Nabble removed Mailing-list integration from the Forum.
This killed the Forum. This is now an ARCHIVE.
It is likely Nabble will shutdown in the future.
So basically the Forum is now out of date, we are looking into migrating the history.
OpenSCAD support is now provided by the Mailing List.
See the first pinned post here for instructions on subscribing to the mailing list.
Fit an rectangle into another rectangle
Locked
12
12
Fit an rectangle into another rectangle
 
|
Task is to fit a rectangle with given width 'w' into another rectangle with given size 'a' x 'b', so that all four edges of inner rectangle touches the outer rectangle ( at [x,0],[0,y],[a-x,b],[a,b-y] ). Now I need a formula to calculate x and y from given a,b,w
 I have made an animation, which illustrates the problem. (OpenSCAD script below) If 'x' is known, solution is simple to calculate 'y' and 'w'. (see fit_for_given_x(x) ) Now I need a function fit_for_given_w(w) to calculate 'x' and 'y'
// Animation: FPS=5 STEPS=100
a=13;
b=15;
module fit_for_given_x(x)
{
y=b-(b/2+sqrt(x*x+b*b/4-a*x));
w=sqrt(x*x+y*y);
inner_rect=[[x,0],[0,y],[a-x,b],[a,b-y]];
color("blue")linear_extrude(0.01)polygon(points=inner_rect);
color("black")translate([x,0,0])linear_extrude(0.02)text(str("x=",x),size=1,halign="center",valign="top");
color("black")translate([0,y,0])linear_extrude(0.02)text(str("y=",y),size=1,halign="right",valign="center");
color("black")translate([x/2,y/2,0])linear_extrude(0.02)text(str("w=",w),size=1,halign="left",valign="bottom");
}
if(is_num($t))
{
if($t>0)if($t<1)
{
fit_for_given_x(a*$t);
}
}
color("black")translate([a/2,b,0])linear_extrude(0.02)text(str("a=",a),size=1,halign="center",valign="bottom");
color("black")translate([a,b/2,0])linear_extrude(0.02)text(str("b=",b),size=1,halign="left",valign="center");
outer_rect=[[0,0],[0,b],[a,b],[a,0]];
color("yellow")linear_extrude(0.001)polygon(points=outer_rect);
Sent from the OpenSCAD mailing list archive at Nabble.com. _______________________________________________ OpenSCAD mailing list To unsubscribe send an email to [hidden email] |
Re: Fit an rectangle into another rectangle
|
I think you need to know the height of the internal rectangle as there are many ways to place one of width w that give different heights. On Thu, 25 Mar 2021 at 09:27, bassklampfe <[hidden email]> wrote: Task is to fit a rectangle with given width 'w' into another rectangle with given size 'a' x 'b', so that all four edges of inner rectangle touches the outer rectangle ( at [x,0],[0,y],[a-x,b],[a,b-y] ). Now I need a formula to calculate x and y from given a,b,w _______________________________________________ OpenSCAD mailing list To unsubscribe send an email to [hidden email] |
Re: Fit an rectangle into another rectangle
|
|
Re: Fit an rectangle into another rectangle
|
Re: Fit an rectangle into another rectangle
|
|
Re: Fit an rectangle into another rectangle
|
|
Re: Fit an rectangle into another rectangle
|
|
Sorry, but no.
