mirror of
https://github.com/BelfrySCAD/BOSL2.git
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Various fixes to get example generation working.
This commit is contained in:
Garth Minette
parent
ea88aa8ac2
commit
35e6fdb1aa
3 changed files with 158 additions and 146 deletions
288
geometry.scad
288
geometry.scad
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@ -26,12 +26,12 @@ function point_on_segment2d(point, edge, eps=EPSILON) =
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assert( _valid_line(edge,2,eps=eps), "Invalid segment." )
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let( dp = point-edge[0],
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de = edge[1]-edge[0],
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ne = norm(de) )
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( dp*de >= -eps*ne )
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ne = norm(de) )
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( dp*de >= -eps*ne )
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&& ( (dp-de)*de <= eps*ne ) // point projects on the segment
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&& _dist2line(point-edge[0],unit(de))<eps; // point is on the line
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&& _dist2line(point-edge[0],unit(de))<eps; // point is on the line
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//Internal - distance from point `d` to the line passing through the origin with unit direction n
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//_dist2line works for any dimension
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function _dist2line(d,n) = norm(d-(d * n) * n);
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@ -39,15 +39,15 @@ function _dist2line(d,n) = norm(d-(d * n) * n);
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// Internal non-exposed function.
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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[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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//Internal
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function _valid_line(line,dim,eps=EPSILON) =
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is_matrix(line,2,dim)
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&& ! approx(norm(line[1]-line[0]), 0, eps);
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function _valid_line(line,dim,eps=EPSILON) =
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is_matrix(line,2,dim)
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&& ! approx(norm(line[1]-line[0]), 0, eps);
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//Internal
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function _valid_plane(p, eps=EPSILON) = is_vector(p,4) && ! approx(norm(p),0,eps);
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@ -79,13 +79,13 @@ function point_left_of_line2d(point, line) =
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// eps = Acceptable variance. Default: `EPSILON` (1e-9)
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function collinear(a, b, c, eps=EPSILON) =
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assert( is_path([a,b,c],dim=undef)
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|| ( is_undef(b) && is_undef(c) && is_path(a,dim=undef) ),
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|| ( is_undef(b) && is_undef(c) && is_path(a,dim=undef) ),
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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 positive number." )
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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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// Function: distance_from_line()
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// Usage:
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@ -98,11 +98,11 @@ function collinear(a, b, c, eps=EPSILON) =
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// Example:
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// distance_from_line([[-10,0], [10,0]], [3,8]); // Returns: 8
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function distance_from_line(line, pt) =
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assert( _valid_line(line) && is_vector(pt,len(line[0])),
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assert( _valid_line(line) && is_vector(pt,len(line[0])),
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"Invalid line, invalid point or incompatible dimensions." )
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_dist2line(pt-line[0],unit(line[1]-line[0]));
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// Function: line_normal()
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// Usage:
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// line_normal([P1,P2])
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@ -121,9 +121,9 @@ function distance_from_line(line, pt) =
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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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line_normal(p1[0],p1[1])
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: assert( _valid_line([p1,p2],dim=2), "Invalid line." )
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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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unit([p1.y-p2.y,p2.x-p1.x]);
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@ -157,7 +157,7 @@ function _general_line_intersection(s1,s2,eps=EPSILON) =
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function line_intersection(l1,l2,eps=EPSILON) =
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assert( is_finite(eps) && eps>=0, "The tolerance should be a positive number." )
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assert( _valid_line(l1,dim=2,eps=eps) &&_valid_line(l2,dim=2,eps=eps), "Invalid line(s)." )
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let(isect = _general_line_intersection(l1,l2,eps=eps))
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let(isect = _general_line_intersection(l1,l2,eps=eps))
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isect[0];
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@ -176,7 +176,7 @@ function line_ray_intersection(line,ray,eps=EPSILON) =
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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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)
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is_undef(isect[0]) ? undef :
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(isect[2]<0-eps) ? undef : isect[0];
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@ -217,7 +217,7 @@ function ray_intersection(r1,r2,eps=EPSILON) =
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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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)
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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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@ -237,7 +237,7 @@ function ray_segment_intersection(ray,segment,eps=EPSILON) =
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assert( is_finite(eps) && eps>=0, "The tolerance should be a positive number." )
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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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)
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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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@ -258,7 +258,7 @@ function segment_intersection(s1,s2,eps=EPSILON) =
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assert( is_finite(eps) && eps>=0, "The tolerance should be a positive number." )
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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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)
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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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@ -449,7 +449,7 @@ function segment_closest_point(seg,pt) =
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projection>=seglen ? seg[1] :
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seg[0] + projection*segvec;
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// Function: line_from_points()
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// Usage:
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// line_from_points(points, [fast], [eps]);
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@ -586,25 +586,25 @@ function tri_calc(ang,ang2,adj,opp,hyp) =
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assert(num_defined([ang,ang2,adj,opp,hyp])==2, "Exactly two arguments must be given.")
