Surfaces based on Scattered Data Interpolation
Example 1. We are given a set of scattered data which are obtained from
a model of car, say. We used C^1 quintic splines to find an interpolation
which gives a surface of the model.
Example 2. We are given a set of scattered data which were sampled from a
side panel of
a car. We used C^1 cubic splines to find a surface which interpolates
the data. The interpolatory spline gives the surface of side panel.
Polygonal Hole Filling
Example 1. We are given a surface which has a polygonal hole in the
middle. We used a C^1 cubic spline surface to mend the hole.
Example 2. Besides we are given a surface with a hole, we are also given
a few points to interpolate. We used a C^1 cubic spline surface to mend
the hole as well as interpolate the given data.
Connection of Surfaces
Suppose that we are given two pieces of surface. We use bivariate splines
to connect these two pieces of surface together in a smooth fashion.
Example 1. We used C^1 cubic splines
to connect these two surfaces. Two different
methods are applied: one is the minimal energy method and the other one is
called L1 spline method.
The first figure is obtained based on the minimal
energy method. The other using the L1 spline method.
Example 2. We used C^2 quintic spline surfaces to connect these two
surface patches. Again the minimal energy method and the L1 spline method
are used. The first figure is obtained based on the minimal
energy method. The other using the L1 spline method.
