# Freeform vector graphics with controlled thin-plate splines

ACM Trans. Graphics (SIGGRAPH Asia), 30(6), 2011.

Rich set of curve and point controls for intuitive and expressive color interpolation.

**Abstract:**
Recent work defines vector graphics using diffusion between colored curves. We explore higher-order
fairing to enable more natural interpolation and greater expressive control. Specifically, we build on
thin-plate splines which provide smoothness everywhere except at user-specified tears and creases
(discontinuities in value and derivative respectively). Our system lets a user sketch discontinuity curves
without fixing their colors, and sprinkle color constraints at sparse interior points to obtain smooth
interpolation subject to the outlines. We refine the representation with novel contour and slope curves,
which anisotropically constrain interpolation derivatives. Compound curves further increase editing power
by expanding a single curve into multiple offsets of various basic types (value, tear, crease, slope, and
contour). The vector constraints are discretized over an image grid, and satisfied using a hierarchical
solver. We demonstrate interactive authoring on a desktop CPU.

**Sample inputs and associated output imagery:**
The following pairs of images show the curves and points specified by the user on
the left, and the generated images on the right.
A small number of strokes can produce very rich graphics.