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Adrian Mariano 2021-11-19 22:20:01 -05:00
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@ -32,7 +32,7 @@ $tags_hidden = [];
_ANCHOR_TYPES = ["intersect","hull"];
// Section: Anchors, Spin, and Orientation
// Section: Terminology and Shortcuts
// This library adds the concept of anchoring, spin and orientation to the `cube()`, `cylinder()`
// and `sphere()` builtins, as well as to most of the shapes provided by this library itself.
// - An anchor is a place on an object which you can align the object to, or attach other objects
@ -41,8 +41,13 @@ _ANCHOR_TYPES = ["intersect","hull"];
// - Spin is a simple rotation around the Z axis.
// - Orientation is rotating an object so that its top is pointed towards a given vector.
// An object will first be translated to its anchor position, then spun, then oriented.
// For a detailed step-by-step explanation of attachments, see the [[Attachments Tutorial|Tutorial-Attachments]].
// .
// ## Anchor
// For describing directions, faces, edges, and corners the library provides a set of shortcuts
// all based on combinations of unit direction vectors. You can use these for anchoring and orienting
// attachable objects. You can also them to specify edge sets for rounding or chamfering cuboids,
// or for placing edge, face and corner masks.
// SubSection: Anchor
// Anchoring is specified with the `anchor` argument in most shape modules. Specifying `anchor`
// when creating an object will translate the object so that the anchor point is at the origin
// (0,0,0). Anchoring always occurs before spin and orientation are applied.
@ -51,8 +56,8 @@ _ANCHOR_TYPES = ["intersect","hull"];
// .
// When given as a vector, it points, in a general way, towards the face, edge, or corner of the
// object that you want the anchor for, relative to the center of the object. There are directional
// constants named `TOP`, `BOTTOM`, `FRONT`, `BACK`, `LEFT`, and `RIGHT` that you can add together
// to specify an anchor point.
// constants with names like `TOP`, `BOTTOM`, `LEFT`, `RIGHT` and `BACK` that you can add together
// to specify an anchor point. See ?????? below for the full list of pre-defined directional constants.
// .
// For example:
// - `[0,0,1]` is the same as `TOP` and refers to the center of the top face.
@ -69,24 +74,280 @@ _ANCHOR_TYPES = ["intersect","hull"];
// Some more complex objects, like screws and stepper motors, have named anchors to refer to places
// on the object that are not at one of the standard faces, edges or corners. For example, stepper
// motors have anchors for `"screw1"`, `"screw2"`, etc. to refer to the various screwholes on the
// stepper motor shape. The names, positions, directions, and spins of these anchors will be
// specific to the object, and will be documented when they exist.
// stepper motor shape. The names, positions, directions, and spins of these anchors are
// specific to the object, and are documented when they exist.
// .
// ## Spin
// Spin is specified with the `spin` argume// nt in most shape modules. Specifying a scalar `spin`
// SubSection: Spin
// Spin is specified with the `spin` argument in most shape modules. Specifying a scalar `spin`
// when creating an object will rotate the object counter-clockwise around the Z axis by the given
// number of degrees. If given as a 3D vector, the object will be rotated around each of the X, Y, Z
// axes by the number of degrees in each component of the vector. Spin is always applied after
// anchoring, and before orientation.
// anchoring, and before orientation. Since spin is applied after anchoring it is not what
// you might think of intuitively as spinning the shape. To do that, apply `zrot()` to the shape before anchoring.
// .
// ## Orient
// SubSection: Orient
// Orientation is specified with the `orient` argument in most shape modules. Specifying `orient`
// when creating an object will rotate the object such that the top of the object will be pointed
// at the vector direction given in the `orient` argument. Orientation is always applied after
// anchoring and spin. The constants `UP`, `DOWN`, `FRONT`, `BACK`, `LEFT`, and `RIGHT` can be
// added together to form the directional vector for this. ie: `LEFT+BACK`
// .
// For a more step-by-step explanation of attachments, see the [[Attachments Tutorial|Tutorial-Attachments]].
// SubSection: Specifying Directions
// You can use direction vectors to specify anchors for objects or to specify edges, faces, and
// corners of cubes. You can simply specify these direction vectors numerically, but another
// option is to use named constants for direction vectors. These constants define unit vectors
// for the six axis directions as shown below.
