364 lines
34 KiB
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364 lines
34 KiB
HTML
<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Understanding and using different scales on the axis</title><link rel="stylesheet" type="text/css" href="manual.css"><meta name="generator" content="DocBook XSL Stylesheets V1.76.0"><link rel="home" href="index.html" title="JpGraph Manual"><link rel="up" href="ch14.html" title="Chapter 14. Common features for all Cartesian (x,y) graph types"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Understanding and using different scales on the axis</th></tr><tr><td width="20%" align="left"> </td><th width="60%" align="center">Chapter 14. Common features for all Cartesian (x,y) graph types</th><td width="20%" align="right"> </td></tr></table><hr></div><div class="sect1" title="Understanding and using different scales on the axis"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="id2544834"></a>Understanding and using different scales on the axis</h2></div></div></div>
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<div class="sect2" title="Different scale types"><div class="titlepage"><div><div><h3 class="title"><a name="id2544880"></a>Different scale types</h3></div></div></div>
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<p>The scale of the graph axis are controlled by either</p>
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<p>
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</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
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<p><code class="code">Graph::SetScale()</code> which can take on of the following
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strings as argument</p>
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<p>"intint", "intlin", "intlog", "linint", "linlin", "linlog",
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"logint", "loglin", "loglog", "textint", "textlin", "textlog",
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"datint","datlin","datlog"</p>
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<p>The first half of the string argument specifies the x-axis scale
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and the second half of the string specifies the y-axis scale. When
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an y2 or multiple y-scales (see ?? </p>
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</li></ul></div><p>
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</p>
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<div class="sect3" title="Numerical scale types"><div class="titlepage"><div><div><h4 class="title"><a name="id2544899"></a>Numerical scale types</h4></div></div></div>
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<p>The scale for a basic graph is specified with a call to
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<code class="code">Graph::SetScale()</code> and supplying the wanted scales for the
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x- and y-axis. For numeric data there are three basic scales
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available</p>
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<p>
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</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
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<p>Integer scale "int"</p>
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</li><li class="listitem">
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<p>Linear scale (a.k.a decimal labels)</p>
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</li><li class="listitem">
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<p>Logarithmic scales </p>
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</li></ol></div><p>
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</p>
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<p>The choice of scale will affect how the autoscaling is done and how the
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labels will look. Choosing an integer scale will, as the name suggests,
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restrict the labels to integer and integer interval between the scale step
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(at each tick mark). The linear scale has no such restriction and can be
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considered a superset of the integer scale (even though the implementation
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is done in rather the opposite way). Labels for linear scale can have
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fraction intervals and will shows the decimal values by default in the
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labels. Finally the logarithmic scale will create a deca - logarithmic
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scale.</p>
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<p>The style of the labels can be formatted in two ways</p>
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<p>
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</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
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<p>By specifying a format string (in <code class="code">printf()</code>
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format) to be used by calling the method
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<code class="code">Axis::SetLabelFormatString()</code> The format string
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is interpretated according to the second parameter. If that
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parameter is "<code class="code">true</code>" then the format string will be
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assumed to give a date format as expected by the
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<code class="code">date()</code> function. This is an easy way to
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translate timestamp values to proper time/date labels.</p>
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</li><li class="listitem">
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<p>By specifying a callback function. The callback
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function/method will be called with the label as the only
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argument and must return the label that should be printed
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<code class="code">Axis::SetLabelFormatCallback()</code></p>
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<p>For example. An easy way to get 1000' separators for numbers
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is to add the PHP function number_format() as callback to the
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wanted y-axis as in</p>
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<p>
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</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
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</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$graph->yaxis->SetLabelFormatCallback('number_format');</span></pre></td></tr></table></div><p>
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</p>
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<p>Another example of using a callback function is to "revert"
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the y-axis. By default the y-axis grows from the bottom and up.
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But what if we want the y-axis to grow from top to bottom, i.e.
