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15
.github/check_for_tabs.json vendored Normal file
View file

@ -0,0 +1,15 @@
{
"problemMatcher": [
{
"owner": "check_for_tabs",
"pattern": [
{
"regexp": "^([^:]+):(\\d+):(.*)$",
"file": 1,
"line": 2,
"message": 3
}
]
}
]
}

60
.github/workflows/docsgen.yml vendored
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@ -1,60 +0,0 @@
name: Docs
on:
pull_request:
branches: [master]
types: [closed]
jobs:
GenerateDocs:
if: github.event.pull_request.merged == true
runs-on: ubuntu-latest
steps:
- name: Checkout
uses: actions/checkout@v2
- name: Checkout Wiki
uses: actions/checkout@v2
with:
repository: revarbat/BOSL2.wiki
path: BOSL2.wiki
- name: Apt Update
run: sudo apt update
- name: Install Packages
run: sudo apt-get install -y python3-pip python3-dev python3-setuptools python3-pil gifsicle
- name: Install openscad-docsgen
run: sudo pip3 install openscad_docsgen
- name: Install OpenSCAD
run: |
cd $GITHUB_WORKSPACE
wget https://files.openscad.org/OpenSCAD-2021.01-x86_64.AppImage
sudo mv OpenSCAD-2021.01*-x86_64.AppImage /usr/local/bin/openscad
sudo chmod +x /usr/local/bin/openscad
echo "::add-matcher::.github/openscad_docsgen.json"
- name: Generating Docs Headless
run: |
export OPENSCADPATH=$(dirname $GITHUB_WORKSPACE)
xvfb-run --server-args="-screen 0, 1280x720x24" -a \
openscad-docsgen -ticmI *.scad
- name: Commit Wiki Docs
run: |
cd $GITHUB_WORKSPACE/BOSL2.wiki
git config user.name github-actions
git config user.email github-actions@github.com
git add --all
git commit -m "Wiki docs auto-regen." && git push || true
- name: Bump Release Version
run: |
cd $GITHUB_WORKSPACE
./scripts/increment_version.sh
git config user.name github-actions
git config user.email github-actions@github.com
git add version.scad
git commit -m "Bump release version." && git push || true

49
.github/workflows/forced_docsgen.yml vendored
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@ -1,49 +0,0 @@
name: FDocs
on:
workflow_dispatch:
branches: [master]
jobs:
GenerateDocs:
runs-on: ubuntu-latest
steps:
- name: Checkout
uses: actions/checkout@v2
- name: Checkout Wiki
uses: actions/checkout@v2
with:
repository: revarbat/BOSL2.wiki
path: BOSL2.wiki
- name: Apt Update
run: sudo apt update
- name: Install Packages
run: sudo apt-get install -y python3-pip python3-dev python3-setuptools python3-pil gifsicle
- name: Install openscad-docsgen
run: sudo pip3 install openscad_docsgen
- name: Install OpenSCAD
run: |
cd $GITHUB_WORKSPACE
wget https://files.openscad.org/OpenSCAD-2021.01-x86_64.AppImage
sudo mv OpenSCAD-2021.01*-x86_64.AppImage /usr/local/bin/openscad
sudo chmod +x /usr/local/bin/openscad
echo "::add-matcher::.github/openscad_docsgen.json"
- name: Generating Docs Headless
run: |
export OPENSCADPATH=$(dirname $GITHUB_WORKSPACE)
xvfb-run --server-args="-screen 0, 1280x720x24" -a \
openscad-docsgen -ticmIf *.scad
- name: Commit Wiki Docs
run: |
cd $GITHUB_WORKSPACE/BOSL2.wiki
git config user.name github-actions
git config user.email github-actions@github.com
git add --all
git commit -m "Wiki docs auto-regen." && git push || true

8
.github/workflows/main.yml vendored
View file

@ -1,4 +1,4 @@
name: CI
name: Checks
on: [pull_request]
jobs:
@ -49,6 +49,12 @@ jobs:
sudo mv OpenSCAD-2021.01*-x86_64.AppImage /usr/local/bin/openscad
sudo chmod +x /usr/local/bin/openscad
- name: Tabs Check
run: |
cd $GITHUB_WORKSPACE
echo "::add-matcher::.github/check_for_tabs.json"
./scripts/check_for_tabs.sh
- name: Checking Docs
run: |
cd $GITHUB_WORKSPACE

49
.github/workflows/testwf.yml vendored
View file

@ -1,49 +0,0 @@
name: TestWorkflow
on:
workflow_dispatch:
branches: [master]
jobs:
TestJob:
runs-on: ubuntu-latest
steps:
- name: Checkout
uses: actions/checkout@v2
- name: Checkout Wiki
uses: actions/checkout@v2
with:
repository: revarbat/BOSL2.wiki
path: BOSL2.wiki
- name: Setup OpenGL
uses: openrndr/setup-opengl@v1.1
- name: Apt Update
run: sudo apt update
- name: Install Packages
run: sudo apt-get install -y python3-pip python3-dev python3-setuptools python3-pil gifsicle
- name: Install openscad-docsgen
run: sudo pip3 install openscad_docsgen
- name: Install OpenSCAD
run: |
cd $GITHUB_WORKSPACE
wget https://files.openscad.org/OpenSCAD-2021.01-x86_64.AppImage
sudo mv OpenSCAD-2021.01*-x86_64.AppImage /usr/local/bin/openscad
sudo chmod +x /usr/local/bin/openscad
echo "::add-matcher::.github/openscad_docsgen.json"
- name: Make SCAD File
run: |
cd $GITHUB_WORKSPACE
echo "cube(50, center=100);" > testwf.scad
- name: TestScript
run: |
export OPENSCADPATH=$(dirname $GITHUB_WORKSPACE)
xvfb-run --server-args="-screen 0, 1280x720x24" -a \
glxinfo

