Computer Aided Engineering Design

276 COMPUTER AIDED ENGINEERING DESIGN

Δ =

1

1

1

11

22

33

xy

xy

xy

(9.2)

PointC can relate to AB in three possible ways (Figure 9.2):

Planar

objectB

Curves of intersection

Planar object A

A∩B

(a) Boolean intersection between planar objects

Obstacle

O

A

Start point

Obstacle

B End point

Collision-free path

(b) Collision free path planning for a manipulator

B

C

A

B

C

A

C

B

A

A

C

B

(a)C on left of AB (b)C on right of AB (c)C collinear with AB (d)C on AB

Figure 9.2 Proximity of a point and a line

Figure 9.1 Some examples requiring intersection/proximity analysis.