Profiling of hull- and cylinder-based line drawings
Following a discussion on line drawing algorithm in other thread
http://forum.openscad.org/converting-to-sperical-coordinates-tp25098p25173.html
, I decided to do a profiling to check the speed of hull() in comparison to
that of a cylinder-based one when used in drawing lines of multi-segments.
The cylinder-based one is the Line() here
https://github.com/runsun/OpenSCAD_Tips/blob/master/snippets.md#line .
The hull-based is named Rod(), made by replacing the cylinder part of
Line()
v = pts[i+1]-pts[i]; L = norm(v); if( L > 1e-12)
translate(pts[i]) rotate([0, acos(v[2]/L), atan2(v[1],v[0])])
rotate(45) cylinder(h=L, r=r, $fn=fn);
with hull:
hull() { translate( pts[i] ) sphere(r); translate( pts[i+1] )
sphere(r); }
(See the full code in the end)
Data points of various lengths are generated randomly in advance and saved
and named pts20(20 pts), pts30 ... etc so they are not re-generated anew
in each test. The drawing of pts100 looks like this:
http://forum.openscad.org/file/t602/191a_hull_cylinder_compare_pts100.png
Data length tested are: 20,30,40,50,75,100. Each test is performed with 3
steps: [Flush Cache]+[Preview]+[Render], and repeated at least once. The
time (in sec) required is recorded. The time for [preview] is 0 for all
tests conducted, so it is not displayed in the following table :
n Rod Line Line Rod 20 7 2 2 7 30 13 4 4
13 40 20 8 8 20 50 27 9 9 25 75 69 25 25
67 100 101 35 35 101100 100 36 36 99 (* 2 sets of pts100
are used)
In average, Line (cylinder-based) is about 3 times faster than Rod
(hull-based) in rendering.
http://forum.openscad.org/file/t602/191a_hull_cylinder_compare.png
The [Preview] time is 0 sec in all cases above. However, a quick check (on
[Preview] only) with larger # of pts shows that, for [Preview], Line
(cylinder-based) has a huge advantage, as much as ~50 times faster when n
reaches 2000. This confirms the previous observation that it has an
efficiency the hull-based approach can't compete:
n Rod Line 500 12 0 1000 24 0 2000 47 1
Below is the code for this test. Data points up to pts50 are included.
module Line( pts, r=0.05, closed=false, color=undef, transp=1, fn=4 ){
if(len(pts)>1 && len(pts[0])>1 && r>0) { // Convert to 3d if 2d;
Attach 1st pt if closed pts = concat( [for(p=pts) [
p[0],p[1],p[2]==undef?0:p[2] ]], closed? [[ pts[0][0],
pts[0][1], pts[0][2]==undef?0:pts[0][2] ]] : [] );
color(color,transp) for(i=[0:len(pts)-2]) { v =
pts[i+1]-pts[i]; L = norm(v); if( L > 1e-12)
translate(pts[i]) rotate([0, acos(v[2]/L), atan2(v[1],v[0])])
rotate(45) cylinder(h=L, r=r, $fn=fn); } } }module Rod( pts, r=0.05,
closed=false, color=undef, transp=1, fn=4 ){ if(len(pts)>1 && len(pts[0])>1
&& r>0) { // Convert to 3d if 2d; Attach 1st pt if closed pts =
concat( [for(p=pts) [ p[0],p[1],p[2]==undef?0:p[2] ]],
closed? [[ pts[0][0], pts[0][1], pts[0][2]==undef?0:pts[0][2] ]] : [] );
color(color,transp) for(i=[0:len(pts)-2]) { hull() {
translate( pts[i] ) sphere(r); translate( pts[i+1] ) sphere(r);
} } } }module Rod_test(){ Rod(pts50); } //Rod_test();module
Line_test(){Line(pts50); } //Line_test();pts20= [[-0.59, 0.78, 0.9], [1.31,
-0.99, 1.34], [0.82, -2.75, -2.79], [-2.64, 2.15, -1.27], [0.33, 0.39,
1.29], [0.74, 0.84, -2.01], [2, -1.28, -1.37], [2.66, -1.58, -0.57], [-1.01,
