Practice question · Multiple choice
Graphics uses 4×4 matrices for a three-dimensional world. What does the extra dimension make possible?
Hints
- Is translation a linear transformation? Check where it sends the origin.
- Ask what would have to be true for a single matrix multiply to move every point by a fixed offset.
Show the answer
D. Translation as a matrix, since shifting the origin is not linear
Why
A linear map fixes the origin and translation does not, so no 3×3 matrix can translate. Embedding points as (x, y, z, 1) makes it a shear in four dimensions, linear again, so the whole pipeline becomes matrix multiplication. Perspective division comes free from the same trick.
Practise Matrices and Matrix Operations
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More questions on Matrices and Matrix Operations
- Order the steps to compute entry (2,1) of AB, where A has rows (1,2),(3,4) and B has rows (5,6),(7,8).
- Sort each matrix operation by whether the two matrices must have identical shape.
- Let A be 3x2 and B be 2x3. Select every statement that is TRUE.
- Graphics libraries compose a rotation and a translation by multiplying their matrices, then apply the single…