cadgme conference, linz. july 2009 1/12 teaching computer aided design with the use of dynamic...
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1/12
CADGME conference,
Linz. JULY 2009
TEACHING COMPUTER AIDED DESIGN WITH THE USE OF DYNAMIC GEOMETRY
Francisco PérezUniversidad Politécnica de Madrid.
Spain
2/12
CADGME conference,
Linz. JULY 2009
• Introduction
• Geometry at university level
• The discipline of CAD
• Why Geogebra?
• Examples
• Conclusions
Contents
Introduction
Geometry at University level
The discipline of CAD
Why Geogebra?
Examples
Conclusions
3/12
CADGME conference,
Linz. JULY 2009
• CAD with commercial programs
• + Business, - Teaching
• Little knowledge on how CAD works
• Consolidate theoretical concepts and acquire practice
Introduction (I)
Introduction
Geometry at University level
The discipline of CAD
Why Geogebra?
Examples
Conclusions
4/12
CADGME conference,
Linz. JULY 2009
Introduction (II)
Introduction
Geometry at University level
The discipline of CAD
Why Geogebra?
Examples
Conclusions
• Bezier, B-Splines, NURBS curves: properties DGS.
• Algorithms DGS
• Surfaces CAD programs
• Why? Develop specific applications
5/12
CADGME conference,
Linz. JULY 2009
• Geometry contents very different
• Geometry contents reduced
• CAD: not only buttons, but algorithms
• Shipyard: CAD user, CAD application developer
• DGS: multimedia contents
• DGS shows to be an attractive and effective way to
develop spatial abilities
Geometry at university level
Technical Drawing
Basic CAD
Descriptive Geometry
CAD (Comp. Geometry)
Introduction
Geometry at University level
The discipline of CAD
Why Geogebra?
Examples
Conclusions
6/12
CADGME 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
Introduction
Geometry at University level
The discipline of CAD
Why Geogebra?
Examples
Conclusions
7/12
CADGME conference,
Linz. JULY 2009
• Algorithms graphically and analytically
• Free
• Step by step
Why Geogebra? (I)
Introduction
Geometry at University level
The discipline of CAD
Why Geogebra?
Examples
Conclusions
8/12
CADGME conference,
Linz. JULY 2009
• Geometric commands important for CAD
Why Geogebra? (II)
Introduction
Geometry at University level
The discipline of CAD
Why Geogebra?
Examples
Conclusions
9/12
CADGME conference,
Linz. JULY 2009
• NURBS (Non Uniform Rational B-splines): algebraically
• NURBS (Nobody Understand Rational B-splines)
Examples (I)
Introduction
Geometry at University level
The discipline of CAD
Why Geogebra?
Examples
Conclusions
10/12
CADGME conference,
Linz. JULY 2009
• Conics as NURBS
Examples (II)
• Projective geometry
Introduction
Geometry at University level
The discipline of CAD
Why Geogebra?
Examples
Conclusions
11/12
CADGME conference,
Linz. JULY 2009
• DGS: understanding algorithms bellow CAD programs
• DGS: 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+DGS = positive for developers and programmers
Conclusions
Introduction
Geometry at University level
The discipline of CAD
Why Geogebra?
Examples
Conclusions
12/12
CADGME conference,
Linz. JULY 2009
Thank you!
Thank you!
Introduction
Geometry at University level
The discipline of CAD
Why Geogebra?
Examples
Conclusions