Use recursion instead of iteration.

On Tue, Oct 29, 2024 at 8:56 PM William F. Adams via Discuss <
discuss@lists.openscad.org> wrote:

I didn't try to understand it, but a for() loop just builds a tree of geometry.
Just use an if(<whatever criteria>) before your beam() to include or exclude that branch.

I agree that the right way to solve a problem like this in OpenSCAD is with
recursion.  Any algorithm that involves iterating and changing the
variables as you iterate should be done either with recursion (which is
easier) or with the C-style for() construction, which is hard to use
compared to recursion, but may possibly be faster.  I have written a
generic root finder for 1d function in openscad (root_find() in BOSL2) as
well as a function that finds all the roots of a polynomial.  Both use
iterative algorithms that I implemented in OpenSCAD using recursion.

I also can say that like Michael Marx, I didn't try to figure out the code,
which seemed pretty mystifying.  It looks like you're trying to solve the
problem by testing every point on a grid, which is a very inefficient sover
alogorithm and not how these things are generally done.  But if you really
want to use that kind of algorithm you should do it with a for loop as
follows:

Write your for loop and have it calculate the error, so something like
error_list = [for ( L=..., theta=...) error(L,theta)] and then you find the
minimum error and figure out from the index value which parameter(s) gave
rise to that value.  Then you'll have just one solution (because you can
take the first one that has the minimum value).  To simplify the index
referencing you can include the parameters in the output of the loop.  That
does add an extra step of forming an array of only error values to pass to
min().  And either way you'll want to use search() to track down which
index is actually equal to the min that you find.

On Tue, Oct 29, 2024 at 10:06 PM Father Horton via Discuss <
discuss@lists.openscad.org> wrote:

Thanks!

I'll have to dig through this later. Doing recursion where each copy calls itself until the value matches seems straight-forward enough, and I think that's something I can do in BlockSCAD:

https://www.blockscad3d.com/community/projects/1845977

I did have one correction to the code --- forgot to include the formula for the rotated beam length, so change the translate line to:

  translate([((beamspacing + beamwidth) - cos(i) * beamwidth), 0, 0]){

William

On Tuesday, October 29, 2024 at 10:28:00 PM EDT, Adrian Mariano via Discuss discuss@lists.openscad.org wrote:

I agree that the right way to solve a problem like this in OpenSCAD is with recursion.   Any algorithm that involves iterating and changing the variables as you iterate should be done either with recursion (which is easier) or with the C-style for() construction, which is hard to use compared to recursion, but may possibly be faster.   I have written a generic root finder for 1d function in openscad (root_find() in BOSL2) as well as a function that finds all the roots of a polynomial.  Both use iterative algorithms that I implemented in OpenSCAD using recursion. 

I also can say that like Michael Marx, I didn't try to figure out the code, which seemed pretty mystifying.  It looks like you're trying to solve the problem by testing every point on a grid, which is a very inefficient sover alogorithm and not how these things are generally done.  But if you really want to use that kind of algorithm you should do it with a for loop as follows:

Write your for loop and have it calculate the error, so something like error_list = [for ( L=..., theta=...) error(L,theta)] and then you find the minimum error and figure out from the index value which parameter(s) gave rise to that value.  Then you'll have just one solution (because you can take the first one that has the minimum value).  To simplify the index referencing you can include the parameters in the output of the loop.  That does add an extra step of forming an array of only error values to pass to min().  And either way you'll want to use search() to track down which index is actually equal to the min that you find. 

On Tue, Oct 29, 2024 at 10:06 PM Father Horton via Discuss discuss@lists.openscad.org wrote:

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A question to the general list.  Is "blockscad3d.com" a known/trusted URL?

On Wed, Oct 30, 2024 at 1:07 PM William F. Adams via Discuss <
discuss@lists.openscad.org> wrote:

Here's a direct solution to the problem using a function solver, which is
really the right way to do this kind of problem:

include<BOSL2/std.scad>

width = 8;
height = 12;
beamwidth=3;

// Length of beam so that it achieves the desired width at specified angle
function length(theta) = (width-beamwidth*sin(theta))/cos(theta);

// Height of beam at angle theta with the length chosen to match target
width
function height(theta) = length(theta) * sin(theta) + beamwidth*cos(theta);

ang = root_find(function (theta) height(theta) - height, 1, 89);

echo(ang);

rect([width,height]);
zrot(90-ang)color("red")rect([beamwidth, length(ang)]);

On Wed, Oct 30, 2024 at 1:58 PM John David via Discuss <
discuss@lists.openscad.org> wrote:

On 10/30/2024 10:57 AM, John David via Discuss wrote:

It offers a graphical OpenSCAD-like designer that might well use
OpenSCAD under the covers; I don't know.

Does it also host bad stuff?  No idea.  It sure doesn't look like a
site that would be trying to distribute malware.

Elegantly done!

I hope you don't mind that I posted it (with attribution) to:

https://old.reddit.com/r/openscad/comments/1gf3y69/length_and_angle_of_diagonal_beam_in_a_specific/luoo5ar/

As noted there, a big problem with approaching this angularly is that even a quite small angle can result in a quite large deviation.

William

On Wednesday, October 30, 2024 at 04:36:32 PM EDT, Adrian Mariano via Discuss discuss@lists.openscad.org wrote:

Here's a direct solution to the problem using a function solver, which is really the right way to do this kind of problem:

include<BOSL2/std.scad>

width = 8;
height = 12;
beamwidth=3;

  // Length of beam so that it achieves the desired width at specified angle
function length(theta) = (width-beamwidth*sin(theta))/cos(theta);

  // Height of beam at angle theta with the length chosen to match target width
function height(theta) = length(theta) * sin(theta) + beamwidth*cos(theta);

ang = root_find(function (theta) height(theta) - height, 1, 89);

echo(ang);

rect([width,height]);
zrot(90-ang)color("red")rect([beamwidth, length(ang)]);

On Wed, Oct 30, 2024 at 1:58 PM John David via Discuss discuss@lists.openscad.org wrote:

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