

"Chris R" <car### [at] comcastnet> wrote:
> "Kenneth" <kdw### [at] gmailcom> wrote:
> > "Chris R" <car### [at] comcastnet> wrote:
> > >
> > > So I've been playing around with shapes extruded along one of the axes, by
> > > changing the rounding parameter and the scaling parameters on the other two
> > > axes, as well as translating the center of the rounded box along those two other
> > > axes in various ways, including linear interpolation, spline interpolation, and
> > > various other functions.
> > >
> > > This is the one where the scale decreases linearly from bottom to top, the
> > > rounding factor decreases linearly from bottom to top, and the x and z centers
> > > of the box are translated using sin(y*2*pi/height) and cos(y*2*pi/height).
> > >
> >
> > That's a nice result, and a clever use of functions. And gold colors! I assume
> > that this is just one functionobject, not a 'combination' of several function
> > shapes?
> >
> > I experimented with functionbased isosurfaces years ago, but have forgotten
> > some of the finer points, like how to 'taper' an object (like you did in y.) But
> > I happened to be playing around with this same kind of technique this week! I
> > can make a nice sinewave shape, but what is the trick for getting the shape to
> > taper or scale so nicely? IIRC, it is something relatively simple but I
> > can't remember what :(
>
> Here's a pretty simple example with linear tapering. I did something similar
> with the image above, but embedded the tapering in functions instead.
>
> #macro TaperedBox(SizeBase,SizeTop,RoundingBase,RoundingTop,Height)
> #local _xSlope = (SizeTop.x  SizeBase.x)/(2*Height);
> #local _zSlope = (SizeTop.z  SizeBase.z)/(2*Height);
> #local _rndSlope = (RoundingTop  RoundingBase)/Height;
> #local _xScaleBase = SizeBase.x/2;
> #local _zScaleBase = SizeBase.z/2;
> #local _xScaleFn = function(l) {
> _xScaleBase + _xSlope*l
> }
> #local _zScaleFn = function(l) {
> _zScaleBase + _ySlope*l
> }
> #local _rndFn = function(l) {
> RoundingBase + _rndSlope*l
> }
> #local _sy = Height/2;
> #local _shapeFn = function(x,y,z) {
> f_rounded_box(x, y, z, _rndFn(y+_sy), _xScaleFn(y+_sy), _sy,
> _zScaleFn(y+_sy))
> }
>
> #local _maxx = max(SizeBase.x,SizeTop.x)/2;
> #local _maxz = max(SizeBase.z,SizeTop.z)/2;
> #local _lbounds = <_maxx, _sy, _maxz>;
> #local _ubounds = <_maxx, _sy, _maxz>;
>
> #local _shape = isosurface {
> function {
> _shapeFn(x,y,z)
> }
> threshold 0
> contained_by { box { _lbounds, _ubounds } }
> }
>
> #undef _shapeFn
> #undef _rndFn
> #undef _zScaleFn
> #undef _xScaleFn
>
> _shape
>
> #end
>
> TaperedBox(<2,2>, <1,1>, 0.2, 0.1, 2)
>
> I have purposefully, pedantically, broken things out, because it helps me
> remember why I wrote the code when I go back to it months down the line.
>
> This should give you a truncated pyramid with a rounded bottom, rounded edges,
> with the rounding decreasing as you move up the pyramid.
>
> I use the RC3 Metal macros to create the gold texture.
>
>
>  Chris R.
Sorry, transcription error, yScaleBase should have been zScaleBase in _zScaleFn
 Chris R.
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