110
arrays.scad
View file

@ -951,28 +951,34 @@ function shuffle(list,seed) =
// idx should be an index of the arrays l[i]
function _group_sort_by_index(l,idx) =
len(l) == 0 ? [] :
len(l) == 1 ? [l] :
let( pivot = l[floor(len(l)/2)][idx],
equal = [ for(li=l) if( li[idx]==pivot) li ] ,
lesser = [ for(li=l) if( li[idx]< pivot) li ] ,
greater = [ for(li=l) if( li[idx]> pivot) li ]
)
concat( _group_sort_by_index(lesser,idx),
[equal],
_group_sort_by_index(greater,idx) ) ;
len(l) == 0 ? [] :
len(l) == 1 ? [l] :
let(
pivot = l[floor(len(l)/2)][idx],
equal = [ for(li=l) if( li[idx]==pivot) li ],
lesser = [ for(li=l) if( li[idx]< pivot) li ],
greater = [ for(li=l) if( li[idx]> pivot) li ]
)
concat(
_group_sort_by_index(lesser,idx),
[equal],
_group_sort_by_index(greater,idx)
);
function _group_sort(l) =
len(l) == 0 ? [] :
len(l) == 1 ? [l] :
let( pivot = l[floor(len(l)/2)],
equal = [ for(li=l) if( li==pivot) li ] ,
lesser = [ for(li=l) if( li< pivot) li ] ,
greater = [ for(li=l) if( li> pivot) li ]
)
concat( _group_sort(lesser),
[equal],
_group_sort(greater) ) ;
len(l) == 0 ? [] :
len(l) == 1 ? [l] :
let(
pivot = l[floor(len(l)/2)],
equal = [ for(li=l) if( li==pivot) li ] ,
lesser = [ for(li=l) if( li< pivot) li ] ,
greater = [ for(li=l) if( li> pivot) li ]
)
concat(
_group_sort(lesser),
[equal],
_group_sort(greater)
);
// Sort a vector of scalar values with the native comparison operator
@ -1171,11 +1177,11 @@ function group_sort(list, idx) =
assert(is_list(list), "Input should be a list." )
assert(is_undef(idx) || (is_finite(idx) && idx>=0) , "Invalid index." )
len(list)<=1 ? [list] :
is_vector(list)? _group_sort(list) :
let( idx = is_undef(idx) ? 0 : idx )
assert( [for(entry=list) if(!is_list(entry) || len(entry)<idx || !is_num(entry[idx]) ) 1]==[],
"Some entry of the list is a list shorter than `idx` or the indexed entry of it is not a number." )
_group_sort_by_index(list,idx);
is_vector(list)? _group_sort(list) :
let( idx = is_undef(idx) ? 0 : idx )
assert( [for(entry=list) if(!is_list(entry) || len(entry)<idx || !is_num(entry[idx]) ) 1]==[],
"Some entry of the list is a list shorter than `idx` or the indexed entry of it is not a number.")
_group_sort_by_index(list,idx);
// Function: unique()
@ -1197,23 +1203,27 @@ function unique(list) =
is_string(list)? str_join(unique([for (x = list) x])) :
len(list)<=1? list :
is_homogeneous(list,1) && ! is_list(list[0])
? _unique_sort(list)
? _unique_sort(list)
: let( sorted = sort(list))
[ for (i=[0:1:len(sorted)-1])
if (i==0 || (sorted[i] != sorted[i-1]))
sorted[i]
];
[
for (i=[0:1:len(sorted)-1])
if (i==0 || (sorted[i] != sorted[i-1]))
sorted[i]
];
function _unique_sort(l) =
len(l) <= 1 ? l :
let( pivot = l[floor(len(l)/2)],
equal = [ for(li=l) if( li==pivot) li ] ,
lesser = [ for(li=l) if( li<pivot ) li ] ,
greater = [ for(li=l) if( li>pivot) li ]
)
concat( _unique_sort(lesser),
equal[0],
_unique_sort(greater) ) ;
len(l) <= 1 ? l :
let(
pivot = l[floor(len(l)/2)],
equal = [ for(li=l) if( li==pivot) li ] ,
lesser = [ for(li=l) if( li<pivot ) li ] ,
greater = [ for(li=l) if( li>pivot) li ]
)
concat(
_unique_sort(lesser),
equal[0],
_unique_sort(greater)
);
// Function: unique_count()
@ -1232,13 +1242,23 @@ function unique_count(list) =
assert(is_list(list) || is_string(list), "Invalid input." )
list == [] ? [[],[]] :
is_homogeneous(list,1) && ! is_list(list[0])
? let( sorted = _group_sort(list) )
[ [for(s=sorted) s[0] ], [for(s=sorted) len(s) ] ]
: let( list=sort(list) )
let( ind = [0, for(i=[1:1:len(list)-1]) if (list[i]!=list[i-1]) i] )
[ select(list,ind), deltas( concat(ind,[len(list)]) ) ];
? let( sorted = _group_sort(list) ) [
[for(s=sorted) s[0] ],
[for(s=sorted) len(s) ]
]
: let(
list=sort(list),
ind = [
0,
for(i=[1:1:len(list)-1])
if (list[i]!=list[i-1]) i
]
) [
select(list,ind),
deltas( concat(ind,[len(list)]) )
];
// Section: List Iteration Helpers
// Function: idx()

2
bottlecaps.scad
View file

@ -502,7 +502,7 @@ module generic_bottle_neck(
}
function generic_bottle_neck(
neck_d,
neck_d,
id,
thread_od,
height,

