World: r3wp

a is a value between 0,1

I know bezier really is just an iterated break up of an algorythm 
between control points..  I could implement the math, but if you've 
got some stuff all done  ;-)

all the algorythms are available on the web via siggraph and other 
sources, but coding that stuff usually isn't very fun.

I was asking, cause I saw a demo once of someone rebuilding the AGG 
spline manually right over the AGG one.. so some code definitely 
exists.

no, i use it to interpolate colors, not coordinates, so it is no 
use as it is in my script.

But it's easy to figure how to interpolate coordinates instead of 
colors gradiants, i gues...

Giving 2 points as input , i can write it if you want, but give me 
the paremeters you want and the result expected (an image, a block 
of coordinates ?).
Give the specs

for linear interpolation its pretty easy.
  
this is the complicated use...

give me the (x.y)  at length z of (bezier, nurbs, quadratic, etc) 
spline defined by points  p1, p2, p3, p4, pn

We wrote our own spline (arc function for a Paint program we did). 
 

DPaint had this, which implies John's RPaint has this code too, no?

ho i see, your input is a length and you want the coordinates in 
return ?

tricky need

The nice thing is that it works backwards, which is, you give it 
XY, and a control point, and it draws thorugh the control point.

Of note, if you want another way to think of an arc.

Think of drawing 3 points A B C (C is the "pull")

Now, you have what looks like a triangle.


If you make a tic halfway between A and C, and B and C, and draw 
a line been these tics, then keep doing this, you will eventually 
make an Arc.

The last tic is where your Mouse cursor would end up.

That is why Arc in RPaint is "backwards".

Cool, eh?

Wow, i understood nothing...

What do you mean?

reichart  that is the exact bezier algorythm.

Yup.

ok, so I should bother john for his function... he probably profiled 
it and such... I'm just lazy.

now I have a real math problem... I didn't even find a direct solution 
on wolfram mathematica site.


do you know of an algorythm (expressed in code, not in math) that 
can give me the ellipse with two supplied coordinates.
center and one point which touches the ellipse?

Steeve, was there something you wanted described?

Maxim, probably not, since you need to first find an example in a 
real program that uses that UI.  Perhaps GIMP though?

My paint program let you draw a start point, and drag a line in some 
direction, then show an ellipse on that "angle".

Then, you could size the width and length, in real time, then when 
you released the mouse it snapped perfect....it was VERY fast, and 
very cool.

some graphic app I'm writting ;-) does the ellipse dragging in real 
time, but uses x-radius and y-radius which is snapped to the edge 
of the ellipse... 


I just prefer single point editing... but for that to be intuitive, 
the point really has to be exactly on the ellipse... and since ellipse 
have 2 center points... ellipse seem to be very complex challenge, 
by what I've read, there isn't even today an exact method to calculate 
the arclen of an ellipse... only very close approximations!

Yup, all circles (ellipses) are doe with an error correction routine.

We too had to correct "to a pixel"

How will you set the "width" of your ellipse?

basically, two points reside on the major and minor axis and a reference 
center is used.  if rotation is needed, I can easily calculate the 
vector from any of the axis to the center.

but right now the rotation is locked, cause I'm not sure its a good 
thing to rotate the ellipse for this specific application.

but the powerfull thing, is that you can drag the ellipse itself, 
by clicking on any part of the line itself, no cvs to drag the shape. 
 :-)

and just hovering over the line (the arc) the cvs appear, so they 
don't clutter the drawing while you're editing other parts of it.

A REBOL Bezier algorithm:

do http://www.fys.ku.dk/~niclasen/rebol/fysik/bezier.r

Move the points around with the mouse.

that's the demo I was talking about   ;-)

so you don't mind if I use that code in my own projects?

first use will be to build a keyframe editor, which will be distributed 
with liquid-paint, with MIT license.

(for spline-based animation curves.)

Use as you like.

do you know of an algorythm (expressed in code, not in math) that 
can give me the ellipse with two supplied coordinates.
center and 
one point which touches the ellipse?

Isn't there an infinite number of ways, you can do that?

thanks! for the spline code, with a few changes, one in three points 
should pass directly through the point and the two other points will 
be used as tangeants.

its not really obvious... I'm not a math expert, even if I've done 
some pretty cool 3D engines (crowd simulation, for example) it takes 
me a lot of time to get the math part of things done when its question 
of doing math mix and match.

Let's say, you have center and a point with same y-coordinate as 
center. So it's just horizontal out from the center. Now the ellipse 
can be any height, so you can make infinite many ellipses with those 
two points.

I did whole evening of research on the ellipse and didn't find a 
single exact procedure to do it... some math dr have done their thesis 
just on finding ways to calculate its arc len ! 


though I think its possible to resolve the two foci based on the 
angle and distance of the point we want to pass through the arc, 
all the math needed to get to the proper major and minor axis (eventually 
equating to what people call the x and y radius) is pretty intensive.

In DPaint (and Canvas RPaint), you specify center and corner of ellipse. 
It's then not rotated. After specifying size this way with two points, 
you can rotate it.

yes but the corner is not *ON* the line, its equal to the major and 
minor axis of the elipse.

if I where to drag one of those points to an angle of 30 degres, 
I still want the arc to touch my point.

Yup, but you can't make just one ellipse with center and point on 
the ellipse.

there is definitely a way to calculate it mathematically, but there 
are so many steps, I get lost in the procedure to get to it.

:-) Think of my example with center and point horizontal out from 
the center. What height should your ellipse  be?

The problem is not, that it's hard. It's impossible.

in that case, its can be treated as a special case... like a like 
since one of the axis is = 0  just like the up vector of a 3d object 
cannot be (0,0,0)

Ah, I now think, I understand, what you want. It's like the arc drawing 
routine, where you want the point to be on the line. Same thing with 
ellipse.

but if x and y axis aren't = 0  then the angle of the point, can 
let you calculate the two foci, which are relation to x/y.