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Merge pull request #678 from adrianVmariano/master

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doc fixes, vnf_halfspace bugfix
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Revar Desmera 2021-10-05 20:21:07 -07:00 committed by GitHub
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35
geometry.scad
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@ -646,14 +646,14 @@ function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) =
// bounded = If false, the line is considered unbounded. If true, it is treated as a bounded line segment. If given as `[true, false]` or `[false, true]`, the boundedness of the points are specified individually, allowing the line to be treated as a half-bounded ray. Default: false (unbounded) // bounded = If false, the line is considered unbounded. If true, it is treated as a bounded line segment. If given as `[true, false]` or `[false, true]`, the boundedness of the points are specified individually, allowing the line to be treated as a half-bounded ray. Default: false (unbounded)
// nonzero = set to true to use the nonzero rule for determining it points are in a polygon. See point_in_polygon. Default: false. // nonzero = set to true to use the nonzero rule for determining it points are in a polygon. See point_in_polygon. Default: false.
// eps = Tolerance in geometric comparisons. Default: `EPSILON` (1e-9) // eps = Tolerance in geometric comparisons. Default: `EPSILON` (1e-9)
// Example: The line intersects the 3d hexagon in a single point. // Example(3D): The line intersects the 3d hexagon in a single point.
// hex = zrot(140,p=rot([-45,40,20],p=path3d(hexagon(r=15)))); // hex = zrot(140,p=rot([-45,40,20],p=path3d(hexagon(r=15))));
// line = [[5,0,-13],[-3,-5,13]]; // line = [[5,0,-13],[-3,-5,13]];
// isect = polygon_line_intersection(hex,line); // isect = polygon_line_intersection(hex,line);
// stroke(hex,closed=true); // stroke(hex,closed=true);
// stroke(line); // stroke(line);
// color("red")move(isect)sphere(r=1); // color("red")move(isect)sphere(r=1,$fn=12);
// Example: In 2D things are more complicated. The output is a list of intersection parts, in the simplest case a single segment. // Example(2D): In 2D things are more complicated. The output is a list of intersection parts, in the simplest case a single segment.
// hex = hexagon(r=15); // hex = hexagon(r=15);
// line = [[-20,10],[25,-7]]; // line = [[-20,10],[25,-7]];
// isect = polygon_line_intersection(hex,line); // isect = polygon_line_intersection(hex,line);
@ -665,7 +665,7 @@ function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) =
// move(part[0]) sphere(r=1); // move(part[0]) sphere(r=1);
// else // else
// stroke(part); // stroke(part);
// Example: In 2D things are more complicated. Here the line is treated as a ray. // Example(2D): Here the line is treated as a ray.
// hex = hexagon(r=15); // hex = hexagon(r=15);
// line = [[0,0],[25,-7]]; // line = [[0,0],[25,-7]];
// isect = polygon_line_intersection(hex,line,RAY); // isect = polygon_line_intersection(hex,line,RAY);
@ -677,7 +677,7 @@ function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) =
// move(part[0]) circle(r=1,$fn=12); // move(part[0]) circle(r=1,$fn=12);
// else // else
// stroke(part); // stroke(part);
// Example: Here the intersection is a single point, which is returned as a single point "path" on the path list. // Example(2D): Here the intersection is a single point, which is returned as a single point "path" on the path list.
// hex = hexagon(r=15); // hex = hexagon(r=15);
// line = [[15,-10],[15,13]]; // line = [[15,-10],[15,13]];
// isect = polygon_line_intersection(hex,line,RAY); // isect = polygon_line_intersection(hex,line,RAY);
@ -689,7 +689,7 @@ function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) =
// move(part[0]) circle(r=1,$fn=12); // move(part[0]) circle(r=1,$fn=12);
// else // else
// stroke(part); // stroke(part);
// Example: Another way to get a single segment // Example(2D): Another way to get a single segment
// hex = hexagon(r=15); // hex = hexagon(r=15);
// line = rot(30,p=[[15,-10],[15,25]],cp=[15,0]); // line = rot(30,p=[[15,-10],[15,25]],cp=[15,0]);
// isect = polygon_line_intersection(hex,line,RAY); // isect = polygon_line_intersection(hex,line,RAY);
@ -701,7 +701,7 @@ function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) =
// move(part[0]) circle(r=1,$fn=12); // move(part[0]) circle(r=1,$fn=12);
// else // else
// stroke(part); // stroke(part);
// Example: Single segment again // Example(2D): Single segment again
// star = star(r=15,n=8,step=2); // star = star(r=15,n=8,step=2);
