So then the mass-spring models used for these types of simulations are represented with PDEs?
idontknow
In general is every physical simulation just a PDE? For example, a pile of bricks falling, hair bouncing, water spilling, etc.
graphic_content
In the hair example, do each of the strands have a permanent configuration that can be deformed?
keenan
@dtorresr Mass-spring models can be used as a simplification of the true physics. If you look at a hair under a microscope, it has all sorts of complex geometry and physical behavior. E.g., it stretches and twists in some directions better than others. At a large scale, this behavior can mean that a simple mass-spring model looks almost, but not quite like real hair---resulting in an uncanny valley between reality and simulation. More sophisticated hair models may end up looking, computationally, not so different from simple mass-spring models, but have just the right tweaks and modifications to give the right behavior. If you then want to incorporate effects like wetting of hair, things start to get really complicated! And you need to go back to the physical origins of the equations again.
keenan
In general is every physical simulation just a PDE?
@idontknow Boy, that's an excellent question. Can every physical phenomenon be modeled using partial differential equations? Well, certainly people try to do that, yes. But there are certain phenomena, like contact, where thinking about the relationship between rates of change doesn't quite provide the computational tools you need. For instance, simulating discrete grains (like sand) is a place where you really need to consider both continuous models (based on PDEs) and discrete models, and how they interact.
keenan
In the hair example, do each of the strands have a permanent configuration that can be deformed?
My understanding is that, yes, one reasonable model for hair is to use an elastic rod, which can bend and twist but always tries to restore its original configuration. Real, physical hair will definitely have a yield point past which it breaks; it may also experience some plastic deformation (changing its rest configuration) near this yield point. But since this scenario is pretty uncommon in animation (e.g., pulling someone's hair until it breaks!) these phenomena are generally ignored in the computational model.
So then the mass-spring models used for these types of simulations are represented with PDEs?
In general is every physical simulation just a PDE? For example, a pile of bricks falling, hair bouncing, water spilling, etc.
In the hair example, do each of the strands have a permanent configuration that can be deformed?
@dtorresr Mass-spring models can be used as a simplification of the true physics. If you look at a hair under a microscope, it has all sorts of complex geometry and physical behavior. E.g., it stretches and twists in some directions better than others. At a large scale, this behavior can mean that a simple mass-spring model looks almost, but not quite like real hair---resulting in an uncanny valley between reality and simulation. More sophisticated hair models may end up looking, computationally, not so different from simple mass-spring models, but have just the right tweaks and modifications to give the right behavior. If you then want to incorporate effects like wetting of hair, things start to get really complicated! And you need to go back to the physical origins of the equations again.
@idontknow Boy, that's an excellent question. Can every physical phenomenon be modeled using partial differential equations? Well, certainly people try to do that, yes. But there are certain phenomena, like contact, where thinking about the relationship between rates of change doesn't quite provide the computational tools you need. For instance, simulating discrete grains (like sand) is a place where you really need to consider both continuous models (based on PDEs) and discrete models, and how they interact.
My understanding is that, yes, one reasonable model for hair is to use an elastic rod, which can bend and twist but always tries to restore its original configuration. Real, physical hair will definitely have a yield point past which it breaks; it may also experience some plastic deformation (changing its rest configuration) near this yield point. But since this scenario is pretty uncommon in animation (e.g., pulling someone's hair until it breaks!) these phenomena are generally ignored in the computational model.