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This idea is from the new user mclarekin. Not sure it is at all feasible but I think his idea is interesting. I know in boxplorer there is a way to visualize the camera path for editing - that is the basically what he's asking for...

From mclarekin...

Mandlebulber Feature requests

 USING THE CATMULL-ROM SPLINE

My basic visualization is as follows:
Firstly onto a still single image (like say Kraftworks Infinitely O'Clock @ The Watchmaker's or FonkyBonkers by Ixh), render a "red" line ( the Catmull-Rom Spline) depicting the path of an animation flight in and out and around the features that has been recorded in keyframes.

 I can now visually see the whole or parts of the flight path winding it's way through the fractal ( and could possibly be used as a visual tool if i want to modify the path)

 Now this winding path could then be replaced by two parallel lines which are now iron tracks for a rollercoaster or tram, train, etc ("U" shaped trough for taboggin) (large translucent sphere chasing you along the tracks from backwards facing camera, as in Indianna Jones).

 Then I would want to render my animation again showing these tracks existing in the same 3D space as the fractal.

 Further I could create a new set of key frames, initially following the first path but choosing to deviate at some point along a new flight path, to produce a fork in the path (alternative route(s)), this would look good in a high speed rollercoaster ride through or around a fractal.
 This idea is probably not very original, but as the Catmull-Rom Spline exists it would be fun to have it easily useable within the program and to be able to give it various cross sectional characteristics .

 

http://code.google.com/p/boxplorer2/wiki/ScreenShots shows what that looks like in boxplorer2.

Catmull-Rom gets pretty annoying with sparse keyframes, or deep-dive keyframes. Lots of hard to control overshoot at times. But it does have the nice property of hitting all the keyframes.

With boxplorer2 I use a color coding hack (255 shades of pure blue) to allow for interactive grabbing and dragging of the spline keyframes. All this is only barely fun under interactive frame rates.
Showing the path statically would not require much more than a z-buffer obeying linedraw.

this is how my workaround looks

My math is quite weak.  I started learning about splines about 4 years ago though, so I could (try) to make smoother flame animations.
Recently I saw a paper that may be of interest, though I believe it probably won't help much with overshoot:
"A minimum-energy quadratic curve through three points and corresponding cubic Hermite spline" which you can download here:
http://arxiv.org/abs/1010.4615

There are some representative graphs in the presentation as well as pseudocode at the end of the paper.  From that example I was able to work out a routine for my (next, yet unreleased) flame animation script, but I am not so confident that my implementation is correct.