0.39, -1.52], [-1.79, 2.68, -0.63], [2.48, -1.23, -1.02], [0.81, 0.55,
1.15], [-0.43, -0.99, -1.55], [0.27, 0.76, -0.85], [-2.21, -2.16, 2.34],
[-2.98, 0.91, 0.8], [-2.47, 2.03, -2.25], [1.88, -2.05, 1.42], [0.94, 2.11,
2.74], [-1.47, -0.3, -2.18]];pts30= [[2.86, -0.25, -0.93], [2.22, -0.59,
-0.58], [-1.46, 1.22, 1.27], [1.11, -2.13, -2.58], [-2.25, 1.22, -0.93],
[-2.01, -2.3, 0.05], [-1.34, 1.42, -1.56], [0.04, 1.35, 1.4], [-0.93, -2.72,
-2.12], [-1.58, 1.89, -2.59], [1.19, 0.67, 1.13], [-2.07, 2.35, -2.66],
[0.05, 1.51, 0.88], [0.84, 2.7, -0.85], [-2.3, 1.58, -0.04], [-2.4, -2.63,
1.54], [0.97, 2.65, -1.5], [1.68, -0.96, -1.1], [-0.65, -1.87, -1.2], [2.02,
0.03, -2.13], [1.56, -2.42, 1.37], [-2.41, 1.45, 2.88], [1.87, 2.7, 2.65],
[1.1, -0.98, -0.72], [2.32, 1, 2.11], [2.35, 2.92, -1.23], [-1.85, 0.12,
-2.23], [1.43, -0.43, -1.1], [0.05, 2, 0.18], [-1.43, -2.28, -1.07]];pts40=
[[0.65, -0.85, -1.26], [2.68, 0.92, 0.53], [-0.47, -0.41, 1.79], [0.71, 1.8,
0.06], [-1.41, -0.44, -1.38], [-2.56, 2.24, 2.09], [1.26, 0.81, 1.46],
[2.58, 2.74, -1.24], [-0.99, 2.69, 2.79], [-2.6, -2.55, 2.61], [1.87, -2.7,
0.78], [0.6, -0.44, -1.15], [2.13, -2.8, 1.57], [0.43, -0.25, -1.23],
[-1.86, -0.88, 1.92], [1.35, 2.12, -1.8], [2.86, -2.28, -1.54], [2.13, 0.39,
2.95], [-2.54, -0.83, 1.74], [0.99, 1.92, 2.12], [2.23, -0.07, -0.97],
[-0.65, -2.04, -0.24], [0.12, -0.98, -1.86], [1.21, -2.97, 2.76], [-1.1,
2.8, -1.98], [-0.37, 0.89, 0.66], [0.5, 0.71, -2.12], [0.01, 0.58, -2.14],
[1.05, -1.34, -0.4], [1.63, -0.26, -2.35], [-2.76, -0.57, 1.94], [-0.14,
-0.12, -0.66], [-1.88, 0, 0.95], [1.14, -0.9, 2.26], [1.03, -2.49, -0.23],
[-2.07, -1.56, -0.47], [-2.81, 2.79, -1.22], [-0.74, 1.71, -1.49], [2.74,
0.29, 2.56], [-0.14, 1.51, 0.45]];pts50= [[2.83, 2.08, 0.25], [-0.56, -0.02,
-0.5], [2.12, -2.13, 0.42], [2.24, -0.67, -2.29], [1.24, 1.57, -1.1], [0.02,
1.41, -0.99], [-0.28, 1.73, -1.53], [-0.15, 1.15, -0.93], [-2.24, 0.09,
1.88], [2.44, 2.64, 0.61], [0.02, -1.33, 1.46], [2.11, -1.09, -0.36], [2.51,
-1.51, -2.86], [-0.84, -2.48, 1.62], [1.09, -0.98, 0.99], [2.32, -1.3,
-0.26], [-1.95, 2.21, 1.61], [0.1, 1.95, -1.55], [-0.32, 2.1, 1.08], [-2.76,
-0.97, 0.09], [-1.48, 1.54, -1.97], [-1.42, 0.4, 1.96], [1.73, 0.42, 2.55],
[2.47, 0.34, -2.51], [-1.52, -0.45, 0.02], [0.81, 0.16, -1.28], [-0.62,
0.43, -1.93], [0.06, -1.16, -1.74], [2.18, 0.38, 2.95], [1.17, 1.78, 1.54],
[-2.54, 1.92, -0.96], [0.44, -1.65, -2.2], [0.85, -2, 0.64], [-2.76, -2.46,
2.23], [-1.08, 0.49, -2.18], [-2.35, -0.96, 1.39], [-2.1, 1.23, -2.87],
[1.44, -1.32, -0.35], [-0.91, -1.3, 2.02], [-2.72, 0.03, -1.44], [-0.08,
1.6, -2.02], [-0.94, 0.1, 0.92], [-2.5, -1.61, 2.76], [0.81, 1.48, -1.68],
[-0.55, 0.81, 2.94], [1.17, -2.06, 2.49], [-1.22, 0.62, 1.39], [2.41, 1.74,
2.82], [1.93, 0.8, -1.87], [-0.67, -0.63, -0.12]];
$ Runsun Pan, PhD $ libs: scadx , doctest , faces ( git ), offline doc ( git ), runscad.py ( 2 , git ), editor of choice: CudaText ( OpenSCAD lexer ); $ Tips ; $ Snippets
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I think you are comparing apples to pears. Without the hull() the preview
does nothing but draw the cylinders on top of each other. With the hull()
the actual hull has to be computed because OpenCSG cannot fake it like it
can with union() and differences(). Not sure if CGAL is involved there to
union the spheres first or not.
