mirror of
https://github.com/BelfrySCAD/BOSL2.git
synced 2024-12-29 00:09:41 +00:00
Fix tab indents.
This commit is contained in:
Garth Minette
parent
7a3720a812
commit
48c5139099
6 changed files with 320 additions and 267 deletions
110
arrays.scad
110
arrays.scad
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@ -951,28 +951,34 @@ function shuffle(list,seed) =
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// idx should be an index of the arrays l[i]
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function _group_sort_by_index(l,idx) =
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len(l) == 0 ? [] :
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len(l) == 1 ? [l] :
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let( pivot = l[floor(len(l)/2)][idx],
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equal = [ for(li=l) if( li[idx]==pivot) li ] ,
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lesser = [ for(li=l) if( li[idx]< pivot) li ] ,
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greater = [ for(li=l) if( li[idx]> pivot) li ]
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)
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concat( _group_sort_by_index(lesser,idx),
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[equal],
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_group_sort_by_index(greater,idx) ) ;
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len(l) == 0 ? [] :
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len(l) == 1 ? [l] :
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let(
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pivot = l[floor(len(l)/2)][idx],
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equal = [ for(li=l) if( li[idx]==pivot) li ],
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lesser = [ for(li=l) if( li[idx]< pivot) li ],
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greater = [ for(li=l) if( li[idx]> pivot) li ]
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)
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concat(
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_group_sort_by_index(lesser,idx),
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[equal],
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_group_sort_by_index(greater,idx)
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);
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function _group_sort(l) =
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len(l) == 0 ? [] :
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len(l) == 1 ? [l] :
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let( pivot = l[floor(len(l)/2)],
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equal = [ for(li=l) if( li==pivot) li ] ,
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lesser = [ for(li=l) if( li< pivot) li ] ,
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greater = [ for(li=l) if( li> pivot) li ]
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)
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concat( _group_sort(lesser),
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[equal],
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_group_sort(greater) ) ;
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len(l) == 0 ? [] :
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len(l) == 1 ? [l] :
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let(
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pivot = l[floor(len(l)/2)],
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equal = [ for(li=l) if( li==pivot) li ] ,
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lesser = [ for(li=l) if( li< pivot) li ] ,
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greater = [ for(li=l) if( li> pivot) li ]
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)
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concat(
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_group_sort(lesser),
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[equal],
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_group_sort(greater)
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);
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// Sort a vector of scalar values with the native comparison operator
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@ -1171,11 +1177,11 @@ function group_sort(list, idx) =
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assert(is_list(list), "Input should be a list." )
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assert(is_undef(idx) || (is_finite(idx) && idx>=0) , "Invalid index." )
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len(list)<=1 ? [list] :
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is_vector(list)? _group_sort(list) :
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let( idx = is_undef(idx) ? 0 : idx )
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assert( [for(entry=list) if(!is_list(entry) || len(entry)<idx || !is_num(entry[idx]) ) 1]==[],
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"Some entry of the list is a list shorter than `idx` or the indexed entry of it is not a number." )
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_group_sort_by_index(list,idx);
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is_vector(list)? _group_sort(list) :
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let( idx = is_undef(idx) ? 0 : idx )
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assert( [for(entry=list) if(!is_list(entry) || len(entry)<idx || !is_num(entry[idx]) ) 1]==[],
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"Some entry of the list is a list shorter than `idx` or the indexed entry of it is not a number.")
