Homework2
A reminder: you are free to collaborate, but you must understand and write up the final answers by yourself!
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Show that perspective projection preserves lines.
Hint: the easiest argument to make is a geometric one using the 3D line, the center of projection, and the image plane. - For a \( 4 \times 4\) matrix whose top three rose are arbitrary and whose bottom row is \((0, 0, 0, 1)\), show that the points \((x, y, z, 1)\) and \((hx, hy, hz, h)\) transform to the same point after homogenization.
- For the eye position \(\mathbf{e} = (0, 1, 0)\), a look vector \(\mathbf{g} = (0, -1, 0)\), and an up vector \(\mathbf{t} = (1, 1, 0)\), what is the resulting \(\mathbf{uvw}\) basis used for coordinate rotations?