On Thu, 10 Jan 2019 at 18:48, runsun runsun@gmail.com wrote:
Following a discussion on line drawing algorithm in other thread
http://forum.openscad.org/converting-to-sperical-coordinates-tp25098p25173.html,
I decided to do a profiling to check the speed of hull() in comparison to
that of a cylinder-based one when used in drawing lines of multi-segments.
The cylinder-based one is the Line() here
https://github.com/runsun/OpenSCAD_Tips/blob/master/snippets.md#line.
The hull-based is named Rod(), made by replacing the cylinder part of
Line()
v = pts[i+1]-pts[i];
L = norm(v);
if( L > 1e-12)
translate(pts[i])
rotate([0, acos(v[2]/L), atan2(v[1],v[0])])
rotate(45) cylinder(h=L, r=r, $fn=fn);
with hull:
hull()
{ translate( pts[i] ) sphere(r);
translate( pts[i+1] ) sphere(r);
}
(See the full code in the end)
Data points of various lengths are generated randomly in advance and saved
and named pts20(20 pts), pts30 ... etc so they are not re-generated
anew in each test. The drawing of pts100 looks like this:
Data length tested are: 20,30,40,50,75,100. Each test is performed with 3
steps: [Flush Cache]+[Preview]+[Render], and repeated at least once.
The time (in sec) required is recorded. The time for [preview] is 0 for all
tests conducted, so it is not displayed in the following table :
n Rod Line Line Rod
20 7 2 2 7
30 13 4 4 13
40 20 8 8 20
50 27 9 9 25
75 69 25 25 67
100 101 35 35 101
100 100 36 36 99 (* 2 sets of pts100 are used)
In average, Line (cylinder-based) is about 3 times faster than Rod
(hull-based) in rendering.
The [Preview] time is 0 sec in all cases above. However, a quick check (on
[Preview] only) with larger # of pts shows that, for [Preview], Line
(cylinder-based) has a huge advantage, as much as ~50 times faster when n
reaches 2000. This confirms the previous observation that it has an
efficiency the hull-based approach can't compete:
n Rod Line
500 12 0
1000 24 0
2000 47 1
Below is the code for this test. Data points up to pts50 are included.