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the 0-value should be at the top and the largest value at the
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bottom?</p>
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<p>The way to accomplish this is to use a negative y-scale which
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the plot is made against (by negating all the data values in the
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data serie). This would then give the appearance that we want
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apart from the act that all labels will have a minus sign in
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front of them. By creating a callback function that just returns
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the absolute value of the label we can adjust that and we get
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the effect that we want. <a class="xref" href="ch14s07.html#fig.inyaxisex2" title="Figure 14.19. Inverted y-scale to show a dive profile (inyaxisex2.php)">Figure 14.19. Inverted y-scale to show a dive profile <code class="uri"><a class="uri" href="example_src/inyaxisex2.html" target="_top">(<code class="filename">inyaxisex2.php</code>)</a></code> </a>
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shows an example of a "dive-curve" where the sea-level is at the
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top of the graph to give better connection to this particular
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use-case.</p>
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<p>
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</p><div class="figure"><a name="fig.inyaxisex2"></a><p class="title"><b>Figure 14.19. Inverted y-scale to show a dive profile <code class="uri"><a class="uri" href="example_src/inyaxisex2.html" target="_top">(<code class="filename">inyaxisex2.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/inyaxisex2.png" alt="Inverted y-scale to show a dive profile (inyaxisex2.php)"></span> </div></div><p><br class="figure-break">
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</p>
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<p>
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</p><div class="note" title="Note" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Note</h3>
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<p>The dive profile in <a class="xref" href="ch14s07.html#fig.inyaxisex2" title="Figure 14.19. Inverted y-scale to show a dive profile (inyaxisex2.php)">Figure 14.19. Inverted y-scale to show a dive profile <code class="uri"><a class="uri" href="example_src/inyaxisex2.html" target="_top">(<code class="filename">inyaxisex2.php</code>)</a></code> </a> is an actual dive of one of the authors dives in the
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<span class="italic">Gulf of
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Bothnia</span></p>
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</div><p>
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</p>
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</li></ol></div><p>
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</p>
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</div>
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<div class="sect3" title="Textual scale types"><div class="titlepage"><div><div><h4 class="title"><a name="id2545118"></a>Textual scale types</h4></div></div></div>
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<p>There is only one pure textual scale type</p>
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<p>
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</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
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<p>Text scale ("text")</p>
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</li></ol></div><p>
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</p>
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<p>This type of scale is exclusively used for the x-axis.</p>
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<p>The primary use of this scale is to label bars in a bar graph. However, as
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will be shown this can also be used at other occasions to achieve various
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wanted effects. There is no concept of autoscaling for text scales. Instead
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the whole purpose of this type of scale is for the user to manually supply
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the wanted labels in an array using the method
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<code class="code">Axis::SetTickLabels()</code>.</p>
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<p>The other key difference for a text scale as compared to the numeric
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scales is that the labels are positioned in between the tick marks and not
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directly under them. This is the common practice to label bar graphs and
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hence this is the way text scale works.</p>
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</div>
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<div class="sect3" title="Date scale types"><div class="titlepage"><div><div><h4 class="title"><a name="id2545179"></a>Date scale types</h4></div></div></div>
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<p>This scale type only has one valid scale</p>
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<p>
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</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
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<p>Date scale ("dat")</p>
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</li></ol></div><p>
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</p>
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<p>This specific scale type will assume that the data values are timestamps
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and will properly format them to give "even" steps (in a time/date
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sense).</p>
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</div>
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</div>
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<div class="sect2" title="Manual vs automatic scale handling"><div class="titlepage"><div><div><h3 class="title"><a name="id2545212"></a>Manual vs automatic scale handling</h3></div></div></div>
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<p>Normally the scale is determined automatically in the library by analyzing the
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input data and making sure that a suitable scale is established that fulfill the
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following criteria:</p>
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<p>
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</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
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<p>The full dynamic scope of the data series can be displayed</p>
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</li><li class="listitem">
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<p>The step size between major tick marks (tick marks that have a
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label) is a multiple of either (1, 2, 5, 10 ) * 10 ^n, where the
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size of 'n' is determined by the dynamic range of the data.</p>
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</li><li class="listitem">
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<p>In addition the number of labels is dependent on the size of the
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graph. A smaller graph will have fewer labels since there is
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"physically" not enough room to show too many labels.</p>
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</li></ol></div><p>
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</p>
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<p>
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</p><div class="note" title="Note" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Note</h3>
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<p>Internally the auto scaling algorithm has fair amount of intelligence
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to try to make the scale in the same way a human would so ti. For