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let(
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ang = ang!=undef
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? assert(ang>0&&ang<90, "The input angles should be acute angles." ) ang
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: ang2!=undef ? (90-ang2)
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: adj==undef ? asin(constrain(opp/hyp,-1,1))
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: opp==undef ? acos(constrain(adj/hyp,-1,1))
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? assert(ang>0&&ang<90, "The input angles should be acute angles." ) ang
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: ang2!=undef ? (90-ang2)
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: adj==undef ? asin(constrain(opp/hyp,-1,1))
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: opp==undef ? acos(constrain(adj/hyp,-1,1))
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: atan2(opp,adj),
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ang2 = ang2!=undef
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? assert(ang2>0&&ang2<90, "The input angles should be acute angles." ) ang2
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? assert(ang2>0&&ang2<90, "The input angles should be acute angles." ) ang2
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: (90-ang),
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adj = adj!=undef
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? assert(adj>0, "Triangle side lengths should be positive." ) adj
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? assert(adj>0, "Triangle side lengths should be positive." ) adj
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: (opp!=undef? (opp/tan(ang)) : (hyp*cos(ang))),
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opp = opp!=undef
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? assert(opp>0, "Triangle side lengths should be positive." ) opp
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? assert(opp>0, "Triangle side lengths should be positive." ) opp
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: (adj!=undef? (adj*tan(ang)) : (hyp*sin(ang))),
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hyp = hyp!=undef
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? assert(hyp>0, "Triangle side lengths should be positive." )
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? assert(hyp>0, "Triangle side lengths should be positive." )
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assert(adj<hyp && opp<hyp, "Hyphotenuse length should be greater than the other sides." )
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hyp
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: (adj!=undef? (adj/cos(ang))
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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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@ -622,7 +622,7 @@ function tri_calc(ang,ang2,adj,opp,hyp) =
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// Example:
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// hyp = hyp_opp_to_adj(5,3); // Returns: 4
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function hyp_opp_to_adj(hyp,opp) =
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assert(is_finite(hyp+opp) && hyp>=0 && opp>=0,
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assert(is_finite(hyp+opp) && hyp>=0 && opp>=0,
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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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@ -672,7 +672,7 @@ function opp_ang_to_adj(opp,ang) =
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// Example:
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// opp = hyp_adj_to_opp(5,4); // Returns: 3
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function hyp_adj_to_opp(hyp,adj) =
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assert(is_finite(hyp) && hyp>=0 && is_finite(adj) && adj>=0,
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assert(is_finite(hyp) && hyp>=0 && is_finite(adj) && adj>=0,
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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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@ -720,7 +720,7 @@ function adj_ang_to_opp(adj,ang) =
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// Example:
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// hyp = adj_opp_to_hyp(3,4); // Returns: 5
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function adj_opp_to_hyp(adj,opp) =
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assert(is_finite(opp) && opp>=0 && is_finite(adj) && adj>=0,
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assert(is_finite(opp) && opp>=0 && is_finite(adj) && adj>=0,
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"Triangle side lengths should be a positive numbers." )
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norm([opp,adj]);
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@ -768,7 +768,7 @@ function opp_ang_to_hyp(opp,ang) =
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// Example:
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// ang = hyp_adj_to_ang(8,4); // Returns: 60 degrees
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function hyp_adj_to_ang(hyp,adj) =
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assert(is_finite(hyp) && hyp>0 && is_finite(adj) && adj>=0,
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assert(is_finite(hyp) && hyp>0 && is_finite(adj) && adj>=0,
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"Triangle side lengths should be positive numbers." )
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acos(adj/hyp);
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@ -784,7 +784,7 @@ function hyp_adj_to_ang(hyp,adj) =
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// Example:
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// ang = hyp_opp_to_ang(8,4); // Returns: 30 degrees
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function hyp_opp_to_ang(hyp,opp) =
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assert(is_finite(hyp+opp) && hyp>0 && opp>=0,
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assert(is_finite(hyp+opp) && hyp>0 && opp>=0,
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"Triangle side lengths should be positive numbers." )
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asin(opp/hyp);
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@ -800,7 +800,7 @@ function hyp_opp_to_ang(hyp,opp) =
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// Example:
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// ang = adj_opp_to_ang(sqrt(3)/2,0.5); // Returns: 30 degrees
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function adj_opp_to_ang(adj,opp) =
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assert(is_finite(adj+opp) && adj>0 && opp>=0,
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assert(is_finite(adj+opp) && adj>0 && opp>=0,
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"Triangle side lengths should be positive numbers." )
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atan2(opp,adj);
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@ -814,10 +814,10 @@ function adj_opp_to_ang(adj,opp) =
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// Examples:
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// triangle_area([0,0], [5,10], [10,0]); // Returns -50
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// triangle_area([10,0], [5,10], [0,0]); // Returns 50
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function triangle_area(a,b,c) =
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assert( is_path([a,b,c]), "Invalid points or incompatible dimensions." )
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len(a)==3
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? 0.5*norm(cross(c-a,c-b))
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function triangle_area(a,b,c) =
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assert( is_path([a,b,c]), "Invalid points or incompatible dimensions." )
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len(a)==3
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? 0.5*norm(cross(c-a,c-b))
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: 0.5*cross(c-a,c-b);
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@ -830,7 +830,7 @@ function triangle_area(a,b,c) =
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// plane3pt(p1, p2, p3);
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// Description:
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// Generates the normalized cartesian equation of a plane from three 3d points.
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// Returns [A,B,C,D] where Ax + By + Cz = D is the equation of a plane.
