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Merged
adrianVmariano merged 2 commits into from
Mar 18, 2026
+98 −51
Merged

add rounded caps to path_join; handle parameter lists in debug_nurbs #1945

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2bcd3b1
add rounded caps to path_join
adrianVmariano Mar 17, 2026
739a743
remove echo from random_polygon()
adrianVmariano Mar 17, 2026
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1 change: 0 additions & 1 deletion math.scad
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Original file line number Diff line number Diff line change
Expand Up @@ -1262,7 +1262,6 @@ function random_polygon(n=3,size=1, angle_sep=0.2, seed) =
max(dang)<180 ? angs : randang(seed=u_add(seed,angs[0])),
angs = randang(seed),
rads = is_undef(seed) ? rands(rmin,rmax,n) : rands(rmin,rmax,n,seed+angs[0])
,f=echo(rads=rads)
)
[for(i=count(n)) rads[i]*[cos(angs[i]), -sin(angs[i])]];

Expand Down
87 changes: 46 additions & 41 deletions nurbs.scad
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Expand Up @@ -360,7 +360,6 @@ function _calc_mult(knots) =
deltas(ind);



// Module: debug_nurbs()
// Synopsis: Shows a NURBS curve and its control points, knots and weights
// SynTags: Geom
Expand All @@ -370,9 +369,10 @@ function _calc_mult(knots) =
// debug_nurbs(control, degree, [width], [splinesteps=], [type=], [mult=], [knots=], [size=], [show_weights=], [show_knots=], [show_idx=]);
// Description:
// Displays a 2D or 3D NURBS and the associated control points to help debug NURBS curves. You can display the
// control point indices and weights, and can also display the knot points.
// control point indices and weights, and can also display the knot points.
// Instead of providing separate parameters you can give a first parameter of the form of a NURBS parameter list: `[type degree, control, knots, weights]`.
// Arguments:
// control = control points for NURBS
// control = list of control points in any dimension or a NURBS parameter list
// degree = degree of NURBS
// splinesteps = number of segments between each pair of knots. Default: 16
// width = width of the line. Default: 1
Expand All @@ -395,42 +395,50 @@ function _calc_mult(knots) =
// debug_nurbs(pts,4,type="closed",weights=weights);

module debug_nurbs(control,degree,splinesteps=16,width=1, size, mult,weights,type="clamped",knots, show_weights, show_knots=false, show_index=true)
{
$fn=8;
size = default(size, 3*width);
show_weights = default(show_weights, is_def(weights));
N=len(control);
twodim = len(control[0])==2;
curve = nurbs_curve(control=control,degree=degree,splinesteps=splinesteps, mult=mult,weights=weights, type=type, knots=knots);
stroke(curve, width=width, closed=type=="closed");//, color="green");
stroke(control, width=width/2, color="lightblue", closed=type=="closed");
if (show_knots){
knotpts = nurbs_curve(control=control, degree=degree, splinesteps=1, mult=mult, weights=weights, type=type, knots=knots);
echo(knotpts);
color([1,.5,1])
move_copies(knotpts)
if (twodim)circle(r=width);
else sphere(r=width);
{
if (is_list(control) && in_list(control[0], ["closed","open","clamped"])) {
assert(len(control)>=5, "Invalid NURBS parameter list")
assert(num_defined([degree,mult,weights,knots])==0,
"Cannot give degree, mult, weights or knots when you provide a NURBS parameter list")
debug_nurbs(control[2], control[1], splinesteps, width, size, weights=control[4], type=control[0], knots=control[3],
show_weights=show_weights, show_knots=false, show_index=true);
}
color("blue")
if (show_index)
move_copies(control){
let(label = str($idx),
anch = show_weights && is_def(weights[$idx]) && weights[$idx]!=1 ? FWD : CENTER)
if (twodim) text(text=label, size=size, anchor=anch);
else rot($vpr) text3d(text=label, size=size, anchor=anch);
else {
$fn=8;
size = default(size, 3*width);
show_weights = default(show_weights, is_def(weights));
N=len(control);
twodim = len(control[0])==2;
curve = nurbs_curve(control=control,degree=degree,splinesteps=splinesteps, mult=mult,weights=weights, type=type, knots=knots);
stroke(curve, width=width, closed=type=="closed");//, color="green");
stroke(control, width=width/2, color="lightblue", closed=type=="closed");
if (show_knots){
knotpts = nurbs_curve(control=control, degree=degree, splinesteps=1, mult=mult, weights=weights, type=type, knots=knots);
echo(knotpts);
color([1,.5,1])
move_copies(knotpts)
if (twodim)circle(r=width);
else sphere(r=width);
}
color("blue")
if ( show_weights)
move_copies(control){
if(is_def(weights[$idx]) && weights[$idx]!=1)
let(label = str("w=",weights[$idx]),
anch = show_index ? BACK : CENTER
)
if (twodim) fwd(size/2*0)text(text=label, size=size, anchor=anch);
else rot($vpr) text3d(text=label, size=size, anchor=anch);
}