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_group_sort_by_index(list,idx);
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// Function: unique()
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@ -1197,23 +1203,27 @@ function unique(list) =
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is_string(list)? str_join(unique([for (x = list) x])) :
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len(list)<=1? list :
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is_homogeneous(list,1) && ! is_list(list[0])
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? _unique_sort(list)
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? _unique_sort(list)
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: let( sorted = sort(list))
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[ for (i=[0:1:len(sorted)-1])
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if (i==0 || (sorted[i] != sorted[i-1]))
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sorted[i]
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];
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[
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for (i=[0:1:len(sorted)-1])
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if (i==0 || (sorted[i] != sorted[i-1]))
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sorted[i]
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];
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function _unique_sort(l) =
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len(l) <= 1 ? l :
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let( pivot = l[floor(len(l)/2)],
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equal = [ for(li=l) if( li==pivot) li ] ,
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lesser = [ for(li=l) if( li<pivot ) li ] ,
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greater = [ for(li=l) if( li>pivot) li ]
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)
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concat( _unique_sort(lesser),
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equal[0],
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_unique_sort(greater) ) ;
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len(l) <= 1 ? l :
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let(
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pivot = l[floor(len(l)/2)],
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equal = [ for(li=l) if( li==pivot) li ] ,
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lesser = [ for(li=l) if( li<pivot ) li ] ,
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greater = [ for(li=l) if( li>pivot) li ]
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)
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concat(
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_unique_sort(lesser),
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equal[0],
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_unique_sort(greater)
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);
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// Function: unique_count()
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@ -1232,13 +1242,23 @@ function unique_count(list) =
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assert(is_list(list) || is_string(list), "Invalid input." )
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list == [] ? [[],[]] :
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is_homogeneous(list,1) && ! is_list(list[0])
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? let( sorted = _group_sort(list) )
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[ [for(s=sorted) s[0] ], [for(s=sorted) len(s) ] ]
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: let( list=sort(list) )
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let( ind = [0, for(i=[1:1:len(list)-1]) if (list[i]!=list[i-1]) i] )
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[ select(list,ind), deltas( concat(ind,[len(list)]) ) ];
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? let( sorted = _group_sort(list) ) [
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[for(s=sorted) s[0] ],
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[for(s=sorted) len(s) ]
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]
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: let(
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list=sort(list),
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ind = [
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0,
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for(i=[1:1:len(list)-1])
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if (list[i]!=list[i-1]) i
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]
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) [
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select(list,ind),
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deltas( concat(ind,[len(list)]) )
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];
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// Section: List Iteration Helpers
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// Function: idx()
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@ -502,7 +502,7 @@ module generic_bottle_neck(
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}
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function generic_bottle_neck(
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neck_d,
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neck_d,
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id,
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thread_od,
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height,
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425
geometry.scad
425
geometry.scad
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@ -20,7 +20,7 @@
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// eps = Tolerance in geometric comparisons. Default: `EPSILON` (1e-9)
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function point_on_segment2d(point, edge, eps=EPSILON) =
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assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
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point_segment_distance(point, edge)<eps;
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point_segment_distance(point, edge)<eps;
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//Internal - distance from point `d` to the line passing through the origin with unit direction n
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@ -31,8 +31,8 @@ function _dist2line(d,n) = norm(d-(d * n) * n);
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function _point_above_below_segment(point, edge) =
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let( edge = edge - [point, point] )
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edge[0].y <= 0
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? (edge[1].y > 0 && cross(edge[0], edge[1]-edge[0]) > 0) ? 1 : 0
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: (edge[1].y <= 0 && cross(edge[0], edge[1]-edge[0]) < 0) ? -1 : 0 ;
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? (edge[1].y > 0 && cross(edge[0], edge[1]-edge[0]) > 0) ? 1 : 0
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: (edge[1].y <= 0 && cross(edge[0], edge[1]-edge[0]) < 0) ? -1 : 0;
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//Internal
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function _valid_line(line,dim,eps=EPSILON) =
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@ -74,8 +74,8 @@ function collinear(a, b, c, eps=EPSILON) =
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"Input should be 3 points or a list of points with same dimension.")
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assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
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let( points = is_def(c) ? [a,b,c]: a )
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len(points)<3 ? true
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: noncollinear_triple(points,error=false,eps=eps)==[];
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len(points)<3 ? true :
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noncollinear_triple(points,error=false,eps=eps) == [];
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// Function: point_line_distance()
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@ -124,8 +124,7 @@ function point_segment_distance(pt, seg) =
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// dist = segment_distance([[-14,3], [-15,9]], [[-10,0], [10,0]]); // Returns: 5
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// dist2 = segment_distance([[-5,5], [5,-5]], [[-10,3], [10,-3]]); // Returns: 0
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function segment_distance(seg1, seg2) =
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assert( is_matrix(concat(seg1,seg2),4),
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"Inputs should be two valid segments." )
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assert( is_matrix(concat(seg1,seg2),4), "Inputs should be two valid segments." )
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convex_distance(seg1,seg2);
