Hierarchical Modeling - Essentials of Interactive Computer Graphics - page 304

OC of
Left Palm

C p0

R p1

M lp

OC of
Left Arm

M w2 n

NDC

M la

OC of
Body

M p2w

WC

M b

Figure 11.18.

Transformation of the left palm OC space.

transformations that correspond to the transformation operators in the scene
hierarchy must be considered. We will discuss this issue in Section 11.4.1.

• Collision. We must transform primitives into a common coordinate space
before the primitives can interact. For example, if we want the left palm in
the human model of Figure 11.13 to bounce off a ball, we would need to
detect collisions between the primitives that define the palm and the ball. In
order to perform the collision detection, we must transform all primitives
into a common coordinate space (e.g., WC). We will discuss this issue in
Section 11.4.2.

As mentioned, thus far we have worked with the drawing aspect of OC spaces.
For example, when drawing the left palm of Figure 11.13, we computed M dlp
(Equation (11.6)):

M dlp = M lp M la M b M V M P

M p 2 w M w 2 n .
Figure 11.18 shows that one way to understand M dlp is that

=

M w 2 n = M V M P

is the WC-to-NDC transformation (as discussed in Section 10.3), and we can
consider

M p 2 w = M lp M la M b

to be the palm-OC-to-WC transformation that transforms the left palm primitives
( C p 0 and R p 1 ) into the WC space.