If we scale x1, x2 and x3 uniformly, the result is the original shape, because with homogeneous coordinates, x1 and x2 need to be divided by x3 in order to be mapped to 2D.
jlessioh
if we scaled x1, x2, and x3 uniformly, wouldn't the result appear to be bigger than it actually is, since it would be closer to the viewing point? This is assuming that we are viewing it along the x3 axis.
Max
@jlessioh yeah, you can see that in this slide. However, when we're using homogeneous coordinates we won't be viewing the scene along the homogeneous axis - we divide out the homogeneous term to find the final scene coordinates (this is also how we implement perspective projection).
tib
I agree with @CMUScottie that you would get back the original shape (before scaling), because by the definition of homogenous coordinates, you would "un-scale" the x1, x2 coordinates when dividing by z.
If we scale x1, x2 and x3 uniformly, the result is the original shape, because with homogeneous coordinates, x1 and x2 need to be divided by x3 in order to be mapped to 2D.
if we scaled x1, x2, and x3 uniformly, wouldn't the result appear to be bigger than it actually is, since it would be closer to the viewing point? This is assuming that we are viewing it along the x3 axis.
@jlessioh yeah, you can see that in this slide. However, when we're using homogeneous coordinates we won't be viewing the scene along the homogeneous axis - we divide out the homogeneous term to find the final scene coordinates (this is also how we implement perspective projection).
I agree with @CMUScottie that you would get back the original shape (before scaling), because by the definition of homogenous coordinates, you would "un-scale" the x1, x2 coordinates when dividing by z.