

"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) {
_yScaleBase + _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.
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