Homogeneous coordinates

I've been learning webgl recently, and I've been learning for a while, and I want to express my opinion on the secondary coordinates.

First, let us first understand the meaning of homogeneous coordinates. Little two, the picture above!

 
The existence of homogeneous coordinates, like the existence of the denominator 21, allows two fractions with different denominators to be added or subtracted. Maybe you have already thought that the existence of homogeneous coordinates is to allow coordinates of different dimensions to participate in the operation together

Second, let's take a look at how homogeneous coordinates allow coordinates of different dimensions to participate in the operation. Second, serve

   

      As shown in the figure, we want to put the coordinates of two different dimensions together to operate, and we must expand the lower dimension. We will add one dimension to the point of one dimension, a1 = (x = 5,y =0), then a1 can be regarded as a homogeneous coordinate of a

      I'm a rookie, please forgive me if I'm not good enough

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