To understand a Signed Distance Function (SDF), imagine a circle with radius R and center at [0,0]. The equation of its boundary is x^2+y^2=R^2. Rearrange it to x^2+y^2−R^2=0. This represents the SDF, where f(x,y)=0 defines the boundary. The function f(x,y)0 represents points outside. Essentially, the SDF indicates how far a point is from the boundary, with the sign showing whether it's inside or outside. You can also write a similar equation for a sphere, but SDF algorithms allow you to do this for any arbitrary geometry.
So how it captures geometry,let say 3d geometry with the help of neural network, as we know neural network is just a function approximation which helps in learning the equation of level/ scalar curves….I am still not clear with how it captures 3d geometry from 3d point given as input to neural network
To understand a Signed Distance Function (SDF), imagine a circle with radius R and center at [0,0]. The equation of its boundary is x^2+y^2=R^2. Rearrange it to x^2+y^2−R^2=0. This represents the SDF, where f(x,y)=0 defines the boundary. The function f(x,y)0 represents points outside. Essentially, the SDF indicates how far a point is from the boundary, with the sign showing whether it's inside or outside. You can also write a similar equation for a sphere, but SDF algorithms allow you to do this for any arbitrary geometry.
So how it captures geometry,let say 3d geometry with the help of neural network, as we know neural network is just a function approximation which helps in learning the equation of level/ scalar curves….I am still not clear with how it captures 3d geometry from 3d point given as input to neural network
good one