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// Returns [A,B,C,D] where Ax + By + Cz = D is the equation of a plane.
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// Returns [], if the points are collinear.
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// Arguments:
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// p1 = The first point on the plane.
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@ -838,11 +838,11 @@ function triangle_area(a,b,c) =
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// p3 = The third point on the plane.
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function plane3pt(p1, p2, p3) =
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assert( is_path([p1,p2,p3],dim=3) && len(p1)==3,
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"Invalid points or incompatible dimensions." )
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"Invalid points or incompatible dimensions." )
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let(
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crx = cross(p3-p1, p2-p1),
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nrm = norm(crx)
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)
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)
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approx(nrm,0) ? [] :
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concat(crx, crx*p1)/nrm;
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@ -869,7 +869,7 @@ function plane3pt_indexed(points, i1, i2, i3) =
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p1 = points[i1],
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p2 = points[i2],
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p3 = points[i3]
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)
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)
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plane3pt(p1,p2,p3);
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@ -881,7 +881,7 @@ function plane3pt_indexed(points, i1, i2, i3) =
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// Example:
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// plane_from_normal([0,0,1], [2,2,2]); // Returns the xy plane passing through the point (2,2,2)
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function plane_from_normal(normal, pt=[0,0,0]) =
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assert( is_matrix([normal,pt],2,3) && !approx(norm(normal),0),
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assert( is_matrix([normal,pt],2,3) && !approx(norm(normal),0),
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"Inputs `normal` and `pt` should 3d vectors/points and `normal` cannot be zero." )
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concat(normal, normal*pt) / norm(normal);
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@ -946,7 +946,7 @@ function plane_from_polygon(poly, fast=false, eps=EPSILON) =
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poly = deduplicate(poly),
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n = polygon_normal(poly),
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plane = [n.x, n.y, n.z, n*poly[0]]
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)
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)
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fast? plane: coplanar(poly,eps=eps)? plane: [];
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@ -955,7 +955,7 @@ function plane_from_polygon(poly, fast=false, eps=EPSILON) =
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// plane_normal(plane);
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// Description:
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// Returns the unit length normal vector for the given plane.
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function plane_normal(plane) =
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function plane_normal(plane) =
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assert( _valid_plane(plane), "Invalid input plane." )
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unit([plane.x, plane.y, plane.z]);
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@ -964,10 +964,10 @@ function plane_normal(plane) =
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// Usage:
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// d = plane_offset(plane);
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// Description:
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// Returns coeficient D of the normalized plane equation `Ax+By+Cz=D`, or the scalar offset of the plane from the origin.
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// Returns coeficient D of the normalized plane equation `Ax+By+Cz=D`, or the scalar offset of the plane from the origin.
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// This value may be negative.
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// The absolute value of this coefficient is the distance of the plane from the origin.
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function plane_offset(plane) =
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function plane_offset(plane) =
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assert( _valid_plane(plane), "Invalid input plane." )
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plane[3]/norm([plane.x, plane.y, plane.z]);
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@ -994,7 +994,7 @@ function plane_transform(plane) =
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plane = normalize_plane(plane),
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n = point3d(plane),
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cp = n * plane[3]
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)
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)
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rot(from=n, to=UP) * move(-cp);
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@ -1002,7 +1002,7 @@ function plane_transform(plane) =
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// Usage:
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// projection_on_plane(points);
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// Description:
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// Given a plane definition `[A,B,C,D]`, where `Ax+By+Cz=D`, and a list of 2d or 3d points, return the 3D orthogonal
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// Given a plane definition `[A,B,C,D]`, where `Ax+By+Cz=D`, and a list of 2d or 3d points, return the 3D orthogonal
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// projection of the points on the plane.
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// Arguments:
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// plane = The `[A,B,C,D]` plane definition where `Ax+By+Cz=D` is the formula of the plane.
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@ -1014,13 +1014,13 @@ function plane_transform(plane) =
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function projection_on_plane(plane, points) =
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assert( _valid_plane(plane), "Invalid plane." )
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assert( is_path(points), "Invalid list of points or dimension." )
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let(
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let(
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p = len(points[0])==2
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? [for(pi=points) point3d(pi) ]
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: points,
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: points,
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plane = normalize_plane(plane),
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n = point3d(plane)
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)
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)
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[for(pi=p) pi - (pi*n - plane[3])*n];
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@ -1069,7 +1069,7 @@ function closest_point_on_plane(plane, point) =
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let( plane = normalize_plane(plane),
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n = point3d(plane),
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d = n*point - plane[3] // distance from plane
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)
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)
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point - n*d;
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@ -1078,7 +1078,7 @@ function closest_point_on_plane(plane, point) =
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// Returns undef if line is parallel to, but not on the given plane.
