Bob, I did I think exactly the same thing in my code and didn't notice
anything, but now that you mention it, doing chamfers on an angular basis
is of course not going to match doing them on a linear basis.  So that
means the geometry changes a bit if you change the chamfer size.  This
isn't necessarily catastrophic, but is a little unexpected, I suppose.
Generally speaking you can't mate two parts produced with different chamfer
size anyway, so I'm not sure this is crucial to get right.  But in order to
get it right, I think both thetaCA2 and phiCA are going to need to be
computed with trig---either that or there's some complicated way of
computing just one.  The question is whether these two parameters can be
computed independently or are they related in some complicated way.
Treated as a 2d problem you are trying to get the angle that corresponds to
a fraction of a chord of the circle, which is a reasonably straight forward
triangle calculation.  I got atan(chamfer*tan(angle)) where angle is
180/tooth_count for the ridge chamfer.  But the chamfered one still doesn't
align with the unchamfered.  For example:

[image: image.png]

Yellow is unchamfered.  Blue has huge chamfer applied only at ridge
(and slightly larger radius so we can see it clearly).  And we see that the
angle has changed.  I actually got less error with the original
calculation, but that might be because I didn't correct the phi angle only
the theta angle.  (Or maybe I botched the trig.)  So I tried computing a
correction for phi and got ridge_angle-atan(ridge_angle -
chamfer*(tan(ridge_angle)-tan(valley_angle))), but still things don't line
up correctly.  (And the horizontal correction is still worse than not,
which makes me wonder if the horizontal correction needs to take into
account the vertical position of the chamfer somehow.)  Doing the phi
correction alone actually is an improvement over no correction.

Here's my current code (without any chamfer corrections).  It does
rounding and skew teeth.

module hirth(n, ir, or, id, od, tooth_angle=60, cone_angle=0, chamfer,
rounding, base=1, crop=false,skew=0, rot=false, orient,anchor,spin)
{
ir = get_radius(r=ir,d=id);
or = get_radius(r=or,d=od);
dummy = assert(all_positive([ir]), "ir/id must be a positive value")
assert(all_positive([or]), "or/od must be a positive value")
assert(is_int(n) && n>1, "n must be an integer larger than 1")
assert(is_finite(skew) && abs(skew)<=1, "skew must be a
number between -1 and 1")
assert(ir<or, "inside radius (ir/id) must be smaller than
outside radius (or/od)")
assert(all_positive([tooth_angle]) &&
tooth_angle<360*(n-1)/2/n, str("tooth angle must be between 0 and
",360*(n-1)/2/n," for spline with ",n," teeth."))
assert(num_defined([chamfer,rounding]) <=1, "Cannot define
both chamfer and rounding")
assert(is_undef(chamfer) || all_nonnegative([chamfer]) &&
chamfer<1/2, "chamfer must be a non-negative value smaller than 1/2")
assert(is_undef(rounding) || all_nonnegative([rounding]) &&
rounding<1/2, "rounding must be a non-negative value smaller than 1/2")
assert(all_positive([base]), "base must be a positive value")
;
tooth_height = sin(180/n) / tan(tooth_angle/2);    // Normalized
tooth height
cone_height = -tan(cone_angle);                        // Normalized
height change corresponding to the cone angle
ridge_angle = atan(tooth_height/2 + cone_height);
valley_angle = atan(-tooth_height/2 + cone_height);
angle = 180/n;    // Half the angle occupied by each tooth going
around the circle

factor = crop ? 3 : 1;  // Make it oversized when crop is true

profile = is_undef(rounding) || rounding==0 ?
let(
chamfer=default(chamfer,0),
vchamf = chamfer*(ridge_angle-valley_angle),
pts = [
[-angle*(1-chamfer/2),
valley_angle+vchamf/2],
[-anglechamfer, ridge_angle-vchamf]
],
full = deduplicate(concat(pts,
reverse(xflip(pts))))
)
back(valley_angle,
skew(sxy=skewangle/(ridge_angle-valley_angle),fwd(valley_angle,full)))
: let(
vround=rounding*(ridge_angle-valley_angle),
profpts = [
[  -angle, valley_angle+vround/2],
[  -angle*(1-rounding/2),
valley_angle+vround/2],
[  -anglerounding, ridge_angle-vround],
],
segs = max(16,segs(orrounding)),
full = concat(profpts, reverse(xflip(profpts))),
skewed = back(valley_angle,
skew(sxy=skew*angle/(ridge_angle-valley_angle),fwd(valley_angle,full))),
// Using computed values for the joints
lead to round-off error issues
joints = [(skewed[1]-skewed[0]).x,
(skewed[3]-skewed[2]).x/2,
(skewed[3]-skewed[2]).x/2,(skewed[5]-skewed[4]).x ],
roundpts = round_corners(skewed, joint=joints,
closed=false,$fn=segs)
)
roundpts;

