File:Lagrange simple.svg
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Size of this PNG preview of this SVG file: 512 × 450 pixels. Other resolutions: 273 × 240 pixels | 546 × 480 pixels | 874 × 768 pixels | 1,165 × 1,024 pixels | 2,330 × 2,048 pixels.
Original file (SVG file, nominally 512 × 450 pixels, file size: 5.6 MB)
This file is from a shared repository and may be used by other projects. The description on its file description page there is shown below.
Summary
DescriptionLagrange simple.svg |
English: derivative of https://en.wikipedia.org/wiki/File:Lagrange_simple.jpg |
Date | |
Source | Own work based on: Lagrange simple.svg en:File:Lagrange simple.jpg |
Author |
Original: Jacobmelgaard Vector: |
SVG development InfoField | This oversized trigonometry was created with Inkscape. This trigonometry uses embedded text that can be easily translated using a text editor. |
Source Code
The graph was made in Matlab with the following source code
% Function data [X,Y] = meshgrid(-2:0.1:2, -2:0.1:2); Z = (X.^2).*Y; % Constraint data t = -pi:0.01:pi; xc = sqrt(3)*cos(t); yc = sqrt(3)*sin(t); zc = xc.^2 .* yc; % Plot graph and constraint figure(); surface = surfc(X,Y,Z); hold on; plot3(xc, yc, zc, 'k', 'LineWidth', 2); plot3(xc, yc ,-10*ones(1,length(t)), 'k', 'LineWidth', 1); set(gcf, 'Color', [1 1 1]); set(gcf, 'Position', [46 107 767 682]); % Axis labels text(0.2, -3, -10, 'x'); text(2.5, -.5, -10, 'y'); text(-2.4, -2, 0, 'z'); % Annotations of the max and min points % Point indicating max #1 plot3(sqrt(2), 1, 2, 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(sqrt(2), 1, -10, 'kx', 'MarkerSize', 10, 'LineWidth', 2); text('Interpreter', 'latex',... 'String', '$$(\sqrt{2}, 1, 2)$$',... 'Position', [1.1 .1 2.1],... 'FontSize', 20); % Point indicating max #2 plot3(-sqrt(2), 1, 2, 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(-sqrt(2), 1, -10, 'kx', 'MarkerSize', 10, 'LineWidth', 2); text('Interpreter', 'latex',... 'String', '$$(-\sqrt{2}, 1, 2)$$',... 'Position', [-1.6 .1 2.1],... 'FontSize', 20); % Point indicating min #1 plot3(sqrt(2), -1, -2, 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(sqrt(2), -1, -10, 'kx', 'MarkerSize', 10, 'LineWidth', 2); plot3(0,1,-3,'kx') text('Interpreter', 'latex',... 'String', '$$(\sqrt{2}, -1, -2)$$',... 'Position', [.5 -.8 -1.4],... 'FontSize', 20); % Point indicating min #2 plot3(-sqrt(2), -1, -2, 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(-sqrt(2), -1, -10, 'kx', 'MarkerSize', 10, 'LineWidth', 2); text('Interpreter', 'latex',... 'String', '$$(-\sqrt{2}, -1, -2)$$',... 'Position', [-1.9 -.8 -1],... 'FontSize', 20); hold off; shading interp; view([25 18]); %plot2svg must be retrieved from http://www.zhinst.com/blogs/schwizer/ plot2svg;
Corresponding Mathematica code:
Block[{x, y, f = #^2 #2 &, g = #^2 + #2^2 &, c = 3}, sol = With[{max = MaxValue[{f[x, y], g[x, y] == c}, {x, y}]}, Solve[{f[x, y] == max, g[x, y] == c}, {x, y}, Reals] ]; Show[ Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2}, Mesh -> {{c}}, MeshFunctions -> g, PlotRange -> All, Boxed -> False, AspectRatio -> 1, PlotPoints -> 30, MeshStyle -> Cyan, PerformanceGoal -> "Quality", ColorFunction -> "DeepSeaColors"], Graphics3D[{Red, PointSize[Large], Point[{x, y, f[x, y]} /. sol]}] ] ]
Licensing
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- 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.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
Items portrayed in this file
depicts
7 August 2012
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 16:52, 7 August 2012 | 512 × 450 (5.6 MB) | commons>Zerodamage | Optimized, layers and text relocated |
File usage
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Metadata
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If the file has been modified from its original state, some details may not fully reflect the modified file.
Image title | Matlab Figure Converted by PLOT2SVG written by Juerg Schwizer |
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