WORKSHOP/SEMINAR
PARAMETRIC RAPID PROTOTYPING

INSTRUCTOR Earl Mark ejmark@virginia.edu 225 Campbell Hall
TEACHING ASSISTANTS David Malda dcm9b@virginia.edu, Micheal Plehn mep4d@virginia.edu

Spring 2009 Syllabus

SUMMARY: The primary objective of the workshop/seminar is to exploremethods of harnessing a computer to generate parametrically controlled three-dimensional forms. The course examines a design workshop paradigm that ties together 1) 3D six-axis scanning, 2) parametrical programming and 3) three-dimensional printing or CNC fabrication as an cyclical activity.

SEMESTER LAYOUT: The first half of the term will focus predominantly on parametrical description. Through these activities, the workshops experiment with generative approaches to form description. Our goal will be to generate forms that could not as easily be achieved with traditional paper based media or single step CAD command processes. The second half of the term will focus on the link from parametrical programming to physical prototyping. The emhasis will be on 3D Printing (fuse deposition modeling). CNC milling and routing will also be examined in hands-on workshops.

SETTING: We will meet on Tuesdays and Thursdays in Campbell 105 from 2:00 to 3:30 p.m.. On some occasions the class will meet in Cambell 132, the CNC Fabrication Lab. Class participation will count towards 10 percent of the grade. Each of the first seven exercises will count towards 60 percent of the grade. The final exercise is a cumulative term project that will count towards 30 percent of the final grade. The atmosphere in the class is intended to be workshop based with relatively small enrollment to facilitate more dialog and interaction with the instructor and teaching assistant. The first-half of the term is somewhat more tightly structured with week to week exercises based upon the text developed on-line. Individually defined projects will be a signifant part of the second half of the term. There are no exams. Full attendance is expected. The primary software used this term, Generative Components, will be provided free to students enrolled in the subject. Although not the primary focus of the class, it may be possible for some students to adapt the lessons of the course to other 3D modeling programs and macro programming languages.

TEXT: Note, due to copyright issues, the links below will be available only from within the School of Architecture. The text Parametric Rapid Prototyping a draft manuscript authored by the instructor in web browser accessible format and intended for use in the seminar only. Individual Chapters in the book and the seminar exercises are not likely to be available until the week during which they are assigned. A course userID and password will be provided for access by students in the class.

PREMISE: The quantitative basis and invisible geometrical order of shapes found in nature and architecture may serve as a point of departure in design. A step-by-step computer scripted procedure can reduce to a simpler and more easily grasped understanding the development of a complex form. Such a procedure can be harnessed to a three-dimensional printer to produce forms, in some cases with interoperable components, not easily arrived at by manual construction. We will explore the development of computer scripted procedures to construct two and three-dimensional geometrical compositions that have architectural possibilities. Parameters used to drive these procedures may be based on fractal processes, such as found in cellular and crystalline forms, or based on other kinds of growth procedures that may describe trees, snowflakes, shells, radiolaria and other organic forms. Rapid prototyping the resulting forms provides a means for testing and analysis that can serve a designer's speculative imagination.

The following schedule is subject to revision.

• Introduction to course concepts and technology
• Introduction to macro programming and parametrical concepts
• Exercise 1: Geometrical modeling exercise
• Begin Reading Parametric Rapid Prototyping, Chapter 1: Introduction

• Procedures and the Object Oriented Geometrical Modeling
• Multiple Coordinate System(s)
• Procedures
• Continue to Read Parametric Rapid Prototyping, Chapter 1: Introduction
• Exercise 2: Geometric Primtiives and Serlio's Book on Geometry

• Variable declarations data-types in GC script
• Arithmatic Operations
• Procedure Abstraction
• Read Parametric Rapid Prototyping, Chapter 2: Introducing the Graphics Coordinate System and Simple Graphics Programs

• D’Arcy Thompson, On Growth and Form
• For loop
• While loop
• Relational Operators
• Conditional Operators
• Logarithmic Spiral
• Archimedes Curves
• Read Parametric Rapid Prototyping, Chapter 3: Relations Among Parts of a Graphic Figure
• Exercise 3: Simple Graphics Procedures [only available from within the School of Architecture]
  

• Tiling Pattens
• Rustication Patterns
• Greek Fret Pattern
• Exercise 4: Recurring Relations and Composition
• Read Parametric Rapid Prototyping, Chapter 4: Conditional Expressions

