RoboSense RS-LiDAR-16 - Page 33

RS-LiDAR-16 User Manual
33
objects. Therefore, in a rectangular environment, the section lines of the conical surfaces and the
rectangular planes are hyperbolas as shown in Figure 15.
Figure 15:Contour lines plotted on X, Z coordinates.
Figure 16: RS-LiDAR-16 Scanning Illustration.
The hyperbolas contour lines phenomenon can also be explained by transforming polar coordinates into
orthogonal coordinates. As shown in Figure 17, we deduced the function of a hyperbolas
1
))tan((
2
2
2
2

y
x
y
z

. When y and

are definite values, it indicates a hyperbola with focus on z
coordinate. When y is a definite value, as

gains in value, the asymptote slope and eccentricity will
decline thereof, which resulted a more curved hyperbola. On the contrary, as

loses in value, a more
flat hyperbola is resulted. When

is a definite value, as y gains in value, the asymptote of the same
angle presents same slope, the value of y determines the width between scanning contours.
Figure 17: Hyperbolic Function.
);sin(
);sin()cos(
);cos()cos(



rz
ry
rx



)(sin/)(cos
22222
 zyx 
1
))tan((
2
2
2
2

y
x
y
z