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example the origin has a specially strong attraction meaning that the
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autoscaling will try hard to make sure 0 is included in the scale as
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long as it "makes sense".</p>
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</div><p>
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</p>
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<p>Usually this works fine in most cases but there are always exception where
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exact control over the scale is wanted. For example to be able to compare
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several graphs that might otherwise get different scales. There are two ways of
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manually adjusting the scales.</p>
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<p>
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</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
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<p><span class="bold"><strong>Manual min/max values but with the tick
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marks automatically determined</strong></span></p>
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<p>In this case the exact min/max value of the scale is submitted to
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the SetScale() method call to set either (or both) of the x- and
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y-scale. Since the first two argument after the scale type
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determines the y min/max and the fourth and fifth argument specifies
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the x min/max this means that in order to specify the x scale the y
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scale must have some values. If the y axis should be left alone
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(i.e. to be autoscaled) then just put the "dummy" values (0,0) as
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placeholder in the method call. The following examples clarifies
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this.</p>
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<p>
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</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
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<p><code class="code">$graph->SetScale('intlin',0,0,-10,20);</code></p>
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<p>Y-scale is autoscaled and the x-scale is set to
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[-10,20]</p>
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</li><li class="listitem">
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<p><code class="code">$graph->SetScale('intlin',0,50);</code></p>
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<p>Automatic x-scale and manual y-scale with range
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[0,50]</p>
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</li><li class="listitem">
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<p><code class="code">$graph->SetScale('intlin','-10,10,-20,20);</code></p>
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<p>Manual x- and y-scale</p>
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</li></ul></div><p>
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</p>
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</li><li class="listitem">
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<p><span class="bold"><strong>Semi automatic (or semi
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manual)</strong></span></p>
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<p>This is a away to lock either the min or max value and let the
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auto scaling algorithm determine a suitable corresponding max and
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min value. This can be very useful to make sure that for example the
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0 value is always includeded even if the minimal value is so high
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that the autoscaling algorithm have chosen to start at a larger
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value. These two locked down values are set with the two
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methods</p>
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<p>
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</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
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<p><code class="code">Scale::SetAutoMin()</code></p>
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<p>Example:
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<code class="code">$graph->yaxis->scale->SetAutoMin(0);</code>
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This will lock the y-min to 0</p>
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</li><li class="listitem">
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<p><code class="code">Scale::SetAutoMax()</code></p>
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<p>Example:
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<code class="code">$graph->xaxis->scale->SetAutoMax(1000);</code>
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This will lock the x.max to 0</p>
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</li></ul></div><p>
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</p>
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</li></ol></div><p>
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</p>
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</div>
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<div class="sect2" title="Major and minor ticks"><div class="titlepage"><div><div><h3 class="title"><a name="id2545421"></a>Major and minor ticks</h3></div></div></div>
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<p>The final step in understanding the scaling is to understand tick marks. There
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are two types of tick marks, major and minor. Major tick marks are tick marks
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that have a label associated. Up to now we have assumed that the library adjusts
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where the tick marks are positioned and the inter spacing between tick marks. </p>
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<p>The tick object is available as an instance variable of the scale class which
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means that you can access and adjust the tick mark properties by
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accessing:</p>
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<p><code class="code">$Graph::Axis::Scale::ticks</code></p>
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<p>For further fine control of the scale it is possible to manually adjust the
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major and minor ticks using one of the three methods</p>
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<p>
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</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
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<p><span class="bold"><strong>Adjusting how dense the auto scaling
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algorithm should put the tick marks.</strong></span></p>
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<p>Even when using a fully automatic scaling it is possible to adjust
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how many tick marks that the algorithm should try to place on the
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scale. This is controlled with the method </p>
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<p>
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</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
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<p><code class="code">Graph::SetTickDensity($aYDensity,
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$aXDensity)</code></p>
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</li></ul></div><p>
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</p>
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<p>The y- and x-scale density can be set to one of the following
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(symbolic) values</p>