color("blue")
if (show_index)
move_copies(control){
let(label = str($idx),
anch = show_weights && is_def(weights[$idx]) && weights[$idx]!=1 ? FWD : CENTER)
if (twodim) text(text=label, size=size, anchor=anch);
else rot($vpr) text3d(text=label, size=size, anchor=anch);
}
color("blue")
if ( show_weights)
move_copies(control){
if(is_def(weights[$idx]) && weights[$idx]!=1)
let(label = str("w=",weights[$idx]),
anch = show_index ? BACK : CENTER
)
if (twodim) fwd(size/2*0)text(text=label, size=size, anchor=anch);
else rot($vpr) text3d(text=label, size=size, anchor=anch);
}
}
}


Expand Down Expand Up @@ -496,7 +504,6 @@ function is_nurbs_patch(x) =
// move_copies(flatten(pts)) sphere(r=2,$fn=16);

function nurbs_patch_points(patch, degree, splinesteps, u, v, weights, type=["clamped","clamped"], mult=[undef,undef], knots=[undef,undef]) =
let(fo=echo(intype=type))
is_list(patch) && _valid_surface_type(patch[0]) ?
assert(len(patch)>=5, "NURBS parameter list is invalid")
assert(num_defined([degree,weights])==0 && mult==[undef,undef] && knots==[undef,undef],
Expand All @@ -518,9 +525,7 @@ let(fo=echo(intype=type))
u=is_range(u) ? list(u) : u,
v=is_range(v) ? list(v) : v,
degree = force_list(degree,2),
feee=echo(type=type),
type = force_list(type,2),
fda= echo(type=type, force_list(type,2)),
splinesteps = is_undef(splinesteps) ? [undef,undef] : force_list(splinesteps,2),
mult = is_vector(mult) || is_undef(mult) ? [mult,mult]
: assert((is_undef(mult[0]) || is_vector(mult[0])) && (is_undef(mult[1]) || is_vector(mult[1])), "mult must be a vector or list of two vectors")
Expand All @@ -535,11 +540,11 @@ fda= echo(type=type, force_list(type,2)),
: is_num(v) ? column(nurbs_patch_points(patch, degree, u=u, v=[v], knots=knots, mult=mult, type=type),0)
:
let(

vsplines = [for (i = idx(patch[0])) nurbs_curve(column(patch,i), degree[0], splinesteps=splinesteps[0],u=u, type=type[0],mult=mult[0],knots=knots[0])]
)
[for (i = idx(vsplines[0])) nurbs_curve(column(vsplines,i), degree[1], splinesteps=splinesteps[1], u=v, mult=mult[1], knots=knots[1], type=type[1])];