// line = [[20,-5],[-5,20]]; // line = [[20,-5],[-5,20]];
// isect = polygon_line_intersection(star,line,RAY); // isect = polygon_line_intersection(star,line,RAY);
@ -713,7 +713,7 @@ function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) =
// move(part[0]) circle(r=1,$fn=12); // move(part[0]) circle(r=1,$fn=12);
// else // else
// stroke(part); // stroke(part);
// Example: Solution is two points // Example(2D): Solution is two points
// star = star(r=15,n=8,step=3); // star = star(r=15,n=8,step=3);
// line = rot(22.5,p=[[15,-10],[15,20]],cp=[15,0]); // line = rot(22.5,p=[[15,-10],[15,20]],cp=[15,0]);
// isect = polygon_line_intersection(star,line,SEGMENT); // isect = polygon_line_intersection(star,line,SEGMENT);
@ -725,7 +725,7 @@ function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) =
// move(part[0]) circle(r=1,$fn=12); // move(part[0]) circle(r=1,$fn=12);
// else // else
// stroke(part); // stroke(part);
// Example: Solution is list of three segments // Example(2D): Solution is list of three segments
// star = star(r=25,ir=9,n=8); // star = star(r=25,ir=9,n=8);
// line = [[-25,12],[25,12]]; // line = [[-25,12],[25,12]];
// isect = polygon_line_intersection(star,line); // isect = polygon_line_intersection(star,line);
@ -737,7 +737,7 @@ function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) =
// move(part[0]) circle(r=1,$fn=12); // move(part[0]) circle(r=1,$fn=12);
// else // else
// stroke(part); // stroke(part);
// Example: Solution is a mixture of segments and points // Example(2D): Solution is a mixture of segments and points
// star = star(r=25,ir=9,n=7); // star = star(r=25,ir=9,n=7);
// line = [left(10,p=star[8]), right(50,p=star[8])]; // line = [left(10,p=star[8]), right(50,p=star[8])];
// isect = polygon_line_intersection(star,line); // isect = polygon_line_intersection(star,line);
@ -1591,22 +1591,17 @@ function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
// poly = Array of vertices for the polygon. // poly = Array of vertices for the polygon.
// ind = A list indexing the vertices of the polygon in `poly`. // ind = A list indexing the vertices of the polygon in `poly`.
// eps = A maximum tolerance in geometrical tests. Default: EPSILON // eps = A maximum tolerance in geometrical tests. Default: EPSILON
// Example: // Example(2D):
// poly = star(id=10, od=15,n=11); // poly = star(id=10, od=15,n=11);
// tris = polygon_triangulate(poly); // tris = polygon_triangulate(poly);
// polygon(poly); // for(tri=tris) stroke(select(poly,tri), width=.1, closed=true);
// up(1) // Example(3D):
// color("blue"); // include <BOSL2/polyhedra.scad>
// for(tri=tris) trace_path(select(poly,tri), size=.1, closed=true);
//
// Example:
// include<BOSL2/polyhedra.scad>
// vnf = regular_polyhedron_info(name="dodecahedron",side=5,info="vnf"); // vnf = regular_polyhedron_info(name="dodecahedron",side=5,info="vnf");
// %vnf_polyhedron(vnf); // %vnf_polyhedron(vnf);
// vnf_tri = [vnf[0], [for(face=vnf[1]) each polygon_triangulate(vnf[0], face) ] ]; // vnf_tri = [vnf[0], [for(face=vnf[1]) each polygon_triangulate(vnf[0], face) ] ];
// color("blue") // color("blue")
// vnf_wireframe(vnf_tri, d=.15); // vnf_wireframe(vnf_tri, width=.15);
function polygon_triangulate(poly, ind, eps=EPSILON) = function polygon_triangulate(poly, ind, eps=EPSILON) =
assert(is_path(poly), "Polygon `poly` should be a list of 2d or 3d points") assert(is_path(poly), "Polygon `poly` should be a list of 2d or 3d points")
assert(is_undef(ind) assert(is_undef(ind)

525
vnf.scad
View file

@ -206,35 +206,35 @@ function vnf_vertex_array(
// points = List of point lists for each row // points = List of point lists for each row
// row_wrap = If true then add faces connecting the first row and last row. These rows must differ by at most 2 in length. // row_wrap = If true then add faces connecting the first row and last row. These rows must differ by at most 2 in length.
// reverse = Set this to reverse the direction of the faces // reverse = Set this to reverse the direction of the faces
// Example: Each row has one more point than the preceeding one. // Example(3D): Each row has one more point than the preceeding one.
// pts = [for(y=[1:1:10]) [for(x=[0:y-1]) [x,y,y]]]; // pts = [for(y=[1:1:10]) [for(x=[0:y-1]) [x,y,y]]];
// vnf = vnf_tri_array(pts); // vnf = vnf_tri_array(pts);
// vnf_wireframe(vnf,d=.1); // vnf_wireframe(vnf,width=0.1);
// color("red")move_copies(flatten(pts)) sphere(r=.15,$fn=9); // color("red")move_copies(flatten(pts)) sphere(r=.15,$fn=9);
// Example: Each row has one more point than the preceeding one. // Example(3D): Each row has one more point than the preceeding one.
