Study and Application of NURBS and Free-Form Surfaces for Design and Architecture

This paper studies different mechanisms and options that make possible the use of free-form curves for architectural design and drawing. The advantages and disadvantages of the different possibilities to choose from for the study of complex curves and surfaces are presented. Both architectural design and geometry subjects benefit from rigorous control of form and geometry, as well as the ability to modify and adjust curves and surfaces. Examples include generating a new drawing, vector digitizing, mathematical translation of freehand drawings, or applying cases in architecture or design. Some examples of the use of NURBS for the study of curves and surfaces used in the teaching of architectural design and geometry are shown. Its procedures could be applied to other examples. Among these are the accurate drawing of the apparent contour of a quadric surface, the drawing of its conic sections, the determination of the elements and intersection curves of two quadric surfaces, or the analysis of ruled surfaces such as helicoids. This requires knowledge and control of NURBS surfaces and curves as well as their contextualization in the mentioned areas.