Thanks Damien,
you saved me a lot of trouble explaining about curve domains :)
There's one thing I'd like to add to those who want to know more about
nurbs mathematics. This is not required knowledge even for Plugin
programmers. So if you skip this, you'll be no worse off:
The domain of a curve is an emergent property of the knot-vector. I
always hated the word "knot-vector", because it conjures up images
that have nothing to do with what it's supposed to describe. Every
nurbs curve is defined by 3 things:
1) the control point position + weights
2) the degree of the curve
3) the knot-vector
The control points are 4D points (3d points if you omit weighting
factors).
The degree is a single integer number between 1 and infinity (or 1 and
11 in the case of Rhino).
And the knot-vector is a list of floating point numbers that controls
the area of influence of individual control points. (it's a bit more
complicated than that, but this is only a flying survey)
The thing to realise about the knot vector is that the only thing that
matters are the relative ratios of the subsequent numbers. Hence, a
curve with the knot vector:
{0, 0, 0, 1, 2, 3, 3, 3}
will look exactly the same as a curve with the same degree and control
points but with the knot vector:
{10, 10, 10, 11, 12, 13, 13, 13}
and exactly the same as a curve with the knot vector:
{0, 0, 0, 2, 4, 6, 6, 6}
The celebrated domain of the curve is nothing more than the numeric
interval between the first and the last number in the knot-vector. We
can fit the knot-vector into any non-zero domain we wish, because we
can easily scale and offset all the knots so that their relative
ratios remain unmolested.
If you want a hands on example, create a curve in Rhino (degree=3, 5
control points, don't make it closed), and use the _List command to
sneak a peek at the knot-vector. Then use the _Reparameterize command
to change the domain and use _List again to see what's changed in the
knot-vector.
--
David Rutten
[email protected]
Robert McNeel & Associates
On Jan 16, 5:35 am, damien_alomar <[email protected]> wrote:
> Evaluating the curve in more of a geometric matter just requires
> switching out the Evaluate Curve for the Evaluate Length component
> (forgot about that one), and disconnecting the curve domain from the
> random component....the Evaluate length component will default to
> evaluating the curve between 0 and 1, so the standard output of the
> random component is fine
>
> http://grasshopper3d.googlegroups.com/web/rndCrvDivLen.jpg?hl=en&gsc=...
>
> -Damien
>
> On Jan 15, 11:26 pm, damien_alomar <[email protected]> wrote:
>
>
>
> > Domains are equivalent to the mathematical "length" of the curve.
> > There's a start parameter and an end parameter value and any values in
> > between those two can be solved through the mathematical equations and
> > the control points that dictate the final shape of the curve. The
> > three key things to understand are that the domain does not really
> > relate to the length of the curve at all (although by default when
> > Rhino creates curves it does its best to try and match the domain to
> > the length), the domain of the curve can be reexpressed (ie changed
> > from 0 to 1), and lastly that evenly spaced values in parametric space
> > will not be evenly placed in terms of distance along the curve.
>
> > So far the suggested solutions are really over complicating this
> > problem. Right now you guys aren't using the random component as its
> > intended and are thinking of crazy ways to get around it. Random
> > number generators will only generate numbers from 0 to 1, so if you
> > look at the R node you'll find that the random component can except a
> > range and defaults to that 0 to 1 range. Ideally we want to use the
> > domain of our curve to set the range of our random number set. There
> > use to be an explicit Curve Domain component in grasshopper, but it
> > was taken out because David has added the implicit conversions almost
> > everywhere in GH. An implicit conversion is simple the concept that I
> > can feed one data type (a curve for instance) into another data type
> > (a range/domain for instance) and that data type is able to be
> > extracted from another, the it will do so automatically. Because of
> > this, we can just feed our curve directly into the R node and we'll
> > get the domain that is need...no dotNet scripts. After that just feed
> > that to the Curve Parameter component and you're on your way.
>
> >http://grasshopper3d.googlegroups.com/web/rndCrvDiv.jpg?hl=en&gsc=Ql9...
>
> > The only thing about this solution is that you'll get a higher
> > concentration of points, geometrically speaking, where the parametric
> > space of the curve is more compressed. This kind of makes the
> > randomness jaded, but probably doesn't matter that much. I'll see if
> > there's a way to randomly divide the curve more based on geometric
> > space than parametric.
>
> > HTH,
> > Damien
>
> > On Jan 15, 8:31 pm, visose <[email protected]> wrote:
>
> > > I'll leave that to David. He's a man of much more knowledge. He will
> > > probably have to end up correcting me any way.
> > > :P
>
> > > On Jan 16, 1:42 am, Chris Wilkins <[email protected]> wrote:
>
> > > > Visose,
>
> > > > That worked. You are a man of much knowledge.
>
> > > > Can you explain the "reparameterize" and the "domain" of the curves
> > > > any further?
>
> > > > Thanks much,
> > > > Chris
>
> > > > On Jan 15, 7:29 pm, visose <[email protected]> wrote:
>
> > > > > Right-click on the curve component and check 'reparametrize'. It
> > > > > should normalize the domain range from 0 to 1.
>
> > > > > On Jan 16, 1:22 am, Chris Wilkins <[email protected]> wrote:
>
> > > > > > Baldino,
>
> > > > > > I tried building your solution (since I hadn't used the Random
> > > > > > component yet), and found a problem when there are more than 3
> > > > > > control
> > > > > > points on the curve. I found that the domain of the curve rises when
> > > > > > more control points are there, and the Evaluate Point on Curve
> > > > > > component would only divide a portion of the curves. Here's a pic of
> > > > > > that:
>
> > > > > >http://groups.google.com/group/grasshopper3d/web/RandomDivideVB1.jpg
> > > > > > (I crossreferenced the input in the last component to show the five
> > > > > > curves with same random values)
>
> > > > > > The domains are listed under each curve and you can see how the
> > > > > > affected portion is shorter when the domain rises over 1.
>
> > > > > > I couldn't find a GH component that output the number of control
> > > > > > points, so I tried out the VB component (finally). I got the domain
> > > > > > of
> > > > > > the curve that way and multiplied the random numbers by the domain
> > > > > > to
> > > > > > divide the whole length of the curve. Here's the two additional
> > > > > > components:
>
> > > > > >http://groups.google.com/group/grasshopper3d/web/RandomDivideVB2.jpg
> > > > > > (I could only make it do one curve at a time without more thought).
>
> > > > > > Chris
>
> > > > > > PS. I have no idea if changing the degree of the curve will mess
> > > > > > this
> > > > > > solution up. I had no idea what "domain" of curve was before this.
>
> > > > > > On Jan 15, 12:37 pm, baldino <[email protected]> wrote:
>
> > > > > > > this will
> > > > > > > work:http://groups.google.com/group/grasshopper3d/web/divide_crv_randomlen...
>
> > > > > > > On Jan 15, 6:15 pm, Alvin <[email protected]> wrote:
>
> > > > > > > > Hi,
>
> > > > > > > > I'm just getting into Grasshopper and need some initial help.
>
> > > > > > > > I would like to divide a curve into a certain # of segments,
> > > > > > > > with each
> > > > > > > > segment being a random length. I cant see how to any of the
> > > > > > > > functions
> > > > > > > > in the curve>division section of grasshopper can do this.
> > > > > > > > Little help
> > > > > > > > please?
>
> > > > > > > > thanks much,
>
> > > > > > > > Alvin- Hide quoted text -
>
> > > > > > > - Show quoted text -- Hide quoted text -
>
> > > > > - Show quoted text -- Hide quoted text -
>
> - Show quoted text -
