This problem concerns a flight of a ski jumper at the Winter Olympics. Assume that the path
followed by the jumper consists of three curve segments: one for the jump, one for his flight, and
one after landing, See the schematic below.
Ski Jump, 3 Bezier Curves
Control vertices for the curve that models flight are: p_(0)=(220,70),p_(1)=(170,62),p_(2)=(150,60),
p_(3)=(100,30). Control vertices for the curve that models the jump are: ,
, q_(2)=(235,72),q_(3)=(220,70). Assume the units are meters.
Answer the following questions:
a. Derive the equation for the cubic Bezier curve that corresponds to the given control vertices.
Simplify the equation into the form: a_(3)u^(3)+a_(2)u^(2)+a_(1)u+a_(0)=k(u)
b. Compute the point on the curve at u=0.7
c. Derive or state the relationship between Bezier curve control vertices and Hermite curve
tangent vectors. Compute the tangent vectors at the end of the jump curve ( {:q_(3)) and the beginning
of the flight curve ).
d. What is the continuity condition between the jump and flight curves? Justify your answer
quantitatively (i.e., with calculations).
e. Compute the control vertices in the flight curve for C^(1) continuity between the jump and flight
curves.This problem concerns a flight of a ski jumper at the Winter Olympics. Assume that the path
followed by the jumper consists of three curve segments: one for the jump, one for his flight, and
one after landing, See the schematic below.
Control vertices for the curve that models flight are: p0=(220,70), p1=(170, 62), p2=(150, 60),
p3=(100, 30). Control vertices for the curve that models the jump are: q0=(270, 130), q1=(256,
80), q2=(235, 72), q3= (220, 70). Assume the units are meters.
Answer the following questions:
a. Derive the equation for the cubic Bezier curve that corresponds to the given control vertices.
Simplify the equation into the form: a3u3 + a2u2 + a1u + a0 = k(u)
b. Compute the point on the curve at u = 0.7
c. Derive or state the relationship between Bezier curve control vertices and Hermite curve
tangent vectors. Compute the tangent vectors at the end of the jump curve (q3) and the beginning
of the flight curve (p0).
d. What is the continuity condition between the jump and flight curves? Justify your answer
quantitatively (i.e., with calculations).
e. Compute the control vertices in the flight curve for C1 continuity between the jump and flight
curves.
This problem concerns a flight of a ski jumper at the Winter Olympics. Assume that the path followed by the jumper consists of three curve segments: one for the jump, one for his flight, and one after landing, See the schematic below. Ski Jump,3 Bezier Curves
160
140
Jump Curve
120
100
Flight Curve P1 Pz
60 E 60
Po93
92
40
Pa
20
Hill surface
0
50
100
150 X [m]
200
250
Control vertices for the curve that models flight are:p=220,70,p=170,62p=150,60 ps=(100, 30). Control vertices for the curve that models the jump are: qo=(270, 130), qi=(256 80), q=235, 72), q=(220, 70).Assume the units are meters.
Answer the following questions: a. Derive the equation for the cubic Bezier curve that corresponds to the given control vertices
b.Compute the point on the curve at u =0.7
c. Derive or state the relationship between Bezier curve control vertices and Hermite curve
of the flight curve (po).
d. What is the continuity condition between the jump and flight curves? Justify your answer quantitatively (i.e., with calculations).
e. Compute the control vertices in the flight curve for C continuity between the jump and flight curves.