Stabilization of Curve Directions

Let me start from what I’d like to make:

I.e., we got two curves, between which I’d like to, for example, stretch Blend or do the previously described center curve procedure by spreading points in Ratio Mode, connect them with lines, and through center points of those lines lead Spline (our approximate center curve). Those two curves have opposite vectors (I’ll purposefully start from such example), meaning, when you indicate them using the tree, Blend won’t pass through without correcting vector of one of the curves… That will give us:

So the condition for the procedure is, to direct two curves so that they have the same direction. When marking out center curve, we’ll get false curve, because the straight lines will intersect each other. And something like that will always happen during any change in Parent orientation. How do we avoid that? We need to carry out a procedure, that will somehow connect vectors of those two curves, and keep them together, pointing in the same direction…

Here’s an example procedure:

– create a Spine curve between our two curves, it will define common direction for both of our curves

– next, create normal plane for the Spine:

Now let’s stabilize the first of our curves:

– create intersections between the normal plane for Spine and the one from our curves,

– using that intersection, create normal line for the plane, let’s say 20 mm long (that line will adopt the orientation of the plane),

– create a line outgoing from intersection and contacting our curve – keep the 20 mm length (the line will adopt the orientation of our curve),

– then, on both lines create a point in Ratio mode (on the ends) :

– then create inverse out of our curve, and parameterize it with the following formula:

the distance between two points > 20 mm

– do the same procedure with the other curve.

Now we got two, so to speak, “intelligent” inverses, which react to the change in Parent orientation, and are interconnected through the Spine curve. That will result in two curves with vectors pointing in the same direction… Now we can stretch Blend over, and it will never reverse.

Here is a clip showing that procedure:

In the end, they’ve developed a template for Blend – for a stable one. And what’s the advantage of that template?? You don’t have to mind the directions of inputs when inserting a template – all you need to do is blindly click them out, and the stabilization procedure will do the rest… A good early approach to templates, at the stage of their creation, i.e., by stabilizing all directions of input elements. An example of such template is already included in the entry about pipe axis – follow that procedure, because there’s a direction that’s been stabilized in a similar way… Soon, I’ll describe how to make a stable parallel curve, and finally, a spatial middle curve (having half of the job already done :-).
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}