There is of course the case of points on import() or surface().

From: Adrian Mariano [mailto:avm4@cornell.edu]
Sent: Wed, 1 Sep 2021 04:42
To: OpenSCAD general discussion
Subject: [OpenSCAD] Re: Provide a simple measurement tool

I see that nophead has given one solution to the problem of finding the tip of this cone:

rotate([80,40,20])cylinder(h=10, d1=10, d2=0);

It's also easy to do with BOSL2.  (I note I neglected to include the "include<BOSL2/std.scad>" in my previous example.)

include<BOSL2/std.scad>
echo(rot([80,40,20], p=[0,0,10]));

If you want to know how this is actually working, basically you construct the same rotation matrix that rotate() is using and apply it to the cone tip.  If you want to do stuff like this then in my opinion you should do it once and put it in a library.  (Or do it zero times yourself and use nopscadlib or BOSL2, or dotSCAD.)  There is a certain amount of "reinventing OpenSCAD" in that doing this requires writing code that does the same thing that rotate() does.  There was vague talk of a proposal to expose object geometry to users using the new function literals.  I don't know if it's something likely to happen someday.  But even if it did, you still have the problem of: given a cone as a list of points and faces, how do you find the vertex?

But again I wonder about the use case for this.  Personally I never invoke rotate with more than one angle---do you actually use vector angles like this?  Why do you want to know where the tip of the cone is at that weird angle?    If it's because you want to put an object there then you don't need to know where the point is.  You just need to be able to make an object go there.  That's a different requirement.  That's why I'm wondering about what the real use case is.  In the case of Jordan's models he wants to design by trial and error and in that case there's no way around needing to measure your model so that you can determine what the error is.  But I remain curious about other situations where you need to know where something is that are not artificial, because I wonder if there's a different way to solve them.  In my own modeling I usually want to position things in relation to other things, and this does NOT require that I actually know the coordinates of any of the objects in my model.  The case that's problematic is if you want to create an object in relation to TWO (or more) other things, but I have not encountered that case in my own modeling.  That is, if something needs to be sized based on 2 things there's really some other fundamental size underlying it all.  So I don't understand a practical situation where you need the distance between the tips of two arbitrarily rotated cones.

On Tue, Aug 31, 2021 at 8:42 AM Ray West raywest@raywest.com wrote:

Going back to my original bit of code with the two cones, I would like to be able to calculate the xyz coordinates of this cone tip. (it being 60 years since 'I did O-level Maths', and I can't get my head around this)

rotate([80,40,20])cylinder(h=10, d1=10, d2=0);

Thanks.

On 30/08/2021 20:43, Adrian Mariano wrote:

Yes, geometrical calculations can be painful.  I know people here are fond of doing everything from first principles every time, which makes them more painful than might be necessary.  But my quick solution to your squares problem:

sq1 = rot(a,p=square(10));
sq2 = right(20,p=rot(b,p=square(10)));
stroke(sq1,closed=true);
stroke(sq2,closed=true);
alldist = [for(i=[0:3], j=[0:3]) segment_distance(select(sq1,i,i+1), select(sq2,j,j+1))];
echo(min(alldist));

But your examples also gets at the question of what allowed definitions of points are, the "random" points.  Your definitions both have to do with optimization, which means you've gone up a leap in complexity from simple geometry.  Points derived from optimization aren't going to be clickable on a model.  You can't "see" them.  The only way you can find these points is by doing the math.

I can't run your model because it's full of parameters.  But I would think that in that case, at least, it would be possible to define your model in terms of the width.  If you start from the width and build everything from there then you'll have the right width.  That's the kind of thing I meant when I wondered about the need for access to distance values.  The notion that you need to know the width of your model after the fact so you can fix your botched model by trial and error to make it the right width....doesn't appeal to me as a design strategy.  But if you really want to pursue trial-and-error design then having a way to measure does seem very important.  (It's unclear to me if starting from the width just shifts the measurement problem somewhere else, but it seems like if you have measurable parameters you should be able to measure them and then design to the measurements directly.)

On Mon, Aug 30, 2021 at 12:45 PM Jordan Brown openscad@jordan.maileater.net wrote:

On 8/29/2021 5:57 PM, Adrian Mariano wrote:

The question I have is: why do you need to know where a point is?  What are you trying to do that requires this knowledge in a real model?  I wonder if there might be alternative approaches that don't require that information, or where the model can be structured so that it's easy to know where the point is.  I suspect that at least some of the time, such alternative approaches may exist.

I think the problem with straight "calculation" schemes is that they can get very hard, very fast.

Quick, what's the distance between the closest points in these squares?

rotate(a) square(10);
translate([20,20]) rotate(b) square(10);

You're a much stronger math guy than I am, so maybe you can do that off the top of your head, but it would take me some pretty serious thinking.  And that's a simple case.