// Function&Module: nurbs_vnf()
// Synopsis: Generates a (possibly non-manifold) VNF for a single NURBS surface patch.
// SynTags: VNF
Expand Down
61 changes: 52 additions & 9 deletions rounding.scad
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Expand Up @@ -781,13 +781,15 @@ function _scalar_to_vector(value,length,varname) =
// back by the joint length. Rounding is using continous curvature 4th order bezier splines and
// the parameter `k` specifies how smooth the curvature match is. This parameter ranges from 0 to 1 with
// a default of 0.5. Use a larger k value to get a curve that is bigger for the same joint value. When
// k=1 the curve may be similar to a circle if your curves are symmetric. As the path is built up, the joint
// k=0.9 the curve may be similar to a circle if your curves are symmetric. As the path is built up, the joint
// parameter applies to the growing path, so if you pick a large joint parameter it may interact with the
// previous path sections. See [Types of Roundover](rounding.scad#subsection-types-of-roundover) for more details
// on continuous curvature rounding.
// .
// The rounding is created by extending the two clipped paths to define a corner point. If the extensions of
// the paths do not intersect, the function issues an error. When closed=true the final path should actually close
// the paths do not intersect they will be capped by a curve resembling a semi-circle if this is possible. But sometimes
// the connecting path will need to be S-shaped, which is not supported. If this situation arises, the function issues an error.
// When closed=true the final path should actually close
// the shape, repeating the starting point of the shape. If it does not, then the rounding fills the gap.
// .
// The number of segments in the roundovers is set based on $fn and $fs. If you use $fn it specifies the number of
Expand Down Expand Up @@ -881,6 +883,16 @@ function _scalar_to_vector(value,length,varname) =
// tri = regular_ngon(n=3, r=7);
// stroke(path_join([tri], joint=3,closed=true,$fn=12),
// closed=true,width=.5);
// Example(2D): Here lines are joined that do not intersect when they are extended, so the joint is sort of like a semi-circle. We show the effect of the `k` parameter at its default value of 0.5 or at 0.92 which is close to a circle.
// p=path_join([
// [[1,3],[15,8]],
// [[17,0],[0,0]],
// [[0,-8],[15,-3]]
// ],
// k=[.5,.9],
// relocate=false);
// stroke(p);

module path_join(paths,joint=0,k=0.5,relocate=true,closed=false) { no_module();}
function path_join(paths,joint=0,k=0.5,relocate=true,closed=false)=
assert(is_list(paths),"Input paths must be a list of paths")
Expand Down Expand Up @@ -935,14 +947,21 @@ function _path_join(paths,joint,k=0.5,i=0,result=[],relocate=true,closed=false)
corner = approx(firstcut[0],nextcut[0]) ? firstcut[0]
: line_intersection([firstcut[0], firstcut[0]-first_dir], [nextcut[0], nextcut[0]-next_dir],RAY,RAY)
)
assert(is_def(corner), str("Curve directions at cut points don't intersect in a corner when ",
loop?"closing the path":str("adding path ",i+1)))
let(
bezpts = _smooth_bez_fill([firstcut[0], corner, nextcut[0]],k[i]),
N = max(3,$fn>0 ?$fn : ceil(bezier_length(bezpts)/$fs)),
bezpath = approx(firstcut[0],corner) && approx(corner,nextcut[0])
? []
: bezier_curve(bezpts,N),
bezpath =
is_def(corner) ? let(
bezpts = _smooth_bez_fill([firstcut[0], corner, nextcut[0]],k[i]),
N = max(3,$fn>0 ?$fn : ceil(bezier_length(bezpts)/$fs)),
bezpath = approx(firstcut[0],corner) && approx(corner,nextcut[0])
? []
: bezier_curve(bezpts,N)
)
bezpath
: let(bezpath = _smooth_bezier_cap([firstcut[0]+first_dir, firstcut[0]],
[nextcut[0]+next_dir, nextcut[0]], k[i]))
assert(is_def(bezpath),str("Curve directions at cut points requires an S-curve joint (which is not supported) when ",
loop?"closing the path":str("adding path ",i+1)))
bezpath,
new_result = [each select(result,loop?nextcut[1]:0,len(revresult)-1-firstcut[1]),
each bezpath,
nextcut[0],
Expand All @@ -955,6 +974,30 @@ function _path_join(paths,joint,k=0.5,i=0,result=[],relocate=true,closed=false)



// connect tails of v1 and v2, starting at v1
// returns undef if an S curve is needed instead of a cap
function _smooth_bezier_cap(v1,v2,k=0.8,r) =
let(
r=default(r,norm(v1[1]-v2[1])/2),
n=line_normal(v1[1],v2[1]),
sign = (v1[1]-v1[0])*n>0 ? 1 : -1,
check= (v2[1]-v2[0])*n>0 ? 1 : -1
)
check != sign ? undef
:
let(
tangent = move(sign*n*r, [(v1[1]+v2[1])/2,v2[1]]),
corner1 = line_intersection(tangent, v1, LINE),
corner2 = line_intersection(tangent, v2, LINE)
)
concat(
list_head(_bezcorner([v1[1],corner1, tangent[0]],k)),
_bezcorner([tangent[0], corner2, v2[1]],k)
);




// Function&Module: offset_stroke()
// Synopsis: Draws a line along a path with options to specify angles and roundings at the ends.
// SynTags: Path, Region
Expand Down
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