Fractal sets patch. Second version.

	Bugs corrected:

	. Bounding slabs now work. Thank to Egon (egon@ugcs.caltech.edu) who
	found the bug in 'lighting.c'. This correction may arrouse problems
	with shadows one day, but until now, no one was detected. Well.

	. CSG is operational, but slows even more the computations. It
	can be used optionaly.

	. The necessary file 'tokenize.c' was not included in the
	previous archive. Unforgivable neglecting. 

					Pascal.
-----------------------------------------------------------------------

	julia_patch_2.tar contents and description:

	. 'frame.h'		( new primitive fields )
	. 'parse.h'		( new tokens: julia, z3 and fractal )
	. 'tokenize.c'		( new tokens spelling )
	. 'parse.c'		( syntax )
	. 'povproto.h'		( prototype for routines in 'julia.c' )
	. 'julia.c'		( primitive routines )
	. 'lighting.c'		( Lines 269 and 270 have been changed to
				  make bounding slabs work.)

	These files should replace those in the POV-ray 2.2 sources. Add
	the primitive 'julia.c' in the Makefile before re-compiling.

	Syntax:

	<keyword> { C.x, C.y, C.z, C.w, n, s (,csg)
		    USUAL_TRANSFORMATIONS
		    USUAL_TEXTURES
		    ...
	}

	where <keyword> is either: julia, z3 or fractal.

	The fractal is generated by taking the point (x,y,z,0.0) in
	4D space (quaternion) and iterating a certain map, which depends
	on the four parameters given by C.x, C.y, C.z and C.w.

	If, after n iterations, the iterated point did not get out of
	the bounding sphere (radius=2), the initial point is in the set.

	For 'julia' set, the map is : 	z -> z^2 + C
	For 'z3' set, it is:		z -> z^3 + C
	For 'fractal' set, the map is currently:

		| x		| x^2-y^2-z^2-w^2
		| y		| 2*w*y	
		| z	---->	| 2*x*z		      + C
		| w		| 2*y*z

	but it can be changed at will in 'julia.c'. Look at routines:
	'Iteration_Fractal' and 'Normal_Calc_Fractal'...

	The integer s gives the number of steps in which is a ray divided
	in inside the sphere. Each point is tested, starting from eye,
	until a likely intersection is detected. The higher s, the slower,
	but smoother will look the set... 300 is commonly a good value.

	A better algo would use distance-estimator to perform the tests, 
	and be much faster, but that does not work for any iteration map,
	or when the initial point is *inside* the set. If someone wants to
	enhance that point... I'll try when I find time :(

        csg: this keyword is optional and must be used when the fractal
	set takes part in a CSG operation. Because, in such case, *all*
	intersection points (or at least the MAX_INTERSECTIONS first
	ones. Check in file 'parse.h' if problems) must be detected.
	It is therefore much slower.

	Hope you'll enjoy, even if it is a slow primitive...

			Pascal.

------------------------------
Pascal Massimino
Ecole Normale Superieure
45, rue d'Ulm
75005 Paris.
Pascal.Massimino@ens.fr	     	(any comments/bugs/enhancements
				welcome )
http://acacia.ens.fr:8080/home/massimin/index.ang.html