Graphs

((('''Index'''
* [#AddGraph|How to add an empty graph]
* [#PlotEquations|Plot equations]
* [#PlotMatrices|Plot matrices]
* [#MultiplePlots|Multiple plots]
* [#SpecialPlots|Special plots (words, points, colors...)]
* [#AnimatedPlots|Animated plots]
* [#PlotDomains|Plot domains]
* [#PlotByIndex|Plot vectors by index]
* [#PlotHandling|Plot handling]
* [#KnownIssues|Known issues]
* [#History|History]
* [#SeeAlso|See also]
* [#References|References])))


{BR}[anchor|#AddGraph]
==How to add an empty graph==

You can add a 2D/3D Graph from the '''Insert''' item in the menu bar:

{{{{Insert > Plot > 2D / 3D

[image|add new graph|{UP}graphs/wiki-01-01.png]}}}}

{{{{Keyboard shortcut: a 2D Graph can be added directly typing &#64;}}}}

Now an empty graph will be added:

{{{{[image|empty graphs|{UP}graphs/wiki-01-02.png]}}}}


{BR}[anchor|#PlotEquations]
==Plot equations==

Variables to plot equations must be:

* '''x''' for 2D graphs

* '''x''' and/or '''y''' for 3D graphs

* '''t''' to [Animations|animate 2D and 3D graphs]

{{{{NOTE: variables are case sensitive (x is different from X)}}}}

You have multiple ways to plot equations:

{{{{Directly from the plot window

[image|single equation - direct input|{UP}graphs/wiki-02-01.png]}}}}

{{{{Indirectly, building your equation outside the plot window

[image|single equation - indirect input|{UP}graphs/wiki-02-02.png]}}}}


{BR}[anchor|#PlotMatrices]
==Plot matrices==

You can plot figures from [Matrices|matrices] (directly or indirectly):

* 2 columns matrices for 2D plots

* 3 columns matrices for 3D plots

{{{{[image|single equation - matrices|{UP}graphs/wiki-03-01.png]}}}}


{BR}[anchor|#MultiplePlots]
==Multiple plots==

You can plot multiple equations/matrices on the same graph using the [Multiple values|Multiple values item] on the Functions [Toolbox|toolbox]:

{{{{[image|multiple equations/matrices - example|{UP}graphs/wiki-04-01.png]}}}}

Each "value" will be colored differently (cycling between 6 colours, in the following order: blue, red, green, magenta, orange and brown)

{{{{[image|multiple equations/matrices - colours|{UP}graphs/wiki-04-02.png]}}}}


{BR}[anchor|#SpecialPlots]
==Special plots (words, points, colors...)==

You can plot words or characters (strings) on your 2D graphs;

{{{{[image|special plots|{UP}graphs/wiki-05-01.png]}}}}

* Special characters (case sensitive) have position fixed on center on the given coordinates: '''+ . * o x''';

* Words, phrases or non-special characters have top-left corner of (virtual) textbox fixed on the given coordinates;

* Size and color columns are not required (so you can use a 3, 4 or 5 columns matrix);

* Values of size column are absolute, so the resize action does not affect the appearance of special plots;

* Many colors are allowed, using web format (like "#6699CC" or "#FF6699CC") or by name; here is a complete list of possible colors:

{{{{<!--PLEASE GROUP COLORS BY NAME-->
aliceblue, antiquewhite, aqua, aquamarine, azure,

beige, bisque, blanchedalmond, black, blue, blueviolet, brown, burlywood,

cadetblue, chartreuse, chocolate, coral, cornflowerblue, cornsilk, crimson, cyan,

darkblue, darkcyan, darkgoldenrod, darkgray, darkgreen, darkkhaki, darkmagenta, darkolivegreen, darkorange, darkorchid, darkred,
darksalmon, darkseagreen, darkslateblue, darkslategray, darkturquoise, darkviolet, deeppink, deepskyblue, dimgray, dodgerblue,