409
geometry.scad
View file

@ -21,7 +21,7 @@
// eps = Tolerance in geometric comparisons. Default: `EPSILON` (1e-9)
function point_on_segment2d(point, edge, eps=EPSILON) =
assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
point_segment_distance(point, edge)<eps;
point_segment_distance(point, edge)<eps;
//Internal - distance from point `d` to the line passing through the origin with unit direction n
@ -32,8 +32,8 @@ function _dist2line(d,n) = norm(d-(d * n) * n);
function _point_above_below_segment(point, edge) =
let( edge = edge - [point, point] )
edge[0].y <= 0
? (edge[1].y > 0 && cross(edge[0], edge[1]-edge[0]) > 0) ? 1 : 0
: (edge[1].y <= 0 && cross(edge[0], edge[1]-edge[0]) < 0) ? -1 : 0 ;
? (edge[1].y > 0 && cross(edge[0], edge[1]-edge[0]) > 0) ? 1 : 0
: (edge[1].y <= 0 && cross(edge[0], edge[1]-edge[0]) < 0) ? -1 : 0;
//Internal
function _valid_line(line,dim,eps=EPSILON) =
@ -77,8 +77,8 @@ function collinear(a, b, c, eps=EPSILON) =
"Input should be 3 points or a list of points with same dimension.")
assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
let( points = is_def(c) ? [a,b,c]: a )
len(points)<3 ? true
: noncollinear_triple(points,error=false,eps=eps)==[];
len(points)<3 ? true :
noncollinear_triple(points,error=false,eps=eps) == [];
// Function: point_line_distance()
@ -131,8 +131,7 @@ function point_segment_distance(pt, seg) =
// dist = segment_distance([[-14,3], [-15,9]], [[-10,0], [10,0]]); // Returns: 5
// dist2 = segment_distance([[-5,5], [5,-5]], [[-10,3], [10,-3]]); // Returns: 0
function segment_distance(seg1, seg2) =
assert( is_matrix(concat(seg1,seg2),4),
"Inputs should be two valid segments." )
assert( is_matrix(concat(seg1,seg2),4), "Inputs should be two valid segments." )
convex_distance(seg1,seg2);
@ -155,9 +154,9 @@ function segment_distance(seg1, seg2) =
// color("blue") move_copies([p1,p2]) circle(d=2, $fn=12);
function line_normal(p1,p2) =
is_undef(p2)
? assert( len(p1)==2 && !is_undef(p1[1]) , "Invalid input." )
? assert( len(p1)==2 && !is_undef(p1[1]) , "Invalid input." )
line_normal(p1[0],p1[1])
: assert( _valid_line([p1,p2],dim=2), "Invalid line." )
: assert( _valid_line([p1,p2],dim=2), "Invalid line." )
unit([p1.y-p2.y,p2.x-p1.x]);
@ -172,7 +171,8 @@ function line_normal(p1,p2) =
function _general_line_intersection(s1,s2,eps=EPSILON) =
let(
denominator = det2([s1[0],s2[0]]-[s1[1],s2[1]])
) approx(denominator,0,eps=eps)? [undef,undef,undef] : let(
) approx(denominator,0,eps=eps)? [undef,undef,undef] :
let(
t = det2([s1[0],s2[0]]-s2) / denominator,
u = det2([s1[0],s1[0]]-[s2[0],s1[1]]) / denominator
) [s1[0]+t*(s1[1]-s1[0]), t, u];
@ -211,11 +211,10 @@ function line_intersection(l1,l2,eps=EPSILON) =
function line_ray_intersection(line,ray,eps=EPSILON) =
assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
assert( _valid_line(line,dim=2,eps=eps) && _valid_line(ray,dim=2,eps=eps), "Invalid line or ray." )
let(
isect = _general_line_intersection(line,ray,eps=eps)
)
let( isect = _general_line_intersection(line,ray,eps=eps) )
is_undef(isect[0]) ? undef :
(isect[2]<0-eps) ? undef : isect[0];
(isect[2]<0-eps) ? undef :
isect[0];
// Function: line_segment_intersection()
@ -232,9 +231,7 @@ function line_ray_intersection(line,ray,eps=EPSILON) =
function line_segment_intersection(line,segment,eps=EPSILON) =
assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
assert( _valid_line(line, dim=2,eps=eps) &&_valid_line(segment,dim=2,eps=eps), "Invalid line or segment." )
let(
isect = _general_line_intersection(line,segment,eps=eps)
)
let( isect = _general_line_intersection(line,segment,eps=eps) )
is_undef(isect[0]) ? undef :
isect[2]<0-eps || isect[2]>1+eps ? undef :
isect[0];
@ -254,11 +251,10 @@ function line_segment_intersection(line,segment,eps=EPSILON) =
function ray_intersection(r1,r2,eps=EPSILON) =
assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
assert( _valid_line(r1,dim=2,eps=eps) && _valid_line(r2,dim=2,eps=eps), "Invalid ray(s)." )
let(
isect = _general_line_intersection(r1,r2,eps=eps)
)
let( isect = _general_line_intersection(r1,r2,eps=eps) )
is_undef(isect[0]) ? undef :
isect[1]<0-eps || isect[2]<0-eps ? undef : isect[0];
isect[1]<0-eps || isect[2]<0-eps ? undef :
isect[0];
// Function: ray_segment_intersection()
@ -275,9 +271,7 @@ function ray_intersection(r1,r2,eps=EPSILON) =
function ray_segment_intersection(ray,segment,eps=EPSILON) =
assert( _valid_line(ray,dim=2,eps=eps) && _valid_line(segment,dim=2,eps=eps), "Invalid ray or segment." )
assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
let(
isect = _general_line_intersection(ray,segment,eps=eps)
)
let( isect = _general_line_intersection(ray,segment,eps=eps) )
is_undef(isect[0]) ? undef :
isect[1]<0-eps || isect[2]<0-eps || isect[2]>1+eps ? undef :
isect[0];
@ -297,9 +291,7 @@ function ray_segment_intersection(ray,segment,eps=EPSILON) =
function segment_intersection(s1,s2,eps=EPSILON) =
assert( _valid_line(s1,dim=2,eps=eps) && _valid_line(s2,dim=2,eps=eps), "Invalid segment(s)." )
assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
let(
isect = _general_line_intersection(s1,s2,eps=eps)
)
let( isect = _general_line_intersection(s1,s2,eps=eps) )
is_undef(isect[0]) ? undef :
isect[1]<0-eps || isect[1]>1+eps || isect[2]<0-eps || isect[2]>1+eps ? undef :
isect[0];
@ -361,7 +353,7 @@ function line_closest_point(line,pt) =
assert(_valid_line(line), "Invalid line." )
assert( is_vector(pt,len(line[0])), "Invalid point or incompatible dimensions." )
let( n = unit( line[0]- line[1]) )
line[1]+((pt- line[1]) * n) * n;
line[1] + ((pt- line[1]) * n) * n;
// Function: ray_closest_point()
@ -503,7 +495,9 @@ function line_from_points(points, fast=false, eps=EPSILON) =
assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
let( pb = furthest_point(points[0],points) )
norm(points[pb]-points[0])<eps*max(norm(points[pb]),norm(points[0])) ? undef :
fast || collinear(points) ? [points[pb], points[0]] : undef;
fast || collinear(points)
? [points[pb], points[0]]
: undef;
@ -576,7 +570,8 @@ function law_of_sines(a, A, b, B) =
// a/sin(A) = b/sin(B) = c/sin(C)
assert(num_defined([b,B]) == 1, "Must give exactly one of b= or B=.")
let( r = a/sin(A) )
is_undef(b) ? r*sin(B) : asin(constrain(b/r, -1, 1));
is_undef(b) ? r*sin(B) :
asin(constrain(b/r, -1, 1));
// Function: tri_calc()