In a real project... as I've mentioned, a lot of my work is in scale models.  I was designing an armchair:
https://cdn.thingiverse.com/assets/ed/00/42/d1/65/featured_preview_WIN_20200407_22_06_02_Pro.jpg

Here's what generates the sides and arms:

    // Sides
    for (s=[-1, 1]) {
        translate([s*w/2, d, leg_h+seat_h]) {
            rotate([90, 0, -90])
                clip(v=[0,0,s]) {
                    pipe_polygon(r=wing_t, fill=true, open=true, [
                        [3*inch, 0],
                        [18*inch, 0],
                        [18*inch, 8.5*inch],
                        [4*inch, 8.5*inch],
                        [3.5*inch, 17*inch],
                        [4*inch, 26*inch],
                        [-3.8*inch, 28*inch]
                    ]);
                }
            // Arms
            translate([s*0*inch, -20.75*inch, 8.75*inch])
                rotate([-86.5,0,4*s])
                cylinder(d2=wing_t*1.3, d1=wing_t*2, h=16*inch);
        }
    }

All of those dimensions are measured by hand off the real object, and the angles are eyeballed.

Now, what's the width, measured between the outsides of the two arms?  I want to tweak the angles and sizes so that's it's pretty close to correct.

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A reminder, in the editor put the cursor next to a number and Alt-Up/Down changes it and previews, handy for such adjustments.

And/or you could restructure it to use customizer to move them around??

From: Ray West [mailto:raywest@raywest.com]
Sent: Thu, 2 Sep 2021 08:57
To: discuss@lists.openscad.org
Subject: [OpenSCAD] Re: Provide a simple measurement tool

I've simplified my eyeballing technique, distances can be measured fairly quickly.

I start off by defining the tolerance I'm happy with.

I've made a module named tol() and set it to 0.5 for this example

module tol(t){

# sphere(t);

}

then I place a tolerance sphere at each of the two points I'm measuring between

e.g. like

p1=([0,0,10]);
translate(p1)tol();  // first point
p2=([54.5,11.2,41.3]);
translate(p2)tol(); // second point

They are easy to position, one at a time, by positioning x,y from the top or bottom view, adjusting the appropriate values in PI or P2, and then  position z from one of the other views.  zooming or rotating the view as required.

then the distance can be echoed by  something like

module dist(p1,p2){
dx= p2.x-p1.x;
dy= p2.y-p1.y;
dz= p2.z-p2.y;
l= sqrt((dxdx) +(dydy) +(dz*dz));
echo(distance = l);
}

provided the points of interest lie within the tolerance spheres, I get the distance between the points within my defined tolerance,. If I want a more accurate result, I can reduce the tolerance and zoom in closer when positioning the spheres. If the tolerance sphere is too small, to see on the full size view, then I could easily  place a few rings around them, or similar.

On 31/08/2021 22:31, Ray West wrote:

The idea was to generate a couple of points, that i would not have any precise idea where they were, for what I originally thought was a test for the measuring tool that i mistakenly thought was being  talked about earlier. Now, I have gone back to thinking that If I calculate the positions, then I can check my eyeballing technique errors, just a test. I am also thinking, in the back of my mind, of the possibility of using the openscad scad text file as the input to some other program, to see if distance can be calculated there. I've a thought  that it could be possible for designs made of simple shapes, but the maths would be beyond me for anything complicated. From what I've seen, for rotating points, as per cone, it involves matrix calculations, which if I ever learnt anything about them, now, I've completely forgotten.

Best wishes,

Ray

On 31/08/2021 19:42, Adrian Mariano wrote:

I see that nophead has given one solution to the problem of finding the tip of this cone:

rotate([80,40,20])cylinder(h=10, d1=10, d2=0);

It's also easy to do with BOSL2.  (I note I neglected to include the "include<BOSL2/std.scad>" in my previous example.)

include<BOSL2/std.scad>
echo(rot([80,40,20], p=[0,0,10]));

If you want to know how this is actually working, basically you construct the same rotation matrix that rotate() is using and apply it to the cone tip.  If you want to do stuff like this then in my opinion you should do it once and put it in a library.  (Or do it zero times yourself and use nopscadlib or BOSL2, or dotSCAD.)  There is a certain amount of "reinventing OpenSCAD" in that doing this requires writing code that does the same thing that rotate() does.  There was vague talk of a proposal to expose object geometry to users using the new function literals.  I don't know if it's something likely to happen someday.  But even if it did, you still have the problem of: given a cone as a list of points and faces, how do you find the vertex?

