Xref: utzoo alt.fractals:1230 sci.math:17218 comp.graphics:17746 Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!usc!apple!spies!zorch!xanthian From: xanthian@zorch.SF-Bay.ORG (Kent Paul Dolan) Newsgroups: alt.fractals,sci.math,comp.graphics Subject: Re: 3-d fractal raytracer? Message-ID: <1991May3.085302.18527@zorch.SF-Bay.ORG> Date: 3 May 91 08:53:02 GMT References: <1991Apr30.074427.29894@milton.u.washington.edu> Organization: SF-Bay Public-Access Unix Lines: 21 > bungi@u.washington.edu writes: > Failing this, does anyone know a fairly accurate method for computing > the a normal to a procedurally defined surface (in this case M or > J_c)? Which brought to mind this sudden realization: the boundary of a fractal object like a snowflake curve or the Mandelbrot set, being everywhere of discontinuous first derivative (in the > 2D case, Jacobian), what in the world does one intend when one says the "normal" to such an object at a particular point? Does one limit resolution, do some local smoothing, and take the normal to the resultant bounding surface? Most of the interesting rendering algorithms I know misbehave at surface derivative discontinuities; how in the world does one proceed when the surface derivative is everywhere discontinuous? Kent, the man from xanth.