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Geometric Continuity and Shape Parameters

2013
Given 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, 1991
This 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

1998
The 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

2013
Analogous 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, 2005
Wang Wen-tao, Wang Guo-zhao
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Geometrical Interpretation of the Shape Parameters

2013
The 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, 2021
Fenghua Zhang, Yanju Liu, Jin-Song Leng
exaly  

Optimal approach to shape parameter control

2006
When 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, 2019
Andreas Lendlein, Oliver E C Gould
exaly  

Bacterial cell shape

Nature Reviews Microbiology, 2005
Christine Jacobs-Wagner
exaly  

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