i
i
i
i
i
i
i
i
384 15. Curves
(u =0.5) position, p
3
is the first derivative at the middle, p
4
is the position
at the end, and p
5
is the first derivative at the end.
5. The Lagrange Form (Equation (15.12)) can be used to represent the inter-
polating cubic of Exercise 3. Use it at several different parameter values to
confirm that it does produce the same results as the basis functions derived
in Exercise 3.
6. Devise an arc-length parameterization for the curve representedby the para-
metric function
f(u)=(u, u
2
).
7. Given the four control points of a segment of a Hermite spline, compute the
control points of an equivalent B´ezier segment.
8. Use the de Castijeau algorithm to evaluate the position of the cubic B´ezier
curve with its control points at (0,0), (0,1), (1,1) and (1,0) for parameter
values u =0.5 and u =0.75. Drawing a sketch will help you do this.
9. Use the Cox / de Boor recurrence to derive Equation (15.16).
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.