// pts = [for(y=[0:2:10]) [for(x=[-y/2:y/2]) [x,y,y]]]; // pts = [for(y=[0:2:10]) [for(x=[-y/2:y/2]) [x,y,y]]];
// vnf = vnf_tri_array(pts); // vnf = vnf_tri_array(pts);
// vnf_wireframe(vnf,d=.1); // vnf_wireframe(vnf,width=0.1);
// color("red")move_copies(flatten(pts)) sphere(r=.15,$fn=9); // color("red")move_copies(flatten(pts)) sphere(r=.15,$fn=9);
// Example: Chaining two VNFs to construct a cone with one point length change between rows. // Example(3D): Chaining two VNFs to construct a cone with one point length change between rows.
// pts1 = [for(z=[0:10]) path3d(arc(3+z,r=z/2+1, angle=[0,180]),10-z)]; // pts1 = [for(z=[0:10]) path3d(arc(3+z,r=z/2+1, angle=[0,180]),10-z)];
// pts2 = [for(z=[0:10]) path3d(arc(3+z,r=z/2+1, angle=[180,360]),10-z)]; // pts2 = [for(z=[0:10]) path3d(arc(3+z,r=z/2+1, angle=[180,360]),10-z)];
// vnf = vnf_tri_array(pts1, // vnf = vnf_tri_array(pts1,
// vnf=vnf_tri_array(pts2)); // vnf=vnf_tri_array(pts2));
// color("green")vnf_wireframe(vnf,d=.1); // color("green")vnf_wireframe(vnf,width=0.1);
// vnf_polyhedron(vnf); // vnf_polyhedron(vnf);
// Example: Cone with length change two between rows // Example(3D): Cone with length change two between rows
// pts1 = [for(z=[0:1:10]) path3d(arc(3+2*z,r=z/2+1, angle=[0,180]),10-z)]; // pts1 = [for(z=[0:1:10]) path3d(arc(3+2*z,r=z/2+1, angle=[0,180]),10-z)];
// pts2 = [for(z=[0:1:10]) path3d(arc(3+2*z,r=z/2+1, angle=[180,360]),10-z)]; // pts2 = [for(z=[0:1:10]) path3d(arc(3+2*z,r=z/2+1, angle=[180,360]),10-z)];
// vnf = vnf_tri_array(pts1, // vnf = vnf_tri_array(pts1,
// vnf=vnf_tri_array(pts2)); // vnf=vnf_tri_array(pts2));
// color("green")vnf_wireframe(vnf,d=.1); // color("green")vnf_wireframe(vnf,width=0.1);
// vnf_polyhedron(vnf); // vnf_polyhedron(vnf);
// Example: Point count can change irregularly // Example(3D): Point count can change irregularly
// lens = [10,9,7,5,6,8,8,10]; // lens = [10,9,7,5,6,8,8,10];
// pts = [for(y=idx(lens)) lerpn([-lens[y],y,y],[lens[y],y,y],lens[y])]; // pts = [for(y=idx(lens)) lerpn([-lens[y],y,y],[lens[y],y,y],lens[y])];
// vnf = vnf_tri_array(pts); // vnf = vnf_tri_array(pts);
// vnf_wireframe(vnf,d=.1); // vnf_wireframe(vnf,width=0.1);
// color("red")move_copies(flatten(pts)) sphere(r=.15,$fn=9); // color("red")move_copies(flatten(pts)) sphere(r=.15,$fn=9);
function vnf_tri_array(points, row_wrap=false, reverse=false, vnf=EMPTY_VNF) = function vnf_tri_array(points, row_wrap=false, reverse=false, vnf=EMPTY_VNF) =
let( let(
@ -422,234 +422,6 @@ function vnf_triangulate(vnf) =
// Section: Turning a VNF into geometry
// Module: vnf_polyhedron()
// Usage:
// vnf_polyhedron(vnf);
// vnf_polyhedron([VNF, VNF, VNF, ...]);
// Description:
// Given a VNF structure, or a list of VNF structures, creates a polyhedron from them.
// Arguments:
// vnf = A VNF structure, or list of VNF structures.
// convexity = Max number of times a line could intersect a wall of the shape.
// extent = If true, calculate anchors by extents, rather than intersection. Default: true.
// cp = Centerpoint of VNF to use for anchoring when `extent` is false. Default: `[0, 0, 0]`
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `"origin"`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#orient). Default: `UP`
module vnf_polyhedron(vnf, convexity=2, extent=true, cp=[0,0,0], anchor="origin", spin=0, orient=UP) {
vnf = is_vnf_list(vnf)? vnf_merge(vnf) : vnf;
cp = is_def(cp) ? cp : vnf_centroid(vnf);
attachable(anchor,spin,orient, vnf=vnf, extent=extent, cp=cp) {
polyhedron(vnf[0], vnf[1], convexity=convexity);
children();
}
}
// Module: vnf_wireframe()
// Usage:
// vnf_wireframe(vnf, <r|d>);
// Description:
// Given a VNF, creates a wire frame ball-and-stick model of the polyhedron with a cylinder for
// each edge and a sphere at each vertex. The width parameter specifies the width of the sticks
// that form the wire frame.
