Graphics Reference
In-Depth Information
14.11
E
XERCISES
Section 14.2
14.2.1.
Carefully describe an algorithm that finds the distance between a point and a polygo-
nal curve.
Find the the point
q
on the curve p(u) = (u,u
2
) that is closest to
p
= (-3,1).
14.2.2.
Find the two nearest points on the curves p: [-•,3] Æ
R
2
, p(u) = (2u,u
2
), and q:
R
Æ
R
, q(u) = (-u + 1,u + 5).
14.2.3.
Consider the surface p:
D
Æ
R
3
, p(u,v) = (u,v,u
2
+ v
2
).
(a) Find the the point
q
on the surface that is closest to
p
= (0,3,0) if
D
=
R
2
.
(b) Find the the point
q
on the surface that is closest to
p
= (0,3,0) if
D
=
R
¥(-•,-1].
14.2.4.
Find the two nearest points on the surfaces p(u,v) = (u,v,u
2
+v
2
) and q(u,v) = (u,v,2u-
6).
14.2.5.
Section 14.5.1
Consider the curve defined implicitly by the equation y
2
- x
3
= 0. Resolve the singu-
larity of this curve at (0,0) using the method described in Section 14.5. Work through
and explain the details just like we did in Example 14.5.1.2.
14.5.1.1
Section 14.9.1
Consider the planar curve p(u) = (u,u
2
). Analyze the offset curve p
d
(u) defined by equa-
tion (14.28) with respect to cusps, turning points, inflection points, vertices, and self-
intersections for the following values of d:
14.9.1.1
(a) 0 < d < 0.5
(b) 0.5 < d
(c) d = 0.5
14.12
P
ROGRAMMING
P
ROJECTS
Section 14.2
14.2.1.
Implement a point-curve distance algorithm for planar
(a) polygonal curves, and
(b) B-spline curves.
Let the user define a curve interactively with a mouse or specify a previously created
one. Then let him/her pick a point with the mouse and display both the distance and
the point on the curve that is closest to the picked point.
