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Implement fix for issue #174.

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Garth Minette 2020-09-25 00:01:45 -07:00
parent 4f88775ef9
commit f193871a34
5 changed files with 119 additions and 48 deletions
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115
geometry.scad
View file

@ -1220,16 +1220,25 @@ function in_front_of_plane(plane, point) =
// Section: Circle Calculations
// Function: find_circle_2tangents()
// Usage:
// find_circle_2tangents(pt1, pt2, pt3, r|d, <tangents>);
// Function&Module: circle_2tangents()
// Usage: As Function
// circ = circle_2tangents(pt1, pt2, pt3, r|d, <tangents>);
// Usage: As Module
// circle_2tangents(pt1, pt2, pt3, r|d, <h>, <center>);
// Description:
// Given a pair of rays with a common origin, and a known circle radius/diameter, finds
// the centerpoint for the circle of that size that touches both rays tangentally.
// Both rays start at `pt2`, one passing through `pt1`, and the other through `pt3`.
// If the rays given are collinear, `undef` is returned. Otherwise, if `tangents` is
// true, then `[CP,NORMAL]` is returned. If `tangents` is false, the more extended
// `[CP,NORMAL,TANPT1,TANPT2,ANG1,ANG2]` is returned
// .
// When called as a module with an `h` height argument, creates a 3D cylinder of `h`
// length at the found centerpoint, aligned with the found normal.
// .
// When called as a module with 2D data and no `h` argument, creates a 2D circle of
// the given radius/diameter, tangentially touching both rays.
// .
// When called as a function with collinear rays, returns `undef`.
// Otherwise, when called as a function with `tangents=false`, returns `[CP,NORMAL]`.
// Otherwise, when called as a function with `tangents=true`, returns `[CP,NORMAL,TANPT1,TANPT2,ANG1,ANG2]`.
// - CP is the centerpoint of the circle.
// - NORMAL is the normal vector of the plane that the circle is on (UP or DOWN if the points are 2D).
// - TANPT1 is the point where the circle is tangent to the ray `[pt2,pt1]`.
@ -1242,13 +1251,15 @@ function in_front_of_plane(plane, point) =
// pt3 = A point that the second ray passes though.
// r = The radius of the circle to find.
// d = The diameter of the circle to find.
// h = Height of the cylinder to create, when called as a module.
// center = When called as a module, center the cylinder if true, Default: false
// tangents = If true, extended information about the tangent points is calculated and returned. Default: false
// Example(2D):
// pts = [[60,40], [10,10], [65,5]];
// rad = 10;
// stroke([pts[1],pts[0]], endcap2="arrow2");
// stroke([pts[1],pts[2]], endcap2="arrow2");
// circ = find_circle_2tangents(pt1=pts[0], pt2=pts[1], pt3=pts[2], r=rad);
// circ = circle_2tangents(pt1=pts[0], pt2=pts[1], pt3=pts[2], r=rad);
// translate(circ[0]) {
// color("green") {
// stroke(circle(r=rad),closed=true);
@ -1259,14 +1270,29 @@ function in_front_of_plane(plane, point) =
// translate(circ[0]) color("red") circle(d=2, $fn=12);
// labels = [[pts[0], "pt1"], [pts[1],"pt2"], [pts[2],"pt3"], [circ[0], "CP"], [circ[0]+[cos(315),sin(315)]*rad*0.7, "r"]];
// for(l=labels) translate(l[0]+[0,2]) color("black") text(text=l[1], size=2.5, halign="center");
function find_circle_2tangents(pt1, pt2, pt3, r, d, tangents=false) =
// Example(2D):
// pts = [[-5,25], [5,-25], [45,15]];
// rad = 12;
// color("blue") stroke(pts, width=0.75, endcaps="arrow2");
// circle_2tangents(pt1=pts[0], pt2=pts[1], pt3=pts[2], r=rad);
// Example: Non-centered Cylinder
// pts = [[45,15,10], [5,-25,5], [-5,25,20]];
// rad = 12;
// color("blue") stroke(pts, width=0.75, endcaps="arrow2");
// circle_2tangents(pt1=pts[0], pt2=pts[1], pt3=pts[2], r=rad, h=10, center=false);
// Example: Non-centered Cylinder
// pts = [[45,15,10], [5,-25,5], [-5,25,20]];
// rad = 12;
// color("blue") stroke(pts, width=0.75, endcaps="arrow2");
// circle_2tangents(pt1=pts[0], pt2=pts[1], pt3=pts[2], r=rad, h=10, center=true);
function circle_2tangents(pt1, pt2, pt3, r, d, tangents=false) =
let(r = get_radius(r=r, d=d, dflt=undef))
assert(r!=undef, "Must specify either r or d.")