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@ -147,9 +146,9 @@ function segment_distance(seg1, seg2) =
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// color("blue") move_copies([p1,p2]) circle(d=2, $fn=12);
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function line_normal(p1,p2) =
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is_undef(p2)
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? assert( len(p1)==2 && !is_undef(p1[1]) , "Invalid input." )
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? assert( len(p1)==2 && !is_undef(p1[1]) , "Invalid input." )
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line_normal(p1[0],p1[1])
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: assert( _valid_line([p1,p2],dim=2), "Invalid line." )
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: assert( _valid_line([p1,p2],dim=2), "Invalid line." )
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unit([p1.y-p2.y,p2.x-p1.x]);
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@ -164,7 +163,8 @@ function line_normal(p1,p2) =
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function _general_line_intersection(s1,s2,eps=EPSILON) =
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let(
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denominator = det2([s1[0],s2[0]]-[s1[1],s2[1]])
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) approx(denominator,0,eps=eps)? [undef,undef,undef] : let(
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) approx(denominator,0,eps=eps)? [undef,undef,undef] :
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let(
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t = det2([s1[0],s2[0]]-s2) / denominator,
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u = det2([s1[0],s1[0]]-[s2[0],s1[1]]) / denominator
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) [s1[0]+t*(s1[1]-s1[0]), t, u];
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@ -201,11 +201,10 @@ function line_intersection(l1,l2,eps=EPSILON) =
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function line_ray_intersection(line,ray,eps=EPSILON) =
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assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
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assert( _valid_line(line,dim=2,eps=eps) && _valid_line(ray,dim=2,eps=eps), "Invalid line or ray." )
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let(
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isect = _general_line_intersection(line,ray,eps=eps)
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)
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let( isect = _general_line_intersection(line,ray,eps=eps) )
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is_undef(isect[0]) ? undef :
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(isect[2]<0-eps) ? undef : isect[0];
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(isect[2]<0-eps) ? undef :
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isect[0];
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// Function: line_segment_intersection()
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@ -221,9 +220,7 @@ function line_ray_intersection(line,ray,eps=EPSILON) =
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function line_segment_intersection(line,segment,eps=EPSILON) =
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assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
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assert( _valid_line(line, dim=2,eps=eps) &&_valid_line(segment,dim=2,eps=eps), "Invalid line or segment." )
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let(
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isect = _general_line_intersection(line,segment,eps=eps)
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)
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let( isect = _general_line_intersection(line,segment,eps=eps) )
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is_undef(isect[0]) ? undef :
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isect[2]<0-eps || isect[2]>1+eps ? undef :
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isect[0];
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@ -242,11 +239,10 @@ function line_segment_intersection(line,segment,eps=EPSILON) =
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function ray_intersection(r1,r2,eps=EPSILON) =
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assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
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assert( _valid_line(r1,dim=2,eps=eps) && _valid_line(r2,dim=2,eps=eps), "Invalid ray(s)." )
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let(
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isect = _general_line_intersection(r1,r2,eps=eps)
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)
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let( isect = _general_line_intersection(r1,r2,eps=eps) )
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is_undef(isect[0]) ? undef :
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isect[1]<0-eps || isect[2]<0-eps ? undef : isect[0];
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isect[1]<0-eps || isect[2]<0-eps ? undef :
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isect[0];
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// Function: ray_segment_intersection()
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@ -262,9 +258,7 @@ function ray_intersection(r1,r2,eps=EPSILON) =
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function ray_segment_intersection(ray,segment,eps=EPSILON) =
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assert( _valid_line(ray,dim=2,eps=eps) && _valid_line(segment,dim=2,eps=eps), "Invalid ray or segment." )
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assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
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let(
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isect = _general_line_intersection(ray,segment,eps=eps)
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)
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let( isect = _general_line_intersection(ray,segment,eps=eps) )
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is_undef(isect[0]) ? undef :
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isect[1]<0-eps || isect[2]<0-eps || isect[2]>1+eps ? undef :
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isect[0];
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@ -283,9 +277,7 @@ function ray_segment_intersection(ray,segment,eps=EPSILON) =
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function segment_intersection(s1,s2,eps=EPSILON) =
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assert( _valid_line(s1,dim=2,eps=eps) && _valid_line(s2,dim=2,eps=eps), "Invalid segment(s)." )
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assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
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let(
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isect = _general_line_intersection(s1,s2,eps=eps)
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)
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let( isect = _general_line_intersection(s1,s2,eps=eps) )
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is_undef(isect[0]) ? undef :
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isect[1]<0-eps || isect[1]>1+eps || isect[2]<0-eps || isect[2]>1+eps ? undef :
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isect[0];
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@ -346,7 +338,7 @@ function line_closest_point(line,pt) =
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assert(_valid_line(line), "Invalid line." )
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assert( is_vector(pt,len(line[0])), "Invalid point or incompatible dimensions." )
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let( n = unit( line[0]- line[1]) )
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line[1]+((pt- line[1]) * n) * n;
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line[1] + ((pt- line[1]) * n) * n;
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// Function: ray_closest_point()
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@ -485,7 +477,9 @@ function line_from_points(points, fast=false, eps=EPSILON) =
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assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
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let( pb = furthest_point(points[0],points) )
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norm(points[pb]-points[0])<eps*max(norm(points[pb]),norm(points[0])) ? undef :
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fast || collinear(points) ? [points[pb], points[0]] : undef;
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fast || collinear(points)
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? [points[pb], points[0]]
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: undef;
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@ -556,7 +550,8 @@ function law_of_sines(a, A, b, B) =
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// a/sin(A) = b/sin(B) = c/sin(C)
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assert(num_defined([b,B]) == 1, "Must give exactly one of b= or B=.")
