Re: [Lib2geom-devel] cy2geom questions

[Nathan H. <nj...@nj...>]

On Sun, Sep 30, 2012 at 05:12:27PM -0500, Susan Spencer wrote:
> Hi developers,
> 
> Here are some examples of current output using
> the tmtp library <https://github.com/sconklin/tmtp.git> for pattern design.
> 
> https://docs.google.com/open?id=0BxsnjDIHW4yvNGZEMGlNSGpzblk
> https://docs.google.com/open?id=0BxsnjDIHW4yvTVFndHIyYnBoZjA
> https://docs.google.com/open?id=0BxsnjDIHW4yvck9iMGVVTWFXMFU

freaken awesome.  I just spent several hours reverse engineering a
teeshirt pattern I liked: this would have been very handy!

Something I would like is a way of tracing the support lines from body
measurements and using them to adjust the pattern.  I have no idea how
to do this :)

> It would improve the tmtp project to replace functions like
> pointOnCurveAtLength() and lengthOnCurveAtPoint()
> with calls to cy2geom/lib2geom code.
> 
> The data structures are very simple,
> a point is a python object with x & y values.
> Point A is A.x, A.y, and A.name = 'A'
> Curve paths are python lists where a cubic curve P0 c1 c2 P1
> is stored as curve[0],curve[1],curve[2],curve[3]
> Longer curves P0 c11 c12 P1 c21 c22 P2 are stored as
> curve[0],curve[1],curve[2],curve[3], curve[4],curve[5],curve[6]
> where the shared points (eg P1 in example) are not repeated.
> 
> Can anyone give me examples for:
> 1.) returning a point at a known length on a curve,

There are two ways to go about this, depending on how many points you
want.  If you just want a single point then you could do it with a
root find on length, but if you want it for many values it would be
more efficient to use arc_length_parametrization(D2<SBasis> const &M, 
                           unsigned order=3, 
                           double tol=.01);

which returns a new path which 't' is in length.

> 2.) returning the length at a known or interpolated point on a
> curve,

double length(path.portion(0,t));

should do that.

> 3.) the point at an intersection of a line and a curve,
> 4.) the point at an intersection of two curves

void find_intersections_bezier_clipping (std::vector<
std::pair<double, double> > & xs,
                         std::vector<Point> const& A,
                         std::vector<Point> const& B,
                         double precision = 1e-5);

will find the intersection of two bezier curves (including lines)


> 5.) interpolating a curve.

What do you mean by this?  the simplest interpolation would be to just
Lerp the control points.  If you want something like the stretchy
rubber mat transforms in the toys/2dsb2d you are actually composing
curves.  If you want something like path-along-path you are composing
with a 2d arc length parameterisation.

For patterns I think the solution is somewhere in the middle of these
approaches: it's not an affine scaling transform because people aren't
all the same shape and you are actually also ensuring that both sides
of seam are the same length.  I will think about it for a bit.

> I have very simple code for these functions in tmtp,
> but I need to improve accuracy.

Jan is the expert on the cy2geom bindings and I'm sure he'll be able
to give example code for these better than me.

> Bonus points if anyone can produce an example for Bend Path!!!
> I obviously don't have code for this - see the 2nd file in list
> above.

yeah, I think it's a variant of path-along-path.

njh