Given a cube with diagonal corners at (0,0,0) and at (2,2,2), which is the follo

Question

Given a cube with diagonal corners at (0,0,0) and at (2,2,2), which is the following transformation expressed as a 4x4 matrix that will scale the cube into a board with dimensions 10x2x4 along the x,y,z axes respectively? (C++/Calculus?)

Given a cube with diagonal corners a (0.0.0) and at (2.2.2), which is the following transformation expressed as a 4x4 matrix that will scale the cube into a board with dimensions 10x2x4 along the x,yz axes respectively? 01. 5 0 0 0 0 1 0 0 0 0 2 0 0 0 0 1 O 2. 10 0 0 0 0 2 0 0 0 0 4 0 0 0 0 O 3. 1 0 0 5 0 1 0 1 0 0 1 2 0 0 0 1 O 4. 1 0 0 10 0 1 0 2 0 0 1 4 0 0 0 1 (0,0,0) (2,2,2)

Explanation / Answer

Using Linear transformations – local scaling

{{s_x, 0, 0, 0},

{0, s_y, 0, 0},

{0, 0, s_z, 0},

{0, 0, 0, 1}}

Scaling with respect a selected fixed position (xf, yf, zf) can be represented with the following transformation sequence:

The equations for this sequence of transformation is (where s is scaling factor)

ANSWER : [2]

1. Translate the fixed point to the origin 2. Scale the object relative to the coordinate origin 3. Translate the fixed point back to its original position

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