module Line( pts, r=0.05, closed=false, color=undef, transp=1, fn=4 )
{
if(len(pts)>1 && len(pts[0])>1 && r>0)
{
// Convert to 3d if 2d; Attach 1st pt if closed
pts = concat( [for(p=pts) [ p[0],p[1],p[2]==undef?0:p[2] ]],
closed? [[ pts[0][0], pts[0][1], pts[0][2]==undef?0:pts[0][2] ]] : []
);
color(color,transp)
for(i=[0:len(pts)-2])
{
v = pts[i+1]-pts[i];
L = norm(v);
if( L > 1e-12)
translate(pts[i])
rotate([0, acos(v[2]/L), atan2(v[1],v[0])])
rotate(45) cylinder(h=L, r=r, $fn=fn);
}
}
}
module Rod( pts, r=0.05, closed=false, color=undef, transp=1, fn=4 )
{
if(len(pts)>1 && len(pts[0])>1 && r>0)
{
// Convert to 3d if 2d; Attach 1st pt if closed
pts = concat( [for(p=pts) [ p[0],p[1],p[2]==undef?0:p[2] ]],
closed? [[ pts[0][0], pts[0][1], pts[0][2]==undef?0:pts[0][2] ]] : []
);
color(color,transp)
for(i=[0:len(pts)-2])
{
hull()
{ translate( pts[i] ) sphere(r);
translate( pts[i+1] ) sphere(r);
}
}
}
}
module Rod_test(){ Rod(pts50); } //Rod_test();
module Line_test(){Line(pts50); } //Line_test();
pts20= [[-0.59, 0.78, 0.9], [1.31, -0.99, 1.34], [0.82, -2.75, -2.79], [-2.64, 2.15, -1.27], [0.33, 0.39, 1.29], [0.74, 0.84, -2.01], [2, -1.28, -1.37], [2.66, -1.58, -0.57], [-1.01, 0.39, -1.52], [-1.79, 2.68, -0.63], [2.48, -1.23, -1.02], [0.81, 0.55, 1.15], [-0.43, -0.99, -1.55], [0.27, 0.76, -0.85], [-2.21, -2.16, 2.34], [-2.98, 0.91, 0.8], [-2.47, 2.03, -2.25], [1.88, -2.05, 1.42], [0.94, 2.11, 2.74], [-1.47, -0.3, -2.18]];
pts30= [[2.86, -0.25, -0.93], [2.22, -0.59, -0.58], [-1.46, 1.22, 1.27], [1.11, -2.13, -2.58], [-2.25, 1.22, -0.93], [-2.01, -2.3, 0.05], [-1.34, 1.42, -1.56], [0.04, 1.35, 1.4], [-0.93, -2.72, -2.12], [-1.58, 1.89, -2.59], [1.19, 0.67, 1.13], [-2.07, 2.35, -2.66], [0.05, 1.51, 0.88], [0.84, 2.7, -0.85], [-2.3, 1.58, -0.04], [-2.4, -2.63, 1.54], [0.97, 2.65, -1.5], [1.68, -0.96, -1.1], [-0.65, -1.87, -1.2], [2.02, 0.03, -2.13], [1.56, -2.42, 1.37], [-2.41, 1.45, 2.88], [1.87, 2.7, 2.65], [1.1, -0.98, -0.72], [2.32, 1, 2.11], [2.35, 2.92, -1.23], [-1.85, 0.12, -2.23], [1.43, -0.43, -1.1], [0.05, 2, 0.18], [-1.43, -2.28, -1.07]];
pts40= [[0.65, -0.85, -1.26], [2.68, 0.92, 0.53], [-0.47, -0.41, 1.79], [0.71, 1.8, 0.06], [-1.41, -0.44, -1.38], [-2.56, 2.24, 2.09], [1.26, 0.81, 1.46], [2.58, 2.74, -1.24], [-0.99, 2.69, 2.79], [-2.6, -2.55, 2.61], [1.87, -2.7, 0.78], [0.6, -0.44, -1.15], [2.13, -2.8, 1.57], [0.43, -0.25, -1.23], [-1.86, -0.88, 1.92], [1.35, 2.12, -1.8], [2.86, -2.28, -1.54], [2.13, 0.39, 2.95], [-2.54, -0.83, 1.74], [0.99, 1.92, 2.12], [2.23, -0.07, -0.97], [-0.65, -2.04, -0.24], [0.12, -0.98, -1.86], [1.21, -2.97, 2.76], [-1.1, 2.8, -1.98], [-0.37, 0.89, 0.66], [0.5, 0.71, -2.12], [0.01, 0.58, -2.14], [1.05, -1.34, -0.4], [1.63, -0.26, -2.35], [-2.76, -0.57, 1.94], [-0.14, -0.12, -0.66], [-1.88, 0, 0.95], [1.14, -0.9, 2.26], [1.03, -2.49, -0.23], [-2.07, -1.56, -0.47], [-2.81, 2.79, -1.22], [-0.74, 1.71, -1.49], [2.74, 0.29, 2.56], [-0.14, 1.51, 0.45]];
