mnb96
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"obvious" question on angles and solid-angles
Hello,
I have found in http://www.cg.tuwien.ac.at/hostings/cescg/CESCG97/csebfalvi/node2.html" an important statement about solid angles. Namely, the differential solid angle [itex]d\omega[/itex] is related to an oriented differential surface area [itex]dA[/itex] placed at distance [itex]r[/itex] from the origin in the following way:
[tex]d\omega = \frac{dA \cdot cos\theta}{r^2}[/tex]
where [itex]\theta[/itex] is the angle between the normal of [itex]dA[/itex] and the direction from the origin (see the figure in the http://www.cg.tuwien.ac.at/hostings/cescg/CESCG97/csebfalvi/node2.html" ), and [itex]r^2[/itex] is the squared distance between the origin and the "centre" of dA.
The authors say that this very "obvious", but it is not for me, not even in the 2D case with ordinary angles.
How can I derive this result?
Hello,
I have found in http://www.cg.tuwien.ac.at/hostings/cescg/CESCG97/csebfalvi/node2.html" an important statement about solid angles. Namely, the differential solid angle [itex]d\omega[/itex] is related to an oriented differential surface area [itex]dA[/itex] placed at distance [itex]r[/itex] from the origin in the following way:
[tex]d\omega = \frac{dA \cdot cos\theta}{r^2}[/tex]
where [itex]\theta[/itex] is the angle between the normal of [itex]dA[/itex] and the direction from the origin (see the figure in the http://www.cg.tuwien.ac.at/hostings/cescg/CESCG97/csebfalvi/node2.html" ), and [itex]r^2[/itex] is the squared distance between the origin and the "centre" of dA.
The authors say that this very "obvious", but it is not for me, not even in the 2D case with ordinary angles.
How can I derive this result?
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