firebrick, floralwhite, forestgreen, fuchsia,

gainsboro, ghostwhite, gold, goldenrod, gray, green, greenyellow,

honeydew, hotpink,

indianred, indigo, ivory,

khaki,

lavender, lavenderblush, lawngreen, lemonchiffon, lightblue, lightcoral, lightcyan, lightgoldenrodyellow, lightgray, lightgreen,
lightpink, lightsalmon, lightseagreen, lightskyblue, lightslategray, lightsteelblue, lightyellow, lime, limegreen, linen,

magenta, maroon, mediumaquamarine, mediumblue, mediumorchid, mediumpurple, mediumseagreen, mediumslateblue, mediumspringgreen,
mediumturquoise, mediumvioletred, midnightblue, mintcream, mistyrose, moccasin,

navajowhite, navy,

oldlace, olive, olivedrab, orange, orangered, orchid,

palegoldenrod, palegreen, paleturquoise, palevioletred, papayawhip, peachpuff, peru, pink, plum, powderblue, purple,

red, rosybrown, royalblue,

saddlebrown, salmon, sandybrown, seagreen, seashell, sienna, silver, skyblue, slateblue, slategray, snow, springgreen, steelblue,

tan, teal, thistle, tomato, turquoise,

violet,

wheat, white, whitesmoke,

yellow, yellowgreen
}}}}

{{{{[image|colors|{UP}graphs/wiki-05-02.png]}}}}

{{{{NOTE: You can use darkblue, DarkBlue, Dark Blue (recommended), DARKBLUE, D a R k B l U e ant etc...
::::   all spaces will be removed and color name will be converted to lower case chars.}}}}

{{{{[image|colors|{UP}graphs/wiki-05-03.png]
[image|colors|{UP}graphs/wiki-05-04.png]
[image|colors|{UP}graphs/wiki-05-05.png]}}}}

{{{{NOTE: web colors are allowed both in hexadecimal RGB ("#RRGGBB") or hexadecimal aRGB ("#aaRRGGBB") format.}}}}

{{{{NOTE: You can use number instead of color name or web-color.

Number composing rule is a bit complex, but it is similar with web-colors: color represented as a hexadecimal number where
- first pair is opacity;
- second pair is a Red Component;
- third pair is a Green Component;
- fourth pair is a Blue Component;
For example FF00FF00 is a full-opacity Green color (FF 00 FF 00).

When you have a hexadecimal number you need to convert it to decimal number to use it in SMath Studio.
There are snippets to make easy this conversion ([#color snippets|see References]).

Note that because of the maximum 32-bit integer is 2147483647 (0xFFFFFFFF/2) and FF00FF00 = 4278255360 (i.e. greater then the max. integer),
then Green is FF00FF00-0xFFFFFFFF-1=-16711936.
}}}}


{BR}[anchor|#AnimatedPlots]
==Animated plots==

See [Animations|animations]

{{{{[image|animated plot|{UP}graphs/wiki-06-01.gif]}}}}


{BR}[anchor|#PlotDomains]
==Plot domains==

If you want to define a plot inside a specified domain you can follow two ways:

{{{{Using an if/else statement

[image|single equation - direct input|{UP}graphs/wiki-08-01.png]}}}}

{{{{NOTE: Any text (empty or not) or message from the [error|error] function will be ignored.}}}}

{{{{Using booleans as function parameters

[image|single equation - indirect input|{UP}graphs/wiki-08-02.png]}}}}

{{{{NOTE: infinite values will be ignored.}}}}


{BR}[anchor|#PlotByIndex]
==Plot vectors by index==

It is possible to plot a single column vector using as index the x variable.

In the plot any x value will be rounded and, if possible, the corresponding vector element will be used as y value:

{{{{[image|plot by index|{UP}graphs/wiki-09-01.png]}}}}


{BR}[anchor|#Units]
==Units==

It is possible to use [Units|units of measurement] inside plots.

Because the output units of calculations are base units (f.e. meters for any length unit), you have to scale the input or adjust the viewport.

{{{{[image|plot using units|{UP}graphs/wiki-10-01.png]}}}}


{BR}[anchor|#PlotHandling]
==Plot handling==

A dedicated plot palette allow some operations on the graph.

