1. GEOGEBRA conference, Linz. JULY 2009 1/12 Teaching Computer Aided Design with the use of Geogebra Francisco Pérez Universidad Politécnica de Madrid. Spain

2. GEOGEBRA conference, Linz. JULY 2009 2/12 Presentation Introduction The discipline of CAD Why Geogebra? Examples Conclusions Contents Presentation Introduction The discipline of CAD Why GeoGebra? Examples Conclusions

3. GEOGEBRA conference, Linz. JULY 2009 3/12 Francisco Pérez Arribas Naval Architecture School. Technical University Madrid Technical Drawing: Euclidean Geometry (160 students) http://debin.etsin.upm.es/~geometria/ CAD (Computer Aided Design) (<10 students) Presentation Technical Drawing Basic CAD Descriptive Geometry CAD (Comp. Geometry) Presentation Introduction The discipline of CAD Why GeoGebra? Examples Conclusions

4. GEOGEBRA conference, Linz. JULY 2009 4/12 CAD with commercial programs + Business, - Teaching Little knowledge on how CAD works Consolidate theoretical concepts and acquire practice Introduction (I) Presentation Introduction The discipline of CAD Why GeoGebra? Examples Conclusions

5. GEOGEBRA conference, Linz. JULY 2009 5/12 Introduction (II) Bezier, B-Splines, NURBS curves: properties Geog. Algorithms GeoGebra Surfaces CAD programs Why? Develop specific applications Presentation Introduction The discipline of CAD Why GeoGebra? Examples Conclusions

6. GEOGEBRA conference, Linz. JULY 2009 6/12 1962 Sketchpad 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 The discipline of CAD Presentation Introduction The discipline of CAD Why GeoGebra? Examples Conclusions

7. GEOGEBRA conference, Linz. JULY 2009 7/12 Algorithms graphically and analytically Free Step by step Why Geogebra? (I) Presentation Introduction The discipline of CAD Why GeoGebra? Examples Conclusions

8. GEOGEBRA conference, Linz. JULY 2009 8/12 Geometric commands important for CAD Why Geogebra? (II) Presentation Introduction The discipline of CAD Why GeoGebra? Examples Conclusions

9. GEOGEBRA conference, Linz. JULY 2009 9/12 NURBS (Non Uniform Rational B-splines): algebraically NURBS (Nobody Understand Rational B-splines) Examples (I) Presentation Introduction The discipline of CAD Why GeoGebra? Examples Conclusions

10. GEOGEBRA conference, Linz. JULY 2009 10/12 Conics as NURBS Examples (II) Projective geometry Presentation Introduction The discipline of CAD Why GeoGebra? Examples Conclusions

11. GEOGEBRA conference, Linz. JULY 2009 11/12 Geo: understanding algorithms bellow CAD programs Geo: active learning, not push buttons, not black boxes Classes as laboratories More time on class preparation, more time for students CAD programs are necessary CAD+Geog.=positive for developers and programmers Conclusions Presentation Introduction The discipline of CAD Why GeoGebra? Examples Conclusions

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