Tutorial
Parametric Cubic Curves 2
( The tutorial solutions are also available)
- A B-spline vector is defined by four points, namely
a geometry vector
G = [ P1 P2 P3 P4 ]^t.
See your course notes
for the B-spline basis matrix.
-
What is the effect of choosing P1=P2, i.e, what does
the resulting curve look like? Does it pass through any
of the control points? How are the tangents at either end
of the curve related to the control points?
-
What is the effect of choosing P1=P2=P3?
- Show that two B-spline curve segments, defined by
Ga = [ P1 P2 P3 P4 ] and Gb = [ P2 P3 P4 P5 ] are C2 continuous.
-
One of the simplest ways to render a parametric surface patch
is to subdivide the patch into (possibly non-planar) quadrilaterals,
as determined by a grid in terms of the parameters s and t.
Describe how one might clip patches rendered using subdivision in an
efficient way.