Sin-thesis


 

How Sin-thesizing is done

Creating a straight segment is rather easy. Simply set the end vertex to the desired distance on the negative Z-axis. Any X- and Y- values are zero. But where are we to put the control points?
 
We will call the mathematicaly correct solution 'equidistant' (you may also have found 'equidistant' with these 'Push Straight...' operations already). So the 1st control point will be on exactly one third of the straight's lenght, the 2nd on two thirds of it.
 
However: when 'making straight' any segment within the Nolimits-Editor you will get different positions for the two control points. This other characteristic is available as an option also.
 
 
Calculating Bows (arcs, curves, turns, call these whatever you like) is a bit more tricky. Due to the nature of the 3rd-order beziers we're using with NoLimits there is no mathematical exact solution of creating a perfect circle or any part of it. You simply can't model sine/cosine functions with a 3rd-order Bezier polynom. (Tiny voice: "B-splines, get B-splines!" Redunzelizer: "Forget it!")
 
So we have to find a Bezier-curve that represents the 'apperance' of a circle/bow as close as possible.
 
The initial values for this calculation are based on a 'best fit - least error' algorithm and will not be discussed here. For you it's most important to reckognize that the error of this calculation (the 'non-perfect behaviour' so to say) increases dramaticaly with larger angle values! It's therefor strongly recommended using angles smaller than aproximately 65 degrees.
 
 
Designing A Parabolic Hat using Bezier's is possible with mathematical perfection. The quadratic parabola segment(s) created here are a subset of the Bezier's third-order eqations, thus can be modeled with ease. Nevertheless there are lots of different parameters which may define the desired final result.
 
 
Cooking a Bezier by coordinates is something for the 'not faint at heart' (at least mathematicaly spoken). So fire up you spreadsheets and on we go... (Low voice: "Uarghhhhh... Please take that away!")   In case of more complex prefabs please use the import- / export-functions which are described in chapter 'Menus & Commands'.

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Sin-thesis: General

!!! Caution: The Result of any synthesis will immediately become your new 'IN' and thus overwrite any previously existing 'IN' !!!
 
First choose what to do: besides the four existing groups (Straight, Bow, Parabola, Coord's) you will find some 'radiobuttons' by which you may select the type of synthesis you want to do.


Select a Sin-thesis


Then better do some general settings which will affect all (w. one exception) kinds of sin-thesizing:


Synth Panel: General Options

After you have set all the other specific values and finaly pushed the 'Synthesize'-button... (Third voice: "Show me! Show me!".) OK here you are. On special request of the audience, exlusive and only tonight we proudly present the fabulous:

Synthesize Button

... so you've pushed the 'Synthesize'-button and the result will immediately become your new 'IN' and show up.

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Sin-thesis: Straights


Synth Panel: Straight's options


The result will be created within the ZX-plane and thus have zero Y-values. The X-/Y-/Z-Coordinates of the 1st Vertex (Bezier-'P0') will be 0/0/0.
 

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Sin-thesis: Bows


Synth Panel: Bows's options


The result will be created within the ZX-plane and thus have zero Y-values. The X-/Y-/Z-Coordinates of the 1st Vertex (Bezier-'P0') will be 0/0/0. A positive angle will make your bow turn the right, a negative to the left. Input of 'Angle' values is limited to 90.0 degrees.
 
There are three Inputs: values for angle, radius and and bow lenght. Calculation is done out of two of these three which you may then choose by checking one of the following 'By'-options.

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Sin-thesis: Parabolic Hats


CAUTION: the general 'resizing' option on the 'Synth Panel' will NOT influence Parabolas!
 


Synth Panel: Parabola's options


 
The result will be created within the ZY-plane which is 'straight forward' and up and thus have zero X-values. The X-/Y-/Z-Coordinates of the 1st Vertex (Bezier-'P0') will be 0/0/0.
 
The settings will first create and affect a half 'Parabolic Hat' stub! This 'half' may then optionaly (by default) be mirrored to give a fully symmetric 'hat'.
 
The first line will determine the general characteristics. Select one of the following three: In case you have selected 'G&V' above you will have to preset the velocity of the train (precisesly: of the 'mass center' of the virtual train as seen on rail/wheel-level! (Phew...)) as it's passing the 'top' (the highest point of the parabola) Finaly you will have to set the actual dimensions of the resulting segment(s): Additional Parabolic Hat Options:

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Sin-thesis: By Bezier-Coordinates

This will give you the opportunity to create a single segment by user-defined values. In case you want this a bit more elegant or wish to create multiple segments please use the import- / export-functions (from/to CSV-/Text-files) which are available by [Menu]:[Prefab]:[... as CSV-/Text ...]


Synth Panel: Bezier Coord's Input

There is NO VALIDATION done on any of these values! Z-Coordinates are preset -2...-6 to instantly remind you of the existent Z-axis direction. You probably also may ask: 'Where can i set the coordinates for the P0 ?'. These are 0/0/0, remember? Maybe you forgot all this until now? Of course you didn't! I'm sooooo sorry about assuming that...
 
(Tiny voice once more: "This redunzelizer sucks!")

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