The University of Texas at Austin School of Architecture

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fall 2008

ARC 351R:
Advanced Descriptive Geometries in Architecture

Vincent Snyder

This course will examine, define, reconsider, and apply a variety of precise geometrical techniques to analyze, describe, generate and refine three dimensional architectural form. Therefore, we will consider the theoretical and practical applications of numerous historically definitive techniques of constructed representation--both manual and digital-- in conjunction with algebraic and trigonometric mathematical analyses. It is important to highlight that the student will have the option of performing the “manual“ techniques by conventional graphite and/ or a translation into a drafting program and/or a translation into a 3-d modeling program but strictly limited to point/ line operations in two dimensional formats. Additionally, the software program Rhino is preferred, however, the techniques examined may be equally achieved with any 3-d modeling program such as Viz, Form-Z, 3-d AutoCad,etc. (Note: This is not a proprietary 3-d Digital Modeling course)

While students are required to have had instruction to the pre-calculus mathematical fundamentals, any primary material will be re-introduced by the instructor with an emphasis on the development of complexity through base principles rather than many current graphically expedient techniques which tend to alleviate the designer of definitive formal and descriptive responsibility. In fact, the examination of the selective techniques from various architects and artists will illustrate the multi-faceted relationships in which specific, exacting mathematical and geometrical applications have historically engaged the constructional, scientific, artistic, cosmological and religious influences of their time.

The mathematical level of investigation will be determined by the students’ level of interest and successful progression. (While topological geometries embedded within the current modeling programs involving such operations as Bezier curves, parametric design, algorithms, non-uniform rational b-splines, etc. will be briefly discussed, their comprehensive application is not anticipated. However, the extensive material that is covered in this course is specifically intended to provide a natural extension into such topics of advanced manipulations).


Initially, reading and graphic/physical 2-d and 3/d problem assignments will be issued weekly or bi-weekly as preparatory work towards the culmination of geometrically precise, complex 3-dimensional architectonic model(s) designed and manipulated by the student.

Recommend Texts:

Technical Descriptive Geometry, B. Leighton Wellmann

The Projective Cast, Robin Evans

The Science of Art, Martin Kemp

Additional Readings and Texts (partial):

Architectural Principles in the Age of Humanism, R. Wittkower

The Modulor 1 & 2, Le Corbusier

Mathematics of an Ideal Villa, Colin Rowe


Any student with a documented disability (physical or cognitive) who requires academic accommodations should contact the Services for Students with Disabilities Office at 471-6259 or 471-4641 TTY.