Homework2
A reminder: you are free to collaborate, but you must understand and write up the final answers by yourself!
Complete the homework as a pdf, doc, or on paper (and scan), then submit it to the homework2 directory in your class repo.
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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.Prove lines remain lines after perspective 0: No general cases 3: Show single example 6: Show for specific case 10: Show for all general cases -
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.
Prove homogenization 0: No general cases 3: Show for specific cases 10: Show for all possible points -
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?
Basis position 0: No position 1: Basis position given Basis vectors 0: No vectors 3: Basis u,v,w vectors given Basis values 0: Incorrect values 6: Basis values set according to camera equations