@ -647,11 +642,11 @@ function tri_calc(ang,ang2,adj,opp,hyp) =
hyp
: (adj!=undef? (adj/cos(ang))
: (opp/sin(ang)))
)
[adj, opp, hyp, ang, ang2];
) [adj, opp, hyp, ang, ang2];
// Function: hyp_opp_to_adj()
// Alias: opp_hyp_to_adj()
// Usage:
// adj = hyp_opp_to_adj(hyp,opp);
// Topics: Geometry, Triangles
@ -668,8 +663,11 @@ function hyp_opp_to_adj(hyp,opp) =
"Triangle side lengths should be a positive numbers." )
sqrt(hyp*hyp-opp*opp);
function opp_hyp_to_adj(opp,hyp) = hyp_opp_to_adj(hyp,opp);
// Function: hyp_ang_to_adj()
// Alias: ang_hyp_to_adj()
// Usage:
// adj = hyp_ang_to_adj(hyp,ang);
// Topics: Geometry, Triangles
@ -686,8 +684,11 @@ function hyp_ang_to_adj(hyp,ang) =
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
hyp*cos(ang);
function ang_hyp_to_adj(ang,hyp) = hyp_ang_to_adj(hyp, ang);
// Function: opp_ang_to_adj()
// Alias: ang_opp_to_adj()
// Usage:
// adj = opp_ang_to_adj(opp,ang);
// Topics: Geometry, Triangles
@ -704,8 +705,11 @@ function opp_ang_to_adj(opp,ang) =
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
opp/tan(ang);
function ang_opp_to_adj(ang,opp) = opp_ang_to_adj(opp,ang);
// Function: hyp_adj_to_opp()
// Alias: adj_hyp_to_opp()
// Usage:
// opp = hyp_adj_to_opp(hyp,adj);
// Topics: Geometry, Triangles
@ -721,8 +725,11 @@ function hyp_adj_to_opp(hyp,adj) =
"Triangle side lengths should be a positive numbers." )
sqrt(hyp*hyp-adj*adj);
function adj_hyp_to_opp(adj,hyp) = hyp_adj_to_opp(hyp,adj);
// Function: hyp_ang_to_opp()
// Alias: ang_hyp_to_opp()
// Usage:
// opp = hyp_ang_to_opp(hyp,adj);
// Topics: Geometry, Triangles
@ -738,8 +745,11 @@ function hyp_ang_to_opp(hyp,ang) =
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
hyp*sin(ang);
function ang_hyp_to_opp(ang,hyp) = hyp_ang_to_opp(hyp,ang);
// Function: adj_ang_to_opp()
// Alias: ang_adj_to_opp()
// Usage:
// opp = adj_ang_to_opp(adj,ang);
// Topics: Geometry, Triangles
@ -755,8 +765,11 @@ function adj_ang_to_opp(adj,ang) =
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
adj*tan(ang);
function ang_adj_to_opp(ang,adj) = adj_ang_to_opp(adj,ang);
// Function: adj_opp_to_hyp()
// Alias: opp_adj_to_hyp()
// Usage:
// hyp = adj_opp_to_hyp(adj,opp);
// Topics: Geometry, Triangles
@ -772,8 +785,11 @@ function adj_opp_to_hyp(adj,opp) =
"Triangle side lengths should be a positive numbers." )
norm([opp,adj]);
function opp_adj_to_hyp(opp,adj) = adj_opp_to_hyp(adj,opp);
// Function: adj_ang_to_hyp()
// Alias: ang_adj_to_hyp()
// Usage:
// hyp = adj_ang_to_hyp(adj,ang);
// Topics: Geometry, Triangles
@ -789,8 +805,11 @@ function adj_ang_to_hyp(adj,ang) =
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
adj/cos(ang);
function ang_adj_to_hyp(ang,adj) = adj_ang_to_hyp(adj,ang);
// Function: opp_ang_to_hyp()
// Alias: ang_opp_to_hyp()
// Usage:
// hyp = opp_ang_to_hyp(opp,ang);
// Topics: Geometry, Triangles
@ -806,8 +825,11 @@ function opp_ang_to_hyp(opp,ang) =
assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
opp/sin(ang);
function ang_opp_to_hyp(ang,opp) = opp_ang_to_hyp(opp,ang);
// Function: hyp_adj_to_ang()
// Alias: adj_hyp_to_ang()
// Usage:
// ang = hyp_adj_to_ang(hyp,adj);
// Description:
@ -822,8 +844,11 @@ function hyp_adj_to_ang(hyp,adj) =
"Triangle side lengths should be positive numbers." )
acos(adj/hyp);
function adj_hyp_to_ang(adj,hyp) = hyp_adj_to_ang(hyp,adj);
// Function: hyp_opp_to_ang()
// Alias: opp_hyp_to_ang()
// Usage:
// ang = hyp_opp_to_ang(hyp,opp);
// Topics: Geometry, Triangles
@ -839,8 +864,11 @@ function hyp_opp_to_ang(hyp,opp) =
"Triangle side lengths should be positive numbers." )
asin(opp/hyp);
function opp_hyp_to_ang(opp,hyp) = hyp_opp_to_ang(hyp,opp);
// Function: adj_opp_to_ang()
// Alias: opp_adj_to_ang()
// Usage:
// ang = adj_opp_to_ang(adj,opp);
// Topics: Geometry, Triangles
@ -856,6 +884,8 @@ function adj_opp_to_ang(adj,opp) =
"Triangle side lengths should be positive numbers." )
atan2(opp,adj);
function opp_adj_to_ang(opp,adj) = adj_opp_to_ang(adj,opp);
// Function: triangle_area()
// Usage:
@ -900,8 +930,7 @@ function plane3pt(p1, p2, p3) =
let(
crx = cross(p3-p1, p2-p1),
nrm = norm(crx)
)
approx(nrm,0) ? [] :
) approx(nrm,0) ? [] :
concat(crx, crx*p1)/nrm;
@ -928,8 +957,7 @@ function plane3pt_indexed(points, i1, i2, i3) =
p1 = points[i1],
p2 = points[i2],
p3 = points[i3]
)
plane3pt(p1,p2,p3);
) plane3pt(p1,p2,p3);
// Function: plane_from_normal()
@ -953,7 +981,7 @@ function plane_from_normal(normal, pt=[0,0,0]) =
// Based on: https://en.wikipedia.org/wiki/Eigenvalue_algorithm
function _eigenvals_symm_3(M) =
let( p1 = pow(M[0][1],2) + pow(M[0][2],2) + pow(M[1][2],2) )
(p1<EPSILON)
(p1<EPSILON)
? -sort(-[ M[0][0], M[1][1], M[2][2] ]) // diagonal matrix: eigenvals in decreasing order
: let( q = (M[0][0]+M[1][1]+M[2][2])/3,
B = (M - q*ident(3)),
@ -964,19 +992,19 @@ function _eigenvals_symm_3(M) =
ph = acos(constrain(r,-1,1))/3,
e1 = q + 2*p*cos(ph),
e3 = q + 2*p*cos(ph+120),
e2 = 3*q - e1 - e3 )
e2 = 3*q - e1 - e3 )
[ e1, e2, e3 ];
// the i-th normalized eigenvector of a 3x3 symmetrical matrix M from its eigenvalues
// using Cayley–Hamilton theorem according to:
// https://en.wikipedia.org/wiki/Eigenvalue_algorithm
function _eigenvec_symm_3(M,evals,i=0) =
let(
I = ident(3),
// https://en.wikipedia.org/wiki/Eigenvalue_algorithm
function _eigenvec_symm_3(M,evals,i=0) =
let(
I = ident(3),
A = (M - evals[(i+1)%3]*I) * (M - evals[(i+2)%3]*I) ,
k = max_index( [for(i=[0:2]) norm(A[i]) ])
)
k = max_index( [for(i=[0:2]) norm(A[i]) ])
)
norm(A[k])<EPSILON ? I[k] : A[k]/norm(A[k]);
@ -1013,15 +1041,16 @@ function _covariance_evec_eval(points) =
function plane_from_points(points, fast=false, eps=EPSILON) =
assert( is_path(points,dim=3), "Improper 3d point list." )
assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
len(points) == 3
? let( plane = plane3pt(points[0],points[1],points[2]) )
plane==[] ? [] : plane
: let(
len(points) == 3
? let( plane = plane3pt(points[0],points[1],points[2]) )
plane==[] ? [] : plane
: let(
covmix = _covariance_evec_eval(points),
pm = covmix[0],
evec = covmix[1],
eval0 = covmix[2],
plane = [ each evec, pm*evec] )
plane = [ each evec, pm*evec]
)
!fast && _pointlist_greatest_distance(points,plane)>eps*eval0 ? undef :
plane ;
@ -1054,8 +1083,8 @@ function plane_from_polygon(poly, fast=false, eps=EPSILON) =
triple==[] ? [] :
