the initial default patch size is 17x17 knots, ie. 13x13 control points, and is a cubic b-spline. actually, the surface in this project is rendered with opengl nurbs. i would like to switch to rendering my own, but didn't have the time for this project.

anywhere there are 2 control points on either side of the selected control point, the surface can be "refined", ie. a smaller but more detailed patch can be overlaid on top of the base patch, or on top of another overlay. this refined patch will have 7x7 control points, which will cause the surface to coincide with the one it is lying on top of. the middle vertex can be selected and moved about, which gives a finer level of resolution than the base layer, due to the control points lying twice as close to each other, approximately.

the refinement algorithm is called the oslo algorithm, and can be found in [2]. basically, it calculates a weighted average of the surrounding control points on the layer below. i used 7x7 new control points, but by using a knot vector with quadrupled end knots, it should be possible to use a 5x5 control point array instead. these control points would have to be calculated from evaluating the surface, as opposed to averaging the existing control points, however, to get down to the surface and attaching there.

although i could have used various schemes to keep memory use to a minimum, i preferred going for interactive speed, which means keeping as much as possible in memory, and recalculating as little as possible. for this reason each overlay has a complete set of control points stored, as well as the offsets required to recalculate in case the parent surface is changed. this way while the control points for a single layer are modified, little calculation is done. when a parent is modified, the changes recurse down the tree to the children, but this is unavoidable. memory being as cheap as it is, and given that any computer can be brought to its knees by merely upping the resolution, this seemed a sane approach.

here are two images of a session in progress in fill mode, and in wireframe mode, so that the layers of refinement can be seen. one middle layer is currently selected in the second image.





here is a face i made in about 2 minutes. with higher resolution, and a couple of minor feature additions, it should be possible to make quite realistic faces, but it would be time-consuming, and i would need to measure someone's face. yes, it never got measured last time :)



finally, here is a link to an avi of a session in progress. note that the currently selected patch is red, and the control points can be seen for this patch. the blue ones are not selected, and the green ones are selected. one can move selected vertices around. the unselected areas are skin coloured. i have also included an animated gif, although it tends to run slower than it is supposed to.

smooth.avi

smooth.gif

[1] Hierarchical B-Spline Refinement, Forsey, Bartels,
Computer Graphics, Volume 22, Number 4, August 1988

[2] An Introduction to Splines for Use in Computer Graphics & Geometric Modeling,
Bartels, Beatty, Barsky; Morgan Kaufmann