Hi Chris,
That seems like it will work, but I'm not sure I "get" the reasoning behind
your proposed step 2. That is, once you have the B-spline chopped up into
a bunch of circular arcs, why not simply use the algorithm Sean proposed to
tesselate the area via the critical points on the contour? Since the
contour will only consist of circular arcs and straight lines, this step is
almost trivial. From there, the area of each patch can be computed
directly via Green's Theorem. Plus, one can also compute the first and
second moments of inertia for the shape as well with only 2 extra lines of
code...
Cheers!
-Matt-
On Wed, Jul 11, 2012 at 8:09 AM, crdueck <crdu...@uwaterloo.ca> wrote:
> i've come up with an algorithm that i think will work a bit better for
> my purposes, which i'd like to get some feedback on. it would proceed
> like this:
>
> 1.) convert any bezier/NURBS segments to piecewise circular arcs using
> the approach found here: http://itc.ktu.lt/itc354/Riskus354.pdf
> 2.) create a polygon inside the sketch by connecting the new vertices
> created by the circular arc approximation of the bezier/NURBS segments
> and any endpoints from line segments or existing circular arc segments.
> The area of this interior polygon can be calculated exactly, and is very
> easy to tesselate with a delaunay triangulation for the rt_sketch_tess()
> function.
> 3.) calculate the area of each circular arc segment exactly and add to
> the area of the interior polygon to find the total area.
>
> the interior polygon should be a close approximation to the original
> sketch since its vertices will be created by the bezier curve->circular
> arcs function which will divide the bezier segment into more circular
> arcs the greater the change in curvature.
>
> On 07/10/2012 07:23 AM, Christopher Sean Morrison wrote:
> > On Jul 10, 2012, at 2:12 AM, crdueck wrote:
> >
> >> finding the new inside corners is working now for sketches consisting
> of only line segments and circular arcs as the important points used to
> divide the sketch into rectangular sections are simply their end points.
> but for bezier/NURBS segments I'll need their critical points.
> >>
> >> plussai mentioned some useful looking functions for NURBS in
> src/librt/opennurbs_ext.cpp, which i'll take a look at, but i'd have to
> promote the nurb_seg into a full ON_Curve in order to use those. however, i
> think i'll need to use some of the NURBS API functions anyways in order to
> evaluate the bezier/NURBS segments so it makes sense to do that unless
> there is already some simpler way to analyze the curve segments.
> > That seems like an acceptable form of reuse -- just take care to make
> sure any openNURBS API you are intending to call actually has an
> implementation defined (either in src/librt/opennurbs_ext.* or in
> src/other/openNURBS/*). Many of their API functions do not have an
> implementation, which is why we provide extensions in opennurbs_ext
> implementing some of the pieces they removed.
> >
> >> also, i havent touched any of the C++ codebase yet, will there be any
> issues calling ON functions in librt/primitives/sketch.c? where should I
> look for examples of opennurbs API functions being used in librt?
> > There's not any issues other than proper containment. You cannot make
> any changes that would expose a C++ type to LIBRT's API. That is, you
> can't make a new public function or change an existing one (any defined by
> RT_EXPORT) to make it pass a C++ object. You CAN, however, use C++
> properly encapsulated.
> >
> > I'd suggest adding a new sketch_tess.cpp and including all of the C++
> guts related to tessellation in there. Make sense?
> >
> > Cheers!
> > Sean
> >
> >
> >
> >
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