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<p>
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</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
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<p><code class="code">TICKD_DENSE</code>k</p>
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</li><li class="listitem">
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<p><code class="code">TICKD_NORMAL</code></p>
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</li><li class="listitem">
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<p><code class="code">TICKD_SPARSE</code></p>
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</li><li class="listitem">
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<p><code class="code">TICKD_VERYSPARSE</code></p>
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</li></ul></div><p>
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</p>
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<p>By default the density for all scales are set to
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<code class="code">TICKD_NORMAL</code>
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</p>
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<p>As a comparison <a class="xref" href="ch14s07.html#fig.manscaleex2" title="Figure 14.21. Fully automatic not so good scaling (manscaleex2.php)">Figure 14.21. Fully automatic not so good scaling <code class="uri"><a class="uri" href="example_src/manscaleex2.html" target="_top">(<code class="filename">manscaleex2.php</code>)</a></code> </a> is the exact
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same as <a class="xref" href="ch14s07.html#fig.manscaleex3" title="Figure 14.20. Setting tick density to TICKD_DENSE (manscaleex3.php)">Figure 14.20. Setting tick density to TICKD_DENSE <code class="uri"><a class="uri" href="example_src/manscaleex3.html" target="_top">(<code class="filename">manscaleex3.php</code>)</a></code> </a> with the difference
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that in this figure the density for the y-scale has been set to
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<code class="code">TICKD_DENSE</code></p>
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<p>
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</p><div class="figure"><a name="fig.manscaleex3"></a><p class="title"><b>Figure 14.20. Setting tick density to TICKD_DENSE <code class="uri"><a class="uri" href="example_src/manscaleex3.html" target="_top">(<code class="filename">manscaleex3.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/manscaleex3.png" alt="Setting tick density to TICKD_DENSE (manscaleex3.php)"></span> </div></div><p><br class="figure-break">
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</p>
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</li><li class="listitem">
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<p><span class="bold"><strong>Manually specifying the step size between
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each minor and major tick.</strong></span></p>
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<p>This is done using the method</p>
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<p><code class="code">LinearTicks::Set($aMajStep,$aMinStep=false)</code></p>
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<p>please note that this is a method of the Tick class which is
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available as an instance variable in the scale class</p>
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<p>Example:
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<code class="code">$graph->xaxis->scale->ticks->Set(20,5);</code></p>
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<p>This type of manual positioning of the tick marks might be useful
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if the scale has been set to some non-multiples of 1,2,5,10. The
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following examples will clarify this. In ?? the left graph is what
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we get after manually specifying the y min/max values to (3,35). In
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this case the auto scaling algorithm fails to assign "nice" steps to
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the y-axis so that the tick marks starts and begins at the min/max
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of the scale. If we manually set the tick distance to be (8,2), i.e.
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we set the major tick marks 8 units apart and the minor
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(non-labeled) tick marks 2 steps apart we get the much nicer result
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as shown in the right graph in ??</p>
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<p>
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</p><div class="informaltable">
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<table border="0"><colgroup><col class="c1"><col class="c2"></colgroup><tbody><tr><td>
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<p>
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</p><div class="figure"><a name="fig.manscaleex2"></a><p class="title"><b>Figure 14.21. Fully automatic not so good scaling <code class="uri"><a class="uri" href="example_src/manscaleex2.html" target="_top">(<code class="filename">manscaleex2.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/manscaleex2.png" alt="Fully automatic not so good scaling (manscaleex2.php)"></span> </div></div><p><br class="figure-break">
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</p>
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</td><td>
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<p>
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</p><div class="figure"><a name="fig.manscaleex1"></a><p class="title"><b>Figure 14.22. Manually specified tick distance which gives a much better appearance <code class="uri"><a class="uri" href="example_src/manscaleex1.html" target="_top">(<code class="filename">manscaleex1.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/manscaleex1.png" alt="Manually specified tick distance which gives a much better appearance (manscaleex1.php)"></span> </div></div><p><br class="figure-break">
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</p>
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</td></tr></tbody></table>
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</div><p>
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</p>
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<p>
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</p><div class="caution" title="Caution" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Caution</h3>
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<p>The major tick step must be an even multiple of the minor
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tick step. If this is not the case the library will
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automatically adjust the major step size to be the closest
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multiple of the minor step size.</p>
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</div><p>
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</p>
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</li><li class="listitem">
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<p><span class="bold"><strong>Specify the exact position for each single
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tick mark</strong></span></p>
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<p>This is often used to position only the major tick marks to be
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able to have labels at very specific points in the graph. One
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example of how to use this was shown in <a class="xref" href="ch08s07.html#fig.manualtickex2" title="Figure 8.8. Specifying manual ticks as fraction of Pi. (manualtickex2.php)">Figure 8.8. Specifying manual ticks as fraction of Pi. <code class="uri"><a class="uri" href="example_src/manualtickex2.html" target="_top">(<code class="filename">manualtickex2.php</code>)</a></code> </a> where the tick marks were
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positioned at factions of π. Another typical example is to place a
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label at exactly the beginning of a month. Since months have
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different lengths there is no other way if 100% precision is wanted.
