I have:
- point A (x,y,z) as a "view point"
- point A2 (x,y,z) as center of quadrangular prism
- prism size (width, length, height)
So it's something like this (clickable)
Imagine that you are standing at point A and looking at our prism. I need to get a quad, representating part that is visible from point A. In my example (img) it will be quad from points FBDH. I was thinking about some kind of projection to the plane perpendicular to line connecting point A and center of my prism, but i am not very good at geometry so i need help.
My question is: how can i get the coordinates of this quad using my source data (coordinates of "view point", center and sizes of prism).
Thanks in advance.
Edit: Point A can have any coordinates, higher of lower it doesn't matter. Prism is also could be rotated around every axis.
If you see a face, you see all the four points on it.
Compute the centers $C_k$ of all the faces, and the outer normal to that face $\bf n_k$.
Compute the vectors $\bf{v_k} = \vec {AC_k}$. Only the faces for which $\bf {v_k} \cdot \bf{n_k} <0$ will be visible.
In another way, associate to each vertex $P_k$, the normals $\bf n_{k,j}$ corresponding to each of the three concurrent faces.
The visible points will be those for which at least one of the dot products $\vec {AP_k} \cdot \bf n_{k,j }$ is negative.
In this way you also can arrange the points as having $3,2,1,0$ negative dot products, and those with $0$ will be the obscured points.