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Author SHA1 Message Date
Alex Matulich
11b801ec46 added error check for 'uniform' parameter, reformatted some code 2025-01-05 08:06:52 -08:00
Alex Matulich
eb66ba3e9d fixed description indentation error in rounding.scad 2025-01-05 06:19:12 -08:00
Alex Matulich
4940551b05 fixed 2D example that should have been 3D in squircle 2025-01-05 05:52:39 -08:00
3 changed files with 76 additions and 67 deletions

View file

@ -634,7 +634,7 @@ function path_to_bezpath(path, closed, tangents, uniform=false, size, relsize) =
second + L*tangent2
],
select(path,lastpt)
];
];
@ -689,7 +689,8 @@ function path_to_bezcornerpath(path, closed, size, relsize) =
sizevect[i], relative),
[path[pathlen-1]]
]
) flatten(roundpath);
)
flatten(roundpath);
/// Internal function: _bez_path_corner()
@ -743,9 +744,7 @@ let(
// bz6 is p3
bz3 = p2 + middir * bzdist, // center control point
bz2 = bz3 + midto12unit*(d1<d3 ? cornerlegmin : cornerlegmax),
bz1 = p1 - (d1<=d3 ? leglenmin :
leglenmax)*p21unit,
//norm(0.333*(bz2-p1)))*p21unit,
bz1 = p1 - (d1<=d3 ? leglenmin : leglenmax)*p21unit,
bz4 = bz3 - midto12unit*(d3<d1 ? cornerlegmin : cornerlegmax),
bz5 = p3 - (d3<=d1 ? leglenmin : leglenmax)*p23unit
) [p1, bz1, bz2, bz3, bz4, bz5]; // do not include last control point

View file

@ -735,18 +735,20 @@ function _rounding_offsets(edgespec,z_dir=1) =
// pts = [[-3.3, 1.7], [-3.7, -2.2], [3.8, -4.8], [-0.9, -2.4]];
// stroke(smooth_path(pts, uniform=false, relsize=0.1),width=.1);
// color("red")move_copies(pts)circle(r=.15,$fn=12);
module smooth_path(path, tangents, size, relsize, method="edges", splinesteps=10, uniform=false, closed=false) {no_module();}
function smooth_path(path, tangents, size, relsize, method="edges", splinesteps=10, uniform=false, closed) =
is_1region(path) ? smooth_path(path[0], tangents, size, relsize, method, splinesteps, uniform, default(closed,true)) :
assert(method=="edges" || method=="corners", "method must be \"edges\" or \"corners\".")
assert(method=="edges" || is_undef(tangent), "The tangents parameter is incompatible with method=\"corners\".")
let (
bez = method=="edges" ?
path_to_bezpath(path, tangents=tangents, size=size, relsize=relsize, uniform=uniform, closed=default(closed,false))
module smooth_path(path, tangents, size, relsize, method="edges", splinesteps=10, uniform, closed=false) {no_module();}
function smooth_path(path, tangents, size, relsize, method="edges", splinesteps=10, uniform, closed) =
is_1region(path)
? smooth_path(path[0], tangents, size, relsize, method, splinesteps, uniform, default(closed,true))
: assert(method=="edges" || method=="corners", "method must be \"edges\" or \"corners\".")
assert(method=="edges" || (is_undef(tangents) && is_undef(uniform)), "The tangents and uniform parameters are incompatible with method=\"corners\".")
let (
uniform = default(uniform,false),
bez = method=="edges"
? path_to_bezpath(path, tangents=tangents, size=size, relsize=relsize, uniform=uniform, closed=default(closed,false))
: path_to_bezcornerpath(path, size=size, relsize=relsize, closed=default(closed,false)),
smoothed = bezpath_curve(bez,splinesteps=splinesteps)
)
closed ? list_unwrap(smoothed) : smoothed;
)
closed ? list_unwrap(smoothed) : smoothed;

View file

@ -1793,7 +1793,7 @@ module glued_circles(r, spread=10, tangent=30, d, anchor=CENTER, spin=0) {
// Examples(2D):
// squircle(size=50, squareness=0.4);
// squircle([80,60], 0.7, $fn=64);
// Example(2D,VPD=48,VPR=[40,0,40],NoAxes): Corner differences between the three squircle styles for squareness=0.5. Style "superellipse" is pink, "fg" is gold, "bezier" is blue.
// Example(3D,VPD=48,VPR=[40,0,40],NoAxes): Corner differences between the three squircle styles for squareness=0.5. Style "superellipse" is pink, "fg" is gold, "bezier" is blue.
// color("pink") squircle(size=50, style="superellipse", squareness=0.5, $fn=256);
// color("yellow") up(1) squircle(size=50, style="fg", squareness=0.5, $fn=256);
// color("lightblue") up(2) squircle(size=50, style="bezier", squareness=0.5, $fn=256);
@ -1854,9 +1854,11 @@ function _squircle_fg(size, squareness) = [
) p*[cos(theta), aspect*sin(theta)]
];
function squircle_radius_fg(squareness, r, angle) = let(
function squircle_radius_fg(squareness, r, angle) =
let(
s2a = abs(squareness*sin(2*angle))
) s2a>0 ? r*sqrt(2)/s2a * sqrt(1 - sqrt(1 - s2a*s2a)) : r;
)
s2a>0 ? r*sqrt(2)/s2a * sqrt(1 - sqrt(1 - s2a*s2a)) : r;
function _linearize_squareness(s) =
// from Chamberlain Fong (2016). "Squircular Calculations". arXiv.
@ -1884,27 +1886,33 @@ function _squircle_se(size, squareness) = [
) [ra*x, rb*y] / r
];
function squircle_radius_se(n, r, angle) = let(
function squircle_radius_se(n, r, angle) =
let(
x = cos(angle),
y = sin(angle)
) (abs(x)^n + abs(y)^n)^(1/n) / r;
)
(abs(x)^n + abs(y)^n)^(1/n) / r;
function _squircle_se_exponent(squareness) = let(
function _squircle_se_exponent(squareness) =
let(
// limit squareness; error if >0.99889, limit is smaller for r>1
s=min(0.998,squareness),
rho = 1 + s*(sqrt(2)-1),
x = rho / sqrt(2)
) log(0.5) / log(x);
)
log(0.5) / log(x);
/* Bezier squircle function */
function _squircle_bz(size, squareness) = let(
function _squircle_bz(size, squareness) =
let(
splinesteps = $fn>=12 ? round($fn/4) : 10,
size = is_num(size) ? [size,size] : point2d(size),
sq = square(size, center=true),
bez = path_to_bezcornerpath(sq, relsize=1-squareness, closed=true)
) bezpath_curve(bez, splinesteps=splinesteps);
)
bezpath_curve(bez, splinesteps=splinesteps);