Chapter 3: Implicit Surface Patches
نویسنده
چکیده
Everything should be made as simple as possible, but not simpler.
منابع مشابه
Chapter 3: Piecewise Polynomial Curves and Surfaces (Finite Elements)
1 Piecewise Polynomials 2 1.1 Barycentric and Bernstein-Bézier Bases . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 B-Spline Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Trimmed Freeform Patches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Implicit Algebraic Surface Patches . . . . . . . . . . . . . . . . . . . . . ....
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We propose an approach to model a smooth surface from a surface triangulation by implicit surface patches which are subsets of zero contours of trivariate functions defined on a collection of irregular triangular prisms. Comparing with the earlier approaches of surface modeling by implicit surfaces, the proposed scheme uses much less patches, and can easily capture sharp features. Furthermore, ...
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While it is possible to model a general closed surface of arbitrary genus as a single implicit surface patch, the geometry of such a global surface is di cult to specify, interactively control, and polygonize. The main di culties stem from the fact that implicit representations are iso-contours which generally have multiple real sheets, self{intersections and several other undesirable singulari...
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An implicit surface is defined as the zero set of a scalar function over 3-space. Sign of implicit function determines whether a point is inside or outside the implicit surface: f (P ) = 0 P is on the surface. < 0 P is inside the surface. > 0 P is outside the surface. An algebraic function is an implicit function where the function is polynomial. By using an A-patch representation of algebra...
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تاریخ انتشار 1997