• Passing Arguments to Graphical Functions
• Kits of Parts
• Hierarchical Figures
• Read Parametric Rapid Prototyping, Chapter 5: Introducing Three Dimensional Geometry and Polynomial Surfaces

• Shape Generation Procedure with Variable Input
• The Classical Orders, Fermat Spiral, Daisy Head
• Exercise 5: Procedures that Express Conditional Patterns

• Printing 3D geometry
• Read Parametric Rapid Prototyping, Chapter 6: Recursion and Fractals
• Exercise 6: Polynomial Surfaces - Graphics to Physical Protyping
  

• Koch Curve
• Blancmange Curve
• Carpenter’s Algorithm
• Snow Flake variations
• Mountains, Trees and other Forms

• Conversion to alternative file formats 
• Tools, bits, and tool sets
• Axes and paths of description
• Translating 3-D object desriptions
• SAFETY

•  Tools, bits, and tool sets continued
• Axes and paths of description continued
• 3D scanning
  

• Boolean Operations - Logical Operators
• Read Parametric Rapid Prototyping, Chapter 7: Logic and Solid Geometry
• Final Exercise: Fractals, recursive, and other patterns
  
• Optional Exercise 8: Solid modeling and Boolean operators

• Read Parametric Rapid Prototyping, Chapter 8: Pre-fabrication Planning

• Preliminary review of computer procedures
• Review of CNC prototype
• Course summary and discussion
  

• One-on-one tutorial assistance - preparation for final submission
  

Selected Bibliography

Mark, Earl , Parametric Rapid Prototyping, 2009 (in draft)

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Arnheim, Rudolf. The dynamics of architectural form. Berkeley : University of California Press, 1977.

Bovill, Carl. Fractal geometry in architecture and design. Boston : Birkhluser, 1996.

Critchlow, Keith. Islamic patterns : an analytical and cosmological approach. London : Thames and Hudson, 1976.

Critchlow, Keith. Order in space: a design source book. London: Thames & Hudson, 1969.

Bergamini, David, Mathematics. New York, Time-Life Books, 1972.

Berkowitz, Jeff, Fracal Cosmos: The Art of Mathematics Design. Oakland, Ca.: Dharma Enterprises/Amber Lotus, 1994.

Hastings, Harold, and Sugihara, George. Fractals: A User’s Guide For The Natural Sciences, Oxford University Press, 1995.

Dixon, Robert. Mathographics. New York: Dover Publications, 1991.

Minsky, Marvin, The Society of Mind. Published by Simon and Schuster, 1986.

Mark, Earl (2003) Programming Architectural Geometry and CNC: Advancing A Design Paradigm with Mathematical Abstraction, Digital Design [21th eCAADe Conference Proceedings / ISBN 0-9541183-1-6] Graz (Austria) 17-20 September 2003, pp. 337-342.

Mark, Earl (2008) Animated Parametric Rapid Prototyping, Architecture in Computing [26th eCAADe Conference Proceedings / ISBN 978-0-9541183-7-2] Antwerpen (Belgium) 17-20 September 2008, pp. 897-904.

Mark, Earl, A Design Automation Paradox, Proceedings of CIB conference Conceptual Modeling of Buildings, CIB Working Commissions W74 and W78. Lund Institute of Technology, Lund, Sweden, 10.1988.

Mitchell, William and Stiny George. The Palladian Grammar, Environment and Planning B. May 1978, 5 - 18.

Serlio, Sebastiano, 1475-1554. The five books of architecture : an unabridged reprint of the English edition of 1611 / Sebastiano Serlio. Dover ed. New York : Dover Publications, 1982.

Books I-V of 'Tutte l'opere d'architettura et prospetiva' / by Sebastiano Serlio ; translated from the Italian with an introduction and commentary by Vaughan Hart and Peter Hicks. New Haven [Conn.] : Yale University Press, c1996-

Shore, John, The Sachertorte algorithm and other antidotes to computer anxiety, Viking, 1985

Stewart, Ian, From Here to Infininity: A Guide to Today’s Mathematics, Oxford University Press, 1996.

Stiny, George, Computing with Form & Meaning in Architecture, Journal of Architectural Education, Fall 1985.

Thomson, D’Arcy.On Growth and Form, Cambridge University Press, 1992.

Wittkower, Rudolf, Architectural principles in the age of humanism. Publication info: New York, W. W. Norton, 1971.