// project spherical coordinate point onto cylinder of radius r
cyl_proj = function (r,theta_phi)
[for(pt=theta_phi)
let(xyz = spherical_to_xyz(1,pt[0], 90-pt[1]))
r * xyz / norm(point2d(xyz))];

bottom =
min([tan(valley_angle)ir,tan(valley_angle)or])-base-cone_heightir;
safebottom =
min([tan(valley_angle)ir/factor,tan(valley_angle)orfactor])-base-(crop?1:0)-cone_heightir;
ang_ofs = !rot ? -skewangle
:  n%2==0 ? -(angle-skewangle)  - skewangle
:  -angle*(2-skew)-skewangle;
topinner = down(cone_heightir,[for(ang=lerpn(0,360,n,endpoint=false))
each
zrot(ang+ang_ofs,cyl_proj(ir/factor,profile))]);
topouter = down(cone_heightir,[for(ang=lerpn(0,360,n,endpoint=false))
each
zrot(ang+ang_ofs,cyl_proj(factoror,profile))]);
botinner = [for(val=topinner) [val.x,val.y,safebottom]];
botouter = [for(val=topouter) [val.x,val.y,safebottom]];
vert = [topouter, topinner, botinner, botouter];

anchors = [
named_anchor("teeth_bot", [0,0,bottom], DOWN)
];
attachable(anchor=anchor,spin=spin,orient=orient, r=or,
h=-2*bottom,anchors=anchors){
intersection(){
vnf_polyhedron(vnf_vertex_array(vert, reverse=true,
col_wrap=true, row_wrap=true),convexity=min(10,n));
if (crop)

zmove(bottom)tube(or=or,ir=ir,height=4*or,anchor=BOT,$fa=1,$fs=1);
}
children();
}
}

On Wed, Nov 6, 2024 at 7:55 PM Bob Carlson via Discuss <
discuss@lists.openscad.org> wrote:

OpenSCAD mailing list
To unsubscribe send an email to discuss-leave@lists.openscad.org

Bob, I did I think exactly the same thing in my code and didn't notice
anything, but now that you mention it, doing chamfers on an angular basis
is of course not going to match doing them on a linear basis.  So that
means the geometry changes a bit if you change the chamfer size.  This
isn't necessarily catastrophic, but is a little unexpected, I suppose.
Generally speaking you can't mate two parts produced with different chamfer
size anyway, so I'm not sure this is crucial to get right.  But in order to
get it right, I think both thetaCA2 and phiCA are going to need to be
computed with trig---either that or there's some complicated way of
computing just one.  The question is whether these two parameters can be
computed independently or are they related in some complicated way.
Treated as a 2d problem you are trying to get the angle that corresponds to
a fraction of a chord of the circle, which is a reasonably straight forward
triangle calculation.  I got atan(chamfer*tan(angle)) where angle is
180/tooth_count for the ridge chamfer.  But the chamfered one still doesn't
align with the unchamfered.  For example:

[image: image.png]

Yellow is unchamfered.  Blue has huge chamfer applied only at ridge
(and slightly larger radius so we can see it clearly).  And we see that the
angle has changed.  I actually got less error with the original
calculation, but that might be because I didn't correct the phi angle only
the theta angle.  (Or maybe I botched the trig.)  So I tried computing a
correction for phi and got ridge_angle-atan(ridge_angle -
chamfer*(tan(ridge_angle)-tan(valley_angle))), but still things don't line
up correctly.  (And the horizontal correction is still worse than not,
which makes me wonder if the horizontal correction needs to take into
account the vertical position of the chamfer somehow.)  Doing the phi
correction alone actually is an improvement over no correction.

