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78 lines
5.3 KiB
Markdown
78 lines
5.3 KiB
Markdown
# Example (JKQTPlotter): Plotting Parsed Mathematical Functions as Line Graphs {#JKQTPlotterParsedFunctionPlot}
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# Plot Function f(x)
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This project (see `./examples/simpletest_parsedfunctionplot/`) demonstrates how to plot mathematical functions as line graphs. The functions are defined as strings that will be evaluated with the equation parser, integrated into JKQTPlotter.
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Note: See the example [Plotting Mathematical Functions as Line Graphs](https://github.com/jkriege2/JKQtPlotter/tree/master/examples/simpletest_functionplot) if you don't want to draw parsed functions, but want to provide a C function, or C++ functor!
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Adding an evaluated funtion to a graph is very simple:
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```.cpp
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JKQTPXParsedFunctionLineGraph* parsedFunc=new JKQTPXParsedFunctionLineGraph(plot);
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parsedFunc->setFunction("sin(x*8)*exp(-x/4)");
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parsedFunc->setTitle("user function");
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```
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As you can see a graph of the type `JKQTPXParsedFunctionLineGraph` is used, which plots a function that depends on the variable `x`. The given function is parsed and evaluated (see [`lib/jkqtcommon/jkqtpmathparser.h`](https://github.com/jkriege2/JKQTPlotter/blob/master/lib/jkqtcommon/jkqtpmathparser.h) for details on the features of the math parser). An intelligent drawing algorithm chooses the number of control points for drawing a smooth graph, with sufficient amount of details, by evaluating locally the slope of the function.
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In the example in [`test/simpletest_parsedfunctionplot/simpletest_parsedfunctionplot.cpp`](https://github.com/jkriege2/JKQtPlotter/tree/master/examples/simpletest_parsedfunctionplot/simpletest_parsedfunctionplot.cpp) we do not simply set a fixed function, but add a `QLineEdit` which allows to edit the function and redraws it, once ENTER is pressed:
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```.cpp
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JKQTPlotter* plot=new JKQTPlotter(&mainWin);
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QLineEdit* edit=new QLineEdit(&mainWin);
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edit->setToolTip("enter a function in dependence of the variable <tt>x</tt> and press ENTER to update the graph");
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// ...
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// 2. now we add a JKQTPXParsedFunctionLineGraph object, which will draw the function from
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// the line edit
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JKQTPXParsedFunctionLineGraph* parsedFunc=new JKQTPXParsedFunctionLineGraph(plot);
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plot->addGraph(parsedFunc);
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// finally we connect the line edit with the graph, whenever RETURN is pressed,
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// the graph is updated:
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auto updateGraphFunctor=
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[=]() {
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parsedFunc->setTitle("user function: \\verb{"+edit->text()+"}");
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parsedFunc->setFunction(edit->text());
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plot->redrawPlot();
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};
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QObject::connect(edit, &QLineEdit::returnPressed, updateGraphFunctor);
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QObject::connect(edit, &QLineEdit::editingFinished, updateGraphFunctor);
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edit->setText("sin(x*8)*exp(-x/4)");
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updateGraphFunctor();
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```
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This code snippet results in a plot like this:
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# Plotting with parameters
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As shown in [Plotting Mathematical Functions as Line Graphs](https://github.com/jkriege2/JKQtPlotter/tree/master/examples/simpletest_functionplot) you can also use externally set parameters in a plot function. These parameters can be double numbers and may be set with either as an internal parameter vector, or may be read from a parameter column (as shown in the [linked example](https://github.com/jkriege2/JKQtPlotter/tree/master/examples/simpletest_functionplot)). These parameters are available as variables `p1`, `p2`, ... in the function string. Here is a small example:
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```.cpp
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JKQTPXParsedFunctionLineGraph* parsedFunc=new JKQTPXParsedFunctionLineGraph(plot);
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parsedFunc->setFunction("sin(x*p1)*exp(-x/p2)");
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parsedFunc->setParamV(/*p1=*/8, /*p2=*/4);
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parsedFunc->setTitle("user function");
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```
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# Plot Function f(y)
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If you use the graph class `JKQTPYParsedFunctionLineGraph` instead of `JKQTPXParsedFunctionLineGraph`, you can plot functions `x=f(y)` (instead of `y=f(x)`). The function from the example above will then ahve to be changed to `sin(y*8)*exp(-y/4)` and the result will look like this:
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# Properties of the Adaptive Plotting Algorithm
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The adaptive capabilities of the rendering algorithm can be seen, when plotting e.g. `2/x`, which is drawn smoothely, even around the undefined value at `x=0`:
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With an additional checkbox in this example, you can switch drawing the actual sample points of the drawing algorithm on and off, by calling `parsedFunc->setDisplaySamplePoints(...)`. This can be used to debug the drawing algorithm and explore its parameters (which you can set with `setMinSamples()`, `setMaxRefinementDegree()`, `setSlopeTolerance()`, `setMinPixelPerSample()`). Here is an example of a 2/x function with shown sample points:
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