File:Tangente par Bezier cubique.svg
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Size of this PNG preview of this SVG file: 320 × 600 pixels. Other resolutions: 256 × 480 pixels | 409 × 768 pixels | 546 × 1,024 pixels | 1,092 × 2,048 pixels.
Original file (SVG file, nominally 320 × 600 pixels, file size: 1 KB)
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Summary
[edit]| Description |
Français : Fonction tangentee approchée par une courbe de Bézier cubique (chemin SVG). NB : une courbe de Bézier quadratique ne donne pas une approximation satisfaisante.
English: Tangent function approximated by a quadraticic Bézier curve (SVG path). NB: a quadratic Bézier curve does not give a satisfying approximation. |
| Date | |
| Source | Own work |
| Author | Cdang |
This vector image was created with a text editor.
Please do not replace the simplified code of this file with a version created with Inkscape or any other vector graphics editor
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg width="320px" height="600px" version="1.1"
viewBox="0 0 320 200"
xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink">
<title> Titre </title>
<desc> Description </desc>
<defs>
<style type="text/css"><![CDATA[
path {
fill: none;
stroke: black;
stroke-width: 1
}
]]></style>
</defs>
<g id="tangenteC" transform="scale(0.5093, -0.5) translate(157.1, -100)">
<path
id="c1"
d="M0 0
C113.4 105.6, 129.7 192.5, 141.4 631.4"
/>
<use xlink:href="#c1"
transform="translate(0, 0) scale(-1, -1)" />
</g>
</svg>
The control points are obtained by optimisation, using Scilab:
n=10;
t = linspace(0, 1, n+1);
t($) = [];
x = %pi/2*t;
y = tan(x);
P0C = [x(1) ; y(1)] ;
P3C = [x($) ; y($)];
P1initC = 1/3*(P0 + P2);
P2initC = 2/3*(P0 + P2);
P12initC = [P1initC, P2initC];
// ****************************
// * Courbe de Bézier cubique *
// ****************************
function [X] = bezierC(P, t)
unMoinsT = [1 ; 1]*(1 - t);
tMat = [1 ; 1]*t;
tMat2 = tMat.*tMat;
tMat3 = tMat2.*tMat;
unVec = ones(t);
P0 = P(:, 1)*unVec;
P1 = P(:, 2)*unVec;
P2 = P(:, 3)*unVec;
P3 = P(:, 4)*unVec;
X = ((P0.*unMoinsT + 3*P1.*tMat).*unMoinsT + 3*P2.*tMat2).*unMoinsT...
+ P3.*tMat3;
endfunction
function [f] = diffquadC(P)
X = bezierC(P, t);
x = X(1, :); ybez = X(2, :); ytan = tan(x);
difference = ybez-ytan;
f = sum(difference.*difference);
endfunction
function [f, g, ind] = costfC(P12, ind)
epsilon = 1e-3;
P = [P0C, P12, P3C];
f = diffquadC(P);
g = zeros(P1);
for i = 1:4;
epsilonMat = zeros(P12);
epsilonMat(i) = epsilon;
dP = P + [[0 ; 0], epsilonMat, [0 ; 0]];
g(i) = diffquadC(dP)-f;
end
endfunction
// ***********************
// * programme principal *
// ***********************
[foptC, P12optC] = optim(costfC, P12initC);
PoptC = [P0C, P12optC, P3C];
X = bezierC(PoptC, t);
x1=linspace(0, X(1, $), 100);
y1 = tan(x1);
scf(1);
clf();
plot(X(1 ,:), X(2, :), "+");
plot(x1, y1, "g");
Licensing
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I, the copyright holder of this work, hereby publish it under the following license:
 
|
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 00:35, 1 December 2018 | | 320 × 600 (1 KB) | Cdang (talk | contribs) | better size, +axes |
| 17:18, 29 November 2018 |  | 320 × 600 (830 bytes) | Cdang (talk | contribs) | User created page with UploadWizard |
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