Here's my current code (without any chamfer corrections).  It does
rounding and skew teeth.

module hirth(n, ir, or, id, od, tooth_angle=60, cone_angle=0, chamfer,
rounding, base=1, crop=false,skew=0, rot=false, orient,anchor,spin)
{
ir = get_radius(r=ir,d=id);
or = get_radius(r=or,d=od);
dummy = assert(all_positive([ir]), "ir/id must be a positive value")
assert(all_positive([or]), "or/od must be a positive value")
assert(is_int(n) && n>1, "n must be an integer larger than 1")
assert(is_finite(skew) && abs(skew)<=1, "skew must be a
number between -1 and 1")
assert(ir<or, "inside radius (ir/id) must be smaller than
outside radius (or/od)")
assert(all_positive([tooth_angle]) &&
tooth_angle<360*(n-1)/2/n, str("tooth angle must be between 0 and
",360*(n-1)/2/n," for spline with ",n," teeth."))
assert(num_defined([chamfer,rounding]) <=1, "Cannot define
both chamfer and rounding")
assert(is_undef(chamfer) || all_nonnegative([chamfer]) &&
chamfer<1/2, "chamfer must be a non-negative value smaller than 1/2")
assert(is_undef(rounding) || all_nonnegative([rounding]) &&
rounding<1/2, "rounding must be a non-negative value smaller than 1/2")
assert(all_positive([base]), "base must be a positive value")
;
tooth_height = sin(180/n) / tan(tooth_angle/2);    // Normalized
tooth height
cone_height = -tan(cone_angle);                        // Normalized
height change corresponding to the cone angle
ridge_angle = atan(tooth_height/2 + cone_height);
valley_angle = atan(-tooth_height/2 + cone_height);
angle = 180/n;    // Half the angle occupied by each tooth going
around the circle

factor = crop ? 3 : 1;  // Make it oversized when crop is true

profile = is_undef(rounding) || rounding==0 ?
let(
chamfer=default(chamfer,0),
vchamf = chamfer*(ridge_angle-valley_angle),
pts = [
[-angle*(1-chamfer/2),
valley_angle+vchamf/2],
[-anglechamfer, ridge_angle-vchamf]
],
full = deduplicate(concat(pts,
reverse(xflip(pts))))
)
back(valley_angle,
skew(sxy=skewangle/(ridge_angle-valley_angle),fwd(valley_angle,full)))
: let(
vround=rounding*(ridge_angle-valley_angle),
profpts = [
[  -angle, valley_angle+vround/2],
[  -angle*(1-rounding/2),
valley_angle+vround/2],
[  -anglerounding, ridge_angle-vround],
],
segs = max(16,segs(orrounding)),
full = concat(profpts, reverse(xflip(profpts))),
skewed = back(valley_angle,
skew(sxy=skew*angle/(ridge_angle-valley_angle),fwd(valley_angle,full))),
// Using computed values for the joints
lead to round-off error issues
joints = [(skewed[1]-skewed[0]).x,
(skewed[3]-skewed[2]).x/2,
(skewed[3]-skewed[2]).x/2,(skewed[5]-skewed[4]).x ],
roundpts = round_corners(skewed, joint=joints,
closed=false,$fn=segs)
)
roundpts;

// project spherical coordinate point onto cylinder of radius r
cyl_proj = function (r,theta_phi)
[for(pt=theta_phi)
let(xyz = spherical_to_xyz(1,pt[0], 90-pt[1]))
r * xyz / norm(point2d(xyz))];

bottom =
min([tan(valley_angle)ir,tan(valley_angle)or])-base-cone_heightir;
safebottom =
min([tan(valley_angle)ir/factor,tan(valley_angle)orfactor])-base-(crop?1:0)-cone_heightir;
ang_ofs = !rot ? -skewangle
:  n%2==0 ? -(angle-skewangle)  - skewangle
:  -angle*(2-skew)-skewangle;
topinner = down(cone_heightir,[for(ang=lerpn(0,360,n,endpoint=false))
each
zrot(ang+ang_ofs,cyl_proj(ir/factor,profile))]);
topouter = down(cone_heightir,[for(ang=lerpn(0,360,n,endpoint=false))
each
zrot(ang+ang_ofs,cyl_proj(factoror,profile))]);
botinner = [for(val=topinner) [val.x,val.y,safebottom]];
botouter = [for(val=topouter) [val.x,val.y,safebottom]];
vert = [topouter, topinner, botinner, botouter];

anchors = [
named_anchor("teeth_bot", [0,0,bottom], DOWN)
];
attachable(anchor=anchor,spin=spin,orient=orient, r=or,
h=-2*bottom,anchors=anchors){
intersection(){
vnf_polyhedron(vnf_vertex_array(vert, reverse=true,
col_wrap=true, row_wrap=true),convexity=min(10,n));
if (crop)

zmove(bottom)tube(or=or,ir=ir,height=4*or,anchor=BOT,$fa=1,$fs=1);
}
children();
}
}

On Wed, Nov 6, 2024 at 7:55 PM Bob Carlson via Discuss <
discuss@lists.openscad.org> wrote:

OpenSCAD mailing list
To unsubscribe send an email to discuss-leave@lists.openscad.org