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Geometric Continuity and Shape Parameters
2013Given the two curves Q 1(u) and Q 2(u), consider the joint \(\frac{{{\text{Q}}_1 \left( u \right)}} {{{\text{Q}}_2 \left( u \right)}}\). Recalling equation (4.1), continuity of the unit tangent vector is achieved if $$\frac{{{\text{Q}}_1^{\left( 1 \right)} \left( 1 \right)}} {{\left| {{\text{Q}}_1^{\left( 1 \right)} \left( 1 \right)} \right ...
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Shape parameter deletion for Pólya curves
Numerical Algorithms, 1991This paper presents a simply change of basis technique for transforming one type of Pólya curves to another closely related Pólya curve form. Repeated use of this method yields algorithms for transforming one arbitrary Pólya form to another, as well as algorithms for evaluating, subdividing and differentiating Pólya curves.
Barry, Phillip J., Goldman, Ronald N.
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Microcalcification Evaluation Based on Shape Parameters
1998The study of mammographic microcalcifications provides useful information for the diagnosis of breast cancer in early stages. In order to develop a computer-aided diagnostc method to assist radiologists in differentiating malignant from benignant clustered microcalcifications in mammograms, this work has focused on the selection of a set of shape-based
J. Español +8 more
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Controlling Surfaces Using the Shape Parameters
2013Analogous to the demonstration of Beta-spline curves in Chapter 17, this chapter illustrates the use of the shape parameters in controlling surfaces. The effect of bias is shown in Figures 18.1, 18.2, and 18.3. These figures show Beta-spline surfaces with uniform shape parameter values of β1 = 1 with β2 = 0, of β1 = 2 with β2 = 0, and of β1 = 0.5 with ...
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Bézier curves with shape parameter
Journal of Zhejiang University-SCIENCE A, 2005Wang Wen-tao, Wang Guo-zhao
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Geometrical Interpretation of the Shape Parameters
2013The two inherent shape parameters of the Beta-spline, β1 and β2, provide further control of shape in addition to, and independent of, that supplied by the positional information specified by the control vertices. These shape parameters have the property that β1 = 1 indicates continuity of the parametric first derivative vector and β1 = 1 with β2 = 0 ...
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A Review of Shape Memory Polymers and Composites: Mechanisms, Materials, and Applications
Advanced Materials, 2021Fenghua Zhang, Yanju Liu, Jin-Song Leng
exaly
Optimal approach to shape parameter control
2006When describing the shape of a deformable object, two different approaches can be employed, referring either to local features or to global properties of the shape. Operating this choice influences both the modelling process of the system and the possibility of control- ling it.
CENEDESE, ANGELO, BEGHI, ALESSANDRO
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Reprogrammable recovery and actuation behaviour of shape-memory polymers
Nature Reviews Materials, 2019Andreas Lendlein, Oliver E C Gould
exaly