// Arguments:
// vnf = A vnf structure
// width = width of the cylinders forming the wire frame. Default: 1
// Example:
// $fn=32;
// ball = sphere(r=20, $fn=6);
// vnf_wireframe(ball,width=1);
// Example:
// include <BOSL2/polyhedra.scad>
// $fn=32;
// cube_oct = regular_polyhedron_info("vnf", name="cuboctahedron", or=20);
// vnf_wireframe(cube_oct);
// Example: The spheres at the vertex are imperfect at aligning with the cylinders, so especially at low $fn things look prety ugly. This is normal.
// include <BOSL2/polyhedra.scad>
// $fn=8;
// octahedron = regular_polyhedron_info("vnf", name="octahedron", or=20);
// vnf_wireframe(octahedron,width=5);
module vnf_wireframe(vnf, width=1)
{
vertex = vnf[0];
edges = unique([for (face=vnf[1], i=idx(face))
sort([face[i], select(face,i+1)])
]);
for (e=edges) extrude_from_to(vertex[e[0]],vertex[e[1]]) circle(d=width);
move_copies(vertex) sphere(d=width);
}
// Section: Operations on VNFs
// Function: vnf_volume()
// Usage:
// vol = vnf_volume(vnf);
// Description:
// Returns the volume enclosed by the given manifold VNF. The VNF must describe a valid polyhedron with consistent face direction and
// no holes; otherwise the results are undefined. Returns a positive volume if face direction is clockwise and a negative volume
// if face direction is counter-clockwise.
// Divide the polyhedron into tetrahedra with the origin as one vertex and sum up the signed volume.
function vnf_volume(vnf) =
let(verts = vnf[0])
sum([
for(face=vnf[1], j=[1:1:len(face)-2])
cross(verts[face[j+1]], verts[face[j]]) * verts[face[0]]
])/6;
// Function: vnf_area()
// Usage:
// area = vnf_area(vnf);
// Description:
// Returns the surface area in any VNF by adding up the area of all its faces. The VNF need not be a manifold.
function vnf_area(vnf) =
let(verts=vnf[0])
sum([for(face=vnf[1]) polygon_area(select(verts,face))]);
// Function: vnf_centroid()
// Usage:
// vol = vnf_centroid(vnf);
// Description:
// Returns the centroid of the given manifold VNF. The VNF must describe a valid polyhedron with consistent face direction and
// no holes; otherwise the results are undefined.
// Divide the solid up into tetrahedra with the origin as one vertex.
// The centroid of a tetrahedron is the average of its vertices.
// The centroid of the total is the volume weighted average.
function vnf_centroid(vnf) =
assert(is_vnf(vnf) && len(vnf[0])!=0 )
let(
verts = vnf[0],
pos = sum([
for(face=vnf[1], j=[1:1:len(face)-2]) let(
v0 = verts[face[0]],
v1 = verts[face[j]],
v2 = verts[face[j+1]],
vol = cross(v2,v1)*v0
)
[ vol, (v0+v1+v2)*vol ]
])
)
assert(!approx(pos[0],0, EPSILON), "The vnf has self-intersections.")
pos[1]/pos[0]/4;
// Function: vnf_halfspace()
// Usage:
// newvnf = vnf_halfspace(plane, vnf, [closed]);
// Description:
// Returns the intersection of the vnf with a half space. The half space is defined by
// plane = [A,B,C,D], taking the side where the normal [A,B,C] points: Ax+By+Cz≥D.
// If closed is set to false then the cut face is not included in the vnf. This could
// allow further extension of the vnf by merging with other vnfs.
// Arguments:
// plane = plane defining the boundary of the half space
// vnf = vnf to cut
// closed = if false do not return include cut face(s). Default: true
// Example:
// vnf = cube(10,center=true);
// cutvnf = vnf_halfspace([-1,1,-1,0], vnf);
// vnf_polyhedron(cutvnf);
// Example: Cut face has 2 components
// vnf = path_sweep(circle(r=4, $fn=16),
// circle(r=20, $fn=64),closed=true);
// cutvnf = vnf_halfspace([-1,1,-4,0], vnf);
// vnf_polyhedron(cutvnf);
// Example: Cut face is not simply connected
// vnf = path_sweep(circle(r=4, $fn=16),
// circle(r=20, $fn=64),closed=true);
// cutvnf = vnf_halfspace([0,0.7,-4,0], vnf);
// vnf_polyhedron(cutvnf);
// Example: Cut object has multiple components
// function knot(a,b,t) = // rolling knot
// [ a * cos (3 * t) / (1 - b* sin (2 *t)),
// a * sin( 3 * t) / (1 - b* sin (2 *t)),
// 1.8 * b * cos (2 * t) /(1 - b* sin (2 *t))];
// a = 0.8; b = sqrt (1 - a * a);
// ksteps = 400;
// knot_path = [for (i=[0:ksteps-1]) 50 * knot(a,b,(i/ksteps)*360)];
// ushape = [[-10, 0],[-10, 10],[ -7, 10],[ -7, 2],[ 7, 2],[ 7, 7],[ 10, 7],[ 10, 0]];
// knot=path_sweep(ushape, knot_path, closed=true, method="incremental");
// cut_knot = vnf_halfspace([1,0,0,0], knot);
// vnf_polyhedron(cut_knot);
function vnf_halfspace(plane, vnf, closed=true) =
let(
inside = [for(x=vnf[0]) plane*[each x,-1] >= 0 ? 1 : 0],
vertexmap = [0,each cumsum(inside)],
faces_edges_vertices = _vnfcut(plane, vnf[0],vertexmap,inside, vnf[1], last(vertexmap)),
newvert = concat(bselect(vnf[0],inside), faces_edges_vertices[2])
)
closed==false ? [newvert, faces_edges_vertices[0]] :
let(
allpaths = _assemble_paths(newvert, faces_edges_vertices[1]),
newpaths = [for(p=allpaths) if (len(p)>=3) p
else assert(approx(p[0],p[1]),"Orphan edge found when assembling cut edges.")
