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remove enumerate, zip, ellipse uniform sampling with realign

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Adrian Mariano
2021-11-18 19:02:50 -05:00
parent 96a210b5a4
commit 1ec9faec39
6 changed files with 99 additions and 92 deletions
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97
shapes2d.scad
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@@ -179,7 +179,7 @@ function rect(size=1, center, rounding=0, chamfer=0, anchor, spin=0) =
// circle(r|d=, ...) { attachables }
// Usage: As a Function
// path = circle(r|d=, ...);
// See Also: ellipse()
// See Also: ellipse(), circle_2tangents(), circle_3points()
// Description:
// When called as the builtin module, creates a 2D polygon that approximates a circle of the given size.
// When called as a function, returns a 2D list of points (path) for a polygon that approximates a circle of the given size.
@@ -224,13 +224,14 @@ module circle(r, d, anchor=CENTER, spin=0) {
// Description:
// When called as a module, creates a 2D polygon that approximates a circle or ellipse of the given size.
// When called as a function, returns a 2D list of points (path) for a polygon that approximates a circle or ellipse of the given size.
// Note that the point list or shape is the same as the one you would get by scaling the output of {{circle()}}, but with this module your
// attachments to the ellipse will
// By default the point list or shape is the same as the one you would get by scaling the output of {{circle()}}, but with this module your
// attachments to the ellipse will retain their dimensions, whereas scaling a circle with attachments will also scale the attachments.
// If you set unifom to true then you will get a polygon with congruent sides whose vertices lie on the ellipse.
// Arguments:
// r = Radius of the circle or pair of semiaxes of ellipse
// ---
// d = Diameter of the circle or a pair giving the full X and Y axis lengths.
// realign = If true, rotates the polygon that approximates the circle/ellipse by half of one size.
// realign = If false starts the approximate ellipse with a point on the X+ axis. If true the midpoint of a side is on the X+ axis and the first point of the polygon is below the X+ axis. This can result in a very different polygon when $fn is small. Default: false
// circum = If true, the polygon that approximates the circle will be upsized slightly to circumscribe the theoretical circle. If false, it inscribes the theoretical circle. Default: false
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
@@ -244,6 +245,54 @@ module circle(r, d, anchor=CENTER, spin=0) {
// ellipse(d=50, anchor=FRONT, spin=45);
// Example(NORENDER): Called as Function
// path = ellipse(d=50, anchor=FRONT, spin=45);
// Example(2D,NoAxes): Uniformly sampled hexagon at the top, regular non-uniform one at the bottom
// r=[10,3];
// ydistribute(7){
// union(){
// stroke([ellipse(r=r, $fn=100)],width=0.05,color="blue");
// stroke([ellipse(r=r, $fn=6)],width=0.1,color="red");
// }
// union(){
// stroke([ellipse(r=r, $fn=100)],width=0.05,color="blue");
// stroke([ellipse(r=r, $fn=6,uniform=true)],width=0.1,color="red");
// }
// }
// Example(2D): The realigned hexagons are even more different
// r=[10,3];
// ydistribute(7){
// union(){
// stroke([ellipse(r=r, $fn=100)],width=0.05,color="blue");
// stroke([ellipse(r=r, $fn=6,realign=true)],width=0.1,color="red");
// }
// union(){
// stroke([ellipse(r=r, $fn=100)],width=0.05,color="blue");
// stroke([ellipse(r=r, $fn=6,realign=true,uniform=true)],width=0.1,color="red");
// }
// }
// Example(2D): For odd $fn the result may not look very elliptical:
// r=[10,3];
// ydistribute(7){
// union(){
// stroke([ellipse(r=r, $fn=100)],width=0.05,color="blue");
// stroke([ellipse(r=r, $fn=5,realign=false)],width=0.1,color="red");
// }
// union(){
// stroke([ellipse(r=r, $fn=100)],width=0.05,color="blue");
// stroke([ellipse(r=r, $fn=5,realign=false,uniform=true)],width=0.1,color="red");
// }
// }
// Example(2D): The same ellipse, turned 90 deg, gives a very different result:
// r=[3,10];
// xdistribute(7){
// union(){
// stroke([ellipse(r=r, $fn=100)],width=0.1,color="blue");
// stroke([ellipse(r=r, $fn=5,realign=false)],width=0.2,color="red");
// }
// union(){
// stroke([ellipse(r=r, $fn=100)],width=0.1,color="blue");
// stroke([ellipse(r=r, $fn=5,realign=false,uniform=true)],width=0.2,color="red");
// }
// }
module ellipse(r, d, realign=false, circum=false, uniform=false, anchor=CENTER, spin=0)
{
r = force_list(get_radius(r=r, d=d, dflt=1),2);
@@ -298,13 +347,41 @@ function _ellipse_refine(a,b,N, _theta=[]) =
function _ellipse_refine_realign(a,b,N, _theta=[],i=0) =
len(_theta)==0?
