geogebra conference, linz. july 2009 1/12 teaching computer aided design with the use of geogebra...
TRANSCRIPT
1/12
GEOGEBRA conference,
Linz. JULY 2009
Teaching Computer Aided Design with the use of Geogebra
Francisco PérezUniversidad Politécnica de Madrid.
Spain
2/12
GEOGEBRA conference,
Linz. JULY 2009
• Presentation
• Introduction
• The discipline of CAD
• Why Geogebra?
• Examples
• Conclusions
Contents
Presentation
Introduction
The discipline of CAD
Why GeoGebra?
Examples
Conclusions
3/12
GEOGEBRA conference,
Linz. JULY 2009
• 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
4/12
GEOGEBRA conference,
Linz. JULY 2009
• 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
5/12
GEOGEBRA conference,
Linz. JULY 2009
Introduction (II)
• Bezier, B-Splines, NURBS curves: properties Geog.
• Algorithms GeoGebra
• Surfaces CAD programs
• Why? Develop specific applicationsPresentation
Introduction
The discipline of CAD
Why GeoGebra?
Examples
Conclusions
6/12
GEOGEBRA conference,
Linz. JULY 2009
• 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
7/12
GEOGEBRA conference,
Linz. JULY 2009
• Algorithms graphically and analytically
• Free
• Step by step
Why Geogebra? (I)
Presentation
Introduction
The discipline of CAD
Why GeoGebra?
Examples
Conclusions
8/12
GEOGEBRA conference,
Linz. JULY 2009
• Geometric commands important for CAD
Why Geogebra? (II)
Presentation
Introduction
The discipline of CAD
Why GeoGebra?
Examples
Conclusions
9/12
GEOGEBRA conference,
Linz. JULY 2009
• 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
10/12
GEOGEBRA conference,
Linz. JULY 2009
• Conics as NURBS
Examples (II)
• Projective geometry
Presentation
Introduction
The discipline of CAD
Why GeoGebra?
Examples
Conclusions
11/12
GEOGEBRA conference,
Linz. JULY 2009
• 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