tailieunhanh - From Spiral to Spline: Optimal Techniques in Interactive Curve Design

The total rebuilding of Pier A in 1995 and the construction of a link to Terminal 1 in 1998 was designed by the architect firm Holm & Grut A/S. The most characteristic feature of the pier is its modern version of fan vaulting supporting the aluminium wing structures that make up the roof. These curved roofs and the glass facades form reflecting surfaces that create the space and light that is the hallmark of Nordic architecture. Holm & Grut wanted to create a building that would give arriving passengers an immediate experience of Scandinavian design. And its architectural statement and choice of colours and materials, all emphasised by the. | From Spiral to Spline Optimal Techniques in Interactive Curve Design by Raphael Linus Levien A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Engineering-Electrical Engineering and Computer Sciences in the GRADUATE DIVISION of the UNIVERSITY OF CALIFORNIA BERKELEY Committee in charge Professor Carlo Sequin Chair Professor Jonathan Shewchuk Professor Jasper Rine Fall 2009 From Spiral to Spline Optimal Techniques in Interactive Curve Design Copyright 2009 by Raphael Linus Levien Abstract From Spiral to Spline Optimal Techniques in Interactive Curve Design by Raphael Linus Levien Doctor of Philosophy in Engineering-Electrical Engineering and Computer Sciences University of California Berkeley Professor Carlo Sequin Chair A basic technique for designing curved shapes in the plane is interpolating splines. The designer inputs a sequence of control points and the computer fits a smooth curve that goes through these points. The literature of interpolating splines is rich much of it based on the mathematical idealization of a thin elastic strip constrained to pass through the points. Until now there is little consensus on which if any of these splines is ideal. This thesis explores the properties of an ideal interpolating spline. The most important property is fairness a property often in tension with locality meaning that perturbations to the input points do not affect sections of the curve at a distance. The idealized elastic strip has two serious problems. A sequence of co-circular input points results in a curve deviating from a circular arc. For some other inputs no solution with finite extent exists at all. The idealized elastic strip has two properties worth preserving. First any ideal spline must be extensional meaning that the insertion of a new point on the curve shouldn t change its shape. Second curve segments between any two adjacent control points are drawn from a two-parameter family and this .