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An example of this is shown in <a class="xref" href="ch14s07.html#fig.manualtickex1" title="Figure 14.23. Manually specifying the tick position for each month (manualtickex1.php)">Figure 14.23. Manually specifying the tick position for each month <code class="uri"><a class="uri" href="example_src/manualtickex1.html" target="_top">(<code class="filename">manualtickex1.php</code>)</a></code> </a>
|
||
</p>
|
||
<p>
|
||
</p><div class="figure"><a name="fig.manualtickex1"></a><p class="title"><b>Figure 14.23. Manually specifying the tick position for each month <code class="uri"><a class="uri" href="example_src/manualtickex1.html" target="_top">(<code class="filename">manualtickex1.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/manualtickex1.png" alt="Manually specifying the tick position for each month (manualtickex1.php)"></span> </div></div><p><br class="figure-break">
|
||
</p>
|
||
<p>
|
||
</p><div class="caution" title="Caution" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Caution</h3>
|
||
<p>When the tick position is manually set there should also
|
||
be a corresponding array of labels to be put at these
|
||
positions.</p>
|
||
</div><p>
|
||
</p>
|
||
</li><li class="listitem">
|
||
<p><span class="bold"><strong>Adjusting the size and on what side the tick
|
||
marks should be drawn</strong></span></p>
|
||
<p>The side on the axis which has the tick marks is adjusted with a
|
||
call to</p>
|
||
<p>
|
||
</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
|
||
<p>Axis::SetTickSide($aTickSide)</p>
|
||
<p>Possible options for the tick side are</p>
|
||
<p>
|
||
</p><div class="itemizedlist"><ul class="itemizedlist" type="circle"><li class="listitem">
|
||
<p>SIDE_UP</p>
|
||
</li><li class="listitem">
|
||
<p>SIDE_DOWN</p>
|
||
</li><li class="listitem">
|
||
<p>SIDE_LEFT</p>
|
||
</li><li class="listitem">
|
||
<p>SIDE_RIGHT</p>
|
||
</li></ul></div><p>
|
||
</p>
|
||
</li></ul></div><p>
|
||
</p>
|
||
<p>For example, the following lines added to a script would change
|
||
side of the labels and tick marks for the x-axis.</p>
|
||
<p>
|
||
</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
|
||
2
|
||
3
|
||
4
|
||
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags"><?php</span><span class="hl-code">
|
||
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">xaxis</span><span class="hl-code">-></span><span class="hl-identifier">SetLabelPos</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-identifier">SIDE_UP</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code">;
|
||
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">xaxis</span><span class="hl-code">-></span><span class="hl-identifier">SetTickSide</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-identifier">SIDE_DOWN</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code">;
|
||
</span><span class="hl-inlinetags">?></span></pre></td></tr></table></div><p>
|
||
</p>
|
||
<p>This technique can for example be used to put the x-axis at the
|
||
top of the graph as the following example shows.</p>
|
||
<p>
|
||
</p><div class="figure"><a name="fig.topxaxisex1"></a><p class="title"><b>Figure 14.24. Adjusting the side which have the tick marks and position the x-axis at the top <code class="uri"><a class="uri" href="example_src/topxaxisex1.html" target="_top">(<code class="filename">topxaxisex1.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/topxaxisex1.png" alt="Adjusting the side which have the tick marks and position the x-axis at the top (topxaxisex1.php)"></span> </div></div><p><br class="figure-break">
|
||
</p>
|
||
</li></ol></div><p>
|
||
</p>
|
||
<p>In passing we mention that there are additional ways to adjust the look and
|
||
feel of the tick marks which is discussed in the next section (<a class="xref" href="ch14s08.html" title="Adjusting the appearance of the scale labels">Adjusting the appearance of the scale labels</a>) in detail.</p>
|
||
</div>
|
||
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