Question

Imagine we are working with veretex postions in 3D homogeneous coordinates. Write a 3D matrix that combines the following transformations: 1) First, scale by a factor of 8 along the X axis, by 13 along the Y axis, and by 14 along the Z axis 2) Second, translate by 19 units in the X axis, 16 units in the Y axis, and 13 units in the Z axis

          Imagine we are working with veretex postions in 3D homogeneous coordinates.
Write a 3D matrix that combines the following transformations:
1) First, scale by a factor of 8 along the X axis, by 13 along the Y axis, and by 14 along the Z axis
2) Second, translate by 19 units in the X axis, 16 units in the Y axis, and 13 units in the Z axis

Imagine we are working with veretex postions in 3D homogeneous coordinates.
Write a 3D matrix that combines the following transformations:
1) First, scale by a factor of 8 along the X axis, by 13 along the Y axis, and by 14 along the Z axis
2) Second, translate by 19 units in the X axis, 16 units in the Y axis, and 13 units in the Z axis

Added by Connie W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

02/08/2023

Step 1

Step 1: To create a scaling matrix for scaling by factors of 8 along the x-axis, 13 along the y-axis, and 14 along the z-axis, we can create the following diagonal matrix: \[ S = \begin{bmatrix} 8 & 0 & 0 & 0 \\ 0 & 13 & 0 & 0 \\ 0 & 0 & 14 & 0 \\ 0 & 0 & 0 & 1 Show more…

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Imagine we are working with vertex positions in 3D homogeneous coordinates. Write a 3D matrix that combines the following transformations: First, scale by a factor of 8 along the x-axis, by 13 along the y-axis, and by 14 along the z-axis. Second, translate by 19 units in the x-axis, 16 units in the y-axis, and 13 units in the z-axis.