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Parametric Geometry

Theoretical lectures on mathematical modeling of shapes and objects

The course is about surface and curve modelling by using mathematical functions and Descriptive Geometry.

The students will learn how to build parametric models for many specific purposses, ranging from the fitting of a shape to the animation of CAD created objects.

GrassHopper will be the tool of choice to implement examples and ideas throughout the course.


  1. Coordinate systems and their application to CAD.
  2. Analytic Geometry (Part 1): vectors, lines and planes. Solids. Examples from art, design and architecture.
  3. Analytic Geometry (Part 2): transformation geometry. Emblematic buildings that can be explained as transformations of simple solids.
  4. Introduction to Differential Geometry: the parametrization of curves and surfaces. A mathematical insight into CAD: the freeform tools. The ruled and other simply constructible surfaces. Introduction to resistance through form. Analysis of emblematic buildings.
  5. Putting things at work: from simple CAD geometrical models, via visual programming and abstract algorithms, to mathematically described parametric complex models.


Mathematics at upper secondary level or higher. Basic notions of descriptive geometry and CAD.


  1. Theoretical lectures on the mathematical modeling of shapes and objects, with architectural examples.
  2. Practical lectures on parametrically enhanced geometrical modeling.
  3. Practical elements of data structures and programming in Grasshopper.
  4. Solving mathematical and geometrical short exercises both by hand and in Grasshopper.


The final mark is the overall weighted average of:

  1. Handing in the class exercices (40%)
  2. Writing and presenting an original essay on some freely chosen topic relevant to the course (30%)
  3. A final individual exercise (30%)