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||||
function _general_plane_line_intersection(plane, line, eps=EPSILON) =
|
||||
let(
|
||||
a = plane*[each line[0],-1], // evaluation of the plane expression at line[0]
|
||||
a = plane*[each line[0],-1], // evaluation of the plane expression at line[0]
|
||||
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 ?
|
||||
|
|
@ -1086,10 +1086,10 @@ function _general_plane_line_intersection(plane, line, eps=EPSILON) =
|
|||
? [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()
|
||||
// Usage:
|
||||
// Usage:
|
||||
// nplane = normalize_plane(plane);
|
||||
// Description:
|
||||
// Returns a new representation [A,B,C,D] of `plane` where norm([A,B,C]) is equal to one.
|
||||
|
|
@ -1099,12 +1099,12 @@ function normalize_plane(plane) =
|
|||
|
||||
|
||||
// Function: plane_line_angle()
|
||||
// Usage:
|
||||
// Usage:
|
||||
// angle = plane_line_angle(plane,line);
|
||||
// Description:
|
||||
// Compute the angle between a plane [A, B, C, D] and a line, specified as a pair of points [p1,p2].
|
||||
// The resulting angle is signed, with the sign positive if the vector p2-p1 lies on
|
||||
// the same side of the plane as the plane's normal vector.
|
||||
// The resulting angle is signed, with the sign positive if the vector p2-p1 lies on
|
||||
// the same side of the plane as the plane's normal vector.
|
||||
function plane_line_angle(plane, line) =
|
||||
assert( _valid_plane(plane), "Invalid plane." )
|
||||
assert( _valid_line(line), "Invalid line." )
|
||||
|
|
@ -1113,7 +1113,7 @@ 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);
|
||||
|
||||
|
||||
|
|
@ -1189,19 +1189,19 @@ function polygon_line_intersection(poly, line, bounded=false, eps=EPSILON) =
|
|||
inside = [for (part = parts)
|
||||
if (point_in_polygon(mean(part), poly2d)>0) part
|
||||
]
|
||||
)
|
||||
)
|
||||
!inside? undef :
|
||||
let(
|
||||
isegs = [for (seg = inside) lift_plane(seg, plane) ]
|
||||
)
|
||||
)
|
||||
isegs
|
||||
)
|
||||
)
|
||||
: bounded[0] && res[1]<0? undef :
|
||||
bounded[1] && res[1]>1? undef :
|
||||
let(
|
||||
proj = clockwise_polygon(project_plane(poly, p1, p2, p3)),
|
||||
pt = project_plane(res[0], p1, p2, p3)
|
||||
)
|
||||
)
|
||||
point_in_polygon(pt, proj) < 0 ? undef : res[0];
|
||||
|
||||
|
||||
|
|
@ -1212,7 +1212,7 @@ function polygon_line_intersection(poly, line, bounded=false, eps=EPSILON) =
|
|||
// Compute the point which is the intersection of the three planes, or the line intersection of two planes.
|
||||
// If you give three planes the intersection is returned as a point. If you give two planes the intersection
|
||||
// is returned as a list of two points on the line of intersection. If any two input planes are parallel
|
||||
// or coincident then returns undef.
|
||||
// or coincident then returns undef.
|
||||
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." )
|
||||
|
|
@ -1220,15 +1220,15 @@ function plane_intersection(plane1,plane2,plane3) =
|
|||
? 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];
|
||||
|
||||
|
||||
|
|
@ -1244,13 +1244,13 @@ 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 number." )
|
||||
len(points)<=2 ? false
|
||||
: let( ip = noncollinear_triple(points,error=false,eps=eps) )
|
||||
ip == [] ? false :
|
||||
let( plane = plane3pt(points[ip[0]],points[ip[1]],points[ip[2]]),
|
||||
: let( ip = noncollinear_triple(points,error=false,eps=eps) )
|
||||
ip == [] ? false :
|
||||
let( plane = plane3pt(points[ip[0]],points[ip[1]],points[ip[2]]),
|
||||
normal = point3d(plane) )
|
||||
max( points*normal ) - plane[3]< eps*norm(normal);
|
||||
|
||||
|
||||
|
||||
// Function: points_on_plane()
|
||||
// Usage:
|
||||
// points_on_plane(points, plane, <eps>);
|
||||
|
|
@ -1355,11 +1355,11 @@ function in_front_of_plane(plane, point) =
|
|||
function circle_2tangents(pt1, pt2, pt3, r, d, tangents=false) =
|
||||
let(r = get_radius(r=r, d=d, dflt=undef))
|
||||
assert(r!=undef, "Must specify either r or d.")