pts50= [[2.83, 2.08, 0.25], [-0.56, -0.02, -0.5], [2.12, -2.13, 0.42], [2.24, -0.67, -2.29], [1.24, 1.57, -1.1], [0.02, 1.41, -0.99], [-0.28, 1.73, -1.53], [-0.15, 1.15, -0.93], [-2.24, 0.09, 1.88], [2.44, 2.64, 0.61], [0.02, -1.33, 1.46], [2.11, -1.09, -0.36], [2.51, -1.51, -2.86], [-0.84, -2.48, 1.62], [1.09, -0.98, 0.99], [2.32, -1.3, -0.26], [-1.95, 2.21, 1.61], [0.1, 1.95, -1.55], [-0.32, 2.1, 1.08], [-2.76, -0.97, 0.09], [-1.48, 1.54, -1.97], [-1.42, 0.4, 1.96], [1.73, 0.42, 2.55], [2.47, 0.34, -2.51], [-1.52, -0.45, 0.02], [0.81, 0.16, -1.28], [-0.62, 0.43, -1.93], [0.06, -1.16, -1.74], [2.18, 0.38, 2.95], [1.17, 1.78, 1.54], [-2.54, 1.92, -0.96], [0.44, -1.65, -2.2], [0.85, -2, 0.64], [-2.76, -2.46, 2.23], [-1.08, 0.49, -2.18], [-2.35, -0.96, 1.39], [-2.1, 1.23, -2.87], [1.44, -1.32, -0.35], [-0.91, -1.3, 2.02], [-2.72, 0.03, -1.44], [-0.08, 1.6, -2.02], [-0.94, 0.1, 0.92], [-2.5, -1.61, 2.76], [0.81, 1.48, -1.68], [-0.55, 0.81, 2.94], [1.17, -2.06, 2.49], [-1.22, 0.62, 1.39], [2.41, 1.74, 2.82], [1.93, 0.8, -1.87], [-0.67, -0.63, -0.12]];
$ http://forum.openscad.org/mailing_list/MailingListOptions.jtp?forum=1 Runsun
Pan, PhD
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@nophead, I don't see your statement is valid. The comparison is to check how
efficient an approach is for the user to see the same result. It doesn't
matter how OpenSCAD works it out behind the scene.
$ Runsun Pan, PhD $ libs: scadx , doctest , faces ( git ), offline doc ( git ), runscad.py ( 2 , git ), editor of choice: CudaText ( OpenSCAD lexer ); $ Tips ; $ Snippets
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Hull is much faster than union but in preview unions are faked so it
appears slower. In all my previews I render everything, so for me Hull is
much faster.
On Thu, 10 Jan 2019, 20:23 runsun <runsun@gmail.com wrote:
@nophead, I don't see your statement is valid. The comparison is to check
how
efficient an approach is for the user to see the same result. It doesn't
matter how OpenSCAD works it out behind the scene.
$ Runsun Pan, PhD $ libs: scadx , doctest , faces ( git ), offline doc (
git ), runscad.py ( 2 , git ), editor of choice: CudaText ( OpenSCAD lexer
); $ Tips ; $ Snippets
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nophead wrote
Hull is much faster than union but in preview unions are faked so it
appears slower. In all my previews I render everything, so for me Hull is
much faster.
mmmhhh ... not sure how you conclude that but it's shown in my test that in
average hull is 3 times slower in rendering.
$ Runsun Pan, PhD $ libs: scadx , doctest , faces ( git ), offline doc ( git ), runscad.py ( 2 , git ), editor of choice: CudaText ( OpenSCAD lexer ); $ Tips ; $ Snippets
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By "render" I mean render() { } around all my top level objects. So they
are all calculated by CGAL and then coloured and displayed as polyhedra in
OpenCSG. Union is definitely at least and order of magnitude slower than
hull().
On Thu, 10 Jan 2019 at 22:14, runsun runsun@gmail.com wrote:
nophead wrote
Hull is much faster than union but in preview unions are faked so it
appears slower. In all my previews I render everything, so for me Hull is
much faster.
mmmhhh ... not sure how you conclude that but it's shown in my test that in
average hull is 3 times slower in rendering.
$ Runsun Pan, PhD $ libs: scadx , doctest , faces ( git ), offline doc (
git ), runscad.py ( 2 , git ), editor of choice: CudaText ( OpenSCAD lexer
); $ Tips ; $ Snippets
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My test code is designed to differ ONLY on the part limited to hull vs
cylinder. That's the very first thing I mentioned in the post. There's no
"union" anywhere, and if an implicit union is performed it would have been
performed on both Line() and Rod().