// Figure(3D,Big,VPD=6): Named constants for direction vectors. Some directions have more than one name.
// $fn=12;
// stroke([[0,0,0],RIGHT], endcap2="arrow2", width=.05);
// color("black")right(.05)up(.05)move(RIGHT)atext("RIGHT",size=.1,h=.01,anchor=LEFT,orient=FRONT);
// stroke([[0,0,0],LEFT], endcap2="arrow2", width=.05);
// color("black")left(.05)up(.05)move(LEFT)atext("LEFT",size=.1,h=.01,anchor=RIGHT,orient=FRONT);
// stroke([[0,0,0],FRONT], endcap2="arrow2", width=.05);
// color("black")
// left(.1){
// up(.12)move(FRONT)atext("FRONT",size=.1,h=.01,anchor=RIGHT,orient=FRONT);
// move(FRONT)atext("FWD",size=.1,h=.01,anchor=RIGHT,orient=FRONT);
// down(.12)move(FRONT)atext("FORWARD",size=.1,h=.01,anchor=RIGHT,orient=FRONT);
// }
// stroke([[0,0,0],BACK], endcap2="arrow2", width=.05);
// right(.05)
// color("black")move(BACK)atext("BACK",size=.1,h=.01,anchor=LEFT,orient=FRONT);
// stroke([[0,0,0],DOWN], endcap2="arrow2", width=.05);
// color("black")
// right(.1){
// up(.12)move(BOT)atext("DOWN",size=.1,h=.01,anchor=LEFT,orient=FRONT);
// move(BOT)atext("BOTTOM",size=.1,h=.01,anchor=LEFT,orient=FRONT);
// down(.12)move(BOT)atext("BOT",size=.1,h=.01,anchor=LEFT,orient=FRONT);
// }
// stroke([[0,0,0],TOP], endcap2="arrow2", width=.05);
// color("black")left(.05){
// up(.12)move(TOP)atext("TOP",size=.1,h=.01,anchor=RIGHT,orient=FRONT);
// move(TOP)atext("UP",size=.1,h=.01,anchor=RIGHT,orient=FRONT);
// }
// SubSection: Specifying Faces
// Modules operating on faces accept a list of faces to describe the faces to operate on. Each
// face is given by a vector that points to that face. Attachments of cuboid objects onto their faces also
// work by choosing an attachment face with a single vector in the same manner.
// Figure(3D,Big,NoScales,VPD=275): The six faces of the cube. Some have faces have more than one name.
// ydistribute(50) {
// xdistribute(35){
// _show_cube_faces([BACK], botlabel=["BACK"]);
// _show_cube_faces([UP],botlabel=["TOP","UP"]);
// _show_cube_faces([RIGHT],botlabel=["RIGHT"]);
// }
// xdistribute(35){
// _show_cube_faces([FRONT],toplabel=["FRONT","FWD", "FORWARD"]);
// _show_cube_faces([DOWN],toplabel=["BOTTOM","BOT","DOWN"]);
// _show_cube_faces([LEFT],toplabel=["LEFT"]);
// }
// }
// SubSection: Specifying Edges
// Modules operating on edges use two arguments to describe the edge set they will use: The `edges` argument
// is a list of edge set descriptors to include in the edge set, and the `except` argument is a list of
// edge set descriptors to remove from the edge set.
// The default value for `edges` is `"ALL"`, the set of all edges.
// The default value for `except` is the empty set, meaning no edges are removed.
// If either argument is just a single edge set
// descriptor it can be passed directly rather than in a singleton list.
// Each edge set descriptor must be one of:
// - A vector pointing towards an edge, indicating that single edge.
// - A vector pointing towards a face, indicating all edges surrounding that face.
// - A vector pointing towards a corner, indicating all edges touching that corner.
// - The string `"X"`, indicating all X axis aligned edges.
// - The string `"Y"`, indicating all Y axis aligned edges.
// - The string `"Z"`, indicating all Z axis aligned edges.
// - The string `"ALL"`, indicating all edges.
// - The string `"NONE"`, indicating no edges at all.