assert( ( is_path(pt1) && len(pt1)==3 && is_undef(pt2) && is_undef(pt3))
|| (is_matrix([pt1,pt2,pt3]) && (len(pt1)==2 || len(pt1)==3) ),
"Invalid input points." )
is_undef(pt2)
? find_circle_2tangents(pt1[0], pt1[1], pt1[2], r=r, tangents=tangents)
? circle_2tangents(pt1[0], pt1[1], pt1[2], r=r, tangents=tangents)
: collinear(pt1, pt2, pt3)? undef :
let(
v1 = unit(pt1 - pt2),
@ -1287,11 +1313,29 @@ function find_circle_2tangents(pt1, pt2, pt3, r, d, tangents=false) =
)
[cp, n, tp1, tp2, dang1, dang2];
module circle_2tangents(pt1, pt2, pt3, r, d, h, center=false) {
c = circle_2tangents(pt1=pt1, pt2=pt2, pt3=pt3, r=r, d=d);
assert(!is_undef(c), "Cannot find circle when both rays are collinear.");
cp = c[0]; n = c[1];
if (approx(point3d(cp).z,0) && approx(point2d(n),[0,0]) && is_undef(h)) {
translate(cp) circle(r=r, d=d);
} else {
assert(is_finite(h), "h argument required when result is not flat on the XY plane.");
translate(cp) {
rot(from=UP, to=n) {
cylinder(r=r, d=d, h=h, center=center);
}
}
}
}
// Function: find_circle_3points()
// Usage:
// find_circle_3points(pt1, pt2, pt3);
// find_circle_3points([pt1, pt2, pt3]);
// Function&Module: circle_3points()
// Usage: As Function
// circ = circle_3points(pt1, pt2, pt3);
// circ = circle_3points([pt1, pt2, pt3]);
// Usage: As Module
// circle_3points(pt1, pt2, pt3, <h>, <center>);
// circle_3points([pt1, pt2, pt3], <h>, <center>);
// Description:
// Returns the [CENTERPOINT, RADIUS, NORMAL] of the circle that passes through three non-collinear
// points where NORMAL is the normal vector of the plane that the circle is on (UP or DOWN if the points are 2D).
@ -1305,16 +1349,30 @@ function find_circle_2tangents(pt1, pt2, pt3, r, d, tangents=false) =
// pt1 = The first point.
// pt2 = The second point.
// pt3 = The third point.
// h = Height of the cylinder to create, when called as a module.
// center = When called as a module, center the cylinder if true, Default: false
// Example(2D):
// pts = [[60,40], [10,10], [65,5]];
// circ = find_circle_3points(pts[0], pts[1], pts[2]);
// circ = circle_3points(pts[0], pts[1], pts[2]);
// translate(circ[0]) color("green") stroke(circle(r=circ[1]),closed=true,$fn=72);
// translate(circ[0]) color("red") circle(d=3, $fn=12);
// move_copies(pts) color("blue") circle(d=3, $fn=12);
function find_circle_3points(pt1, pt2, pt3) =
// Example(2D):
// pts = [[30,40], [10,20], [55,30]];
// circle_3points(pts[0], pts[1], pts[2]);
// move_copies(pts) color("blue") circle(d=3, $fn=12);
// Example: Non-Centered Cylinder
// pts = [[30,15,30], [10,20,15], [55,25,25]];
// circle_3points(pts[0], pts[1], pts[2], h=10, center=false);
// move_copies(pts) color("cyan") sphere(d=3, $fn=12);
// Example: Centered Cylinder
// pts = [[30,15,30], [10,20,15], [55,25,25]];
// circle_3points(pts[0], pts[1], pts[2], h=10, center=true);
// move_copies(pts) color("cyan") sphere(d=3, $fn=12);
function circle_3points(pt1, pt2, pt3) =
(is_undef(pt2) && is_undef(pt3) && is_list(pt1))
? find_circle_3points(pt1[0], pt1[1], pt1[2])
: assert( is_vector(pt1) && is_vector(pt2) && is_vector(pt3)
? circle_3points(pt1[0], pt1[1], pt1[2])
: assert( is_vector(pt1) && is_vector(pt2) && is_vector(pt3)
&& max(len(pt1),len(pt2),len(pt3))<=3 && min(len(pt1),len(pt2),len(pt3))>=2,
"Invalid point(s)." )
collinear(pt1,pt2,pt3)? [undef,undef,undef] :
@ -1330,12 +1388,25 @@ function find_circle_3points(pt1, pt2, pt3) =
sc = plane_intersection(
[ each e1, e1*pm[es[1]] ], // planes orthogonal to 2 edges
[ each e2, e2*pm[es[2]] ],
[ each n, n*v[0] ] ) , // triangle plane
cp = len(pt1)+len(pt2)+len(pt3)>6 ? sc: [sc.x, sc.y],
[ each n, n*v[0] ]
), // triangle plane
cp = len(pt1)+len(pt2)+len(pt3)>6 ? sc : [sc.x, sc.y],
r = norm(sc-v[0])
)
[ cp, r, n ];
) [ cp, r, n ];
module circle_3points(pt1, pt2, pt3, h, center=false) {
c = circle_3points(pt1, pt2, pt3);
assert(!is_undef(c[0]), "Points cannot be collinear.");
cp = c[0]; r = c[1]; n = c[2];
if (approx(point3d(cp).z,0) && approx(point2d(n),[0,0]) && is_undef(h)) {
translate(cp) circle(r=r);
} else {
assert(is_finite(h));
translate(cp) rot(from=UP,to=n) cylinder(r=r, h=h, center=center);
}
}
// Function: circle_point_tangents()
// Usage:

