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TEACHING COMPUTER AIDED DESIGN WITH THE USE OF DYNAMIC GEOMETRY

Francisco PérezUniversidad Politécnica de Madrid.

Spain

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CADGME conference,

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• 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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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CADGME conference,

Linz. JULY 2009

Thank you!

Thank you!

Introduction

Geometry at University level

The discipline of CAD

Why Geogebra?

Examples

Conclusions