How would one store this polynomial anyway? Just a list of coefficients, or is there a more clever data structure for dealing with multivariate polynomials? (3 lists?)

goose_r_s

Given a 3d model/mesh is there a way for a computer to generate the algebraic surface or does this process need to be done manually?

shoes

If polynomials are really hard to come up with, how does 3D modeling software (like Blender) represent 3D shapes?

spidey

How do we represent these more intricate shapes in a model if these polynomials are very complicated?

Murrowow

I know it was mentioned that polynomials are rather difficult to come up with, but is there a general mathematical method to consider when coming up with them?

anon

How do programs change the model to reflect deformities (e.g. the sphere being squished, when material allows)? Or would that be considered completely separately with some sort of movement function?

Concurrensee

can geometry also be expressed in matrix format?

derk

Is there a general threshold for whether or not a geometic object should be expressed with a single polynomial?

corgo

How do we decide if we want to express a geometry with polynomial?

BlueCat

I am always curious about how people render complex images on computer. Are there ton of complex equations to be computed and combined to form very real objects? Also, how they know if these equations just produce these shapes which looks like what we want?

How would one store this polynomial anyway? Just a list of coefficients, or is there a more clever data structure for dealing with multivariate polynomials? (3 lists?)

Given a 3d model/mesh is there a way for a computer to generate the algebraic surface or does this process need to be done manually?

If polynomials are really hard to come up with, how does 3D modeling software (like Blender) represent 3D shapes?

How do we represent these more intricate shapes in a model if these polynomials are very complicated?

I know it was mentioned that polynomials are rather difficult to come up with, but is there a general mathematical method to consider when coming up with them?

How do programs change the model to reflect deformities (e.g. the sphere being squished, when material allows)? Or would that be considered completely separately with some sort of movement function?

can geometry also be expressed in matrix format?

Is there a general threshold for whether or not a geometic object should be expressed with a single polynomial?

How do we decide if we want to express a geometry with polynomial?

I am always curious about how people render complex images on computer. Are there ton of complex equations to be computed and combined to form very real objects? Also, how they know if these equations just produce these shapes which looks like what we want?