|
||||
assert( ( is_path(pt1) && len(pt1)==3 && is_undef(pt2) && is_undef(pt3))
|
||||
assert( ( is_path(pt1) && len(pt1)==3 && is_undef(pt2) && is_undef(pt3))
|
||||
|| (is_matrix([pt1,pt2,pt3]) && (len(pt1)==2 || len(pt1)==3) ),
|
||||
"Invalid input points." )
|
||||
is_undef(pt2)
|
||||
? circle_2tangents(pt1[0], pt1[1], pt1[2], r=r, tangents=tangents)
|
||||
is_undef(pt2)
|
||||
? circle_2tangents(pt1[0], pt1[1], pt1[2], r=r, tangents=tangents)
|
||||
: collinear(pt1, pt2, pt3)? undef :
|
||||
let(
|
||||
v1 = unit(pt1 - pt2),
|
||||
|
|
@ -1369,7 +1369,7 @@ function circle_2tangents(pt1, pt2, pt3, r, d, tangents=false) =
|
|||
a = vector_angle(v1, v2),
|
||||
hyp = r / sin(a/2),
|
||||
cp = pt2 + hyp * vmid
|
||||
)
|
||||
)
|
||||
!tangents ? [cp, n] :
|
||||
let(
|
||||
x = hyp * cos(a/2),
|
||||
|
|
@ -1377,7 +1377,7 @@ function circle_2tangents(pt1, pt2, pt3, r, d, tangents=false) =
|
|||
tp2 = pt2 + x * v2,
|
||||
dang1 = vector_angle(tp1-cp,pt2-cp),
|
||||
dang2 = vector_angle(tp2-cp,pt2-cp)
|
||||
)
|
||||
)
|
||||
[cp, n, tp1, tp2, dang1, dang2];
|
||||
|
||||
module circle_2tangents(pt1, pt2, pt3, r, d, h, center=false) {
|
||||
|
|
@ -1438,8 +1438,8 @@ module circle_2tangents(pt1, pt2, pt3, r, d, h, center=false) {
|
|||
// move_copies(pts) color("cyan") sphere(d=3, $fn=12);
|
||||
function circle_3points(pt1, pt2, pt3) =
|
||||
(is_undef(pt2) && is_undef(pt3) && is_list(pt1))
|
||||
? circle_3points(pt1[0], pt1[1], pt1[2])
|
||||
: assert( is_vector(pt1) && is_vector(pt2) && is_vector(pt3)
|
||||
? circle_3points(pt1[0], pt1[1], pt1[2])
|
||||
: assert( is_vector(pt1) && is_vector(pt2) && is_vector(pt3)
|
||||
&& max(len(pt1),len(pt2),len(pt3))<=3 && min(len(pt1),len(pt2),len(pt3))>=2,
|
||||
"Invalid point(s)." )
|
||||
collinear(pt1,pt2,pt3)? [undef,undef,undef] :
|
||||
|
|
@ -1447,17 +1447,17 @@ function circle_3points(pt1, pt2, pt3) =
|
|||
v = [ point3d(pt1), point3d(pt2), point3d(pt3) ], // triangle vertices
|
||||
ed = [for(i=[0:2]) v[(i+1)%3]-v[i] ], // triangle edge vectors
|
||||
pm = [for(i=[0:2]) v[(i+1)%3]+v[i] ]/2, // edge mean points
|
||||
es = sortidx( [for(di=ed) norm(di) ] ),
|
||||
es = sortidx( [for(di=ed) norm(di) ] ),
|
||||
e1 = ed[es[1]], // take the 2 longest edges
|
||||
e2 = ed[es[2]],
|
||||
n0 = vector_axis(e1,e2), // normal standardization
|
||||
n0 = vector_axis(e1,e2), // normal standardization
|
||||
n = n0.z<0? -n0 : n0,
|
||||
sc = plane_intersection(
|
||||
sc = plane_intersection(
|
||||
[ each e1, e1*pm[es[1]] ], // planes orthogonal to 2 edges
|
||||
[ each e2, e2*pm[es[2]] ],
|
||||
[ each n, n*v[0] ]
|
||||
), // triangle plane
|
||||
cp = len(pt1)+len(pt2)+len(pt3)>6 ? sc : [sc.x, sc.y],
|
||||
cp = len(pt1)+len(pt2)+len(pt3)>6 ? sc : [sc.x, sc.y],
|
||||
r = norm(sc-v[0])
|
||||
) [ cp, r, n ];
|
||||
|
||||
|
|
@ -1522,8 +1522,8 @@ function circle_point_tangents(r, d, cp, pt) =
|
|||
// circle 1. If the circles intersect then the interior tangents don't exist and the function
|
||||
// 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.
|
||||
// Example(2D): Four tangents, first in green, second in black, third in blue, last in red.
|
||||
// passes through the point of tangency of the two circles: this degenerate line is NOT returned.
|
||||
// Example(2D): Four tangents, first in green, second in black, third in blue, last in red.
|
||||
// $fn=32;
|
||||
// c1 = [3,4]; r1 = 2;
|
||||
// c2 = [7,10]; r2 = 3;
|
||||
|
|
@ -1541,7 +1541,7 @@ function circle_point_tangents(r, d, cp, pt) =
|
|||
// move(c2) stroke(circle(r=r2), width=.1, closed=true);
|
||||
// colors = ["green","black","blue","red"];
|
||||
// for(i=[0:len(pts)-1]) color(colors[i]) stroke(pts[i],width=.1);
|
||||
// Example(2D): Circles are tangent. Only exterior tangents are returned. The degenerate internal tangent is not returned.
|
||||
// Example(2D): Circles are tangent. Only exterior tangents are returned. The degenerate internal tangent is not returned.
|
||||
// $fn=32;
|
||||
// c1 = [4,4]; r1 = 4;
|
||||
// c2 = [4,10]; r2 = 2;
|
||||
|
|
@ -1550,7 +1550,7 @@ function circle_point_tangents(r, d, cp, pt) =
|
|||
// move(c2) stroke(circle(r=r2), width=.1, closed=true);
|
||||
// colors = ["green","black","blue","red"];
|
||||
// for(i=[0:1:len(pts)-1]) color(colors[i]) stroke(pts[i],width=.1);
|
||||
// Example(2D): One circle is inside the other: no tangents exist. If the interior circle is tangent the single degenerate tangent will not be returned.
|
||||
// Example(2D): One circle is inside the other: no tangents exist. If the interior circle is tangent the single degenerate tangent will not be returned.
|
||||
// $fn=32;
|
||||
// c1 = [4,4]; r1 = 4;
|
||||
// c2 = [5,5]; r2 = 2;
|
||||
|
|
@ -1608,12 +1608,12 @@ function noncollinear_triple(points,error=true,eps=EPSILON) =
|
|||
[]
|
||||
: let(
|
||||
n = (pb-pa)/nrm,
|
||||
distlist = [for(i=[0:len(points)-1]) _dist2line(points[i]-pa, n)]
|
||||
distlist = [for(i=[0:len(points)-1]) _dist2line(points[i]-pa, n)]
|
||||
)
|
||||
max(distlist)<eps
|
||||
? assert(!error, "Cannot find three noncollinear points in pointlist.")
|
||||
[]
|
||||
: [0,b,max_index(distlist)];
|
||||
: [0,b,max_index(distlist)];
|
||||
|
||||
|
||||
// Function: pointlist_bounds()
|
||||
|
|
@ -1626,7 +1626,7 @@ function noncollinear_triple(points,error=true,eps=EPSILON) =
|
|||
// Arguments:
|
||||
// pts = List of points.
|
||||
function pointlist_bounds(pts) =
|
||||
assert(is_matrix(pts) && len(pts)>0 && len(pts[0])>0 , "Invalid pointlist." )
|
||||
assert(is_matrix(pts) && len(pts)>0 && len(pts[0])>0 , "Invalid pointlist." )
|
||||
let(ptsT = transpose(pts))
|
||||
[
|
||||
[for(row=ptsT) min(row)],
|
||||
|
|
@ -1669,7 +1669,7 @@ function furthest_point(pt, points) =
|
|||
// Usage:
|
||||
// area = polygon_area(poly);
|
||||
// Description:
|
||||
// Given a 2D or 3D planar polygon, returns the area of that polygon.
|
||||
// Given a 2D or 3D planar polygon, returns the area of that polygon.
|
||||
// If the polygon is self-crossing, the results are undefined. For non-planar points the result is undef.
|
||||
// When `signed` is true, a signed area is returned; a positive area indicates a counterclockwise polygon.
|
||||
// Arguments:
|
||||
|
|
@ -1678,14 +1678,23 @@ function furthest_point(pt, points) =
|
|||
function polygon_area(poly, signed=false) =
|
||||
assert(is_path(poly), "Invalid polygon." )
|
||||
len(poly)<3 ? 0 :
|
||||
let( cpoly = close_path(simplify_path(poly)) )
|
||||
len(poly[0])==2
|
||||
? sum([for(i=[1:1:len(poly)-2]) cross(poly[i]-poly[0],poly[i+1]-poly[0]) ])/2
|
||||
: let( plane = plane_from_points(poly) )
|
||||
plane==undef? undef :
|
||||
let( n = unit(plane_normal(plane)),
|
||||
total = sum([for(i=[1:1:len(poly)-1]) cross(poly[i]-poly[0],poly[i+1]-poly[0])*n ])/2
|
||||
)
|
||||
signed ? total : abs(total);
|
||||
? sum([for(i=[1:1:len(poly)-2]) cross(poly[i]-poly[0],poly[i+1]-poly[0]) ])/2
|
||||
: let( plane = plane_from_points(poly) )
|
||||
plane==undef? undef :
|
||||
let(
|
||||
n = unit(plane_normal(plane)),
|
||||
total = sum([
|
||||
for(i=[1:1:len(cpoly)-2])
|
||||
let(
|
||||
v1 = cpoly[i] - cpoly[0],
|
||||
v2 = cpoly[i+1] - cpoly[0]
|
||||
)
|
||||
cross(v1,v2) * n
|
||||
])/2
|
||||
)
|
||||
signed ? total : abs(total);
|
||||
|
||||
|
||||
// Function: is_convex_polygon()
|
||||
|
|
@ -1693,7 +1702,7 @@ function polygon_area(poly, signed=false) =
|
|||
// is_convex_polygon(poly);
|
||||
// Description:
|
||||
// Returns true if the given 2D polygon is convex. The result is meaningless if the polygon is not simple (self-intersecting).
|
||||
// If the points are collinear the result is true.
|
||||
// If the points are collinear the result is true.
|
||||
// Example:
|
||||
// is_convex_polygon(circle(d=50)); // Returns: true
|
||||
// Example:
|
||||
|
|
@ -1702,14 +1711,14 @@ function polygon_area(poly, signed=false) =
|
|||
function is_convex_polygon(poly) =
|
||||
assert(is_path(poly,dim=2), "The input should be a 2D polygon." )
|
||||
let( l = len(poly) )
|
||||
len([for( i = l-1,
|
||||
c = cross(poly[(i+1)%l]-poly[i], poly[(i+2)%l]-poly[(i+1)%l]),
|
||||
len([for( i = l-1,
|
||||
c = cross(poly[(i+1)%l]-poly[i], poly[(i+2)%l]-poly[(i+1)%l]),
|
||||
s = sign(c);
|
||||
i>=0 && sign(c)==s;
|
||||
i = i-1,
|
||||
c = i<0? 0: cross(poly[(i+1)%l]-poly[i],poly[(i+2)%l]-poly[(i+1)%l]),
|
||||
i = i-1,
|
||||
c = i<0? 0: cross(poly[(i+1)%l]-poly[i],poly[(i+2)%l]-poly[(i+1)%l]),
|
||||
s = s==0 ? sign(c) : s
|
||||
) i
|
||||
) i
|
||||
])== l;
|
||||
|
||||
|
||||
|
|
@ -1748,7 +1757,7 @@ function polygon_shift_to_closest_point(poly, pt) =
|
|||
// newpoly = reindex_polygon(reference, poly);
|
||||
// Description:
|
||||
// Rotates and possibly reverses the point order of a 2d or 3d polygon path to optimize its pairwise point
|
||||
// association with a reference polygon. The two polygons must have the same number of vertices and be the same dimension.
|
||||
// association with a reference polygon. The two polygons must have the same number of vertices and be the same dimension.
|
||||
// The optimization is done by computing the distance, norm(reference[i]-poly[i]), between
|
||||
// corresponding pairs of vertices of the two polygons and choosing the polygon point order that
|
||||
// makes the total sum over all pairs as small as possible. Returns the reindexed polygon. Note
|
||||
|
|
@ -1772,7 +1781,7 @@ function polygon_shift_to_closest_point(poly, pt) =
|
|||
// move_copies(concat(circ,pent)) circle(r=.1,$fn=32);
|
||||
// color("red") move_copies([pent[0],circ[0]]) circle(r=.1,$fn=32);
|
||||
// color("blue") translate(reindexed[0])circle(r=.1,$fn=32);
|
||||
function reindex_polygon(reference, poly, return_error=false) =
|
||||
function reindex_polygon(reference, poly, return_error=false) =
|
||||
assert(is_path(reference) && is_path(poly,dim=len(reference[0])),
|
||||
"Invalid polygon(s) or incompatible dimensions. " )
|
||||
assert(len(reference)==len(poly), "The polygons must have the same length.")
|
||||
|
|
@ -1784,14 +1793,14 @@ function reindex_polygon(reference, poly, return_error=false) =
|
|||
? clockwise_polygon(poly)
|
||||
: ccw_polygon(poly),
|
||||
I = [for(i=[0:N-1]) 1],
|
||||
val = [ for(k=[0:N-1])
|
||||
[for(i=[0:N-1])
|
||||
val = [ for(k=[0:N-1])
|
||||
[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;
|
||||
|
||||
|
||||
|
||||
// Function: align_polygon()
|
||||
// Usage:
|
||||
|
|
@ -1802,11 +1811,11 @@ function reindex_polygon(reference, poly, return_error=false) =
|
|||
// so if run time is a problem, use a smaller sampling of angles. Returns the rotated and reindexed
|
||||
// polygon.
|
||||
// Arguments:
|
||||
// reference = reference polygon
|
||||
// reference = reference polygon
|
||||
// poly = polygon to rotate into alignment with the reference
|
||||
// angles = list or range of angles to test
|
||||
// cp = centerpoint for rotations
|
||||
// Example(2D): The original hexagon in yellow is not well aligned with the pentagon. Turning it so the faces line up gives an optimal alignment, shown in red.
|
||||
// Example(2D): The original hexagon in yellow is not well aligned with the pentagon. Turning it so the faces line up gives an optimal alignment, shown in red.
|
||||
// $fn=32;
|
||||
// pentagon = subdivide_path(pentagon(side=2),60);
|
||||
// hexagon = subdivide_path(hexagon(side=2.7),60);
|
||||
|
|
@ -1860,7 +1869,7 @@ function centroid(poly) =
|
|||
] )
|
||||
)
|
||||
val[1]/val[0]/3;
|
||||
|
||||
|
||||
|
||||
// Function: point_in_polygon()
|
||||
// Usage:
|
||||
|
|
@ -1888,30 +1897,30 @@ function point_in_polygon(point, poly, eps=EPSILON, nonzero=true) =
|
|||
assert( is_finite(eps) && eps>=0, "Invalid tolerance." )
|
||||
// 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=EPSILON) )
|
||||
on_brd = [for(i=[0:1:len(poly)-1])
|
||||
let( seg = select(poly,i,i+1) )
|
||||
if( !approx(seg[0],seg[1],eps=EPSILON) )
|
||||
point_on_segment2d(point, seg, eps=eps)? 1:0 ]
|
||||
)
|
||||
sum(on_brd) > 0
|
||||
? 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))
|
||||
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(
|
||||
let(
|
||||
n = len(poly),
|
||||
cross =
|
||||
cross =
|
||||
[for(i=[0:n-1])
|
||||
let(
|
||||
p0 = poly[i]-point,
|
||||
let(
|
||||
p0 = poly[i]-point,
|
||||
p1 = poly[(i+1)%n]-point
|
||||
)
|
||||
if( ( (p1.y>eps && p0.y<=0) || (p1.y<=0 && p0.y>eps) )
|
||||
|
|
@ -1970,7 +1979,7 @@ function reverse_polygon(poly) =
|
|||
// n = polygon_normal(poly);
|
||||
// Description:
|
||||
// Given a 3D planar polygon, returns a unit-length normal vector for the
|
||||
// clockwise orientation of the polygon.
|
||||
// clockwise orientation of the polygon.
|
||||
function polygon_normal(poly) =
|
||||
assert(is_path(poly,dim=3), "Invalid 3D polygon." )
|
||||
let(
|
||||
|
|
@ -2082,9 +2091,8 @@ function _split_polygon_at_z(poly, z) =
|
|||
// polys = A list of 3D polygons to split.
|
||||
// xs = A list of scalar X values to split at.
|
||||
function split_polygons_at_each_x(polys, xs, _i=0) =
|
||||
assert( is_consistent(polys) && is_path(poly[0],dim=3) ,
|
||||
"The input list should contains only 3D polygons." )
|
||||
assert( is_finite(xs), "The split value list should contain only numbers." )
|
||||
assert( [for (poly=polys) if (!is_path(poly,3)) 1] == [], "Expects list of 3D paths.")
|
||||
assert( is_vector(xs), "The split value list should contain only numbers." )
|
||||
_i>=len(xs)? polys :
|
||||
split_polygons_at_each_x(
|
||||
[
|
||||
|
|
@ -2092,7 +2100,7 @@ function split_polygons_at_each_x(polys, xs, _i=0) =
|
|||
each _split_polygon_at_x(poly, xs[_i])
|
||||
], xs, _i=_i+1
|
||||
);
|
||||
|
||||
|
||||
|
||||
// Function: split_polygons_at_each_y()
|
||||
// Usage:
|
||||
|
|
@ -2103,9 +2111,8 @@ function split_polygons_at_each_x(polys, xs, _i=0) =
|
|||
// polys = A list of 3D polygons to split.
|
||||
// ys = A list of scalar Y values to split at.
|
||||
function split_polygons_at_each_y(polys, ys, _i=0) =
|
||||
// assert( is_consistent(polys) && is_path(polys[0],dim=3) , // not all polygons should have the same length!!!
|
||||
// "The input list should contains only 3D polygons." )
|
||||
assert( is_finite(ys) || is_vector(ys), "The split value list should contain only numbers." ) //***
|
||||
assert( [for (poly=polys) if (!is_path(poly,3)) 1] == [], "Expects list of 3D paths.")
|
||||
assert( is_vector(ys), "The split value list should contain only numbers." )
|
||||
_i>=len(ys)? polys :
|
||||
split_polygons_at_each_y(
|
||||
[
|
||||
|
|
@ -2124,9 +2131,8 @@ function split_polygons_at_each_y(polys, ys, _i=0) =
|
|||
// polys = A list of 3D polygons to split.
|
||||
// zs = A list of scalar Z values to split at.
|
||||
function split_polygons_at_each_z(polys, zs, _i=0) =
|
||||
assert( is_consistent(polys) && is_path(poly[0],dim=3) ,
|
||||
"The input list should contains only 3D polygons." )
|
||||
assert( is_finite(zs), "The split value list should contain only numbers." )
|
||||
assert( [for (poly=polys) if (!is_path(poly,3)) 1] == [], "Expects list of 3D paths.")
|
||||
assert( is_vector(zs), "The split value list should contain only numbers." )
|
||||
_i>=len(zs)? polys :
|
||||
split_polygons_at_each_z(
|
||||
[
|
||||
|
|
|
|||
|
|
@ -8,7 +8,7 @@
|
|||
//////////////////////////////////////////////////////////////////////
|
||||
|
||||
|
||||
BOSL_VERSION = [2,0,479];
|
||||
BOSL_VERSION = [2,0,480];
|
||||
|
||||
|
||||
// Section: BOSL Library Version Functions
|
||||
|
|
|
|||
14
vnf.scad
14
vnf.scad
|
|
@ -672,8 +672,11 @@ function vnf_validate(vnf, show_warns=true, check_isects=false) =
|
|||
],
|
||||
nonplanars = unique([
|
||||
for (face = faces) let(
|
||||
faceverts = [for (k=face) varr[k]]
|
||||
) if (!coplanar(faceverts)) [
|
||||
faceverts = [for (k=face) varr[k]],
|
||||
area = polygon_area(faceverts)
|
||||
)
|
||||
if (is_num(area) && abs(area) > EPSILON)
|
||||
if (!coplanar(faceverts)) [
|
||||
"ERROR",
|
||||
"NONPLANAR",
|
||||
"Face vertices are not coplanar",
|
||||
|
|
@ -712,9 +715,12 @@ function vnf_validate(vnf, show_warns=true, check_isects=false) =
|
|||
if (v!=edge[0] && v!=edge[1]) let(
|
||||
a = varr[edge[0]],
|
||||
b = varr[v],
|
||||
c = varr[edge[1]],
|
||||
c = varr[edge[1]]
|
||||
)
|
||||
if (a != b && b != c && a != c) let(
|
||||
pt = segment_closest_point([a,c],b)
|
||||
) if (pt == b) [
|
||||
)
|
||||
if (pt == b) [
|
||||
"ERROR",
|
||||
"T_JUNCTION",
|
||||
"Vertex is mid-edge on another Face",
|
||||
|
|
|
|||
Loading…
Reference in a new issue