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let( r = a/sin(A) )
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is_undef(b) ? r*sin(B) : asin(constrain(b/r, -1, 1));
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is_undef(b) ? r*sin(B) :
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asin(constrain(b/r, -1, 1));
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// Function: tri_calc()
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@ -626,11 +621,11 @@ function tri_calc(ang,ang2,adj,opp,hyp) =
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hyp
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: (adj!=undef? (adj/cos(ang))
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: (opp/sin(ang)))
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)
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[adj, opp, hyp, ang, ang2];
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) [adj, opp, hyp, ang, ang2];
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// Function: hyp_opp_to_adj()
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// Alias: opp_hyp_to_adj()
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// Usage:
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// adj = hyp_opp_to_adj(hyp,opp);
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// Description:
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@ -646,8 +641,11 @@ function hyp_opp_to_adj(hyp,opp) =
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"Triangle side lengths should be a positive numbers." )
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sqrt(hyp*hyp-opp*opp);
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function opp_hyp_to_adj(opp,hyp) = hyp_opp_to_adj(hyp,opp);
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// Function: hyp_ang_to_adj()
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// Alias: ang_hyp_to_adj()
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// Usage:
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// adj = hyp_ang_to_adj(hyp,ang);
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// Description:
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@ -663,8 +661,11 @@ function hyp_ang_to_adj(hyp,ang) =
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assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
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hyp*cos(ang);
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function ang_hyp_to_adj(ang,hyp) = hyp_ang_to_adj(hyp, ang);
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// Function: opp_ang_to_adj()
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// Alias: ang_opp_to_adj()
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// Usage:
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// adj = opp_ang_to_adj(opp,ang);
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// Description:
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@ -680,8 +681,11 @@ function opp_ang_to_adj(opp,ang) =
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assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
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opp/tan(ang);
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function ang_opp_to_adj(ang,opp) = opp_ang_to_adj(opp,ang);
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// Function: hyp_adj_to_opp()
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// Alias: adj_hyp_to_opp()
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// Usage:
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// opp = hyp_adj_to_opp(hyp,adj);
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// Description:
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@ -696,8 +700,11 @@ function hyp_adj_to_opp(hyp,adj) =
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"Triangle side lengths should be a positive numbers." )
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sqrt(hyp*hyp-adj*adj);
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||||
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);
|
||||
// Description:
|
||||
|
|
@ -712,8 +719,11 @@ 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);
|
||||
// Description:
|
||||
|
|
@ -728,8 +738,11 @@ 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);
|
||||
// Description:
|
||||
|
|
@ -744,8 +757,11 @@ 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);
|
||||
// Description:
|
||||
|
|
@ -760,8 +776,11 @@ 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);
|
||||
// Description:
|
||||
|
|
@ -776,8 +795,11 @@ 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:
|
||||
|
|
@ -792,8 +814,11 @@ 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);
|
||||
// Description:
|
||||
|
|
@ -808,8 +833,11 @@ 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);
|
||||
// Description:
|
||||
|
|
@ -824,6 +852,8 @@ 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:
|
||||
|
|
@ -866,8 +896,7 @@ 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;
|
||||
|
||||
|
||||
|
|
@ -893,8 +922,7 @@ 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()
|
||||
|
|
@ -917,7 +945,7 @@ 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)),
|
||||
|
|
@ -928,19 +956,19 @@ 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]);
|
||||
|
||||
|
||||
|
|
@ -976,15 +1004,16 @@ 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 ;
|
||||
|
||||
|
|
@ -1016,8 +1045,8 @@ 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:
|
||||
// plane_normal(plane);
|
||||
|
|
@ -1121,10 +1150,10 @@ 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()
|
||||
|
|
@ -1152,8 +1181,7 @@ 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()
|
||||
|
|
@ -1176,8 +1204,7 @@ 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 :
|
||||
|
|
@ -1207,41 +1234,37 @@ 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()
|
||||
|
|
@ -1260,19 +1283,20 @@ 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()
|
||||
|
|
@ -1287,18 +1311,18 @@ 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);
|
||||
|
||||
|
||||
|
|
@ -1429,6 +1453,7 @@ 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.");
|
||||
|
|
@ -1445,6 +1470,7 @@ module circle_2tangents(pt1, pt2, pt3, r, d, h, center=false) {
|
|||
}
|
||||
}
|
||||
|
||||
|
||||
// Function&Module: circle_3points()
|
||||
// Usage: As Function
|
||||
// circ = circle_3points(pt1, pt2, pt3);
|
||||
|
|
@ -1572,7 +1598,7 @@ 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.
