CPSC 424 Assignment 5 - Ugrad.cs.ubc.ca

CPSC 424 Assignment 5
Term: January 2013, Instructor: Alla Sheffer, sheffa@cs.ubc.ca, http://www.ugrad.cs.ubc.ca/˜cs424
Due: March 11th, 2013 in class
Assignment 5.1: B-Splines (10 Points)
Draw a cubic B-spline curve defined by the points on the picture,
a) assuming the first and the last points are replicated 4 times, and all the others are
not replicated.
P 4
P 5
P 6
P 7
=P 8
=P 9
=P 10
P 0
=P 1
=P 2
=P 3
b) assuming no points are replicated.
P 0
P 1
P 2
P 3
P 4
1

Assignment 5.2: Curve equivalence (10 Points)
Given the following 3 curves F i (t), sketch each curve, and for each F i (t) write
down the equations for (some) equivalent curves G 1 i (t), G2 i (t). For each one of the
equivalent curves (check course notes for the definition of equivalence), include the
corresponding parameter domain.
( t
a) (2D) F 0 (t) =
t
)
, t ∈ [0, 1]
b) (2D) F 1 (t) =
( sin(t)
cos(t)
)
, t ∈ [0, π]
⎛
c) (3D) F 2 (t) = ⎝
t
t 2 1
t
⎞
⎠ , t ∈ [0, 1]
Assignment 5.3: Differential geometry (10 Points)
Find an equation of the 2D curve with the following unit tangent vector:
a) τ =
( 1/
√
5
2/ √ 5
)
, t ∈ [0; 1]
b) [BONUS] τ =
( −sinα
cosα
)
, α ∈ [0; ∞)
2

Assignment 5.4: Surface types (10 Points)
For each of the following, describe/sketch an everyday object defined by this type of
surface. Explain.
a) Extrusion surface
b) Surface of revolution
c) Ruled surface
d) Bilinear patch
e) Bezier patch
3