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Speeding up of hull3d
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RonaldoCMP
parent
703e582846
commit
6647c9e0b3
2 changed files with 29 additions and 28 deletions
49
hull.scad
49
hull.scad
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@ -81,8 +81,8 @@ function _backtracking(i,points,h,t,m,all) =
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// clockwise check (2d)
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function _is_cw(a,b,c,all) =
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all ? cross(a-c,b-c)<=EPSILON*norm(a-c)*norm(b-c) :
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cross(a-c,b-c)<-EPSILON*norm(a-c)*norm(b-c);
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all ? cross(a-c,b-c)<=EPSILON*norm(a-c)*norm(b-c) :
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cross(a-c,b-c)<-EPSILON*norm(a-c)*norm(b-c);
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// Function: hull2d_path()
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@ -111,7 +111,7 @@ function hull2d_path(points, all=false) =
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ip = sortidx(points) )
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// lower hull points
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let( lh =
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[ for( i = 2,
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[ for( i = 2,
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k = 2,
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h = [ip[0],ip[1]]; // current list of hull point indices
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i <= n;
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@ -120,7 +120,7 @@ function hull2d_path(points, all=false) =
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i = i+1
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) if( i==n ) h ][0] )
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// concat lower hull points with upper hull ones
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[ for( i = n-2,
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[ for( i = n-2,
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k = len(lh),
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t = k+1,
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h = lh; // current list of hull point indices
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@ -129,7 +129,7 @@ function hull2d_path(points, all=false) =
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h = [for(j=[0:1:k-2]) h[j], if(i>0) ip[i]],
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i = i-1
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) if( i==-1 ) h ][0] ;
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function _hull_collinear(points) =
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let(
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@ -207,25 +207,33 @@ function _hull3d_iterative(points, triangles, planes, remaining, _i=0) =
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let (
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// pick a point
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i = remaining[_i],
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// evaluate the triangle plane equations at point i
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planeq_val = planes*[each points[i], -1],
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// find the triangles that are in conflict with the point (point not inside)
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conflicts = _find_conflicts(points[i], planes),
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// for all triangles that are in conflict, collect their halfedges
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conflicts = [ for (i = [0:1:len(planes)-1]) if (planeq_val[i]>0) i ],
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// collect the halfedges of all triangles that are in conflict
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halfedges = [
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for(c = conflicts, i = [0:2]) let(
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j = (i+1)%3
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) [triangles[c][i], triangles[c][j]]
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for(c = conflicts, i = [0:2])
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[triangles[c][i], triangles[c][(i+1)%3]]
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],
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// find the outer perimeter of the set of conflicting triangles
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horizon = _remove_internal_edges(halfedges),
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// generate a new triangle for each horizon halfedge together with the picked point i
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new_triangles = [ for (h = horizon) concat(h,i) ],
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// calculate the corresponding plane equations
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new_planes = [ for (t = new_triangles) plane3pt_indexed(points, t[0], t[1], t[2]) ]
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// generate new triangles connecting point i to each horizon halfedge vertices
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tri2add = [ for (h = horizon) concat(h,i) ],
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// add tria2add and remove conflict triangles
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new_triangles =
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concat( tri2add,
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[ for (i = [0:1:len(planes)-1]) if (planeq_val[i]<=0) triangles[i] ]
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),
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// add the plane equations of new added triangles and remove the plane equations of the conflict ones
