On 5/8/20 8:09 PM, Bald Eagle wrote:
> 
...

Forgive me, I'm going to forgo answering all the questions in detail. 
You're asking the right questions. Answers there are a many. Shy away 
from extremes that any given approach is all right or all wrong - that 
thinking I've found almost always wrong.

On the fast, distance based stuff. I believe a reason they can be so 
fast - in addition to a lot of optimization - is they set everything up 
distance based (nice gradients). This lets them toss gazillions of 
equations at GPU hardware (or SIMD), run it all in parallel and 'just' 
add up the answers to get an 'effective equation.' By that I mean a 
continuous value field over which one can iterate and find roots. How 
accurate those roots are is a LOT less clear to me... Like our 
isosurface set up, this method has no way to universally find all roots. 
In fact beyond a certain number of equations tossed into the mix, not 
sure the creator of the input really knows...

(In a bisection like solver - see below - they can also test thousands 
of points along the ray 'at once'. Not sure if this done.)

All said, it IS an approach I think could have a place with isosurfaces, 
but then there is the matter of multiple GPU vendors and packages on 
packages of ever changing software to get at it. Needing too to stay 
somewhat an expert in the field to keep it all running over time...

Aside: When I looked at the distance based work I was reminded of all 
the Design Rule Checking (DRC) work I did while working in the 
semiconductor industry for 30 plus years. A very big pile of very old 
methods exists there - on which I the distance stuff is somewhat leaning 
whether they know it or not. A pile of ideas / methods where we might do 
well to beg, borrow and steal too (text object(1)).

(1) - Which if I ever get to back to Christoph's freetype work will be I 
think a new character only object leaving 'text' as it exists with some 
patches in my povr.

> 
>> Your idea and/or a mix of those above there is a key component for
>> usefulness - some way to fade the isosurface function(s) at the hard
>> surface boundaries. Otherwise, we have gradient issues there - unless OK
>> with the container shape cutting or clipping the resultant shape.
> 
> OK, but I still don't understand the gradient issue.  We have CSG and flat
> planes and abrupt discontinuities in shapes all the time that the raytracer
> handles just fine.   Why are the raymarching algorithms not struggling with this
> gradient thing, whereas we find it to be positively crippling in certain
> instances? 
> 

There IS equation/value continuity in ALL the underlying ray-surface 
equations with roots (surfaces) showing up at zero - anywhere we get a 
clean result. All polynomial solvers returning 'all roots' require 
continuity - otherwise the root isolation methods do not work reliably.

The only solver approach handling discontinuities in a general and safe 
way - is a bisection(forward-marching) solver - of which our isosurface 
solver is a form (No I don't know if it lines up with any of the 
published by name ones...).

With bisection you can have discontinuities so long as you sample enough 
to not miss root ranges as the ray approaches actual roots. Once you 
know you have a range with '-' on one end and '+' on the other you can 
always find at least one root (or discontinuity too actually) in that 
range.

Aside: Range in hand with a root is where our isosurface solver - I 
think -  could probably close on the root faster so long as there is 
local continuity. Thinking users would declare this is so by option - 
and come what may. Even with continuity these faster methods are 
something risky, depending. I believe I have in hand a foolproof - coded 
from scratch New-Raphson/bisection uni-variate polynomial solver which 
could be adapted for use inside the isosurface solver.

The disadvantage of bisection / marching solver approaches is you never 
'really' know the number of roots - or whether you've found them all... 
Our parametric and isosurface objects carry this shortcoming. It can be 
a big one in csg and shadow testing, as examples.

I don't have all the answers. I never will. In my solver work I've 
collected a set of books if stacked on the floor would be well over my 
head. Papers, if printed, a stack many, many times that height. The 
whole of it is way, way beyond me to digest.

There is the problem too, in the last 30 years say, of enormous amounts 
of published noise in the field(2)... People need to publish for degrees 
so there is loads of minor-ish, real, but practically, meaningless stuff 
published. Figuring that out some touted by title thing isn't 'really' 
useful takes so blasted much time! There are also niches and notches 
where researchers are off doing things which seem related, but that 
don't really apply to ray tracing. Folks off working on polynomials of 
insane (for us) orders for various reasons...

Anyway, I'm starting to vent. I get frustrated too. :-) You're asking 
the right questions. If the answers were easy - wonderful, fast 
solutions would be everywhere to be had doing everything we want. Be 
thankful! That this not true, gives us a good hobby. ;-)

My philosophy is to push on things. See if something opens up where 
'relatively' easy progress can be made. If so, I work there until it 
gets hard - or I get bored. Then I push on other stuff. I'm also, 
slowly, pruning and changing povr to get it to a place where it's easier 
to try some things on my idea pile.

Apologies for the mistakes - a fair bit of thinking aloud so to speak.

Bill P.

(2) - Book publishers own rights to older stuff - or stuff not selling 
that well - that I can better afford. I believe now, those often spun up 
by an author's students or hired-influence-folks. A fair number of the 
books I've picked up aren't bad I guess. Often though, they're not 
helpful in any practical, get something real done, way. A particular 
popular one which is, has a license for the code there-in which forces 
open source efforts to "keep it on the shelf" for real code work.

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