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Meet the concept What geometric behavior distinguishes valid linear transformations from nonlinear distortions? + ↗ Valid linear transformations keep grid lines straight, parallel, and evenly spaced. Nonlinear distortions involve bending or curving of these lines.
Conditions: Observing the movement of a 2D coordinate grid.; Checking for straightness, parallelism, and equal spacing of lines.
Valid linear transformations keep grid lines straight, parallel, and evenly spaced. Nonlinear distortions involve bending or curving of these lines.
Conditions: Observing the movement of a 2D coordinate grid.; Checking for straightness, parallelism, and equal spacing of lines.
Meet the concept What is the matrix representation of a horizontal shear that slides the y-axis diagonally? + ↗ The matrix representation is [ 1 1 0 1 ] \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix} [ 1 0 1 1 ] i ^ \hat{i} i ^ [ 1 , 0 ] T [1, 0]^T [ 1 , 0 ] T j ^ \hat{j} j ^ [ 1 , 1 ] T [1, 1]^T [ 1 , 1 ] T
Conditions: Horizontal shear keeping i ^ \hat{i} i ^ j ^ \hat{j} j ^ [ 1 , 1 ] T [1, 1]^T [ 1 , 1 ] T
The matrix representation is [ 1 1 0 1 ] \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix} [ 1 0 1 1 ] i ^ \hat{i} i ^ [ 1 , 0 ] T [1, 0]^T [ 1 , 0 ] T j ^ \hat{j} j ^ [ 1 , 1 ] T [1, 1]^T [ 1 , 1 ] T
Conditions: Horizontal shear keeping i ^ \hat{i} i ^ j ^ \hat{j} j ^ [ 1 , 1 ] T [1, 1]^T [ 1 , 1 ] T