how i can use the $BBX or $BBY or @BBZ and what they do with the curve,for example i have curve and then a point and in point the postion is $TX ,$BBY ,$TZ how is my curve to change?
any one have answer?

$BBX relates to the bounding box, as does $BBY and $BBZ and can be used on all types of geometry (except for volumes, which use $X, $Y, and $Z)

It simply gives a value between 0 and 1 depending on where your point is located within the bounding box of your geometry.

So say you have three points in a row on the x axis. One located at -1, one located at 0, and one located at 1.

If you told the alpha attribute to be $BBX, you would see that the point located at -1 would be totally transparent, the point at 0 would be half transparent, and the point at 1 would be opaque because you've assigned alpha values of 0, .5, and 1 to your points. (The values relate to their position in the bounding box, not in world space)

The expression you gave will likely re-order your points in the Y translate to be between 0 and 1 on the Y axis. I often will use a BB values as in the attached file. You can see that by using BBY you can blend between two pieces of geometry, or you can affect the color of the object.

i am very very thankfull to you , you help me very much and now i understand how it to work
thank you

i have another question : what is the different between $TX and $TX2

$TX2 is the point position in x for the second input of the point sop.

and if i want to use the $TX2 the SOPs in the 1input and 2input must have the same count of points

correct

Simon ,thank you very much

($TX*(1-$BBY))+($TX2*($BBY))
($TY*(1-$BBY))+($TY2*($BBY))
($TY*(1-$BBY))+($TY2*($BBY))
Allegro ,you used this equation in your example(attached file) i want to ask you how you know this equations (formulas) , it is very difficult to understand for me , i want to know if this equations is famous in the math or in houdini world, i want to know how you know this

The local expressions are all listed in the help for each node. They use just basic mathematics. Using a line SOP and point SOP see what you can come up with using a combination of the following using just addition and multiplication with :-
sin
cos
$TX , $TY , $TZ
$BBX , $BBY , $BBZ
$FF

The following video just uses those listed

Rob

Ok,that is greate. I can understand how to work {cos($BBX*720)*$BBX}or {sin($BBY)^2} and i can image how is the line SOP or the curve SOP to change when i use them and i can combine some expression to have a Spiral and that is very interesting to build a spiral stairs with some expression but the following expression :
($TX*(1-$BBY))+($TX2*($BBY))
($TY*(1-$BBY))+($TY2*($BBY))
($TY*(1-$BBY))+($TY2*($BBY))
i can image how to change the line or curve when i use them in position of point SOP with line SOP and i had stady the high mathematics a little but i don't remmeber this kind of expression and can you give me the link of help where this expression are listed ?
you can give me how to write this expression in the mathmatics with the X,Y,Z variables,i just want to see how to like its graphics in the XYZ system

These types of expression are not common expressions in maths. They are just the sort of thing you make up to solve a particular problem.

However it is very common to take a variable that goes from 0-1 (like $BBY) and to find the compliment 1-$BBY which then makes the number go from 1-0. Its also quite common to multiple one number (like $TX) by another one that goes from 0-1.

To understand what it is doing try putting some example numbers in for $TX and $BBY and see what comes out in each part of the expression.

Doing the reverse and coming up with the expression in the first place takes some experience of simple mathematics and other houdini expressions.
Again its a good idea to start with some example numbers and write down what you are starting with and what you hope to get out.

now , it is easy to understand . i couldn' t know why i didn't think about what you said.
thank you very much Simon