]
)
len(newpaths)<=1 ? [newvert, concat(faces_edges_vertices[0], newpaths)]
:
let(
faceregion = project_plane(plane, newpaths),
facevnf = region_faces(faceregion,reverse=true)
)
vnf_merge([[newvert, faces_edges_vertices[0]], lift_plane(plane, facevnf)]);
function _assemble_paths(vertices, edges, paths=[],i=0) =
i==len(edges) ? paths :
norm(vertices[edges[i][0]]-vertices[edges[i][1]])<EPSILON ? echo(degen=i)_assemble_paths(vertices,edges,paths,i+1) :
let( // Find paths that connects on left side and right side of the edges (if one exists)
left = [for(j=idx(paths)) if (approx(vertices[last(paths[j])],vertices[edges[i][0]])) j],
right = [for(j=idx(paths)) if (approx(vertices[edges[i][1]],vertices[paths[j][0]])) j]
)
assert(len(left)<=1 && len(right)<=1)
let(
keep_path = list_remove(paths,concat(left,right)),
update_path = left==[] && right==[] ? edges[i]
: left==[] ? concat([edges[i][0]],paths[right[0]])
: right==[] ? concat(paths[left[0]],[edges[i][1]])
: left != right ? concat(paths[left[0]], paths[right[0]])
: paths[left[0]]
)
_assemble_paths(vertices, edges, concat(keep_path, [update_path]), i+1);
function _vnfcut(plane, vertices, vertexmap, inside, faces, vertcount, newfaces=[], newedges=[], newvertices=[], i=0) =
i==len(faces) ? [newfaces, newedges, newvertices] :
let(
pts_inside = select(inside,faces[i])
)
all(pts_inside) ? _vnfcut(plane, vertices, vertexmap, inside, faces, vertcount,
concat(newfaces, [select(vertexmap,faces[i])]), newedges, newvertices, i+1):
!any(pts_inside) ? _vnfcut(plane, vertices, vertexmap,inside, faces, vertcount, newfaces, newedges, newvertices, i+1):
let(
first = search([[1,0]],pair(pts_inside,wrap=true),0)[0],
second = search([[0,1]],pair(pts_inside,wrap=true),0)[0]
)
assert(len(first)==1 && len(second)==1, "Found concave face in VNF. Run vnf_triangulate first to ensure convex faces.")
let(
newface = [each select(vertexmap,select(faces[i],second[0]+1,first[0])),vertcount, vertcount+1],
newvert = [plane_line_intersection(plane, select(vertices,select(faces[i],first[0],first[0]+1)),eps=0),
plane_line_intersection(plane, select(vertices,select(faces[i],second[0],second[0]+1)),eps=0)]
)
true //!approx(newvert[0],newvert[1])
? _vnfcut(plane, vertices, vertexmap, inside, faces, vertcount+2,
concat(newfaces, [newface]), concat(newedges,[[vertcount+1,vertcount]]),concat(newvertices,newvert),i+1)
:len(newface)>3
? _vnfcut(plane, vertices, vertexmap, inside, faces, vertcount+1,
concat(newfaces, [list_head(newface)]), newedges,concat(newvertices,[newvert[0]]),i+1)
:
_vnfcut(plane, vertices, vertexmap, inside, faces, vertcount,newfaces, newedges, newvert, i+1);
// Function: vnf_slice() // Function: vnf_slice()
// Usage: // Usage:
// sliced = vnf_slice(vnf, dir, cuts); // sliced = vnf_slice(vnf, dir, cuts);
@ -657,8 +429,8 @@ function _vnfcut(plane, vertices, vertexmap, inside, faces, vertcount, newfaces=
// Slice the faces of a VNF along a specified axis direction at a given list // Slice the faces of a VNF along a specified axis direction at a given list
// of cut points. You can use this to refine the faces of a VNF before applying // of cut points. You can use this to refine the faces of a VNF before applying
// a nonlinear transformation to its vertex set. // a nonlinear transformation to its vertex set.
