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2021 | Buch

Parametric Geometry of Curves and Surfaces

Architectural Form-Finding


Über dieses Buch

This textbook provides a thorough introduction to the differential geometry of parametrized curves and surfaces, along with a wealth of applications to specific architectural elements.

Geometric elements in architecture respond to practical, physical and aesthetic needs. Proper understanding of the mathematics underlying the geometry provides control over the construction. This book relates the classical mathematical theory of parametrized curves and surfaces to multiple applications in architecture. The presentation is mathematically complete with numerous figures and animations illustrating the theory, and special attention is given to some of the recent trends in the field. Solved exercises are provided to see the theory in practice.

Intended as a textbook for lecture courses, Parametric Geometry of Curves and Surfaces is suitable for mathematically-inclined students in engineering, architecture and related fields, and can also serve as a textbook for traditional differential geometry courses to mathematics students. Researchers interested in the mathematics of architecture or computer-aided design will also value its combination of precise mathematics and architectural examples.


Chapter 1. Parametrizations and Plane Curves
The chapter is devoted to the study of plane curves from the point of view of differential geometry. We focus our attention to classical curves and also on conics, and provide examples and other applications in architectural elements of the mathematical theory.
Alberto Lastra
Chapter 2. Parametrizations and Space Curves
The chapter describes the mathematical theory of space curves from differential geometry, and its application to specific architectural elements. We focus on the study of helices and some transformations on them.
Alberto Lastra
Chapter 3. Parametrizations and Regular Surfaces
The theory of the previous chapters is applied on surfaces and parametrizations. Elements involved in the study of regular surfaces are shown and illustrated with examples. Some classical surfaces in architecture are analyzed from the point of view of the theory described previously in the chapter.
Alberto Lastra
Chapter 4. Special Families of Surfaces
The chapter is devoted to the study of special families of surfaces which are of common use in architecture such as ruled surfaces and some of their subfamilies. The technique followed for achieving a parametrization is also described in detail. Quadrics, minimal and developable surfaces are also considered.
Alberto Lastra
Parametric Geometry of Curves and Surfaces
verfasst von
Dr. Alberto Lastra
Electronic ISBN
Print ISBN