Using Equations To Represent Graphics

[Brian]

Hi, I have one last question about programming:

I read somewhere that programmers sometimes use mathematical equations
to represent graphics, and that the programmers write code that
transforms the equations into the graphics that they want. I didn't
know this was possible. Is it possible to do this?

Brian

[James]

On May 21, 12:19 pm, Brian <briansip...@yahoo.com> wrote:
> I read somewhere that programmers sometimes use mathematical equations
> to represent graphics, and that the programmers write code that
> transforms the equations into the graphics that they want.  I didn't
> know this was possible.  Is it possible to do this?

Hi Brian,

You mean like this webpage?

http://www.onlinefunctiongrapher.com/

Or are you talking about art, or something else?

James

[Brian]

Hi James, I'm talking about using mathematical equations to represent
graphical art. I heard it can be done, but that you have to write
code that transforms the equations into graphical art. Is this
possible?

Brian

[JJ]

Using Unicode characters from the Mathematical Operators subrange. Drawing
each in different sizes and positions as required.

[James]

On May 21, 3:22 pm, Brian <briansip...@yahoo.com> wrote:
>
> Hi James, I'm talking about using mathematical equations to represent
> graphical art.  I heard it can be done, but that you have to write
> code that transforms the equations into graphical art.  Is this
> possible?

Hi Brian,

Some graphics are easily described by mathematics, such as fractals.

I guess you could define any complex image to any resolution you
wanted using piecewise functions. That's what any image display
program does.

James

[Chris M. Thomasson]

> "Brian" wrote in message
> news:dd651185-6c10-4032...@v14g2000yqm.googlegroups.com...

Perhaps IFS might be of interest to you:

http://en.wikipedia.org/wiki/Iterated_function_system

You can mold many shapes indeed!

:^)

[Charles Richmond]

"Brian" <brian...@yahoo.com> wrote in message
news:dd651185-6c10-4032...@v14g2000yqm.googlegroups.com...

Perhaps you are thinking about something like transformation matrices. As I
understand it, each point considered three-dimensionally can be represented
by a 3x3 matrix of values. So for a group of points, you have a group of
matrices... one matrix for each point.

Using the matrix of the point, the point can be projected on the plane of
the computer screen. When some points are joined by lines... the produce a
wire-frame picture. Transformation matrices can be "applied" (i.e., the
matrix for each point is multiplied by a transformation matrix) to produce a
rotation or other modification of the two-dimensional picture by altering
the point's matrix... as the matrix specifies the point's location in three
dimensions. The "projection" on the computer screen is like viewing the
grouping of points from one side or another.

Here are some websites that describe some of this:

http://en.wikipedia.org/wiki/Transformation_matrix

http://www.senocular.com/flash/tutorials/transformmatrix/


If you are interested, I suggest that you find a good book on the subject.

--

numerist at aquaporin4 dot com

[Brian]

Thank you everybody for your replies. James' answer about the piece
part functions is what I was looking for.

[bob]

It sounds like you are talking about Scalable Vector Graphics.

Basically, you use lines and curves to represent complex shapes.

The curves used are often Bezier curves.

You can see many of these SVGs in action at

http://openclipart.org

For instance, here is a ladybug that you can keep zooming in on, and it will still look curvy (not granular):

http://openclipart.org/people/Keistutis/1368310520.svg

Thanks.