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I want to plot functions & integrals with vector variable the present in this paper.

For example the equation (5) at p. 3: I want to plot a chart like figure 5, i.e. the $x$-axis is the angle between vector $\mathbf S$ and $\mathbf V$ of equation (5), and the $y$-axis is the function value, and I also need to set condition that if $\mathbf R_l\cdot\mathbf V<0$, then the function value is $0$.

figure 5

And a more complex one is the $H_s(\mathbf S)$ function at p. 8; this is an integral with vector variable and the integral domain is a hemisphere. How do I plot a chart also like figure 5?

Thanks.

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Welcome to Mathematica.SE, Seila! Please let us know what you have tried so far. Is there a specific problem with your existing code? If so, please post a minimal working example to show where you got stuck, formatting it by indenting with the {} button. You can also use LaTeX markup for math. I'd also recommend that you register your account, so that you can post from more than one machine as the same user. –  Verbeia Oct 8 '12 at 6:27
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