File:Bernstein Polynomials.svg
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DescriptionBernstein Polynomials.svg |
English: Plot of Bernstein polynomial functions up to degree 4 with summation of all four functions to show characteristic of partition of one. Deutsch: Druck von Funktionen der Bernstein Polynome bis Grad 4 mit Summe über alle vier Funktionen zur Verdeutlichung der Partition der Eins. |
Date | |
Source | Own work |
Author | VisorZ |
Code in https://cloud.sagemath.com/projects (with bug fix):
# adapted from file without sum of Bernstein Polynomials by Kilom691
# http://commons.wikimedia.org/wiki/File:Bernstein_poly_4.svg
N = 4
rnb = rainbow(N + 1)
pt1 = sum(
plot(
binomial(N, i) * x ** i * (1 - x) ** (N - i),
0, 1,
legend_label=r'$B^{}_{}(u)$'.format(N, i),
color=rnb[i],
thickness=3,
aspect_ratio=1
)
for i in range(N + 1)
)
almostOne = 0.99999 # bug in sagemath, put it to 1.0 and BSum plot will vanish
var('i')
BSum = sum( binomial(N, i) * x ** i * (1 - x) ** (N - i), i, 0, 3 ) \
+ binomial(N, 4) * x ** 4 * (1 - x) ** (N - 4) * almostOne
pt2 = plot(
BSum,
0, 1,
legend_label='$\sum_{i=0}^{4} \, B^{4}_{i}(u)$', # code between $ .. $ uses LaTeX math commands to format equation
color='orange',
thickness=3
)
pt2.set_legend_options(loc=(0.37,0.5))
show( pt1 + pt2, figsize=6 )
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I, the copyright holder of this work, hereby publish it under the following license:
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- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 09:51, 11 May 2015 | 396 × 390 (41 KB) | VisorZ (talk | contribs) | Put summation equation to bottom of legend for a better logical order. | |
09:42, 11 May 2015 | 396 × 390 (41 KB) | VisorZ (talk | contribs) | Better spacing in sum equation in legend. | ||
09:38, 11 May 2015 | 396 × 390 (41 KB) | VisorZ (talk | contribs) | Bigger legend. | ||
09:29, 11 May 2015 | 531 × 525 (42 KB) | VisorZ (talk | contribs) | User created page with UploadWizard |
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Width | 317pt |
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Height | 312pt |