_ellipse_refine_realign(a,b,N, count(N-1,180/N,360/N))
:
let(
pts = [for(t=_theta) [a*cos(t),b*sin(t)],
[a*cos(_theta[0]), -b*sin(_theta[0])]],
lenlist= path_segment_lengths(pts,closed=true),
meanlen = mean(lenlist),
error = lenlist/meanlen
)
all_equal(error,EPSILON) ? pts
:
let(
dtheta = [each deltas(_theta),
360-last(_theta)-_theta[0],
2*_theta[0]],
newdtheta = [for(i=idx(dtheta)) dtheta[i]/error[i]],
normdtheta = newdtheta / sum(newdtheta) * 360,
adjusted = cumsum([last(normdtheta)/2, each list_head(normdtheta, -3)])
)
_ellipse_refine_realign(a,b,N,adjusted, i+1);
function ellipse(r, d, realign=false, circum=false, uniform=false, anchor=CENTER, spin=0) =
let(
r = force_list(get_radius(r=r, d=d, dflt=1),2),
sides = segs(max(r))
)
uniform ? assert(!circum, "Circum option not allowed when \"uniform\" is true")
reorient(anchor,spin,two_d=true,r=[r.x,r.y],p=_ellipse_refine(r.x,r.y,sides))
reorient(anchor,spin,two_d=true,r=[r.x,r.y],
p=realign ? reverse(_ellipse_refine_realign(r.x,r.y,sides))
: reverse_polygon(_ellipse_refine(r.x,r.y,sides)))
:
let(
offset = realign? 180/sides : 0,
@@ -336,7 +413,7 @@ function ellipse(r, d, realign=false, circum=false, uniform=false, anchor=CENTER
// id = Inside diameter, at center of sides.
// side = Length of each side.
// rounding = Radius of rounding for the tips of the polygon. Default: 0 (no rounding)
// realign = If false, a tip is aligned with the Y+ axis. If true, the midpoint of a side is aligned with the Y+ axis. Default: false
// realign = If false, vertex 0 will lie on the X+ axis. If true then the midpoint of the last edge will lie on the X+ axis, and vertex 0 will be below the X axis. Default: false
// align_tip = If given as a 2D vector, rotates the whole shape so that the first vertex points in that direction. This occurs before spin.
// align_side = If given as a 2D vector, rotates the whole shape so that the normal of side0 points in that direction. This occurs before spin.
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
@@ -471,7 +548,7 @@ module regular_ngon(n=6, r, d, or, od, ir, id, side, rounding=0, realign=false,
// id = Inside diameter, at center of sides.
// side = Length of each side.
// rounding = Radius of rounding for the tips of the polygon. Default: 0 (no rounding)
// realign = If false, a tip is aligned with the Y+ axis. If true, the midpoint of a side is aligned with the Y+ axis. Default: false
// realign = If false, vertex 0 will lie on the X+ axis. If true then the midpoint of the last edge will lie on the X+ axis, and vertex 0 will be below the X axis. Default: false
// align_tip = If given as a 2D vector, rotates the whole shape so that the first vertex points in that direction. This occurs before spin.
// align_side = If given as a 2D vector, rotates the whole shape so that the normal of side0 points in that direction. This occurs before spin.
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
@@ -535,7 +612,7 @@ module pentagon(r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip
// id = Inside diameter, at center of sides.
// side = Length of each side.
// rounding = Radius of rounding for the tips of the polygon. Default: 0 (no rounding)
// realign = If false, a tip is aligned with the Y+ axis. If true, the midpoint of a side is aligned with the Y+ axis. Default: false
// realign = If false, vertex 0 will lie on the X+ axis. If true then the midpoint of the last edge will lie on the X+ axis, and vertex 0 will be below the X axis. Default: false
// align_tip = If given as a 2D vector, rotates the whole shape so that the first vertex points in that direction. This occurs before spin.
// align_side = If given as a 2D vector, rotates the whole shape so that the normal of side0 points in that direction. This occurs before spin.
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
@@ -598,7 +675,7 @@ module hexagon(r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip,
// id = Inside diameter, at center of sides.
// side = Length of each side.
// rounding = Radius of rounding for the tips of the polygon. Default: 0 (no rounding)
// realign = If false, a tip is aligned with the Y+ axis. If true, the midpoint of a side is aligned with the Y+ axis. Default: false
// realign = If false, vertex 0 will lie on the X+ axis. If true then the midpoint of the last edge will lie on the X+ axis, and vertex 0 will be below the X axis. Default: false
// align_tip = If given as a 2D vector, rotates the whole shape so that the first vertex points in that direction. This occurs before spin.
// align_side = If given as a 2D vector, rotates the whole shape so that the normal of side0 points in that direction. This occurs before spin.
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
@@ -808,7 +885,7 @@ module trapezoid(h, w1, w2, angle, shift=0, chamfer=0, rounding=0, anchor=CENTER
// d/od = The diameter to the tips of the star.
// id = The diameter to the inner corners of the star.
// step = Calculates the radius of the inner star corners by virtually drawing a straight line `step` tips around the star. 2 <= step < n/2
// realign = If false, a tip is aligned with the Y+ axis. If true, an inner corner is aligned with the Y+ axis. Default: false
// realign = If false, vertex 0 will lie on the X+ axis. If true then the midpoint of the last edge will lie on the X+ axis, and vertex 0 will be below the X axis. Default: false
// align_tip = If given as a 2D vector, rotates the whole shape so that the first star tip points in that direction. This occurs before spin.
// align_pit = If given as a 2D vector, rotates the whole shape so that the first inner corner is pointed towards that direction. This occurs before spin.
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`