From your responses it seems to me that you made the judgement without
actually checking out my test or code to understand what the test is about.
The test code and data are all there so whoever interested is welcome to
check it out.
nophead wrote
By "render" I mean render() { } around all my top level objects. So they
are all calculated by CGAL and then coloured and displayed as polyhedra in
OpenCSG. Union is definitely at least and order of magnitude slower than
hull().
$ Runsun Pan, PhD $ libs: scadx , doctest , faces ( git ), offline doc ( git ), runscad.py ( 2 , git ), editor of choice: CudaText ( OpenSCAD lexer ); $ Tips ; $ Snippets
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Em qui, 10 de jan de 2019 às 18:48, runsun runsun@gmail.com escreveu:
In average, Line (cylinder-based) is about 3 times faster than Rod
(hull-based) in rendering.
runsun,
Your test code deludes. The cylinder in Line have 8 vertices and the
spheres in Rod have 15 vertices. The hull of the two spheres have 20
vertices. To be fair the Line cylinders should be defined with $fn = 10 and
not the default of 4. (alternatively we could hull cubes instead of spheres
in Rod.)
I have tested your code using fair cylinders ($fn=10) in Line, Rod as is
and a third case where the hull in Rod is dropped. I got the following
times with F6:
Rod Line Rod w/o hull
PT30 15 25 8
PT50 30 56 15
Should we conclude that Line is 70% slower than Rod? Certainly not. The
(implicit) union deals with distinct objects in those cases and it consumes
much more time than the hull. To evaluate the hulling time we have to
discard the union and go to the preview.
With F5, we have a very different framework and a new test is needed. In
Rod, I preceded the hull() with render(). And used the following test code:
N = 2000;
seed = 181;
rnd = rands(-3,3,3N, seed);
pts = [ for(i=[0:N-1])
[ rnd[3i], rnd[3i+1], rnd[3i+2] ] ];
//Rod(pts);
//Line(pts);
I have found out the following times with F5:
N Rod Line
1000 7 0
2000 15 0
4000 28 1
As preview uses a fake union, the Rod times express essentially the hulling
time. And, yes, it is much greater than the time to preview cylinders. The
hull() operation in Rod spends 7ms per rod. And we may conclude that
Rod with F6 spends around 350ms with the hull of pts50 and 30sec with their
union, confirming what nophead has said.
Ronaldo, Thx for checking the test code. I have been wondering that the
discrepancy (between me and you guys) could be due to the lack of knowledge
on my part. But (to me) it's hard to explore that without verifying the
validity of the test code.
A quick question before I do more tests with the code as you corrected it:
both you and nophead argue that the Line() approach requires a union()
which makes it slower. It implies that the approach in Rod(), which uses a
hull() to generate multiple segments, does NOT require or go through a
union() during rendering. Is this correct? Note that they (Line and Rod)
both generate multiple segments of objects.
$ Runsun Pan, PhD $ libs: scadx , doctest , faces ( git ), offline doc ( git ), runscad.py ( 2 , git ), editor of choice: CudaText ( OpenSCAD lexer ); $ Tips ; $ Snippets
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An implicit union is present in both codes of Line and Rod. Under F6, as
the union process time is much greater than the hull, it is irrelevant if
you make the sticks with cylinders or hulling spheres. Under F5 and with a
great number of sticks, there is an efficiency difference as the implicit
union is faked by a fast process. My general use Line uses cylinders and I
apply it just in previews. To illustrate something here in the forum I
define line with hull because it is a simpler and smaller code.
Em sex, 11 de jan de 2019 às 19:36, runsun runsun@gmail.com escreveu:
Ronaldo, Thx for checking the test code. I have been wondering that the
discrepancy (between me and you guys) could be due to the lack of knowledge
on my part. But (to me) it's hard to explore that without verifying the
validity of the test code.
A quick question before I do more tests with the code as you corrected it:
both you and nophead argue that the Line() approach requires a union()
which makes it slower. It implies that the approach in Rod(), which uses
a
hull() to generate multiple segments, does NOT require or go through a
union() during rendering. Is this correct? Note that they (Line and Rod)
both generate multiple segments of objects.
$ Runsun Pan, PhD $ libs: scadx , doctest , faces ( git ), offline doc (
git ), runscad.py ( 2 , git ), editor of choice: CudaText ( OpenSCAD lexer
); $ Tips ; $ Snippets
--
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