OpenGL Insights

236 III Bending the Pipeline

collision force due to collision of the object with other objects. The spring force f

int

may be defined as

f

int

(t) = k

i

(x

i

(t) − x

j

(t)−l

i

)

x

i

(t) − x

j

(t)

x

i

(t) − x

j

(t)

, (17.2)

where k

i

is the spring’s stiffness, l

i

is the resting length of the spring, x

i

is the spring’s

position and x

j

is the position of its neighbor.

The system in Equation (17.1) may be solved using any of the numerical inte-

gration schemes. We may either use the explicit integration schemes [Yan Chen 98,

Georgii and Westermann 05] or the implicit integration schemes [Baraff and Witkin

98]. Some examples of the explicit integration schemes include Euler integrat ...