Re: [Lib2geom-devel] Tangential and perpendicular snapping

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

On Tue, Aug 30, 2011 at 09:00:46PM +0200, Diederik van Lierop wrote:
> Hi all,
> 
> Due to popular demand, I'm thinking of implementing tangential and 
> perpendicular snapping in Inkscape. Well, at least for the case where 
> the user draws a straight line or manipulates a guide. So I have a curve 
> I want to snap to, and some distant point P0. Now I need to find all 
> points P1, for which the line P0-P1 is either tangential or 
> perpendicular to the curve.
> 
> I guess I could first convert the path to sbasis, and then call 
> find_tangents() (see the code snippet below, from sbasis-geometric.cpp). 
> But a few questions come to mind:
> - Can't this be done without having to convert each path to sbasis 
> first? Converting will take CPU time

No more than a matrix multiply.  You need to convert it into a form
with a suitable algebra.  It could be done with bernstein basis
(bezier curves) but we currently lack code to do that.

> - Am I really the first one to need this functionality? find_tangets() 
> is not being used anywhere as far as I can tell. Are there other ways to 
> solve this?

lib2geom is full of solutions looking for problems :)

> - How do I implement perpendicular snapping? There's no method yet 
> called find_normals()

Ok, there are a bunch of operations that are interesting:

* given a direction D, find all points on the curve A that point in that
  direction: roots(dot(derivative(A), rot90(D)))

* given a point P, find all points on the curve A whose tangent passes
  through P: find_tangents(P, A)

* given a point P, find all points on the curve A whose normal passes
  through P, same as find tangents, but use the dot product:
    SBasis crs (dot(A - P, derivative(A)));
    crs = shift(crs*Linear(-1, 0)*Linear(-1, 0), -2); // We know that
  there is a double root at t=0 so we divide out t^2
// JFB points out that this is equivalent to (t-1)^2 followed by a
  divide by s^2 (shift)
    return roots(crs);

* given a pair of curves, find the lines which are normal to both
  curves: collinear_normals

* same, but for tangents (fillets): There is no code for this
  currently, but I'm sure it can be built from collinear_normals.

* snap arcs to matching curvature: filet-minion (I particularly like
  the name of this one :)

There are more snappy things, but I can't think of them right now.
I'm going away for a few days (no internet!!!), but don't hestitate to
ask for more help.

njh