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new_planes =
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concat( [ for (t = tri2add) plane3pt_indexed(points, t[0], t[1], t[2]) ],
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[ for (i = [0:1:len(planes)-1]) if (planeq_val[i]<=0) planes[i] ]
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)
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) _hull3d_iterative(
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points,
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// remove the conflicting triangles and add the new ones
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concat(list_remove(triangles, conflicts), new_triangles),
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concat(list_remove(planes, conflicts), new_planes),
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new_triangles,
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new_planes,
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remaining,
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_i+1
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);
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@ -238,13 +246,6 @@ function _remove_internal_edges(halfedges) = [
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];
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function _find_conflicts(point, planes) = [
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for (i = [0:1:len(planes)-1])
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if (in_front_of_plane(planes[i], point))
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i
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];
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function _find_first_noncoplanar(plane, points, i=0) =
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(i >= len(points) || !points_on_plane([points[i]],plane))? i :
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_find_first_noncoplanar(plane, points, i+1);
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@ -87,12 +87,12 @@ module test_hull() {
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[-4.81079, -0.967785, -10.4726], [-0.949023, 23.1441, -2.08208], [16.1256, -8.2295, -24.0113], [6.45274,
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-7.21416, 23.1409], [22.8274, 1.07038, 19.1756], [-10.6256, -10.0112, -6.12274], [6.29254, -7.81875,
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-24.4037], [22.8538, 8.78163, -6.82567], [-1.96142, 19.1728, -1.726]];
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assert_equal(hull(rand25_3d),[[21, 29, 11], [29, 21, 20], [21, 14, 20], [20, 14, 26], [15, 0, 28], [13, 29, 31], [0, 15,
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assert_equal(sort(hull(rand25_3d)),sort([[21, 29, 11], [29, 21, 20], [21, 14, 20], [20, 14, 26], [15, 0, 28], [13, 29, 31], [0, 15,
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31], [15, 9, 31], [9, 24, 31], [24, 13, 31], [28, 0, 31], [11, 29, 35], [29, 13, 35], [15,
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21, 36], [9, 15, 36], [24, 9, 36], [13, 24, 36], [15, 28, 37], [28, 26, 37], [28, 31, 39],
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[31, 29, 39], [14, 21, 42], [21, 15, 42], [26, 14, 42], [15, 37, 42], [37, 26, 42], [29, 20,
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43], [39, 29, 43], [20, 26, 43], [26, 28, 43], [21, 13, 44], [13, 36, 44], [36, 21, 44],
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[21, 11, 45], [11, 35, 45], [13, 21, 45], [35, 13, 45], [28, 39, 47], [39, 43, 47], [43, 28, 47]]);
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[21, 11, 45], [11, 35, 45], [13, 21, 45], [35, 13, 45], [28, 39, 47], [39, 43, 47], [43, 28, 47]]));
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/* // Inconsistently treats coplanar faces: sometimes face center vertex is included in output, sometimes not
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test_cube_3d = [for(x=[1:3], y=[1:3], z=[1:3]) [x,y,z]];
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@ -178,12 +178,12 @@ module test_hull3d_faces() {
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[-4.81079, -0.967785, -10.4726], [-0.949023, 23.1441, -2.08208], [16.1256, -8.2295, -24.0113], [6.45274,
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-7.21416, 23.1409], [22.8274, 1.07038, 19.1756], [-10.6256, -10.0112, -6.12274], [6.29254, -7.81875,
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-24.4037], [22.8538, 8.78163, -6.82567], [-1.96142, 19.1728, -1.726]];
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assert_equal(hull(rand25_3d),[[21, 29, 11], [29, 21, 20], [21, 14, 20], [20, 14, 26], [15, 0, 28], [13, 29, 31], [0, 15,
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assert_equal(sort(hull(rand25_3d)), sort([[21, 29, 11], [29, 21, 20], [21, 14, 20], [20, 14, 26], [15, 0, 28], [13, 29, 31], [0, 15,
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31], [15, 9, 31], [9, 24, 31], [24, 13, 31], [28, 0, 31], [11, 29, 35], [29, 13, 35], [15,
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21, 36], [9, 15, 36], [24, 9, 36], [13, 24, 36], [15, 28, 37], [28, 26, 37], [28, 31, 39],
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[31, 29, 39], [14, 21, 42], [21, 15, 42], [26, 14, 42], [15, 37, 42], [37, 26, 42], [29, 20,
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43], [39, 29, 43], [20, 26, 43], [26, 28, 43], [21, 13, 44], [13, 36, 44], [36, 21, 44],
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[21, 11, 45], [11, 35, 45], [13, 21, 45], [35, 13, 45], [28, 39, 47], [39, 43, 47], [43, 28, 47]]);
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[21, 11, 45], [11, 35, 45], [13, 21, 45], [35, 13, 45], [28, 39, 47], [39, 43, 47], [43, 28, 47]]));
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}
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test_hull3d_faces();
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