Question:
In 3D transformations, what is the purpose of homogeneous coordinates?
In 3D transformations, what is the purpose of homogeneous coordinates?
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Adding an extra coordinate lets even translation become a matrix operation.
Updated On: Jul 2, 2026
- To represent points using only two coordinates
- To simplify calculations for translation only
- To perform transformations using matrix multiplication
- To remove the need for scaling transformations
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The Correct Option is C
Solution and Explanation
Step 1: In ordinary 3D coordinates, translation is an addition, while scaling and rotation are matrix multiplications. Mixing addition and multiplication makes it hard to combine transformations.
Step 2: Homogeneous coordinates add a fourth component, writing a point as \( (x, y, z, 1) \). This lets translation also be written as a matrix multiplication.
Step 3: With all transformations as 4x4 matrices, a whole sequence can be multiplied into one composite matrix and applied uniformly.
Step 4: So the purpose is to perform transformations using matrix multiplication.
Step 2: Homogeneous coordinates add a fourth component, writing a point as \( (x, y, z, 1) \). This lets translation also be written as a matrix multiplication.
Step 3: With all transformations as 4x4 matrices, a whole sequence can be multiplied into one composite matrix and applied uniformly.
Step 4: So the purpose is to perform transformations using matrix multiplication.
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