let( plane = plane3pt(poly[triple[0]],poly[triple[1]],poly[triple[2]]))
fast? plane: points_on_plane(poly, plane, eps=eps)? plane: [];
// Function: plane_normal()
// Usage:
// vec = plane_normal(plane);
@ -1164,10 +1193,10 @@ function _general_plane_line_intersection(plane, line, eps=EPSILON) =
b = plane*[each(line[1]-line[0]),0] // difference between the plane expression evaluation at line[1] and at line[0]
)
approx(b,0,eps) // is (line[1]-line[0]) "parallel" to the plane ?
? approx(a,0,eps) // is line[0] on the plane ?
? [line,undef] // line is on the plane
: undef // line is parallel but not on the plane
: [ line[0]-a/b*(line[1]-line[0]), -a/b ];
? approx(a,0,eps) // is line[0] on the plane ?
? [line,undef] // line is on the plane
: undef // line is parallel but not on the plane
: [ line[0]-a/b*(line[1]-line[0]), -a/b ];
// Function: normalize_plane()
@ -1197,8 +1226,7 @@ function plane_line_angle(plane, line) =
normal = plane_normal(plane),
sin_angle = linedir*normal,
cos_angle = norm(cross(linedir,normal))
)
atan2(sin_angle,cos_angle);
) atan2(sin_angle,cos_angle);
// Function: plane_line_intersection()
@ -1222,8 +1250,7 @@ function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) =
let(
bounded = is_list(bounded)? bounded : [bounded, bounded],
res = _general_plane_line_intersection(plane, line, eps=eps)
)
is_undef(res) ? undef :
) is_undef(res) ? undef :
is_undef(res[1]) ? res[0] :
bounded[0] && res[1]<0 ? undef :
bounded[1] && res[1]>1 ? undef :
@ -1254,41 +1281,37 @@ function polygon_line_intersection(poly, line, bounded=false, eps=EPSILON) =
bounded = is_list(bounded)? bounded : [bounded, bounded],
poly = deduplicate(poly),
indices = noncollinear_triple(poly)
)
indices==[] ? undef :
) indices==[] ? undef :
let(
p1 = poly[indices[0]],
p2 = poly[indices[1]],
p3 = poly[indices[2]],
plane = plane3pt(p1,p2,p3),
res = _general_plane_line_intersection(plane, line, eps=eps)
)
is_undef(res)? undef :
is_undef(res[1])
? ( let(// Line is on polygon plane.
) is_undef(res)? undef :
is_undef(res[1]) ? (
let(// Line is on polygon plane.
linevec = unit(line[1] - line[0]),
lp1 = line[0] + (bounded[0]? 0 : -1000000) * linevec,
lp2 = line[1] + (bounded[1]? 0 : 1000000) * linevec,
poly2d = clockwise_polygon(project_plane(plane, poly)),
line2d = project_plane(plane, [lp1,lp2]),
parts = split_path_at_region_crossings(line2d, [poly2d], closed=false),
inside = [for (part = parts)
if (point_in_polygon(mean(part), poly2d)>0) part
]
)
!inside? undef :
let(
isegs = [for (seg = inside) lift_plane(plane, seg) ]
)
inside = [
for (part = parts)
if (point_in_polygon(mean(part), poly2d)>0) part
]
) !inside? undef :
let( isegs = [for (seg = inside) lift_plane(plane, seg) ] )
isegs
)
: bounded[0] && res[1]<0? undef :
bounded[1] && res[1]>1? undef :
let(
proj = clockwise_polygon(project_plane([p1, p2, p3], poly)),
pt = project_plane([p1, p2, p3], res[0])
)
point_in_polygon(pt, proj) < 0 ? undef : res[0];
) :
bounded[0] && res[1]<0? undef :
bounded[1] && res[1]>1? undef :
let(
proj = clockwise_polygon(project_plane([p1, p2, p3], poly)),
pt = project_plane([p1, p2, p3], res[0])
) point_in_polygon(pt, proj) < 0 ? undef :
res[0];
// Function: plane_intersection()
@ -1309,19 +1332,20 @@ function plane_intersection(plane1,plane2,plane3) =
assert( _valid_plane(plane1) && _valid_plane(plane2) && (is_undef(plane3) ||_valid_plane(plane3)),
"The input must be 2 or 3 planes." )
is_def(plane3)
? let(
matrix = [for(p=[plane1,plane2,plane3]) point3d(p)],
rhs = [for(p=[plane1,plane2,plane3]) p[3]]
? let(
matrix = [for(p=[plane1,plane2,plane3]) point3d(p)],
rhs = [for(p=[plane1,plane2,plane3]) p[3]]
)
linear_solve(matrix,rhs)
: let( normal = cross(plane_normal(plane1), plane_normal(plane2)) )
: let( normal = cross(plane_normal(plane1), plane_normal(plane2)) )
approx(norm(normal),0) ? undef :
let(
matrix = [for(p=[plane1,plane2]) point3d(p)],
rhs = [plane1[3], plane2[3]],
point = linear_solve(matrix,rhs)
)
point==[]? undef: [point, point+normal];
point==[]? undef:
[point, point+normal];
// Function: coplanar()
@ -1337,18 +1361,18 @@ function coplanar(points, eps=EPSILON) =
assert( is_path(points,dim=3) , "Input should be a list of 3D points." )
assert( is_finite(eps) && eps>=0, "The tolerance should be a non-negative value." )
len(points)<=2 ? false
: let( ip = noncollinear_triple(points,error=false,eps=eps) )
: let( ip = noncollinear_triple(points,error=false,eps=eps) )
ip == [] ? false :
let( plane = plane3pt(points[ip[0]],points[ip[1]],points[ip[2]]) )
_pointlist_greatest_distance(points,plane) < eps;
// the maximum distance from points to the plane
// the maximum distance from points to the plane
function _pointlist_greatest_distance(points,plane) =
let(
let(
normal = point3d(plane),
pt_nrm = points*normal
)
)
abs(max( max(pt_nrm) - plane[3], -min(pt_nrm) + plane[3])) / norm(normal);
@ -1482,6 +1506,7 @@ function 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.");
@ -1498,6 +1523,7 @@ module circle_2tangents(pt1, pt2, pt3, r, d, h, center=false) {
}
}
// Function&Module: circle_3points()
// Usage: As Function
// circ = circle_3points(pt1, pt2, pt3);
@ -1628,7 +1654,7 @@ function circle_point_tangents(r, d, cp, pt) =
// returns only two entries. If one circle is inside the other one then no tangents exist
// so the function returns the empty set. When the circles are tangent a degenerate tangent line
// passes through the point of tangency of the two circles: this degenerate line is NOT returned.
// Arguments:
// Arguments:
// c1 = Center of the first circle.
// r1 = Radius of the first circle.
// c2 = Center of the second circle.
@ -1747,7 +1773,7 @@ function circle_line_intersection(c,r,d,line,bounded=false,eps=EPSILON) =
// If all points are collinear returns [] when `error=true` or an error otherwise .
// Arguments:
// points = List of input points.
// error = Defines the behaviour for collinear input points. When `true`, produces an error, otherwise returns []. Default: `true`.
// error = Defines the behaviour for collinear input points. When `true`, produces an error, otherwise returns []. Default: `true`.
// eps = Tolerance for collinearity test. Default: EPSILON.
function noncollinear_triple(points,error=true,eps=EPSILON) =
assert( is_path(points), "Invalid input points." )
@ -1757,19 +1783,17 @@ function noncollinear_triple(points,error=true,eps=EPSILON) =