// Example: // Example(3D):
// include <BOSL2-fork/polyhedra.scad> // include <BOSL2/polyhedra.scad>
// vnf = regular_polyhedron_info("vnf", "dodecahedron", side=12); // vnf = regular_polyhedron_info("vnf", "dodecahedron", side=12);
// vnf_polyhedron(vnf); // vnf_polyhedron(vnf);
// sliced = vnf_slice(vnf, "X", [-6,-1,10]); // sliced = vnf_slice(vnf, "X", [-6,-1,10]);
@ -753,6 +525,240 @@ function _slice_3dpolygons(polys, dir, cuts) =
// Section: Turning a VNF into geometry
// Module: vnf_polyhedron()
// Usage:
// vnf_polyhedron(vnf);
// vnf_polyhedron([VNF, VNF, VNF, ...]);
// Description:
// Given a VNF structure, or a list of VNF structures, creates a polyhedron from them.
// Arguments:
// vnf = A VNF structure, or list of VNF structures.
// convexity = Max number of times a line could intersect a wall of the shape.
// extent = If true, calculate anchors by extents, rather than intersection. Default: true.
// cp = Centerpoint of VNF to use for anchoring when `extent` is false. Default: `[0, 0, 0]`
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `"origin"`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#orient). Default: `UP`
module vnf_polyhedron(vnf, convexity=2, extent=true, cp=[0,0,0], anchor="origin", spin=0, orient=UP) {
vnf = is_vnf_list(vnf)? vnf_merge(vnf) : vnf;
cp = is_def(cp) ? cp : vnf_centroid(vnf);
attachable(anchor,spin,orient, vnf=vnf, extent=extent, cp=cp) {
polyhedron(vnf[0], vnf[1], convexity=convexity);
children();
}
}
// Module: vnf_wireframe()
// Usage:
// vnf_wireframe(vnf, <r|d>);
// Description:
// Given a VNF, creates a wire frame ball-and-stick model of the polyhedron with a cylinder for
// each edge and a sphere at each vertex. The width parameter specifies the width of the sticks
// that form the wire frame.
// Arguments:
// vnf = A vnf structure
// width = width of the cylinders forming the wire frame. Default: 1
// Example:
// $fn=32;
// ball = sphere(r=20, $fn=6);
// vnf_wireframe(ball,width=1);
// Example:
// include <BOSL2/polyhedra.scad>
// $fn=32;
// cube_oct = regular_polyhedron_info("vnf",
// name="cuboctahedron", or=20);
// vnf_wireframe(cube_oct);
// Example: The spheres at the vertex are imperfect at aligning with the cylinders, so especially at low $fn things look prety ugly. This is normal.
// include <BOSL2/polyhedra.scad>
// $fn=8;
// octahedron = regular_polyhedron_info("vnf",
// name="octahedron", or=20);
// vnf_wireframe(octahedron,width=5);
module vnf_wireframe(vnf, width=1)
{
vertex = vnf[0];
edges = unique([for (face=vnf[1], i=idx(face))
sort([face[i], select(face,i+1)])
]);
for (e=edges) extrude_from_to(vertex[e[0]],vertex[e[1]]) circle(d=width);
move_copies(vertex) sphere(d=width);
}
// Section: Operations on VNFs
// Function: vnf_volume()
// Usage:
// vol = vnf_volume(vnf);
// Description:
// Returns the volume enclosed by the given manifold VNF. The VNF must describe a valid polyhedron with consistent face direction and
// no holes; otherwise the results are undefined. Returns a positive volume if face direction is clockwise and a negative volume
// if face direction is counter-clockwise.
// Divide the polyhedron into tetrahedra with the origin as one vertex and sum up the signed volume.
function vnf_volume(vnf) =
let(verts = vnf[0])
sum([
for(face=vnf[1], j=[1:1:len(face)-2])
cross(verts[face[j+1]], verts[face[j]]) * verts[face[0]]
])/6;
// Function: vnf_area()
// Usage:
// area = vnf_area(vnf);
// Description:
// Returns the surface area in any VNF by adding up the area of all its faces. The VNF need not be a manifold.
function vnf_area(vnf) =
let(verts=vnf[0])
sum([for(face=vnf[1]) polygon_area(select(verts,face))]);
// Function: vnf_centroid()
// Usage:
// vol = vnf_centroid(vnf);
// Description:
// Returns the centroid of the given manifold VNF. The VNF must describe a valid polyhedron with consistent face direction and
// no holes; otherwise the results are undefined.
// Divide the solid up into tetrahedra with the origin as one vertex.
// The centroid of a tetrahedron is the average of its vertices.
