community!
Write the parametric equations of a right circular cone of height $h$ and semi-aperture $α$, lying on the plane $z = 0$, contained in the first octant, so that the segment between its vertex and the centre of its base projects orthogonally on $z = 0$ in the line $x = y$, $z = 0$.
I am really stuck in this exercise of Computational Geometry. I have no idea how to start.
Anyone could give me hints in how to begin? Thank you very much.
I made a sketch with GeoGebra to show you how the cone looks: hope it helps.
You could start writing the parametric equations for a cone whose axis is the z-axis. Then rotate the cone twice: first about y-axis by $(\pi/2-\alpha)$, then about z-axis by $\pi/4$.