b = furthest_point(pa, points),
pb = points[b],
nrm = norm(pa-pb)
)
nrm <= eps*max(norm(pa),norm(pb))
? assert(!error, "Cannot find three noncollinear points in pointlist.")
[]
: let(
n = (pb-pa)/nrm,
distlist = [for(i=[0:len(points)-1]) _dist2line(points[i]-pa, n)]
)
max(distlist) < eps*nrm
? assert(!error, "Cannot find three noncollinear points in pointlist.")
[]
: [0,b,max_index(distlist)];
)
nrm <= eps*max(norm(pa),norm(pb)) ?
assert(!error, "Cannot find three noncollinear points in pointlist.") [] :
let(
n = (pb-pa)/nrm,
distlist = [for(i=[0:len(points)-1]) _dist2line(points[i]-pa, n)]
)
max(distlist) < eps*nrm ?
assert(!error, "Cannot find three noncollinear points in pointlist.") [] :
[0, b, max_index(distlist)];
// Function: pointlist_bounds()
// Usage:
@ -1783,12 +1807,14 @@ function noncollinear_triple(points,error=true,eps=EPSILON) =
// pts = List of points.
function pointlist_bounds(pts) =
assert(is_path(pts,dim=undef,fast=true) , "Invalid pointlist." )
let(
let(
select = ident(len(pts[0])),
spread = [for(i=[0:len(pts[0])-1])
let( spreadi = pts*select[i] )
[min(spreadi), max(spreadi)] ] )
transpose(spread);
spread = [
for(i=[0:len(pts[0])-1])
let( spreadi = pts*select[i] )
[ min(spreadi), max(spreadi) ]
]
) transpose(spread);
// Function: closest_point()
@ -1934,7 +1960,7 @@ function reindex_polygon(reference, poly, return_error=false) =
[for(i=[0:N-1])
(reference[i]*poly[(i+k)%N]) ] ]*I,
optimal_poly = polygon_shift(fixpoly, max_index(val))
)
)
return_error? [optimal_poly, min(poly*(I*poly)-2*val)] :
optimal_poly;
@ -1967,7 +1993,8 @@ function align_polygon(reference, poly, angles, cp) =
"The `angle` parameter must be a range or a non void list of numbers.")
let( // alignments is a vector of entries of the form: [polygon, error]
alignments = [
for(angle=angles) reindex_polygon(
for(angle=angles)
reindex_polygon(
reference,
zrot(angle,p=poly,cp=cp),
return_error=true
@ -1994,22 +2021,21 @@ function centroid(poly, eps=EPSILON) =
assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
let(
n = len(poly[0])==2 ? 1 :
let(
plane = plane_from_points(poly, fast=true) )
let( plane = plane_from_points(poly, fast=true) )
assert( !is_undef(plane), "The polygon must be planar." )
plane_normal(plane),
v0 = poly[0] ,
val = sum([for(i=[1:len(poly)-2])
let(
v1 = poly[i],
v2 = poly[i+1],
area = cross(v2-v0,v1-v0)*n
)
[ area, (v0+v1+v2)*area ]
] )
)
assert(!approx(val[0],0, eps), "The polygon is self-intersecting or its points are collinear.")
val[1]/val[0]/3;
val = sum([
for(i=[1:len(poly)-2])
let(
v1 = poly[i],
v2 = poly[i+1],
area = cross(v2-v0,v1-v0)*n
) [ area, (v0+v1+v2)*area ]
])
)
assert(!approx(val[0],0, eps), "The polygon is self-intersecting or its points are collinear.")
val[1]/val[0]/3;
@ -2040,38 +2066,39 @@ function point_in_polygon(point, poly, nonzero=true, eps=EPSILON) =
assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
// Does the point lie on any edges? If so return 0.
let(
on_brd = [for(i=[0:1:len(poly)-1])
let( seg = select(poly,i,i+1) )
if( !approx(seg[0],seg[1],eps) )
point_on_segment2d(point, seg, eps=eps)? 1:0 ]
)
sum(on_brd) > 0
? 0
: nonzero
? // Compute winding number and return 1 for interior, -1 for exterior
let(
windchk = [for(i=[0:1:len(poly)-1])
let(seg=select(poly,i,i+1))
if(!approx(seg[0],seg[1],eps=eps))
_point_above_below_segment(point, seg)
]
on_brd = [
for (i = [0:1:len(poly)-1])
let( seg = select(poly,i,i+1) )
if (!approx(seg[0],seg[1],eps) )
point_on_segment2d(point, seg, eps=eps)? 1:0
]
)
sum(on_brd) > 0? 0 :
nonzero
? // Compute winding number and return 1 for interior, -1 for exterior
let(
windchk = [
for(i=[0:1:len(poly)-1])
let( seg=select(poly,i,i+1) )
if (!approx(seg[0],seg[1],eps=eps))
_point_above_below_segment(point, seg)
]
) sum(windchk) != 0 ? 1 : -1
: // or compute the crossings with the ray [point, point+[1,0]]
let(
n = len(poly),
cross = [
for(i=[0:n-1])
let(
p0 = poly[i]-point,
p1 = poly[(i+1)%n]-point
)
sum(windchk) != 0 ? 1 : -1
: // or compute the crossings with the ray [point, point+[1,0]]
let(
n = len(poly),
cross =
[for(i=[0:n-1])
let(
p0 = poly[i]-point,
p1 = poly[(i+1)%n]-point
)
if( ( (p1.y>eps && p0.y<=eps) || (p1.y<=eps && p0.y>eps) )
&& -eps < p0.x - p0.y *(p1.x - p0.x)/(p1.y - p0.y) )
1
]
)
2*(len(cross)%2)-1;
if (
( (p1.y>eps && p0.y<=eps) || (p1.y<=eps && p0.y>eps) )
&& -eps < p0.x - p0.y *(p1.x - p0.x)/(p1.y - p0.y)
) 1
]
) 2*(len(cross)%2)-1;
// Function: polygon_is_clockwise()
@ -2124,7 +2151,7 @@ function ccw_polygon(poly) =
// poly = The list of the path points for the perimeter of the polygon.
function reverse_polygon(poly) =
assert(is_path(poly), "Input should be a polygon")
[poly[0], for(i=[len(poly)-1:-1:1]) poly[i] ];
[ poly[0], for(i=[len(poly)-1:-1:1]) poly[i] ];
// Function: polygon_normal()
@ -2307,7 +2334,7 @@ function split_polygons_at_each_z(polys, zs, _i=0) =
// test = is_convex_polygon(poly);
// Topics: Geometry, Convexity, Test
// Description:
// Returns true if the given 2D or 3D polygon is convex.
// Returns true if the given 2D or 3D polygon is convex.
// The result is meaningless if the polygon is not simple (self-intersecting) or non coplanar.
// If the points are collinear an error is generated.
// Arguments:
@ -2321,14 +2348,16 @@ function split_polygons_at_each_z(polys, zs, _i=0) =
// test = is_convex_polygon(spiral); // Returns: false
function is_convex_polygon(poly,eps=EPSILON) =
assert(is_path(poly), "The input should be a 2D or 3D polygon." )
let( lp = len(poly),
p0 = poly[0] )
let(
lp = len(poly),
p0 = poly[0]
)
assert( lp>=3 , "A polygon must have at least 3 points" )
let( crosses = [for(i=[0:1:lp-1]) cross(poly[(i+1)%lp]-poly[i], poly[(i+2)%lp]-poly[(i+1)%lp]) ] )
len(p0)==2
? assert( !approx(sqrt(max(max(crosses),-min(crosses))),eps), "The points are collinear" )
? assert( !approx(sqrt(max(max(crosses),-min(crosses))),eps), "The points are collinear" )
min(crosses) >=0 || max(crosses)<=0
: let( prod = crosses*sum(crosses),
: let( prod = crosses*sum(crosses),
minc = min(prod),
maxc = max(prod) )
assert( !approx(sqrt(max(maxc,-minc)),eps), "The points are collinear" )
@ -2342,9 +2371,9 @@ function is_convex_polygon(poly,eps=EPSILON) =
// See also:
// convex_collision(), hull()
// Description:
// Returns the smallest distance between a point in convex hull of `points1`
