This chapter presents the image-source technique and how to use it to
find all the specular reflection paths in a room geometry. We start
with a single reflection from a surface, and then gradually move to
higher order reflections, and more complex geometries such that in the
end we have a general algorithm that can be used in any room
geometry composed of planar surfaces. The examples here are all in
2D, but they generalize directly to more realistic 3-D geometries as well.
An ideal specular reflection from a rigid surface can be represented by
a mirror image source that is obtained by reflecting the sound source
against the reflecting surface. If the mirror image source emits an
identical wavefront as the original source, it is seen as a reflected
wave-front inside the room.
- Try moving the 'Time' slider to see how a
circular wavefront propagates from a point-source.
- Check the 'Show outside' to see the
reflected image-source and corresponding wavefront as a complete circle.
Note that in all the illustrations the surfaces are single-sided
meaning that only their front-sides are reflective. Each surface has
its normal-vector pointing in this direction. It is seen as a little
red marker at the center of each surface.
Actually, this reflection model is physically accurate if the
reflecting surface is of infinite size and ideally rigid. However, in
practice the surfaces are of limited extent and the edges of a surface
typically cause the sound field to be diffracted. Modeling of
diffraction is a separate topic and will be discussed later in this
book. Also the assumption of ideal rigid surfaces does not usually
hold. In this section the main emphasis is on computation of the
specular reflection paths and handling of acoustic properties of the
reflecting material will be discussed in conjunction with
reconstruction of impulse response from reflection paths.