Which assumptions are placed in mass-spring systems?
point masses, massless springs
What is the role of the stiffness parameter k?
how difficult it is to streach or compress a spring
Name internal and external forces that are acting on the point masses!
external: Gravity, contact forces, all forces not caused by springs
internal: elastic spring forces, viscous damping forces
What does Hooke's law say?
linear spring for small displacement
Write down the internal elastic force of a spring in 3D!
How does the semi-implicit Euler simplify the implicit Euler integration?
linearization of the force in a known state
How do we constrain the banding of hair spring systems?
2 springs, one with the first and second neighbor
Which types of springs do we have for cloth?
structural springs, diagonal springs, interleaved springs
Name problems and limitations of mass-spring systems!
Springs couple different deformation modes
Different behavior for different resolutions
Limitations
▪ Strong dependence on discretization (topology)
▪ No or little control over material behavior
▪ No (explicit) volume preservation (for solids)
Given a quad with a diagonal spring in it: tell which direction has highest/lowest resistance!
along high
across low
What can we use mass-spring systems for?
cloth, hair
What are the inputs and outputs of a constraint in the penalty-based mass-spring systems?
input: positions
output: scalar value which sould go to 0
Why are we not solving for the constraints directly via root finding?
we use the constraint as forces, to directly incorporate it in the mass spring system
How do we derive forces from constraints?
penalty function which goes to 0, negative gradient of that function is force
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