21
C H A P T E R 4
Mass-Spring Models
“May the force be with you”
Obi-Wan Kenobi; … and a lot of Star Wars fans.
In this chapter, we’ll look at how the internal cloth forces are computed.
4.1 INTRODUCTION
You’ve probably heard somewhere before that all material is constructed out of atoms. As such,
it’s no surprise that also cloth is made out of atoms and neighboring atoms exert forces on
each other preventing excessive stretching or compression. In computer graphics, we can take
this idea and represent the continuous cloth by a discrete set of points. Of course, not quite as
many as the number of atoms: : : Unless you’re a very patient person! Continuing on this idea
of having point masses exerting forces on each other to retain certain properties naturally leads
to the mass-spring model.
4.2 COMPUTING MASSES
e name of the model is probably a little bit of a give-away but mass-spring models are none
other than point masses connected by springs. Let’s say you have some geometry that you would
like to simulate as cloth—you can simply take the N vertices of the triangles as the point masses
in our simulation model. Besides being a point, point masses have mass.
A good method to determine the mass is to have a surface density with units
h
kg
m
2
i
defined
for a material. We model the cloth using 2D triangle elements without thickness. Heavier ma-
terial will have a higher density and vice versa. We can loop over all the triangles and compute
the mass as the triangle surface times the density to obtain the mass of that triangle. is mass
is then equally distributed by adding one third of the triangle mass to all three vertices of the
triangles. is is an approximation but works well in practice. A single particle will have mass
contributions from all triangles it is part of. is area is assumed to be the area in the reference
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.