Jiri said:
Line confined between edges of an engraved line... snip ...Example: line 'b', 'd', 'e', 'g' in the image shown
b is not confined between the edges and extends beyond the length.
The line travels through the engraved line between edges, and with the edges. On its way upwards towards the center of the big x-shape it actually forms the right edge of the engraved line. Later, it starts hitting against the left edge. It is exactly as I describe it above. There is practically only one such line for the purposes here.
Nitpicking Saying that it is some sort of a negative that the "line extends beyond the length" is simply inexcusable. It is only natural to extend the line in order to see it better at the exit points, and to see, where it goes. This kind of argument strikes me as very repugnant - a specious argument for the sake of argument.
d is not confined to the original engraved line, includes part of a second line with a right angle and is extend past the ends for form an arbitrary junction.
The derived line 'd' stays entirely in the black for the entire course through the engraved line 'd'. It travels with the right edge, and it touches the lower (left) edge. Travelling with the edge, in effect smoothing it out, counts as staying in the black, according to the rules of this game.
In fact, this is a very nice example of successful translation. There is only one such line for the engraved line 'd'. You missed again..
And what arbitrary junction? Nothing about the line is arbitrary. Its junction with the x-axis is not arbitrary, then.' Oh, you hate me for extending this line, too.
e includes only part of an engraved line, stopping conveniently when the line begins to noticeably curve.
Again, the extrapolated 'e' is perfectly forced by the engraved line 'e'. It travels with both edges, and within the black. It does not curve. It stops, where another straight line begins. All is within the rules. Just look again.
BTW, line 'e' is also perfectly perpendicular to line 'b'.
g includes a number of different engraved lines and extends beyond all of them.[/QUOTE]
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The derived line 'g' stays entirely in the black from the top down to where the engraved line splits into a fork. This is easy to verify. Moreover, since in places it runs with both edges, it is the only such line here. It is entirely forced.
[/QUOTE=Jiri]
Tangential Points. on bowed lines... snip ...Example: line 'c' in the image shown The example shows that in this case the forced line runs with the edge of the engraved line on one side, instead of meeting a single point.[/QUOTE]
c appears entirely arbitrary, starting outside the engraved line and in from the end, and extending beyond a point central to the other end. Also, at no point is line
c tangent with an arc created by the engraved line.[/QUOTE]
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The fact is that the engraved line 'c' is itself an arc, whose two ends rest on the derived line 'c'. Again, there is only one such line, and thus it too belongs to the forced category. To you however it apears arbitrary. By now, I have lost any faith in your observational powers. I had presumed better for you.
Jiri said:
Hybrid lines
A line starts out as one type, but ends as another type.
Example line 'a'. It starts out from the bottom as the type 'bouncing between edges' in the first marked segment, and ends as a tangent in the other segment of the engraved line.
a is not tangent with any curve it intersects.[/QUOTE]
I am not sure what you are trying to say here as being a tangent precludes intersection with the same, but in general the extrapolated line 'c' is tangential to the curve between 'a' and 'd'.
Jiri said:
Of course, this line has an alternative based purely on the "bow" technique. It isn't the lone forced line, it is one of two possible forced lines.
alternate a use two separate lines and may even be tangent to one, just before it takes a sharp turn which you ignore.
The lines neither dilate, nor are they separated by 1/10th of a degree. The divergence, measured from your drawing, is approximately 7.2 degrees.
7.2 degrees, eh? Something tell me we are not looking at the same second line .
Your y axis is entirely arbitrary and the orientation of the engraving has been manipulated.
This is just low of you. The y-axis is part of the so called Cone & Square formation. It is the Square's diagonal, and it is our y-axis for the entire engraving. It never changes, it remains constant throughout my study of the engraving. You must have known that. If not, you had no business involving yourself in this discussion.
And what about your "the orientation of the engraving has been manipulated"? What kind of slander is that? You don't like the fact that I prefer working with the engraving in this orientation? It does not matter, how you twist and turn the engraving - the geometry remains the same.
I was very disappointed by your critique's low level of contact with reality. In fact I was offended by it, because it is so partisan, and antagonistiac. Back on ignore you go, Paul.