tikz-pgf
I would like to plot the shaded region between $y=\sin(x)$ and $y=0$ over $x \in [0, \pi]$ using TikZ and/or possible other packages which I don't know yet. Can you give some examples?
Specifically:
how to do the computation of the special function $\sin$?
how to specify the region in TikZ?
how to shade the region?
Thanks and regards!
Here's another way to do it without using intersections but using path clipping. Each path we draw, we also define a clip against this path. This does mean "drawing" the path twice: once to draw and once to clip against (and I don't see a quick way of merging these two since they have to happen at different times). One thing I like about this approach is that what the graphical package is doing is precisely what the mathematics is doing. That is, each inequality specifies a "clipping" of the plane, saying "After this, we're only interested in one side of this line and we throw away everything else.". That's exactly what a clip does.
\documentclass{article}
\pagestyle{empty}
\usepackage[svgnames]{xcolor}
\usepackage{tikz}
\usepackage{mathtools}
\def\nudge{.5}
\tikzset{axis/.style={ultra thick, Red!75!black, -latex, shorten <=-\nudge cm, shorten >=-2*\nudge cm}}
\tikzset{line/.style={thick,Green}}
\begin{document}
\begin{tikzpicture}
\draw[axis] (0,0) -- (4,0) node[right=2* \nudge cm] {\(x_1\)};
\draw[axis] (0,0) -- (0,4) node[above=2*\nudge cm] {\(x_2\)};
\begin{scope}
\clip (-\nudge ,-\nudge) rectangle (4+\nudge,4+\nudge);
\draw[line] (0,1) -- (4,4) coordinate (ineq1);
\draw[line] (0,5.5) -- (4,-.5) coordinate (ineq2);
\draw[line] (0,-5) -- (4,3) coordinate (ineq3);
\begin{scope}
\clip (0,1) -- (4,4) |- (0,0);
\clip (0,5.5) -- (4,-.5) -| (0,0);
\clip (0,-5) -- (4,3) |- (4,4) -| (0,0);
\fill[Red,opacity=.5] (0,0) rectangle (4,4);
\end{scope}
\draw[dashed,line] (0,1) -- (2,2) -- (3,1) -- (2,0);
\clip (0,1) -- (2,2) -- (3,1) -- (2,0) -| (0,1);
\fill[Blue,opacity=.5] (0,0) rectangle (4,4);
\end{scope}
\node[above right] at (ineq1) {\(\mathllap{-}3 x_1 + 4 x_2 = 4\)};
\node[below right] at (ineq2) {\(3 x_1 + 2 x_2 = 11\)};
\node[above right] at (ineq3) {\(2 x_1 - x_2 = 5\)};
\foreach \coord/\adj in {
{(2,2)}/right,
{(0,1)}/left,
{(0,0)}/below left,
{(2,0)}/below left,
{(2.5,0)}/below right,
{(3,1)}/right,
{(2,2.5)}/right%
} {
\fill \coord circle (2pt) node[\adj] {\coord};
}
\end{tikzpicture}
\end{document}
Other aspects of this answer:
\mathllap to adjust the placement of one of the labels (that's why mathtools is included).Here is my solution:
\documentclass[11pt]{article}
\usepackage{tikz}
\usetikzlibrary{shadings}
\begin{document}
\begin{tikzpicture}
\draw[top color=white,bottom color=red] (0,0) -- (1,2) -- (0,3) -- cycle;
\foreach \coordinate/\label/\pos in {{(0,0)/label1/above left},{(1,2)/label2/right},{(0,3)/label3/above right}}
\node[\pos] at \coordinate {\label};
\draw[->] (-5.0,0) -- (5.0,0) node[right] {$x$} coordinate(x axis);
\draw[->] (0,-5.0) -- (0,5.0) node[above] {$y$} coordinate(y axis);
\end{tikzpicture}
\end{document}
It gives:
The key points are basically two:
the foreach that allows to specify in one shot the coordinate (i.e. (0,0)) in which the label will be placed in a given position (i.e. above left);
the use of the shadings library that allows to shade the region; in the example the shading is vertical, but it is possible to insert different type of shadings (see 47 Shadings Library from the pgfmanual version April 25, 2012 / 46
Shadings Library from the pgfmanual version October 25, 2010).
Best Answer
This is explained in the sections “15.4 Filling a Path” and “19 Plots of Functions” in the TikZ manual (numbers refer to the 2.10 version).
A simple example (note that
\x rinterprets\xas radians; the TikZ'ssinfunction takes degrees as input):