Fix LPE Powerstroke unintuitive / unstable / scale-dependent behavior

(visible for example with Catmul-Rom interpolation)
The instability happens when the width-value of adjacent control knots are the same.
It's technical, but here goes quickly. Knots are treated as [offset along path, width] points.
The offset along path is the segment number + the location along that segment.
The width is (may not be true, but for ease of discussion) in canvas coordinates.
This means that the interpolation is performed in a *very* compressed coordinate system, 
where the x-coords may range from, say, 0 to 5, and the y-coords from 0 to 2000. 
This is also scale dependent; changing the scale of your path and scaling all widths accordingly will change the look of your path.

The fix now does the interpolation in a scaled coordinate system. It stretches the x-coordinates to the arclength of the path.
After interpolation, the inverse scaling is applied to the interpolation result.

(bzr r13341.1.279)

1 files changed, 12 insertions, 0 deletions

diff --git a/src/live_effects/lpe-powerstroke.cpp b/src/live_effects/lpe-powerstroke.cpp
index 58d733b53..03a10807a 100644
--- a/src/live_effects/lpe-powerstroke.cpp
+++ b/src/live_effects/lpe-powerstroke.cpp
@@ -659,6 +659,15 @@ LPEPowerStroke::doEffect_path (std::vector<Geom::Path> const & path_in)
         ts.push_back( Point( pwd2_in.domain().max(),
                              (end_linecap==LINECAP_ZERO_WIDTH) ? 0. : ts.back()[Geom::Y]) );
     }
+
+    // do the interpolation in a coordinate system that is more alike to the on-canvas knots,
+    // instead of the heavily compressed coordinate system of (segment_no offset, Y) in which the knots are stored
+    double pwd2_in_arclength = length(pwd2_in);
+    double xcoord_scaling = pwd2_in_arclength / ts.back()[Geom::X];
+    for (std::size_t i = 0, e = ts.size(); i < e; ++i) {
+        ts[i][Geom::X] *= xcoord_scaling;
+    }
+
     // create stroke path where points (x,y) := (t, offset)
     Geom::Interpolate::Interpolator *interpolator = Geom::Interpolate::Interpolator::create(static_cast<Geom::Interpolate::InterpolatorType>(interpolator_type.get_value()));
     if (Geom::Interpolate::CubicBezierJohan *johan = dynamic_cast<Geom::Interpolate::CubicBezierJohan*>(interpolator)) {
@@ -670,6 +679,9 @@ LPEPowerStroke::doEffect_path (std::vector<Geom::Path> const & path_in)
     Geom::Path strokepath = interpolator->interpolateToPath(ts);
     delete interpolator;
 
+    // apply the inverse knot-xcoord scaling that was applied before the interpolation
+    strokepath *= Scale(1/xcoord_scaling, 1);
+
     D2<Piecewise<SBasis> > patternd2 = make_cuts_independent(strokepath.toPwSb());
     Piecewise<SBasis> x = Piecewise<SBasis>(patternd2[0]);
     Piecewise<SBasis> y = Piecewise<SBasis>(patternd2[1]);