I've been experimenting with some geometry. Three-point perspective is fun to play with. Despite being a mathematician, I've yet to work out the exact relationship between the three vanishing points and the corresponding angles produced in various regions of the drawing.

Perhaps I'll give this task to my Pre-calculus students. Their test scores haven't been good, so I know they'll be wanting some extra credit.

In any case, I think this would be a fun GIMP tutorial to write up: Creating Three-Point Perspective mountain ranges. Here's an example from the project I'm still working on.

"Construction Phase"


The process is to construct basic polygons, then sculpt out the details. I actually learned this trick from one of Griatch's tutorials (drawing a futuristic city).

"Sculpting Phase"


Then add color, etc. Essentially, I'll "paint" the sculpted forms.

"Texture Phase"


There's more to do... but I thought it might be neat to illustrate the technique.

Looks cool Merrak. Looks like way too much work for a simpleton like me though. Hope to see more of your creations too.

Love the "texture phase" image, very cool!

Pretty neat looking results.

Looks very interesting with the added texture
And i did not know you are a mathematician i hope you would not mind help with some question
(not now it took me too time just find the right terminology to explain the question, but i will try next time i stumble over)

well if you forgive the OT i may try:
i know the function to draw a circle of radius N at the center of a image

what i need is find know is how fill the image with concentric circles till filling up also the corners spaces

i want be able to set the first circle radius,
the number of circles i wish OR their Radius Increase "RI" (i.e each larger of 3 px ) and be able to fill the image (the largest circle should have radius = image diagonal - "RI" ) i mean fill any image so image W and H are variables

(wow explaining made it much more clear in my mind..not yet so clear to be able to find a solution

Thanks!



Is this what you're trying to accomplish? (i.e. the upper right corner)

that is cool but i look for something more simple.

let say that if the image would be a square that square will be inscribed in the larger circle...this a poor mock up



but the image are usually rectangle so would be something as



again i want be able to set the the number of circles OR their Radius Increase
and have the rest automatically computed

Here i simplify to give you the whole picture i would also need to manage center off-set
i want to make a pattern filter to create interference patterns as in the examples





where the effect come by offsetting 2 or more identical layers filled with concentric circles

But the math is baffling and if i already felt confused to solve with the circles center in the image center i really feel lost to figure out how to manage circles center off set

This sounds more like a programming problem to me. I'm not sure what language you're using. Does it not have a simple draw_circle type function that takes the radius and center coordinates as arguments?

If you have to calculate the coordinates of every pixel, you'll need to use some trig functions. Make sure whatever libraries you need to do that are loaded.

Here's one way to do it. Let A be an angle. On a circle of radius 1, centered at the origin (0,0), the coordinates of every point on the edge are (cos(A), sin(A)) for some angle A. For a circle of radius R, the coordinates are (R*cos(A), R*sin(A)).

Finally, to shift the circle to some arbitrary location, let (x,y) be the coordinates of the center. Then the edges lie on (R*cos(A) + x, R*sin(A) + y).

What you'll probably want to do is set up a routine that calculates (R*cos(A) + x, R*sin(A) + y) for every angle A between 0 and 360 deg. The step size is up to you. Too small and your code will be slow. Too fast might leave you with a dotted line for an edge instead of a solid line. You'll have to repeat this procedure for increasing values of R until you get the number of circles desired.

That's smart can you put the link up as I wonna try with that pls