// The centroid of the total is the volume weighted average.
function vnf_centroid(vnf) =
assert(is_vnf(vnf) && len(vnf[0])!=0 )
let(
verts = vnf[0],
pos = sum([
for(face=vnf[1], j=[1:1:len(face)-2]) let(
v0 = verts[face[0]],
v1 = verts[face[j]],
v2 = verts[face[j+1]],
vol = cross(v2,v1)*v0
)
[ vol, (v0+v1+v2)*vol ]
])
)
assert(!approx(pos[0],0, EPSILON), "The vnf has self-intersections.")
pos[1]/pos[0]/4;
// Function: vnf_halfspace()
// Usage:
// newvnf = vnf_halfspace(plane, vnf, [closed]);
// Description:
// Returns the intersection of the vnf with a half space. The half space is defined by
// plane = [A,B,C,D], taking the side where the normal [A,B,C] points: Ax+By+Cz≥D.
// If closed is set to false then the cut face is not included in the vnf. This could
// allow further extension of the vnf by merging with other vnfs.
// Arguments:
// plane = plane defining the boundary of the half space
// vnf = vnf to cut
// closed = if false do not return include cut face(s). Default: true
// Example(3D):
// vnf = cube(10,center=true);
// cutvnf = vnf_halfspace([-1,1,-1,0], vnf);
// vnf_polyhedron(cutvnf);
// Example(3D): Cut face has 2 components
// vnf = path_sweep(circle(r=4, $fn=16),
// circle(r=20, $fn=64),closed=true);
// cutvnf = vnf_halfspace([-1,1,-4,0], vnf);
// vnf_polyhedron(cutvnf);
// Example(3D): Cut face is not simply connected
// vnf = path_sweep(circle(r=4, $fn=16),
// circle(r=20, $fn=64),closed=true);
// cutvnf = vnf_halfspace([0,0.7,-4,0], vnf);
// vnf_polyhedron(cutvnf);
// Example(3D): Cut object has multiple components
// function knot(a,b,t) = // rolling knot
// [ a * cos (3 * t) / (1 - b* sin (2 *t)),
// a * sin( 3 * t) / (1 - b* sin (2 *t)),
// 1.8 * b * cos (2 * t) /(1 - b* sin (2 *t))];
// a = 0.8; b = sqrt (1 - a * a);
// ksteps = 400;
// knot_path = [for (i=[0:ksteps-1]) 50 * knot(a,b,(i/ksteps)*360)];
// ushape = [[-10, 0],[-10, 10],[ -7, 10],[ -7, 2],[ 7, 2],[ 7, 7],[ 10, 7],[ 10, 0]];
// knot=path_sweep(ushape, knot_path, closed=true, method="incremental");
// cut_knot = vnf_halfspace([1,0,0,0], knot);
// vnf_polyhedron(cut_knot);
function vnf_halfspace(plane, vnf, closed=true) =
let(
inside = [for(x=vnf[0]) plane*[each x,-1] >= 0 ? 1 : 0],
vertexmap = [0,each cumsum(inside)],
faces_edges_vertices = _vnfcut(plane, vnf[0],vertexmap,inside, vnf[1], last(vertexmap)),
newvert = concat(bselect(vnf[0],inside), faces_edges_vertices[2])
)
closed==false ? [newvert, faces_edges_vertices[0]] :
let(
allpaths = _assemble_paths(newvert, faces_edges_vertices[1]),
newpaths = [for(p=allpaths) if (len(p)>=3) p
else assert(approx(p[0],p[1]),"Orphan edge found when assembling cut edges.")
]
)
len(newpaths)<=1 ? [newvert, concat(faces_edges_vertices[0], newpaths)]
:
let(
M = project_plane(plane),
faceregion = [for(path=newpaths) path2d(apply(M,select(newvert,path)))],
facevnf = region_faces(faceregion,transform=rot_inverse(M),reverse=true)
)
vnf_merge([[newvert, faces_edges_vertices[0]], facevnf]);
function _assemble_paths(vertices, edges, paths=[],i=0) =
i==len(edges) ? paths :
norm(vertices[edges[i][0]]-vertices[edges[i][1]])<EPSILON ? _assemble_paths(vertices,edges,paths,i+1) :
let( // Find paths that connects on left side and right side of the edges (if one exists)
left = [for(j=idx(paths)) if (approx(vertices[last(paths[j])],vertices[edges[i][0]])) j],
right = [for(j=idx(paths)) if (approx(vertices[edges[i][1]],vertices[paths[j][0]])) j]
)
assert(len(left)<=1 && len(right)<=1)
let(
keep_path = list_remove(paths,concat(left,right)),
update_path = left==[] && right==[] ? edges[i]
: left==[] ? concat([edges[i][0]],paths[right[0]])
: right==[] ? concat(paths[left[0]],[edges[i][1]])
: left != right ? concat(paths[left[0]], paths[right[0]])
: paths[left[0]]
)
_assemble_paths(vertices, edges, concat(keep_path, [update_path]), i+1);
function _vnfcut(plane, vertices, vertexmap, inside, faces, vertcount, newfaces=[], newedges=[], newvertices=[], i=0) =
i==len(faces) ? [newfaces, newedges, newvertices] :
let(
pts_inside = select(inside,faces[i])
)
all(pts_inside) ? _vnfcut(plane, vertices, vertexmap, inside, faces, vertcount,
concat(newfaces, [select(vertexmap,faces[i])]), newedges, newvertices, i+1):
!any(pts_inside) ? _vnfcut(plane, vertices, vertexmap,inside, faces, vertcount, newfaces, newedges, newvertices, i+1):
let(
first = search([[1,0]],pair(pts_inside,wrap=true),0)[0],
second = search([[0,1]],pair(pts_inside,wrap=true),0)[0]
)
assert(len(first)==1 && len(second)==1, "Found concave face in VNF. Run vnf_triangulate first to ensure convex faces.")
