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Computer Graphics: Difference between revisions
→Homogeneous Coordinates
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Points and vectors are represented using homogeneous coordinates in computer graphics. | Points and vectors are represented using homogeneous coordinates in computer graphics. | ||
This allows affine transformations in 3D (i.e. rotation and translation) to be represented as a matrix multiplication. | This allows affine transformations in 3D (i.e. rotation and translation) to be represented as a matrix multiplication. | ||
While rotations can typically be represented in a 3x3 matrix multiplication, a translation requires a [[wikipedia:Shear mapping ''shear'']] in 4D. | While rotations can typically be represented in a 3x3 matrix multiplication, a translation requires a [[wikipedia:Shear mapping | ''shear'']] in 4D. | ||
Points are <math>(x,y,z,1)</math> and vectors are <math>(x,y,z,0)</math>. | Points are <math>(x,y,z,1)</math> and vectors are <math>(x,y,z,0)</math>. | ||