Motivation ______________________


Geometry is at the very core of architectural design—from the very early conceptual form finding to the more detailed assembly and construction. In prac¬tice, architecture designers are showing an increasing interest in being able to compute and fabricate non-simple and sometimes intricate geometric forms.

  Olympic Stadium

(Right) Mercedes Benz Museum, UN Studio, Stuttgart


Contemporary approaches to modeling architectural geometry are computational—this is reflected in designers wanting much more parametric control over the generative process; in turn, this enhances the efficiency with which they can navigate design variations, analyze design artifacts and explore design manifestations.

  Olympic Stadium

(Right) Roof of the Olympic Stadium in Munich, Germany
[A minimal surface]

Constructing geometry both parametrically and computationally poses challenges for the designer—particularly to those with little formal geometry training; more so—when required to tackle evolving issues between complex geometry and architecture. There is a compelling and emerging need to better understand concepts that support geometric constructions—to develop (new) computational schemes that can intelligently or ably assist designers in managing geometry data and propagating designs.

  Olympic Stadium

(Right) London City Hall, Norman Foster and Partners

Course Description _____________

This is an introductory course to parametric modeling.  The course has no prerequisites.

This year the course is being offered in two parts each as a mini-course.  Ramesh will instruct the first part of the course, and Josh, lead a project for the second part of the course.  The course will consist of lectures, computer cluster instruction and work/instruction in the digital fabrication (dFab) lab

The first part of the course will introduce:

  • Elements of parametric design and design patterns

    The structure of parametric design processes, their characteristics and reusable parametric design approaches

  • Fundamental concepts of geometric modeling:

    Spatial coordinates, projections, Boolean operations, formal transformations, freeformb surface creation, surface development and deformations aimed at architecture applications, discretization and meshing, digital prototyping and geometry reconstruction. Lectures will focus on concepts in computational geometry that can be applied to parametric architectural geometry modeling.

  • Parametric modeling techniques and tools:

    Tools that are available to model design parametrically will be introduced in this class to illustrate the construction of geometrical relationships among complex shapes. The lectures will focus on hands-on techniques that can be applied to the design process, to extend the efficiency and productivity of work during the process.

  • The second part of the course will reinforce the above fundamentals and introduce students to parametric work flows in digital fabrication:

  • Parametric variation

    Coupling CNC fabrication with parametric modeling allows for mass-customization, high-volume design iteration, custom detailing in architectural design.

  • Modeling of complex assemblies

    Using digital workflows to describe, organize, and construct geometrically complex and dimensionally unique components.

  • Modeling for fabrication

    Using 3D digital modeling to efficiently produce components without the need for 2D representation.  Adjusting global forms can automatically update individual components.

  • For practical reasons, the course uses Rhinoceros 5 and Grasshopper and the following add-ons: Hoopsnake, ghPython, Weaverbird, Kangaroo, Firefly, gHowl, Galapagos, Geometry Gym, and Karamba

    The course is a pre-requisite for a revised extended scripting course to be offered in the Spring Semester.

    Josh Bard will separately supply a more detailed project description for the second half of this course.

    Course Topics __________________

    Part I — The Basics

    The topics covered in the first mini are:

  • Basics of geometric modeling: coordinates and transformations
  • Surface Construction: Freeform curves to surfaces
  • Surface Development: surface offsets, sweeping and evolutions
  • Deformations
  • Discretization: Converting surfaces to meshes
  • Digital Prototyping and Fabrication, Geometry Reconstruction
  • Other topics

    VoronoiSurfaceGuide TS: 01-big+15
  • Surface refinement01

    Surface refinement02

    Surface refinement03

    Surface Refinement

    Relationship definition file for Bird’s Nest
    pattern generations



    Grasshopper Example


    Part II — Drawn Out

    This part deals with parametric techniques for representing constructing architectural space.

    Description —

    Anamorphic projection is a long-standing representational technique closely linked to the abstracting methodologies of perspectival construction. Historically, anamorphosis was used to cloak discursive content – often erotic or political in nature – within an image. The illusion was only to be revealed from a privileged vantage point (e.g. a throne). The technique continues to fascinate, and also suggests new currency for architects, less as a strategy for concealing content or visual trickery and more as a method for disrupting spatial presuppositions thereby pushing physical space to the foreground of perception amidst our overwhelmingly technologically mediated experience. The use of parametric modeling software to study projection also suggests the possibility of multiple viewpoints within a spatial continuum as opposed to a singular privileged view.

    Design Problem —

    In teams, students will construct a parametric drawing machine based on historic modes of projection in visual representation. Students will use these parametric machines to construct material projections in physical space that are legible from multiple viewpoints.

    Course Objective _______________

    This course is to prepare students for modeling architectural geometry through development of parametric schemes for architecture applications.

    This course supplies the basis of understanding parametric geometric construction mechanisms.

    Reference: texts and readings _____

    Other books and readings will be added to this list

    Course Requirements ___________

    Each part has requirements contributing equally to the final grade.

    • (Part I)  Three modeling assignments
    • (Part II) Project