"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 function-object, not a 'combination' of several function
> shapes?
>
> I experimented with function-based 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 sine-wave 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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