منابع مشابه
Parametric Curves
(x, y) (x0, y0) (vx, vy) As shown on the left, the vector from p to a point (x, y) on the line must be either in the direction of (vx, vy) or in its opposite direction. Hence, the cross product of the two vectors must be zero, that is, (x− x0, y − y0)× (vx, vy) = 0. Expansion of the above cross product yields an implicit equation of the line that relates the x and y coordinates of every inciden...
متن کاملConstructing parametric quadratic curves
Constructing a parametric spline curve to pass through a set of data points requires assigning a knot to each data point. In this paper we discuss the construction of parametric quadratic splines and present a method to assign knots to a set of planar data points. The assigned knots are invariant under a ne transformations of the data points, and can be used to construct a parametric quadratic ...
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15 Parametric Curves And Surfaces 15.1 Parametric Curves Designing Curves • We don’t want only polygons. • Curves are used for design. Users require a simple set of controls to allow them to edit and design curves easily. • Curves should have infinite resolution, so we can zoom in and still see a smooth curve. • We want to have a compact representation. Parametric functions are of the form x(t)...
متن کاملComputational Techniques for Parametric Curves and Surfaces
Parametric curves and surfaces have b e en with us for a long time, and their use for object mode ling in Computer Graphics (as opposed to designing in CAD a pplica tions ) is still growing. There is sometimes. however, a r elucta nce t o use them because i t seems that the added power they give is more than otIse t by the complexity of their formulations and their computat.ions. The purpose of...
متن کاملAlgorithms for Intersecting Parametric and Algebraic Curves
The problem of computing the intersection of parametric and algebraic curves arises in many applications of computer graphics, geometric and solid modeling. Earlier algorithms are based on techniques from Elimination theory or subdivision and iteration. The former is however, restricted to low degree curves. This is mainly due to issues of efficiency and numerical stability. In this paper we us...
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ژورنال
عنوان ژورنال: Bulletin of Earthquake Engineering
سال: 2014
ISSN: 1570-761X,1573-1456
DOI: 10.1007/s10518-014-9670-5