CMSC 437 Lecture 14,

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There are many interesting curves and surfaces that are represented
by parametric equations. These may be used in GUI applications.

My reference book is: "CRC Standard Curves and Surfaces" by
David von Seggern, CRC Press, ISBN 0-8493-0196-3.

The uses include defining motion such as the cycloid for
making the robot walk or 3D objects that may be useful or
just interesting.

To understand the examples below, you will have to run the program
read the code. The screen shots are just small samples.

curv_surf.c

The basic idea is to have a standard way to size and parameterize
curves and surfaces. Then a standard set of points can be generated
and these points used either for static drawing or for dynamic
movement, as in a target for a game.

A few simple, crude, codes for spiral and flower:
Spiral.java

spiral_tk.py3

turtle_spiral.py3

spiral.py3 source code
spiral_py3.dat for making .stl
spiral_py3.stl for 3D printer

flower.java

3D surfaces are a bit more complicated.
I tend to write a specific program to generate the 3D surface in
some standard format, I use .dat, then I can combine the 3D objects
into a scene.

make_spiral_635.c is a typical
program to generate a 3D object.

The output is spiral_635.dat which is
not much to look at. The image drawn by light_dat.c is:

spiral_635_3d.py3 source code

A second example, to see the great similarity, is:
make_helix_635.c is a typical
program to generate a 3D object.

The output is helix_635.dat which is
not much to look at. The image drawn by light_dat.c is:

Note that light_dat.c uses datread.h and datread.c
Thus you can read, write and clean the .dat files. Cleaning, removing
redundant vertices, is necessary for good quality rendering when normals
are going to be interpolated.

From the book "Curves and Surfaces" a cylindrical spiral was easily
generated as shown in make_cyl_spiral_635.c
that made the file cyl_spiral_635.dat file displayable in light_dat as:

The same code was dropped into an OpenGL program to create surf3d.c showing the object as a wireframe.

Many python examples in my download directory:

shape_tk.py3

The reason I had so many arcs, I wanted to generate pattern:
shape32.py3

snowflake.py3

New topic:
There are many ways to run "apps" applications over the Internet in a browser.
Plain HTML can be interactive, Java applets and JavaScript are available
along with many others. Now, some want to go significantly farther.
The goal is to have to complete application on a server rather than
have the user istall the application on their computer. Some will
keep the users data on the same server. Do you trust that?

RIA, Rich Internet Applications, fully interactive that can have
fancy graphics use databases may use AJAX, Asynchronous JavaScript
and Xml, Flash (or Microsofts competing Silverlight) in your browser.

Now, groups are working on the equivalent of AppletViewer that runs
Java Applets without a browser. Mozilla Prism is one of the new
RIA Platforms, for Windows, Linux and MacOSX.

You can not stop progress. HTML 5 is available and Flash 5 is available.

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