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GEOGEBRA conference,

Linz. JULY 2009

Teaching Computer Aided Design with the use of Geogebra

Francisco PérezUniversidad Politécnica de Madrid.

Spain

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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

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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

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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

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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

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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

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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

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GEOGEBRA conference,

Linz. JULY 2009

• Geometric commands important for CAD

Why Geogebra? (II)

Presentation

Introduction

The discipline of CAD

Why GeoGebra?

Examples

Conclusions

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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

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GEOGEBRA conference,

Linz. JULY 2009

• Conics as NURBS

Examples (II)

• Projective geometry

Presentation

Introduction

The discipline of CAD

Why GeoGebra?

Examples

Conclusions

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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

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GEOGEBRA conference,

Linz. JULY 2009

Thank you!

Thank you!

Presentation

Introduction

The discipline of CAD

Why GeoGebra?

Examples

Conclusions