{{{{[image|plot handling - palette|{UP}graphs/wiki-07-01.png]
# '''Rotate''': rotate 3D graphs (see [#KnownIssues|Known issues]).
# '''Scale''': if you roll your mouse wheel it zooms both axes together. If you hold 'control' keyboard key (CTRL) at the same time it just zooms the vertical axis;{BR}if you use the mouse wheel holding the 'shift' keyboard key (&uarr;) it zooms the horizontal axis. This does not affect the appearance of special plots.
# '''Move''': drag the graph up or down, left or right; by default you can move the graph also by clicking and holding the left mouse button on the graph.
# '''Graph by points''': show functions/straight lines as a set of points; could be useful to highlight discontinuities.
# '''Graph by lines''': show functions/straight lines as lines (default).
# '''Refresh''': restore the default view of the graph (axes origin moved to the graph center and zoom with default limits).}}}}

Clicking with the right mouse button on the graph appears a context menu that contains other options.

{{{{[image|plot handling - context menu|{UP}graphs/wiki-07-02.png]}}}}


{BR}[anchor|#KnownIssues]
==Known issues==
{| cellspacing="0" cellpadding="8" border="0" style="text-align: center; width: 100%; background-color: #ecffec;"
|-
| style="color: green; font-weight: bold; font-style: italic; font-size: 11px;" | to  inform the developers about issues you found out use the [https://smath.com/bts/|Issues Tracker] or the forum: [https://en.smath.com/forum/yaf_topics15_Bugs-and-Problems.aspx|Bugs & Problems]
|}

There are several main known issues about graphs:
* grids are available in power of two only;
* axes limits are available by mouse wheel only;
* 3D plots loose alignments opening the worksheet;
* 3D coordinates are left-handed;


{BR}[anchor|#History]
==History==

* SMath [http://en.smath.info/forum/default.aspx?g=posts&m=450|0.78] (stable): Added ability to Zoom graphs by mouse wheel;
* SMath [http://en.smath.info/forum/default.aspx?g=posts&m=870|0.82.3477] (stable): Added ability to plot multiple graphs on the canvas (2D & 3D): multiple Graphs can be specified by functions or/and points at the same time; +/- and -/+ operators also can be used; 2D Graphs now can be inserted into the page by pressing "@" symbol;
* SMath [http://en.smath.info/forum/default.aspx?g=posts&m=1013|0.85] (stable): Added ability to separately change axis scale factor on 2D graphs using Ctrl/Shift + Mouse Wheel;
* SMath [http://en.smath.info/forum/default.aspx?g=posts&m=3596|0.89.8] (Beta): Added ability to draw text and special characters on the 2D Plot Control canvas;
* SMath [http://en.smath.info/forum/default.aspx?g=posts&m=5857|0.90] (stable): Graph animation implemented; Plot 2D and Plot 3D buttons removed from the math toolbar panel;
* SMath [http://en.smath.info/forum/default.aspx?g=posts&m=6807|0.94] (stable): Added support for colors specifying for the special objects and strings into the Plot Region using web format (like "#6699CC");


{BR}[anchor|#SeeAlso]
==See also==

* [Animations|Animations]
* [Matrices|Matrices]
* [error|error]


{BR}[anchor|#References]
==References==

Tutorials and examples:
* Graphs Basics ([{UP}Tutorials%2fGraphsBasics10152010.pdf|PDF]|[{UP}Tutorials%2fGraphsBasics10152010.zip|zip])
* [{UP}Tutorials%2fSMathStudioGraphs2%263DExamples.pdf|Examples of 2D & 3D graphs v0.85 (pdf)]
* [{UP}graphs%2fgraphs%20wiki.zip|Graphs wiki] (plots shown in this page)

[anchor|#color snippets]Color snippets (to help with color handling):
* [{UP}graphs%2fwebColors.zip|Color Snippet (hexadecimal with alpha channel)]
* [{UP}graphs%2fRGBcolor.zip|Color Snippet (RGB with 0-255 alpha channel)]
* [{UP}graphs%2fRGB-RGBA colors.zip|Color Snippet (RGB and RGBA with CSS3 compatible behavior)]