gebra? Examples Conclusions 5

GEOGEBRA conference, Linz. JULY 2009 The discipline of CAD • 1962 Sketchpad Presentation Introduction The discipline of CAD Why Geo. Gebra? Examples Conclusions • 60’s Bézier, Casteljau • 1985 NURBS software • CAD is taught very differently: programs, geometric, … • CAD can not exist without commercial CAD programs • Capacity to use CAD tools, and develop programs • CAD algorithms will be the same, not the programs 6

GEOGEBRA conference, Linz. JULY 2009 Why Geogebra? (I) • Algorithms graphically and analytically • Free Presentation • Step by step Introduction The discipline of CAD Why Geo. Gebra? Examples Conclusions 7

GEOGEBRA conference, Linz. JULY 2009 Why Geogebra? (II) • Geometric commands important for CAD Presentation Introduction The discipline of CAD Why Geo. Gebra? Examples Conclusions 8

GEOGEBRA conference, Linz. JULY 2009 Examples (I) • NURBS (Non Uniform Rational B-splines): algebraically • NURBS (Nobody Understand Rational B-splines) Presentation Introduction The discipline of CAD Why Geo. Gebra? Examples Conclusions 9

GEOGEBRA conference, Linz. JULY 2009 Examples (II) • Conics as NURBS Presentation Introduction The discipline of CAD Why Geo. Gebra? Examples Conclusions • Projective geometry 10

GEOGEBRA conference, Linz. JULY 2009 Conclusions • Geo: understanding algorithms bellow CAD programs Presentation • Geo: active learning, not push buttons, not black boxes Introduction The discipline of CAD • Classes as laboratories Why Geo. Gebra? Examples • More time on class preparation, more time for students Conclusions • CAD programs are necessary • CAD+Geog. =positive for developers and programmers 11

GEOGEBRA conference, Linz. JULY 2009 Thank you! Presentation Introduction The discipline of CAD Why Geo. Gebra? Examples Thank you! Conclusions 12