Yes you can prove the triangle inequality property using the Cauchy-Schwarz Inequality.
wxl
Which other norms are used in graphics?
motoole2
I tend to use L1 norms quite a bit in life. An L1 norm of a vector, represented by |x|_1, is simply the sum of the absolute values of the vector elements, i.e.,
|x|_1 = sum_{i=1 to N} |x_i|
This norm comes up in a number of optimization problems, such as compressed sensing which was a really trendy topic used in graphics and vision a few years ago.
In fact, grades for this course will be computed using a weighted L1 norm. :-)
loneliboi
So in order to derive the formula for the form, we basically apply the Cartesian distance formula from an origin to the tip of the 'vector arrow'?
motoole2
Well, technically, we assume vectors start at the origin (0,0) (a.k.a. a basepoint), since a vector only encodes a magnitude and direction.. not an origin. In other words, a vector does not have to be at a fixed location in space. Vectors with a corresponding origin is sometimes referred to as a tangent vector though.
But yes: we are effectively applying the Cartesian distance formula from its origin to the tip.
Yes, it does.
Yes you can prove the triangle inequality property using the Cauchy-Schwarz Inequality.
Which other norms are used in graphics?
I tend to use L1 norms quite a bit in life. An L1 norm of a vector, represented by
|x|_1, is simply the sum of the absolute values of the vector elements, i.e.,|x|_1 = sum_{i=1 to N} |x_i|This norm comes up in a number of optimization problems, such as compressed sensing which was a really trendy topic used in graphics and vision a few years ago.
In fact, grades for this course will be computed using a weighted L1 norm. :-)
So in order to derive the formula for the form, we basically apply the Cartesian distance formula from an origin to the tip of the 'vector arrow'?
Well, technically, we assume vectors start at the origin
(0,0)(a.k.a. a basepoint), since a vector only encodes a magnitude and direction.. not an origin. In other words, a vector does not have to be at a fixed location in space. Vectors with a corresponding origin is sometimes referred to as a tangent vector though.But yes: we are effectively applying the Cartesian distance formula from its origin to the tip.