let(
newface = [each select(vertexmap,select(faces[i],second[0]+1,first[0])),vertcount, vertcount+1],
newvert = [plane_line_intersection(plane, select(vertices,select(faces[i],first[0],first[0]+1)),eps=0),
plane_line_intersection(plane, select(vertices,select(faces[i],second[0],second[0]+1)),eps=0)]
)
true //!approx(newvert[0],newvert[1])
? _vnfcut(plane, vertices, vertexmap, inside, faces, vertcount+2,
concat(newfaces, [newface]), concat(newedges,[[vertcount+1,vertcount]]),concat(newvertices,newvert),i+1)
:len(newface)>3
? _vnfcut(plane, vertices, vertexmap, inside, faces, vertcount+1,
concat(newfaces, [list_head(newface)]), newedges,concat(newvertices,[newvert[0]]),i+1)
:
_vnfcut(plane, vertices, vertexmap, inside, faces, vertcount,newfaces, newedges, newvert, i+1);
function _triangulate_planar_convex_polygons(polys) = function _triangulate_planar_convex_polygons(polys) =
polys==[]? [] : polys==[]? [] :
let( let(
@ -809,7 +815,8 @@ function _triangulate_planar_convex_polygons(polys) =
// bent2 = vnf_bend(vnf2, axis="Y"); // bent2 = vnf_bend(vnf2, axis="Y");
// vnf_polyhedron([bent1,bent2]); // vnf_polyhedron([bent1,bent2]);
// Example(3D): // Example(3D):
// rgn = union(rect([100,20],center=true), rect([20,100],center=true)); // rgn = union(rect([100,20],center=true),
// rect([20,100],center=true));
// vnf0 = linear_sweep(zrot(45,p=rgn), height=10); // vnf0 = linear_sweep(zrot(45,p=rgn), height=10);
// vnf1 = up(50, p=vnf0); // vnf1 = up(50, p=vnf0);
// vnf2 = down(50, p=vnf0); // vnf2 = down(50, p=vnf0);
@ -885,26 +892,24 @@ function vnf_bend(vnf,r,d,axis="Z") =
) [new_vert,sliced[1]]; ) [new_vert,sliced[1]];
// Section: Debugging Polyhedrons // Section: Debugging Polyhedrons
// Module: _show_vertices() /// Internal Module: _show_vertices()
// Usage: /// Usage:
// _show_vertices(vertices, [size]) /// _show_vertices(vertices, [size])
// Description: /// Description:
// Draws all the vertices in an array, at their 3D position, numbered by their /// Draws all the vertices in an array, at their 3D position, numbered by their
// position in the vertex array. Also draws any children of this module with /// position in the vertex array. Also draws any children of this module with
// transparency. /// transparency.
// Arguments: /// Arguments:
// vertices = Array of point vertices. /// vertices = Array of point vertices.
// size = The size of the text used to label the vertices. Default: 1 /// size = The size of the text used to label the vertices. Default: 1
// Example: /// Example:
// verts = [for (z=[-10,10], y=[-10,10], x=[-10,10]) [x,y,z]]; /// verts = [for (z=[-10,10], y=[-10,10], x=[-10,10]) [x,y,z]];
// faces = [[0,1,2], [1,3,2], [0,4,5], [0,5,1], [1,5,7], [1,7,3], [3,7,6], [3,6,2], [2,6,4], [2,4,0], [4,6,7], [4,7,5]]; /// faces = [[0,1,2], [1,3,2], [0,4,5], [0,5,1], [1,5,7], [1,7,3], [3,7,6], [3,6,2], [2,6,4], [2,4,0], [4,6,7], [4,7,5]];
// _show_vertices(vertices=verts, size=2) { /// _show_vertices(vertices=verts, size=2) {
// polyhedron(points=verts, faces=faces); /// polyhedron(points=verts, faces=faces);
// } /// }
module _show_vertices(vertices, size=1) { module _show_vertices(vertices, size=1) {
color("blue") { color("blue") {
dups = vector_search(vertices, EPSILON, vertices); dups = vector_search(vertices, EPSILON, vertices);
@ -924,7 +929,7 @@ module _show_vertices(vertices, size=1) {
} }
/// Module: _show_faces() /// Internal Module: _show_faces()
/// Usage: /// Usage:
/// _show_faces(vertices, faces, [size=]); /// _show_faces(vertices, faces, [size=]);
/// Description: /// Description: