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https://github.com/BelfrySCAD/BOSL2.git
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Update geometry.scad
Removed all double definitions
This commit is contained in:
RonaldoCMP
GitHub
parent
26ff57491e
commit
29672105ed
1 changed files with 1 additions and 160 deletions
161
geometry.scad
161
geometry.scad
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@ -20,16 +20,6 @@
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// point = The point to test.
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// edge = Array of two points forming the line segment to test against.
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// eps = Acceptable variance. Default: `EPSILON` (1e-9)
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function point_on_segment2d(point, edge, eps=EPSILON) =
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assert( is_vector(point,2), "Invalid point." )
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assert( is_finite(eps) && eps>=0, "The tolerance should be a positive number." )
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assert( _valid_line(edge,eps=eps), "Invalid segment." )
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approx(point,edge[0],eps=eps)
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|| approx(point,edge[1],eps=eps) // The point is an endpoint
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|| sign(edge[0].x-point.x)==sign(point.x-edge[1].x) // point is in between the
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|| ( sign(edge[0].y-point.y)==sign(point.y-edge[1].y) // edge endpoints
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&& approx(point_left_of_line2d(point, edge),0,eps=eps) ); // and on the line defined by edge
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function point_on_segment2d(point, edge, eps=EPSILON) =
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assert( is_vector(point,2), "Invalid point." )
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assert( is_finite(eps) && eps>=0, "The tolerance should be a positive number." )
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@ -98,10 +88,6 @@ function collinear(a, b, c, eps=EPSILON) =
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: noncollinear_triple(points,error=false,eps=eps)==[];
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//*** valid for any dimension
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// Function: distance_from_line()
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// Usage:
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// distance_from_line(line, pt);
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@ -330,17 +316,6 @@ function segment_intersection(s1,s2,eps=EPSILON) =
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// stroke(line, endcaps="arrow2");
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// color("blue") translate(pt) sphere(r=1,$fn=12);
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// color("red") translate(p2) sphere(r=1,$fn=12);
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function line_closest_point(line,pt) =
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assert(is_path(line)&&len(line)==2)
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assert(same_shape(pt,line[0]))
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assert(!approx(line[0],line[1]))
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let(
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seglen = norm(line[1]-line[0]),
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segvec = (line[1]-line[0])/seglen,
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projection = (pt-line[0]) * segvec
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)
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line[0] + projection*segvec;
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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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@ -1042,23 +1017,6 @@ function closest_point_on_plane(plane, point) =
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// Returns [POINT, U] if line intersects plane at one point.
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// Returns [LINE, undef] if the line is on the plane.
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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) =
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let(
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p0 = line[0],
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p1 = line[1],
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n = plane_normal(plane),
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u = p1 - p0,
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d = n * u
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) abs(d)<eps? (
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points_on_plane(p0,plane,eps)? [line,undef] : // Line on plane
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undef // Line parallel to plane
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) : let(
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v0 = closest_point_on_plane(plane, [0,0,0]),
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w = p0 - v0,
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s1 = (-n * w) / d,
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pt = s1 * u + p0
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) [pt, s1];
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function _general_plane_line_intersection(plane, line, eps=EPSILON) =
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let( a = plane*[each line[0],-1],
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b = plane*[each(line[1]-line[0]),-1] )
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@ -1345,40 +1303,6 @@ function find_circle_2tangents(pt1, pt2, pt3, r, d, tangents=false) =
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// translate(circ[0]) color("green") stroke(circle(r=circ[1]),closed=true,$fn=72);
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// translate(circ[0]) color("red") circle(d=3, $fn=12);
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// move_copies(pts) color("blue") circle(d=3, $fn=12);
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function find_circle_3points(pt1, pt2, pt3) =
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(is_undef(pt2) && is_undef(pt3) && is_list(pt1))
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? find_circle_3points(pt1[0], pt1[1], pt1[2])
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: assert( is_vector(pt1) && is_vector(pt2) && is_vector(pt3)
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&& max(len(pt1),len(pt2),len(pt3))<=3 && min(len(pt1),len(pt2),len(pt3))>=2,
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"Invalid point(s)." )
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collinear(pt1,pt2,pt3)? [undef,undef,undef] :
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let(
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v1 = pt1-pt2,
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v2 = pt3-pt2,
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n = vector_axis(v1,v2),
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n2 = n.z<0? -n : n
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) len(pt1)+len(pt2)+len(pt3)>6? (
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let(
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a = project_plane(pt1, pt1, pt2, pt3),
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b = project_plane(pt2, pt1, pt2, pt3),
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c = project_plane(pt3, pt1, pt2, pt3),
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res = find_circle_3points(a, b, c)
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) res[0]==undef? [undef,undef,undef] : let(
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cp = lift_plane(res[0], pt1, pt2, pt3),
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r = norm(pt2-cp)
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) [cp, r, n2]
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) : let(
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mp1 = pt2 + v1/2,
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mp2 = pt2 + v2/2,
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mpv1 = rot(90, v=n, p=v1),
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mpv2 = rot(90, v=n, p=v2),
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l1 = [mp1, mp1+mpv1],
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l2 = [mp2, mp2+mpv2],
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isect = line_intersection(l1,l2)
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) is_undef(isect)? [undef,undef,undef] : let(
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r = norm(pt2-isect)
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) [isect, r, n2];
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function find_circle_3points(pt1, pt2, pt3) =
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(is_undef(pt2) && is_undef(pt3) && is_list(pt1))
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? find_circle_3points(pt1[0], pt1[1], pt1[2])
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@ -1403,9 +1327,6 @@ function find_circle_3points(pt1, pt2, pt3) =
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r = norm(sc-v[0])
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)
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[ cp, r, n ];
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// Function: circle_point_tangents()
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@ -1607,19 +1528,6 @@ function furthest_point(pt, points) =
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// Arguments:
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// poly = polygon to compute the area of.
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// signed = if true, a signed area is returned (default: false)
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function polygon_area(poly) =
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assert(is_path(poly), "Invalid polygon." )
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len(poly)<3? 0 :
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len(poly[0])==2? 0.5*sum([for(i=[0:1:len(poly)-1]) det2(select(poly,i,i+1))]) :
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let(
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plane = plane_from_points(poly)
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) plane==undef? undef :
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let(
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n = unit(plane_normal(plane)),
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total = sum([for (i=[0:1:len(poly)-1]) cross(poly[i], select(poly,i+1))]),
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res = abs(total * n) / 2
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) res;
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function polygon_area(poly, signed=false) =
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assert(is_path(poly), "Invalid polygon." )
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len(poly)<3 ? 0 :
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@ -1644,15 +1552,6 @@ function polygon_area(poly, signed=false) =
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// Example:
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// spiral = [for (i=[0:36]) let(a=-i*10) (10+i)*[cos(a),sin(a)]];
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// is_convex_polygon(spiral); // Returns: false
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function is_convex_polygon(poly) =
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assert(is_path(poly,dim=2), "The input should be a 2D polygon." )
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let(
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l = len(poly),
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c = [for (i=idx(poly)) cross(poly[(i+1)%l]-poly[i],poly[(i+2)%l]-poly[(i+1)%l])]
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)
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len([for (x=c) if(x>0) 1])==0 ||
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len([for (x=c) if(x<0) 1])==0;
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function is_convex_polygon(poly) =
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assert(is_path(poly,dim=2), "The input should be a 2D polygon." )
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let( l = len(poly) )
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@ -1726,33 +1625,6 @@ function polygon_shift_to_closest_point(path, pt) =
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// move_copies(concat(circ,pent)) circle(r=.1,$fn=32);
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// color("red") move_copies([pent[0],circ[0]]) circle(r=.1,$fn=32);
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// color("blue") translate(reindexed[0])circle(r=.1,$fn=32);
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function reindex_polygon(reference, poly, return_error=false) =
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assert(is_path(reference) && is_path(poly,dim=len(reference[0])),
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"Invalid polygon(s) or incompatible dimensions. " )
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assert(len(reference)==len(poly), "The polygons must have the same length.")
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let(
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dim = len(reference[0]),
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N = len(reference),
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fixpoly = dim != 2? poly :
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polygon_is_clockwise(reference)? clockwise_polygon(poly) :
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ccw_polygon(poly),
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dist = [
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// Matrix of all pairwise distances
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for (p1=reference) [
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for (p2=fixpoly) norm(p1-p2)
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]
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],
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// Compute the sum of all distance pairs for a each shift
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sums = [
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for(shift=[0:1:N-1]) sum([
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for(i=[0:1:N-1]) dist[i][(i+shift)%N]
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])
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],
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optimal_poly = polygon_shift(fixpoly,min_index(sums))
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)
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return_error? [optimal_poly, min(sums)] :
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optimal_poly;
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function reindex_polygon(reference, poly, return_error=false) =
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assert(is_path(reference) && is_path(poly,dim=len(reference[0])),
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"Invalid polygon(s) or incompatible dimensions. " )
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@ -1774,7 +1646,6 @@ function reindex_polygon(reference, poly, return_error=false) =
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optimal_poly;
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// Function: align_polygon()
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// Usage:
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// newpoly = align_polygon(reference, poly, angles, [cp]);
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@ -1819,26 +1690,6 @@ function align_polygon(reference, poly, angles, cp) =
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// Given a simple 2D polygon, returns the 2D coordinates of the polygon's centroid.
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// Given a simple 3D planar polygon, returns the 3D coordinates of the polygon's centroid.
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// If the polygon is self-intersecting, the results are undefined.
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function centroid(poly) =
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assert( is_path(poly), "The input must be a 2D or 3D polygon." )
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len(poly[0])==2
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? sum([
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for(i=[0:len(poly)-1])
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let(segment=select(poly,i,i+1))
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det2(segment)*sum(segment)
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]) / 6 / polygon_area(poly)
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: let( plane = plane_from_points(poly, fast=true) )
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assert( !is_undef(plane), "The polygon must be planar." )
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let(
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n = plane_normal(plane),
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p1 = vector_angle(n,UP)>15? vector_axis(n,UP) : vector_axis(n,RIGHT),
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p2 = vector_axis(n,p1),
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cp = mean(poly),
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proj = project_plane(poly,cp,cp+p1,cp+p2),
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cxy = centroid(proj)
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)
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lift_plane(cxy,cp,cp+p1,cp+p2);
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function centroid(poly) =
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assert( is_path(poly,dim=[2,3]), "The input must be a 2D or 3D polygon." )
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len(poly[0])==2
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@ -1915,21 +1766,11 @@ function point_in_polygon(point, path, eps=EPSILON) =
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// Results for complex (self-intersecting) polygon are indeterminate.
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// Arguments:
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// path = The list of 2D path points for the perimeter of the polygon.
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function polygon_is_clockwise(path) =
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assert(is_path(path,dim=2), "Input should be a 2d polygon")
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let(
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minx = min(subindex(path,0)),
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lowind = search(minx, path, 0, 0),
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lowpts = select(path, lowind),
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miny = min(subindex(lowpts, 1)),
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extreme_sub = search(miny, lowpts, 1, 1)[0],
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extreme = select(lowind,extreme_sub)
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) det2([select(path,extreme+1)-path[extreme], select(path, extreme-1)-path[extreme]])<0;
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function polygon_is_clockwise(path) =
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assert(is_path(path,dim=2), "Input should be a 2d path")
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polygon_area(path, signed=true)<0;
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// Function: clockwise_polygon()
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// Usage:
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// clockwise_polygon(path);
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