// Returns the smallest distance between a point in convex hull of `points1`
// and a point in the convex hull of `points2`. All the points in the lists
// should have the same dimension, either 2D or 3D.
// should have the same dimension, either 2D or 3D.
// A zero result means the hulls intercept whithin a tolerance `eps`.
// Arguments:
// points1 - first list of 2d or 3d points.
@ -2362,37 +2391,37 @@ function is_convex_polygon(poly,eps=EPSILON) =
// Example(3D):
// sphr1 = sphere(2,$fn=10);
// sphr2 = move([4,0,0], p=sphr1);
// sphr3 = move([4.5,0,0], p=sphr1);
// sphr3 = move([4.5,0,0], p=sphr1);
// vnf_polyhedron(sphr1);
// vnf_polyhedron(sphr2);
// echo(convex_distance(sphr1[0], sphr2[0])); // Returns: 0
// echo(convex_distance(sphr1[0], sphr3[0])); // Returns: 0.5
function convex_distance(points1, points2, eps=EPSILON) =
assert(is_matrix(points1) && is_matrix(points2,undef,len(points1[0])),
assert(is_matrix(points1) && is_matrix(points2,undef,len(points1[0])),
"The input list should be a consistent non empty list of points of same dimension.")
assert(len(points1[0])==2 || len(points1[0])==3 ,
"The input points should be 2d or 3d points.")
let( d = points1[0]-points2[0] )
norm(d)<eps ? 0 :
let( v = _support_diff(points1,points2,-d) )
let( v = _support_diff(points1,points2,-d) )
norm(_GJK_distance(points1, points2, eps, 0, v, [v]));
// Finds the vector difference between the hulls of the two pointsets by the GJK algorithm
// Based on:
// http://www.dtecta.com/papers/jgt98convex.pdf
function _GJK_distance(points1, points2, eps=EPSILON, lbd, d, simplex=[]) =
function _GJK_distance(points1, points2, eps=EPSILON, lbd, d, simplex=[]) =
let( nrd = norm(d) ) // distance upper bound
nrd<eps ? d :
let(
v = _support_diff(points1,points2,-d),
lbd = max(lbd, d*v/nrd), // distance lower bound
close = (nrd-lbd <= eps*nrd)
close = (nrd-lbd <= eps*nrd)
)
// v already in the simplex is a degenerence due to numerical errors
// v already in the simplex is a degenerence due to numerical errors
// and may produce a non-stopping loop
close || [for(nv=norm(v), s=simplex) if(norm(s-v)<=eps*nv) 1]!=[] ? d :
let( newsplx = _closest_simplex(concat(simplex,[v]),eps) )
close || [for(nv=norm(v), s=simplex) if(norm(s-v)<=eps*nv) 1]!=[] ? d :
let( newsplx = _closest_simplex(concat(simplex,[v]),eps) )
_GJK_distance(points1, points2, eps, lbd, newsplx[0], newsplx[1]);
@ -2423,20 +2452,20 @@ function _GJK_distance(points1, points2, eps=EPSILON, lbd, d, simplex=[]) =
// Example(3D):
// sphr1 = sphere(2,$fn=10);
// sphr2 = move([4,0,0], p=sphr1);
// sphr3 = move([4.5,0,0], p=sphr1);
// sphr3 = move([4.5,0,0], p=sphr1);
// vnf_polyhedron(sphr1);
// vnf_polyhedron(sphr2);
// echo(convex_collision(sphr1[0], sphr2[0])); // Returns: true
// echo(convex_collision(sphr1[0], sphr3[0])); // Returns: false
//
function convex_collision(points1, points2, eps=EPSILON) =
assert(is_matrix(points1) && is_matrix(points2,undef,len(points1[0])),
assert(is_matrix(points1) && is_matrix(points2,undef,len(points1[0])),
"The input list should be a consistent non empty list of points of same dimension.")
assert(len(points1[0])==2 || len(points1[0])==3 ,
"The input points should be 2d or 3d points.")
let( d = points1[0]-points2[0] )
norm(d)<eps ? true :
let( v = _support_diff(points1,points2,-d) )
let( v = _support_diff(points1,points2,-d) )
_GJK_collide(points1, points2, v, [v], eps);
@ -2444,8 +2473,8 @@ function convex_collision(points1, points2, eps=EPSILON) =
// http://uu.diva-portal.org/smash/get/diva2/FFULLTEXT01.pdf
// or
// http://www.dtecta.com/papers/jgt98convex.pdf
function _GJK_collide(points1, points2, d, simplex, eps=EPSILON) =
norm(d) < eps ? true : // does collide
function _GJK_collide(points1, points2, d, simplex, eps=EPSILON) =
norm(d) < eps ? true : // does collide
let( v = _support_diff(points1,points2,-d) )
v*d > eps ? false : // no collision
let( newsplx = _closest_simplex(concat(simplex,[v]),eps) )
@ -2457,7 +2486,7 @@ function _GJK_collide(points1, points2, d, simplex, eps=EPSILON) =
// - the smallest sub-simplex of s that contains that point
function _closest_simplex(s,eps=EPSILON) =
assert(len(s)>=2 && len(s)<=4, "Internal error.")
len(s)==2 ? _closest_s1(s,eps) :
len(s)==2 ? _closest_s1(s,eps) :
len(s)==3 ? _closest_s2(s,eps)
: _closest_s3(s,eps);
@ -2466,10 +2495,10 @@ function _closest_simplex(s,eps=EPSILON) =
// Based on: http://uu.diva-portal.org/smash/get/diva2/FFULLTEXT01.pdf
function _closest_s1(s,eps=EPSILON) =
norm(s[1]-s[0])<eps*(norm(s[0])+norm(s[1]))/2 ? [ s[0], [s[0]] ] :
let(
let(
c = s[1]-s[0],
t = -s[0]*c/(c*c)
)
)
t<0 ? [ s[0], [s[0]] ] :
t>1 ? [ s[1], [s[1]] ] :
[ s[0]+t*c, s ];
@ -2499,13 +2528,13 @@ function _closest_s2(s,eps=EPSILON) =
+ (cross(nr,c-a)*a<0 ? 2 : 0 )
+ (cross(nr,b-c)*b<0 ? 4 : 0 )
)
assert( class!=1, "Internal error" )
assert( class!=1, "Internal error" )
class==0 ? [ nr*(nr*a)/(nr*nr), s] : // origin projects (or is) on the tri
// class==1 ? _closest_s1([s[0],s[1]]) :
class==2 ? _closest_s1([s[0],s[2]],eps) :
class==2 ? _closest_s1([s[0],s[2]],eps) :
class==4 ? _closest_s1([s[1],s[2]],eps) :
// class==3 ? a*(a-b)> 0 ? _closest_s1([s[0],s[1]]) : _closest_s1([s[0],s[2]]) :
class==3 ? _closest_s1([s[0],s[2]],eps) :
// class==3 ? a*(a-b)> 0 ? _closest_s1([s[0],s[1]]) : _closest_s1([s[0],s[2]]) :
class==3 ? _closest_s1([s[0],s[2]],eps) :
// class==5 ? b*(b-c)<=0 ? _closest_s1([s[0],s[1]]) : _closest_s1([s[1],s[2]]) :
class==5 ? _closest_s1([s[1],s[2]],eps) :
c*(c-a)>0 ? _closest_s1([s[0],s[2]],eps) : _closest_s1([s[1],s[2]],eps);
@ -2517,13 +2546,13 @@ function _closest_s3(s,eps=EPSILON) =
assert( len(s[0])==3 && len(s)==4, "Internal error." )
let( nr = cross(s[1]-s[0],s[2]-s[0]),
sz = [ norm(s[1]-s[0]), norm(s[1]-s[2]), norm(s[2]-s[0]) ] )
norm(nr)<eps*max(sz)
? let( i = max_index(sz) )
norm(nr)<eps*max(sz)
? let( i = max_index(sz) )
_closest_s2([ s[i], s[(i+1)%3], s[3] ], eps) // degenerate case
// considering that s[3] was the last inserted vertex in s,
// the only possible outcomes will be:
// s or some of the 3 triangles of s containing s[3]
: let(
// considering that s[3] was the last inserted vertex in s,
// the only possible outcomes will be:
// s or some of the 3 triangles of s containing s[3]
: let(
tris = [ [s[0], s[1], s[3]],
[s[1], s[2], s[3]],
[s[2], s[0], s[3]] ],