I did as you suggested. Lets have a=13, b=15, w=9 (to be similar to screenshot of animation) I place the line at an arbitrary location touching a and b, create two right angles. (did this with Inkscape). But – SURPRISE – they don't fit on the other side creating a rectangle. See  There is only ONE x, where the two dotted lines will match, believe me... Sent from the OpenSCAD mailing list archive at Nabble.com. _______________________________________________ OpenSCAD mailing list To unsubscribe send an email to [hidden email] |
Re: Fit an rectangle into another rectangle
|
|
Ok, yes I see the problem now. I think by symmetry and similar triangles y / x = (a-x) / (b- y). And x^2 + y^2 = w^2, so you have to solve those two simultaneous equations. On Thu, 25 Mar 2021 at 14:27, bassklampfe <[hidden email]> wrote: Sorry, but no. _______________________________________________ OpenSCAD mailing list To unsubscribe send an email to [hidden email] |
Re: Fit an rectangle into another rectangle
|
|
Re: Fit an rectangle into another rectangle
|
|
In reply to this post by bassklampfe
When you've solved that, then consider a room, say 14ft by 12ft,
and you need to cut a scaffold plank, 1 foot wide, with square
ends, so that it fits exactly diagonally across the corners, as a
platform for artexing the ceiling, say. What length plank is
required? (The four corners of the plank touch the walls). Has to
be a formula, no iterative process/drawing allowed. On 25/03/2021 09:26, bassklampfe wrote:
Task is to fit a rectangle with given width 'w' into another rectangle with given size 'a' x 'b', so that all four edges of inner rectangle touches the outer rectangle ( at [x,0],[0,y],[a-x,b],[a,b-y] ). Now I need a formula to calculate x and y from given a,b,w _______________________________________________ OpenSCAD mailing list To unsubscribe send an email to [hidden email] |
Re: Fit an rectangle into another rectangle
|
|
I gave the equation to Wolfram to solve. It did but answer is horrible: https://www.wolframalpha.com/input/?i=solve+sqrt%28w%5E2+-x%5E2%29%2Fx+%3D+%28a-x%29+%2F+%28b+-+sqrt%28w%5E2+-x%5E2%29%29 On Thu, 25 Mar 2021 at 17:08, Ray West <[hidden email]> wrote:
_______________________________________________ OpenSCAD mailing list To unsubscribe send an email to [hidden email] |
Re: Fit an rectangle into another rectangle
|
|
Re: Fit an rectangle into another rectangle
|
|
Re: Fit an rectangle into another rectangle
|
|
Re: Fit an rectangle into another rectangle
|
|
In reply to this post by MostlyHarmless
I can tell you, you are not. Solution of this problem is one missing part to build steel constructions like  without mechanical errors and in the final step to build full customizable railway steel bridges in OpenSCAD. When all things are completed, I will happily share the result with you. Sent from the OpenSCAD mailing list archive at Nabble.com. _______________________________________________ OpenSCAD mailing list To unsubscribe send an email to [hidden email] |
Re: Fit an rectangle into another rectangle
|
|
In reply to this post by nophead
 I'm not scared by the answer, as long as it is correct – which still has to be prooved.
But isn't it this, why we use computers? To do calculations, which feels like horror to some people 
Sent from the OpenSCAD mailing list archive at Nabble.com. _______________________________________________ OpenSCAD mailing list To unsubscribe send an email to [hidden email] |
Re: Fit an rectangle into another rectangle
|
|
Re: Fit an rectangle into another rectangle
|
|
In reply to this post by nophead
Nop head was on the right path. But he left the a,b,w as variables for Wolfram. It doesn't complete within the allotted time, so fails to simplify. I tried specifying the example input variables of A=13, B=15 and W=9.16, which allows the algorithm to simplify earlier. Now it solves for x=8.57 (and also some imaginary solutions). The original request was for a formula to set up Fn(a,b,w) returning x. I am not able to solve the problem the way Wolfram did. It appears to use 2 simultaneous equations (see the two lines on the graph). Nop head specified those. Interesting problem that seems like it out to be easy, but seem to actually be computationally complex. Kevin On Thu, Mar 25, 2021 at 1:10 PM nop head <[hidden email]> wrote:
_______________________________________________ OpenSCAD mailing list To unsubscribe send an email to [hidden email] |
Re: Fit an rectangle into another rectangle
|
|
Maybe there's a clever way to solve this using trig, but I'm not seeing it---and the similarity relationship really seems like the fundamental defining property.
Solving a quartic isn't a big deal. But solving one *symbolically* like Wolfram Alpha does is completely pointless. The quartic formula is a horrible mess. Give up on the idea of having a formula, and definitely don't try to use the mess from Worlfram Alpha. You need to solve the equation numerically. BOSL2 has a polynomial root finder that will do the job. https://github.com/revarbat/BOSL2/wiki/math.scad#function-real_roots include<BOSL2/std.scad> a=13; b=15; w=9; function getx(a,b,w) = let( options = real_roots([4,-4*a, a*a+b*b-4*w*w, 2*w*w*a, pow(w,4)-b*b*w*w]), posopt = [for (x=options) if (x>0) x] ) assert(len(posopt)==1) posopt[0]; x=getx(a,b,w); y=b-(b/2+sqrt(x*x+b*b/4-a*x)); echo(x=x,y=y); echo(sqrt(sqr(x)+sqr(y))); inner = [[x,0], [0, y], [a-x,b], [a,b-y]]; linear_extrude(height=1)square([a,b]); color("red")linear_extrude(height=1.1)polygon(inner);  Sent from the OpenSCAD mailing list archive at Nabble.com. _______________________________________________ OpenSCAD mailing list To unsubscribe send an email to [hidden email] |
Re: Fit an rectangle into another rectangle
|
|
| Free forum by Nabble | Edit this page |