One question I have is what if we square a vector or a point? Is that possible? What happens if we do square a point for example, using Homogenous Coordinates? I'm honestly not sure if this is possible or what would happen, though my initial guess would be to square the vector to compensate for squaring the coordinates of a point, but I just thought this would be an interesting thing to know.
Stafftancik
@aramk-hub Squaring a vector is a valid operation, after all it is just a series of additions. In this case you scaling the vector by the length of the vector. We actually do this quite often when calculating distances (a^2 + b^2 = c^2). Squaring a point is undefined in the same way that adding two points is undefined. There is no clear geometric intuition for what adding (or multiplying) two points does.
melodysifry
This slide was super helpful for me in clarifying the purpose of homogenous coordinates and the relationships between points and vectors and how they interact
One question I have is what if we square a vector or a point? Is that possible? What happens if we do square a point for example, using Homogenous Coordinates? I'm honestly not sure if this is possible or what would happen, though my initial guess would be to square the vector to compensate for squaring the coordinates of a point, but I just thought this would be an interesting thing to know.
@aramk-hub Squaring a vector is a valid operation, after all it is just a series of additions. In this case you scaling the vector by the length of the vector. We actually do this quite often when calculating distances (a^2 + b^2 = c^2). Squaring a point is undefined in the same way that adding two points is undefined. There is no clear geometric intuition for what adding (or multiplying) two points does.
This slide was super helpful for me in clarifying the purpose of homogenous coordinates and the relationships between points and vectors and how they interact