Controlling a line from a non zero offset

[vojo]

Trying to build a 30 degree line starting from some non zero offset

Starting from zero offset (lower left corner) is pretty straightforward...top picture attached

Starting from non zero offset (say in the middle of a square) seems tough (or at least I cant figure it out)....bottom picture attached

Tried setatref et al, bound, etc.....can get close but does not work in all cases

Thoughts guys

[Yacine]

Hi Vojo,
The line with offset is of a form y=a*x+b
In your case you bound y to a form a*x (without b)
So you need to modify the formula to something like: GUARD(Controls.Row_1*TAN(30 deg)+40 mm)
You need to do this for both the begin and the end point of the line.
I enclose an adapted shape

[vojo]

Thx....step in right direction, though its a subset of the general problem
Aka what if the line starts in the middle of square

wait...I could do the following
   1) find the point in the middle (your control_1)....when shape is completed...this comes from a more complex calculation
   2) take the X compoenent....do something like controls.row_2.y = - controls.row_1.x * tan (30 deg)     ....controls.row_2.x = 0
   3) then do controls.row_3.x is  BOUND to controls.row_1.x...controls.row_3.y = controls.row_3* tan 30 deg

I will try that

That pesky required reference to width*0 and height*0 for control points made it hard/unclear to do this in one step

thx

[Yacine]

Hi Vojo,

That pesky required reference to width*0 and height*0 for control points made it hard/unclear to do this in one step

If you change the X and Y behavious of the control points to OffsetMin (2), you get distances instead of ratios of width and height.

[wapperdude]

It can be much simpler.  First, the line equation in general terms is (y-y1)= m*(x-x1)  where m is the slope =(y2-y1)/(x2-x1).  Let the pair (x1,y1) be your lines starting point, and the pair (x2,y2) be the end point.  The slope m also equals tan(angle), or in your case, tan(30 deg).

For a completely free form case, let your top group shape have two control points.  Let controls.row_1 be the begin point of your line, e.g., BeginX, and Begin Y.  Let  controls.row_2 be your end points EndX and EndY of the line sub-shape.  Thus, controls.row_1 becomes any arbitrary offset.  Controls.row_2 sets the end point, and the line spans between the two control points.

Now use the equation above to set controls.row_2.y by formula:  y= m*(x-x1)+y1.  Specifically, controls.row_2.y = GUARD((Controls.Row_2-Controls.Row_1)*TAN(30 deg)+Controls.Row_1.Y). 

You can substitute any coordinate pair for the start point by simply replacing the controls.row_1 and controls.row_1.y with values that you desire...just as long as everything is using same coordinate system.

Should do the trick.

HTH
Wapperdude

[vojo]

thx guys

Still had behaviors at 0...will try 2

However, with behaviors at 0...its a bit more complicated than a simple y-y0=M(x-x0) equation.

1.  need to compute the distance of the original offset point aka depth = sqrt (...)
2.  Take the y component of that offset point and subtract the depth*sin (30 deg)     
3.  this new point  (0,offset.y-depth*sin(30 deg) is the start of the line at widht = 0
4   then can use bound and guard

gets me the closest to the correct solution so far (depending on the offset and distance involved with #4, it tends to drift some).
I tried the other examples....they seem to track worse

Here is what I am trying to do (select the manifold at the bottom)

[wapperdude]

Ah!  I see what you're trying to do.  Nice.

After studying what's going on, I focused only on the rectangular shape.  It would seem a slight change will solve your problem.  Controls.row_1 and row_2 are the foundation and controls.row_4 reference what they do.

The changes would be as follows:
  Keep controls.row_1 as starting point for your rectangle, but make
     1. the 2nd point of the rectangle controls.row_2.  Seems logical and simplifies calcs.
     2.  make the 3rd point (the upper right point), be controls_row4.  Just that.  Formula changes will be applied to the control point.
     3.  make the final, upper left point, based upon a formula using controls_row4 and the X-, Y- changes of the baseline.
            X-value = Controls.Row_4-User.Row_7
            Y-value = Controls.Row_4.Y-User.Row_8
            ...and then finish off the shape as usual.

     4.  The two user rows are the delta X and delta y changes of the Line:
             Row_7:  =Controls.Row_2-Controls.Row_1
             Row_8:  =Controls.Row_2.y-Controls.Row_1.y

     5.  Finally, controls.Row_4, you only need to define the Y-value by formula and uses controls.row_2 as its offset reference:
             =GUARD((Controls.Row_4-Controls.Row_2)*TAN(30 deg)+Controls.Row_2.Y)

This seems to work for any position of the control points.  Did not make any changes to controls.Row_3 or Row_5.

HTH
Wapperdude

[vojo]

much appreciated....will give it a try...thx

[vojo]

ok...so the actual solution is this

Controls.row_3 = guard((controls.row_1+controls.row_2)/2)
Controls.row_3.y = guard((controls.row_1.y+controls.row_2.y)/2)

Controls.row_4 = <anything>
Controls.row_4.y = guard((controls.row_4-controls.row_3)*tan(30 deg) + controls.row_3.y)

Geometry
X1 = controls.row_1                                                            Y1 = controls.row_1.y
X2 = controls.row_1+controls.row_4-controls.row_3              Y2 = controls.row_1.y+(controls.row_4-controls.row_3)*tan(30 deg)
X3 = controls.row_2+controls.row_4-controls.row_3              Y3 = controls.row_2.y+(controls.row_4-controls.row_3)*tan(30 deg)
X4 = controls.row_2                                                            Y4 = controls.row_2.y
X5 = geometry1.X1                                                             Y4 = geometry1.Y1

Everything lines up now and controls 4 is midpoint of back edge in all cases