But again I wonder about the use case for this.  Personally I never invoke rotate with more than one angle---do you actually use vector angles like this?  Why do you want to know where the tip of the cone is at that weird angle?    If it's because you want to put an object there then you don't need to know where the point is.  You just need to be able to make an object go there.  That's a different requirement.  That's why I'm wondering about what the real use case is.  In the case of Jordan's models he wants to design by trial and error and in that case there's no way around needing to measure your model so that you can determine what the error is.  But I remain curious about other situations where you need to know where something is that are not artificial, because I wonder if there's a different way to solve them.  In my own modeling I usually want to position things in relation to other things, and this does NOT require that I actually know the coordinates of any of the objects in my model.  The case that's problematic is if you want to create an object in relation to TWO (or more) other things, but I have not encountered that case in my own modeling.  That is, if something needs to be sized based on 2 things there's really some other fundamental size underlying it all.  So I don't understand a practical situation where you need the distance between the tips of two arbitrarily rotated cones.

On Tue, Aug 31, 2021 at 8:42 AM Ray West raywest@raywest.com wrote:

Going back to my original bit of code with the two cones, I would like to be able to calculate the xyz coordinates of this cone tip. (it being 60 years since 'I did O-level Maths', and I can't get my head around this)

rotate([80,40,20])cylinder(h=10, d1=10, d2=0);

Thanks.

On 30/08/2021 20:43, Adrian Mariano wrote:

Yes, geometrical calculations can be painful.  I know people here are fond of doing everything from first principles every time, which makes them more painful than might be necessary.  But my quick solution to your squares problem:

sq1 = rot(a,p=square(10));
sq2 = right(20,p=rot(b,p=square(10)));
stroke(sq1,closed=true);
stroke(sq2,closed=true);
alldist = [for(i=[0:3], j=[0:3]) segment_distance(select(sq1,i,i+1), select(sq2,j,j+1))];
echo(min(alldist));

But your examples also gets at the question of what allowed definitions of points are, the "random" points.  Your definitions both have to do with optimization, which means you've gone up a leap in complexity from simple geometry.  Points derived from optimization aren't going to be clickable on a model.  You can't "see" them.  The only way you can find these points is by doing the math.

I can't run your model because it's full of parameters.  But I would think that in that case, at least, it would be possible to define your model in terms of the width.  If you start from the width and build everything from there then you'll have the right width.  That's the kind of thing I meant when I wondered about the need for access to distance values.  The notion that you need to know the width of your model after the fact so you can fix your botched model by trial and error to make it the right width....doesn't appeal to me as a design strategy.  But if you really want to pursue trial-and-error design then having a way to measure does seem very important.  (It's unclear to me if starting from the width just shifts the measurement problem somewhere else, but it seems like if you have measurable parameters you should be able to measure them and then design to the measurements directly.)

On Mon, Aug 30, 2021 at 12:45 PM Jordan Brown openscad@jordan.maileater.net wrote:

On 8/29/2021 5:57 PM, Adrian Mariano wrote:

The question I have is: why do you need to know where a point is?  What are you trying to do that requires this knowledge in a real model?  I wonder if there might be alternative approaches that don't require that information, or where the model can be structured so that it's easy to know where the point is.  I suspect that at least some of the time, such alternative approaches may exist.

I think the problem with straight "calculation" schemes is that they can get very hard, very fast.

Quick, what's the distance between the closest points in these squares?

rotate(a) square(10);
translate([20,20]) rotate(b) square(10);

You're a much stronger math guy than I am, so maybe you can do that off the top of your head, but it would take me some pretty serious thinking.  And that's a simple case.

In a real project... as I've mentioned, a lot of my work is in scale models.  I was designing an armchair:
https://cdn.thingiverse.com/assets/ed/00/42/d1/65/featured_preview_WIN_20200407_22_06_02_Pro.jpg

Here's what generates the sides and arms:

    // Sides
    for (s=[-1, 1]) {
        translate([s*w/2, d, leg_h+seat_h]) {
            rotate([90, 0, -90])
                clip(v=[0,0,s]) {
                    pipe_polygon(r=wing_t, fill=true, open=true, [
                        [3*inch, 0],
                        [18*inch, 0],
                        [18*inch, 8.5*inch],
                        [4*inch, 8.5*inch],
                        [3.5*inch, 17*inch],
                        [4*inch, 26*inch],
                        [-3.8*inch, 28*inch]
                    ]);
                }
            // Arms
            translate([s*0*inch, -20.75*inch, 8.75*inch])
                rotate([-86.5,0,4*s])
                cylinder(d2=wing_t*1.3, d1=wing_t*2, h=16*inch);
        }
    }

All of those dimensions are measured by hand off the real object, and the angles are eyeballed.

Now, what's the width, measured between the outsides of the two arms?  I want to tweak the angles and sizes so that's it's pretty close to correct.

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