|
||||
|
|
@ -1689,7 +1715,7 @@ 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." )
|
||||
|
|
@ -1699,19 +1725,17 @@ 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:
|
||||
|
|
@ -1724,12 +1748,14 @@ 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()
|
||||
|
|
@ -1782,12 +1808,12 @@ function polygon_area(poly, signed=false) =
|
|||
: let( plane = plane_from_polygon(poly) )
|
||||
plane==[]? undef :
|
||||
let(
|
||||
n = plane_normal(plane),
|
||||
total =
|
||||
sum([ for(i=[1:1:len(poly)-2])
|
||||
cross(poly[i]-poly[0], poly[i+1]-poly[0])
|
||||
]) * n/2
|
||||
)
|
||||
n = plane_normal(plane),
|
||||
total = sum([
|
||||
for(i=[1:1:len(poly)-2])
|
||||
cross(poly[i]-poly[0], poly[i+1]-poly[0])
|
||||
]) * n/2
|
||||
)
|
||||
signed ? total : abs(total);
|
||||
|
||||
|
||||
|
|
@ -1869,7 +1895,7 @@ 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;
|
||||
|
||||
|
|
@ -1901,7 +1927,8 @@ 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
|
||||
|
|
@ -1927,22 +1954,21 @@ 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;
|
||||
|
||||
|
||||
|
||||
|
|
@ -1972,38 +1998,39 @@ 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()
|
||||
|
|
@ -2052,7 +2079,7 @@ 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()
|
||||
|
|
@ -2230,7 +2257,7 @@ function split_polygons_at_each_z(polys, zs, _i=0) =
|
|||
// Usage:
|
||||
// is_convex_polygon(poly);
|
||||
// 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:
|
||||
|
|
@ -2244,14 +2271,16 @@ function split_polygons_at_each_z(polys, zs, _i=0) =
|
|||
// 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" )
|
||||
|
|
@ -2261,12 +2290,12 @@ function is_convex_polygon(poly,eps=EPSILON) =
|
|||
// Function: convex_distance()
|
||||
// Usage:
|
||||
// convex_distance(pts1, pts2,<eps=>);
|
||||
// See also:
|
||||
// See also:
|
||||
// convex_collision
|
||||
// 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.
|
||||
|
|
@ -2284,44 +2313,44 @@ 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]);
|
||||
|
||||
|
||||
// Function: convex_collision()
|
||||
// Usage:
|
||||
// convex_collision(pts1, pts2,<eps=>);
|
||||
// See also:
|
||||
// See also:
|
||||
// convex_distance
|
||||
// Description:
|
||||
// Returns `true` if the convex hull of `points1` intercepts the convex hull of `points2`
|
||||
|
|
@ -2344,20 +2373,20 @@ 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);
|
||||
|
||||
|
||||
|
|
@ -2365,8 +2394,8 @@ 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) )
|
||||
|
|
@ -2378,7 +2407,7 @@ 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);
|
||||
|
||||
|
|
@ -2387,10 +2416,10 @@ 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 ];
|
||||
|
|
@ -2420,13 +2449,13 @@ 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);
|
||||
|
|
@ -2438,13 +2467,13 @@ 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
18
math.scad
|
|
@ -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] ])
|
||||
];
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -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]]) {
|
||||
|
|
|
|||
|
|
@ -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);
|
||||
|
|
|
|||
Loading…
Reference in a new issue