4
shapes.scad
View file

@ -673,7 +673,7 @@ module cyl(
) [p1,p2]
) : !is_undef(fil2)? (
let(
cn = find_circle_2tangents([r2-fil2,l/2], [r2,l/2], [r1,-l/2], r=abs(fil2)),
cn = circle_2tangents([r2-fil2,l/2], [r2,l/2], [r1,-l/2], r=abs(fil2)),
ang = fil2<0? phi : phi-180,
steps = ceil(abs(ang)/360*segs(abs(fil2))),
step = ang/steps,
@ -688,7 +688,7 @@ module cyl(
) [p1,p2]
) : !is_undef(fil1)? (
let(
cn = find_circle_2tangents([r1-fil1,-l/2], [r1,-l/2], [r2,l/2], r=abs(fil1)),
cn = circle_2tangents([r1-fil1,-l/2], [r1,-l/2], [r2,l/2], r=abs(fil1)),
ang = fil1<0? 180-phi : -phi,
steps = ceil(abs(ang)/360*segs(abs(fil1))),
step = ang/steps,

38
tests/test_geometry.scad
View file

@ -57,8 +57,8 @@ test_plane_intersection();
test_coplanar();
test_points_on_plane();
test_in_front_of_plane();
test_find_circle_2tangents();
test_find_circle_3points();
test_circle_2tangents();
test_circle_3points();
test_circle_point_tangents();
test_noncollinear_triple();
@ -470,22 +470,22 @@ module test_segment_closest_point() {
}
*test_segment_closest_point();
module test_find_circle_2tangents() {
module test_circle_2tangents() {
//** missing tests with arg tangent=true
assert(approx(find_circle_2tangents([10,10],[0,0],[10,-10],r=10/sqrt(2))[0],[10,0]));
assert(approx(find_circle_2tangents([-10,10],[0,0],[-10,-10],r=10/sqrt(2))[0],[-10,0]));
assert(approx(find_circle_2tangents([-10,10],[0,0],[10,10],r=10/sqrt(2))[0],[0,10]));
assert(approx(find_circle_2tangents([-10,-10],[0,0],[10,-10],r=10/sqrt(2))[0],[0,-10]));
assert(approx(find_circle_2tangents([0,10],[0,0],[10,0],r=10)[0],[10,10]));
assert(approx(find_circle_2tangents([10,0],[0,0],[0,-10],r=10)[0],[10,-10]));
assert(approx(find_circle_2tangents([0,-10],[0,0],[-10,0],r=10)[0],[-10,-10]));
assert(approx(find_circle_2tangents([-10,0],[0,0],[0,10],r=10)[0],[-10,10]));
assert_approx(find_circle_2tangents(polar_to_xy(10,60),[0,0],[10,0],r=10)[0],polar_to_xy(20,30));
assert(approx(circle_2tangents([10,10],[0,0],[10,-10],r=10/sqrt(2))[0],[10,0]));
assert(approx(circle_2tangents([-10,10],[0,0],[-10,-10],r=10/sqrt(2))[0],[-10,0]));
assert(approx(circle_2tangents([-10,10],[0,0],[10,10],r=10/sqrt(2))[0],[0,10]));
assert(approx(circle_2tangents([-10,-10],[0,0],[10,-10],r=10/sqrt(2))[0],[0,-10]));
assert(approx(circle_2tangents([0,10],[0,0],[10,0],r=10)[0],[10,10]));
assert(approx(circle_2tangents([10,0],[0,0],[0,-10],r=10)[0],[10,-10]));
assert(approx(circle_2tangents([0,-10],[0,0],[-10,0],r=10)[0],[-10,-10]));
assert(approx(circle_2tangents([-10,0],[0,0],[0,10],r=10)[0],[-10,10]));
assert_approx(circle_2tangents(polar_to_xy(10,60),[0,0],[10,0],r=10)[0],polar_to_xy(20,30));
}
*test_find_circle_2tangents();
*test_circle_2tangents();