18
math.scad
View file

@ -791,13 +791,17 @@ function _med3(a,b,c) =
// d = convolve([[1,1],[2,2],[3,1]],[[1,2],[2,1]])); // Returns: [3,9,11,7]
function convolve(p,q) =
p==[] || q==[] ? [] :
assert( (is_vector(p) || is_matrix(p))
&& ( is_vector(q) || (is_matrix(q) && ( !is_vector(p[0]) || (len(p[0])==len(q[0])) ) ) ) ,
"The inputs should be vectors or paths all of the same dimension.")
let( n = len(p),
m = len(q))
[for(i=[0:n+m-2], k1 = max(0,i-n+1), k2 = min(i,m-1) )
sum([for(j=[k1:k2]) p[i-j]*q[j] ])
assert(
(is_vector(p) || is_matrix(p))
&& ( is_vector(q) || (is_matrix(q) && ( !is_vector(p[0]) || (len(p[0])==len(q[0])) ) ) ) ,
"The inputs should be vectors or paths all of the same dimension."
)
let(
n = len(p),
m = len(q)
) [
for (i=[0:n+m-2], k1 = max(0,i-n+1), k2 = min(i,m-1) )
sum([for(j=[k1:k2]) p[i-j]*q[j] ])
];

2
paths.scad
View file

@ -1010,7 +1010,7 @@ module jittered_poly(path, dist=1/512) {
// xcopies(3) circle(3, $fn=32);
// }
module extrude_from_to(pt1, pt2, convexity, twist, scale, slices) {
assert( is_path([pt1,pt2],3), "The points should be 3d points");
assert( is_path([pt1,pt2],3), "The points should be 3d points");
rtp = xyz_to_spherical(pt2-pt1);
translate(pt1) {
rotate([0, rtp[2], rtp[1]]) {

9
scripts/check_for_tabs.sh Executable file
View file

@ -0,0 +1,9 @@
#!/bin/bash
if grep -H -n -P '\t' *.scad ; then
echo "Tabs found in source code." 2>&1
exit 1
fi
exit 0

42
shapes.scad
View file

@ -405,6 +405,8 @@ function cuboid(
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#orient). Default: `UP`
//
// See Also: rounded_prism()
//
// Example: Rectangular Pyramid
// prismoid([40,40], [0,0], h=20);
// Example: Prism
@ -479,8 +481,8 @@ module prismoid(
anchor = get_anchor(anchor, center, BOT, BOT);
vnf = prismoid(
size1=size1, size2=size2, h=h, shift=shift,
rounding=rounding, rounding1=rounding1, rounding2=rounding2,
chamfer=chamfer, chamfer1=chamfer1, chamfer2=chamfer2,
rounding1=rounding1, rounding2=rounding2,
chamfer1=chamfer1, chamfer2=chamfer2,
l=l, center=CENTER
);
attachable(anchor,spin,orient, size=[s1.x,s1.y,h], size2=s2, shift=shift) {
@ -500,12 +502,36 @@ function prismoid(
assert(is_vector(size2,2))
assert(is_num(h) || is_num(l))
assert(is_vector(shift,2))
assert(is_num(rounding) || is_vector(rounding,4), "Bad rounding argument.")
assert(is_undef(rounding1) || is_num(rounding1) || is_vector(rounding1,4), "Bad rounding1 argument.")
assert(is_undef(rounding2) || is_num(rounding2) || is_vector(rounding2,4), "Bad rounding2 argument.")
assert(is_num(chamfer) || is_vector(chamfer,4), "Bad chamfer argument.")
assert(is_undef(chamfer1) || is_num(chamfer1) || is_vector(chamfer1,4), "Bad chamfer1 argument.")
assert(is_undef(chamfer2) || is_num(chamfer2) || is_vector(chamfer2,4), "Bad chamfer2 argument.")
assert(
(is_num(rounding) && rounding>=0) ||
(is_vector(rounding,4) && all_nonnegative(rounding)),
"Bad rounding argument."
)
assert(
is_undef(rounding1) || (is_num(rounding1) && rounding1>=0) ||
(is_vector(rounding1,4) && all_nonnegative(rounding1)),
"Bad rounding1 argument."
)
assert(
is_undef(rounding2) || (is_num(rounding2) && rounding2>=0) ||
(is_vector(rounding2,4) && all_nonnegative(rounding2)),
"Bad rounding2 argument."
)
assert(
(is_num(chamfer) && chamfer>=0) ||
(is_vector(chamfer,4) && all_nonnegative(chamfer)),
"Bad chamfer argument."
)
assert(
is_undef(chamfer1) || (is_num(chamfer1) && chamfer1>=0) ||
(is_vector(chamfer1,4) && all_nonnegative(chamfer1)),
"Bad chamfer1 argument."
)
assert(
is_undef(chamfer2) || (is_num(chamfer2) && chamfer2>=0) ||
(is_vector(chamfer2,4) && all_nonnegative(chamfer2)),
"Bad chamfer2 argument."
)
let(
eps = pow(2,-14),
h = first_defined([h,l,1]),

30
shapes2d.scad
View file

@ -1434,10 +1434,10 @@ function trapezoid(h, w1, w2, angle, shift=0, chamfer=0, rounding=0, anchor=CENT
assert(is_undef(angle) || is_finite(angle))
assert(num_defined([h, w1, w2, angle]) == 3, "Must give exactly 3 of the arguments h, w1, w2, and angle.")
assert(is_finite(shift))
assert(is_finite(chamfer) || is_vector(chamfer,4))
assert(is_finite(rounding) || is_vector(rounding,4))
assert(is_finite(chamfer) || is_vector(chamfer,4))
assert(is_finite(rounding) || is_vector(rounding,4))
let(
simple = chamfer==0 && rounding==0,
simple = chamfer==0 && rounding==0,
h = !is_undef(h)? h : opp_ang_to_adj(abs(w2-w1)/2, abs(angle)),
w1 = !is_undef(w1)? w1 : w2 + 2*(adj_ang_to_opp(h, angle) + shift),
w2 = !is_undef(w2)? w2 : w1 - 2*(adj_ang_to_opp(h, angle) + shift)
@ -1451,23 +1451,23 @@ function trapezoid(h, w1, w2, angle, shift=0, chamfer=0, rounding=0, anchor=CENT
[-w1/2,-h/2],
[w1/2,-h/2],
],
cpath = simple? base_path :
path_chamfer_and_rounding(
base_path, closed=true,
chamfer=chamfer,
rounding=rounding
),
path = reverse(cpath)
) simple?
reorient(anchor,spin, two_d=true, size=[w1,h], size2=w2, shift=shift, p=path) :
reorient(anchor,spin, two_d=true, path=path, p=path);
cpath = simple? base_path :
path_chamfer_and_rounding(
base_path, closed=true,
chamfer=chamfer,
rounding=rounding
),
path = reverse(cpath)
) simple
? reorient(anchor,spin, two_d=true, size=[w1,h], size2=w2, shift=shift, p=path)
: reorient(anchor,spin, two_d=true, path=path, p=path);
module trapezoid(h, w1, w2, angle, shift=0, chamfer=0, rounding=0, anchor=CENTER, spin=0) {
path = trapezoid(h=h, w1=w1, w2=w2, angle=angle, shift=shift, chamfer=chamfer, rounding=rounding);
path = trapezoid(h=h, w1=w1, w2=w2, angle=angle, shift=shift, chamfer=chamfer, rounding=rounding);
union() {
simple = chamfer==0 && rounding==0;
simple = chamfer==0 && rounding==0;
h = !is_undef(h)? h : opp_ang_to_adj(abs(w2-w1)/2, abs(angle));
w1 = !is_undef(w1)? w1 : w2 + 2*(adj_ang_to_opp(h, angle) + shift);
w2 = !is_undef(w2)? w2 : w1 - 2*(adj_ang_to_opp(h, angle) + shift);

10
walls.scad
View file

@ -91,10 +91,10 @@ 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 = 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];
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;
@ -116,7 +116,7 @@ module thinning_wall(h=50, l=100, thick=5, ang=30, braces=false, strut, wall, an
size = [l1, thick, h];
attachable(anchor,spin,orient, size=size, size2=[l2,thick]) {
union() {
zrot(90) {
polyhedron(
points=[
[-x4, -y1, -z1],