Consider a line segment AB parallel to the Z axis with end points A[3 2 2 1] and B[3 2 4 1]. Overall scale to double the size of line AB followed by two point perspective projection with COP along...

The given question is as follows:

Consider a line segment AB parallel to the Z axis with end points A[3 2 2 1] and B[3 2 4 1]. Overall scale to double the size of line AB followed by two point perspective projection with COP along X-axis and Y-axis as Xc=10 and Yc=20 respectively. Also, write the corresponding vanishing points.

So, first of all let us double the size of the line segment. We have been given homogenous coordinates of A and B. Let us apply our scaling matrix to it.

So the new coordinates are [6 4 4 1] and [6 4 8 1]. Now we can apply two point perspective projection along it. Please note that since it is happening along x axis and y axis we will take z=0 plane for this projection. The transformation matrix for two point perspective projection along z=0 plane is given by:

Now let us apply transformation matrix on our endpoints of the line.

As we can see that although it was two point projection it turned out to be one point since both the vanishing points lie at the same coordinates.