Math 128a - Program 2 - Due April 25
Your assignment is to implement a program which computes and plots a curve in the x, y plane,
by fitting a cubic spline curve through a given set of points (xi,y
i) in the plane. You can think of
this as the algorithm underlying various drawing programs like xfig or paint. This set of points may
be from any source, including clicking on your mouse, or arrays computed by another program, like
Program 1 earlier this semester.
The basic idea is that you should be able to click on a matlab graphics window to specify a list
of points in the plane, and have the program connect them with a curve. There is an option to
identify certain points as “corners”, so the program will not try to make the curve smooth there
(have a continuous tangent); this lets you draw curves that are partly smooth and partly polygonal.
There is another option to make the curve closed, i.e. connect the last point to the first point; this
lets you draw circles, for example.
If your points are supplied as an input array, they may be the output of Program 1, which
computed them as solutions to f(x, y ) = 0. So there is also an option to test how well the curve
you compute satisfies f(x, y) = 0 along its entire length, not just the input points.
We will supply most of the Matlab code for this problem, including a program to test it. You
will need to write 4 subroutines, for which we supply detailed input and output descriptions. To
help you debug, we will also tell you what some of the correct output should be from the test
program. You will turn in your code so we can run it and make sure it works.
The main routine is called Param2dSpline.m. Here is a detailed description of its inputs (see
also the comments in the code):
1.Aflagmouse indicating the source of the points in the plane. If mouse = 0, they are supplied
by the next two input arguments x(1 : n)andy(1 : n). If mouse = 1, they should be input
using the mouse by pointing at the graphics window and clicking on the desired location of
each point. A left mouse click means the point is a “non corner point” (explained below),
a right mouse click means the point is a “corner point”, and hitting any other key on the
keyboard means end of input.
2. Two arrays x(1 : n), y(1 : n) defining the x and y coordinates of the points along the curve.
If mouse = 0, these are used as input. If mouse = 1, they are ignored and instead set by the
user clicking on the mouse as just described.
3. The name func of a function that evaluates f(x, y), where the points along the curve including
x(i),y(i) are intended to satisfy f(x(i),y(i)) = 0. If there is no such function (for example if
the points are input by the mouse), then the input function should be the empty string ’’.
This is used to test whether you have correctly implemented the splines.
4. A flag closed indicating whether the curve should be closed, that is (x(1),y(1)) should be
connected to (x(n),y(n)) (if closed =1),ornot(closed =0).
5. An array cn(1 : m) of corner indices. If mouse =0,cn(1 : m) is used as the input, but if
mouse =1,cn is determined by mouse-clicking as described above (right mouse clicks). No
matter how cn(i) is specified, it indicates that (x(cn(i)),y(cn(i))) is to be treated as a corner
in the curve (details below). If closed = 0, the endpoints are defined to be corners as well,
whether or not 1 and nare included in cn.Ifclosed = 1, there may be no corners (cn may
be empty, i.e. have length zero).
6. A flag corners,whichis>0 to indicate that the program should identify additional corners
automatically, and 0 to indicate that it should not. The way a positive value of corners is
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