module test_find_circle_3points() {
module test_circle_3points() {
count = 200;
coords = rands(-100,100,count,seed_value=888);
radii = rands(10,100,count,seed_value=390);
@ -496,7 +496,7 @@ module test_find_circle_3points() {
r = radii[i];
angs = sort(select(angles,i,i+2));
pts = [for (a=angs) cp+polar_to_xy(r,a)];
res = find_circle_3points(pts);
res = circle_3points(pts);
if (!approx(res[0], cp)) {
echo(cp=cp, r=r, angs=angs);
echo(pts=pts);
@ -521,7 +521,7 @@ module test_find_circle_3points() {
r = radii[i];
angs = sort(select(angles,i,i+2));
pts = [for (a=angs) cp+polar_to_xy(r,a)];
res = find_circle_3points(pts[0], pts[1], pts[2]);
res = circle_3points(pts[0], pts[1], pts[2]);
if (!approx(res[0], cp)) {
echo(cp=cp, r=r, angs=angs);
echo(pts=pts);
@ -549,7 +549,7 @@ module test_find_circle_3points() {
n = nrm.z<0? -nrm : nrm;
angs = sort(select(angles,i,i+2));
pts = translate(cp,p=rot(from=UP,to=n,p=[for (a=angs) point3d(polar_to_xy(r,a))]));
res = find_circle_3points(pts);
res = circle_3points(pts);
if (!approx(res[0], cp)) {
echo(cp=cp, r=r, angs=angs, n=n);
echo(pts=pts);
@ -576,7 +576,7 @@ module test_find_circle_3points() {
n = nrm.z<0? -nrm : nrm;
angs = sort(select(angles,i,i+2));
pts = translate(cp,p=rot(from=UP,to=n,p=[for (a=angs) point3d(polar_to_xy(r,a))]));
res = find_circle_3points(pts[0], pts[1], pts[2]);
res = circle_3points(pts[0], pts[1], pts[2]);
if (!approx(res[0], cp)) {
echo(cp=cp, r=r, angs=angs, n=n);
echo(pts=pts);
@ -597,7 +597,7 @@ module test_find_circle_3points() {
}
}
}
*test_find_circle_3points();
*test_circle_3points();
module test_circle_point_tangents() {

2
version.scad
View file

@ -8,7 +8,7 @@
//////////////////////////////////////////////////////////////////////
BOSL_VERSION = [2,0,429];
BOSL_VERSION = [2,0,430];
// Section: BOSL Library Version Functions

8
walls.scad
View file

@ -93,10 +93,10 @@ module thinning_wall(h=50, l=100, thick=5, ang=30, braces=false, strut, wall, an
wall = is_num(wall)? wall : thick/2;
bevel_h = strut + (thick-wall)/2/tan(ang);
cp1 = find_circle_2tangents([0,0,h/2], [l2/2,0,h/2], [l1/2,0,-h/2], r=strut)[0];
cp2 = find_circle_2tangents([0,0,h/2], [l2/2,0,h/2], [l1/2,0,-h/2], r=bevel_h)[0];
cp3 = find_circle_2tangents([0,0,-h/2], [l1/2,0,-h/2], [l2/2,0,h/2], r=bevel_h)[0];
cp4 = find_circle_2tangents([0,0,-h/2], [l1/2,0,-h/2], [l2/2,0,h/2], r=strut)[0];
cp1 = circle_2tangents([0,0,h/2], [l2/2,0,h/2], [l1/2,0,-h/2], r=strut)[0];
cp2 = circle_2tangents([0,0,h/2], [l2/2,0,h/2], [l1/2,0,-h/2], r=bevel_h)[0];
cp3 = circle_2tangents([0,0,-h/2], [l1/2,0,-h/2], [l2/2,0,h/2], r=bevel_h)[0];
cp4 = circle_2tangents([0,0,-h/2], [l1/2,0,-h/2], [l2/2,0,h/2], r=strut)[0];
z1 = h/2;
z2 = cp1.z;