An Approach to Blend Surfaces

Direct micrometer patterning and functionalization of polymer blend surfaces by using hot embossing

European Polymer Journal ◽

10.1016/j.eurpolymj.2014.07.020 ◽

2014 ◽

Vol 59 ◽

pp. 333-340 ◽

Cited By ~ 6

Author(s):

Marta Palacios-Cuesta ◽

Iskandar Vasiev ◽

Nikolaj Gadegaard ◽

Juan Rodríguez-Hernández ◽

Olga García

Keyword(s):

Polymer Blend ◽

Hot Embossing ◽

Blend Surfaces

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Quantification of polystyrene blend surfaces based on end group ToF-SIMS analysis

Applied Surface Science ◽

10.1016/s0169-4332(98)00626-6 ◽

1999 ◽

Vol 141 (1-2) ◽

pp. 1-20 ◽

Cited By ~ 27

Author(s):

X. Vanden Eynde ◽

P. Bertrand

Keyword(s):

Tof Sims ◽

Sims Analysis ◽

Blend Surfaces ◽

End Group

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A Simple Practical Criterion to Guarantee Second Order Smoothness of Blend Surfaces

15th Design Automation Conference: Volume 1 — Computer-Aided and Computational Design ◽

10.1115/detc1989-0024 ◽

1989 ◽

Author(s):

J. Pegna ◽

F.-E. Wolter

Keyword(s):

Second Order ◽

Geometric Design ◽

Computer Aided Geometric Design ◽

Common Boundary ◽

First Order ◽

Computer Aided ◽

The Common ◽

Blend Surfaces ◽

Continuous Curves ◽

Order Smoothness

Abstract Computer Aided Geometric Design of surfaces sometimes presents problems that were not envisioned by mathematicians in differential geometry. This paper presents mathematical results that pertain to the design of second order smooth blending surfaces. Second order smoothness normally requires that normal curvatures agree along all tangent directions at all points of the common boundary of two patches, called the linkage curve. The Linkage Curve Theorem proved here shows that, for the blend to be second order smooth when it is already first order smooth, it is sufficient that normal curvatures agree in one direction other than the tangent to a first order continuous linkage curve. This result is significant for it substantiates earlier works in computer aided geometric design. It also offers simple practical means of generating second order blends for it reduces the dimensionality of the problem to that of curve fairing, and is well adapted to a formulation of the blend surface using sweeps. From a theoretical viewpoint, it is remarkable that one can generate second order smooth blends with the assumption that the linkage curve is only first order smooth. This property may be helpful to the designer since linkage curves can be constructed from low order piecewise continuous curves.

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Geometrical Criteria to Guarantee Curvature Continuity of Blend Surfaces

Journal of Mechanical Design ◽

10.1115/1.2916918 ◽

1992 ◽

Vol 114 (1) ◽

pp. 201-210 ◽

Cited By ~ 30

Author(s):

Joseph Pegna ◽

Franz-Erich Wolter

Keyword(s):

Second Order ◽

Geometric Design ◽

Technical Requirement ◽

Computer Aided Geometric Design ◽

First Order ◽

Surface Patches ◽

Computer Aided ◽

Curvature Continuity ◽

Continuous Surface ◽

Blend Surfaces

Computer Aided Geometric Design (CAGD) of surfaces sometimes presents problems that were not envisioned in classical differential geometry. This paper presents mathematical results that pertain to the design of curvature continuous blending surfaces. Curvature continuity across normal continuous surface patches requires that normal curvatures agree along all tangent directions at all points of the common boundary of two patches, called the linkage curve. The Linkage Curve theorem proved here shows that, for the blend to be curvature continuous when it is already normal continuous, it is sufficient that normal curvatures agree in one direction other than the tangent to a first order continuous linkage curve. This result is significant for it substantiates earlier works in computer aided geometric design. It also offers simple practical means of generating second order blends for it reduces the dimensionality of the problem to that of curve fairing, and is well adapted to a formulation of the blend surface using sweeps. From a theoretical viewpoint, it is remarkable that one can generate second order smooth blends with the assumption that the linkage curve is only first order smooth. The geometric criteria presented may be helpful to the designer since curvature continuity is a technical requirement in hull or cam design problems. The usefulness of the linkage curve theorem is illustrated with a second order blending problem whose implementation will not be detailed here.

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