Springs

Hooke's Law

Force is proportional to displacement

K = spring constant

d = displacement from rest length

Spring is modeled as 2 point masses, linked by the spring

Equal but opposite force is applied to each end

Springs

Springs

Vector between the points is used to compute displacement and the direction of force:

    v = point1 - point0
    displacement = v.length() - restLength
    v.normalize()
    force = springConstant * displacement * v

Springs

• Make one point stay still
• Add other forces

Spring Classes

Two classes needed: PointMass and Spring

PointMass

Attributes:

Mass

Position

Velocity

Acceleration

Functions:

Clear forces

Add force

Update

Freeze

Spring Classes

Spring

Attributes:

Two PointMasses

Spring constant

Rest length

Functions:

Update

Spring-based Objects

Solid objects can be simulated as a collection of springs

Stiff springs (large spring constant) produce rigid objects.
Loose springs produce jello-like objects.

Spring-based Objects

Often, additional internal springs are needed to keep a shape from collapsing

Cloth

Cloth can be simulated by a mesh of springs

Cloth

Diagonal springs are again useful, to keep the mesh from collapsing easily

Numerical Explosion

Spring calculations are prone to "numerical explosion"

This document is by Dave Pape, and is released under a Creative Commons License.