// - A 3x4 array, where each entry corresponds to one of the 12 edges and is set to 1 if that edge is included and 0 if the edge is not. The edge ordering is:
// ```
// [
// [Y-Z-, Y+Z-, Y-Z+, Y+Z+],
// [X-Z-, X+Z-, X-Z+, X+Z+],
// [X-Y-, X+Y-, X-Y+, X+Y+]
// ]
// ```
// You can specify edge descriptors directly by giving a vector, or you can use sums of the
// named direction vectors described above. Below we show all of the edge sets you can
// describe with sums of the direction vectors, and then we show some examples of combining
// edge set descriptors.
// Figure(3D,Big,VPD=300,NoScales): Vectors pointing toward an edge select that single edge
// ydistribute(50) {
// xdistribute(30) {
// _show_edges(edges=BOT+RIGHT);
// _show_edges(edges=BOT+BACK);
// _show_edges(edges=BOT+LEFT);
// _show_edges(edges=BOT+FRONT);
// }
// xdistribute(30) {
// _show_edges(edges=FWD+RIGHT);
// _show_edges(edges=BACK+RIGHT);
// _show_edges(edges=BACK+LEFT);
// _show_edges(edges=FWD+LEFT);
// }
// xdistribute(30) {
// _show_edges(edges=TOP+RIGHT);
// _show_edges(edges=TOP+BACK);
// _show_edges(edges=TOP+LEFT);
// _show_edges(edges=TOP+FRONT);
// }
// }
// Figure(3D,Med,VPD=205,NoScales): Vectors pointing toward a face select all edges surrounding that face.
// ydistribute(50) {
// xdistribute(30) {
// _show_edges(edges=LEFT);
// _show_edges(edges=FRONT);
// _show_edges(edges=RIGHT);
// }
// xdistribute(30) {
// _show_edges(edges=TOP);
// _show_edges(edges=BACK);
// _show_edges(edges=BOTTOM);
// }
// }
// Figure(3D,Big,VPD=300,NoScales): Vectors pointing toward a corner select all edges surrounding that corner.
// ydistribute(50) {
// xdistribute(30) {
// _show_edges(edges=FRONT+LEFT+TOP);
// _show_edges(edges=FRONT+RIGHT+TOP);
// _show_edges(edges=FRONT+LEFT+BOT);
// _show_edges(edges=FRONT+RIGHT+BOT);
// }
// xdistribute(30) {
// _show_edges(edges=TOP+LEFT+BACK);
// _show_edges(edges=TOP+RIGHT+BACK);
// _show_edges(edges=BOT+LEFT+BACK);
// _show_edges(edges=BOT+RIGHT+BACK);
// }
// }
// Figure(3D,Med,VPD=205,NoScales): Named Edge Sets
// ydistribute(50) {
// xdistribute(30) {
// _show_edges(edges="X");
// _show_edges(edges="Y");
// _show_edges(edges="Z");
// }
// xdistribute(30) {
// _show_edges(edges="ALL");
// _show_edges(edges="NONE");
// }
// }
// Figure(3D,Big,VPD=310,NoScales): Next are some examples showing how you can combine edge descriptors to obtain different edge sets. You can specify the top front edge with a numerical vector or by combining the named direction vectors. If you combine them as a list you get all the edges around the front or top faces. Adding `except` removes an edge.
// xdistribute(43){
// _show_edges(_edges([0,-1,1]),toplabel=["edges=[0,-1,1]"]);
// _show_edges(_edges(TOP+FRONT),toplabel=["edges=TOP+FRONT"]);
// _show_edges(_edges([TOP,FRONT]),toplabel=["edges=[TOP,FRONT]"]);
// _show_edges(_edges([TOP,FRONT],TOP+FRONT),toplabel=["edges=[TOP,FRONT]","except=TOP+FRONT"]);
// }
// Figure(3D,Big,VPD=310,NoScales): Using `except=BACK` removes the four edges surrounding the back face if they are present in the edge set. In the first example only one edge needs to be removed. In the second example we remove two of the Z-aligned edges. The third example removes all four back edges from the default edge set of all edges. You can explicitly give `edges="ALL"` but it is not necessary, since this is the default. In the fourth example, the edge set of Y-aligned edges contains no back edges, so the `except` parameter has no effect.
// xdistribute(43){
// _show_edges(_edges(BOT,BACK), toplabel=["edges=BOT","except=BACK"]);
// _show_edges(_edges("Z",BACK), toplabel=["edges=\"Z\"", "except=BACK"]);
// _show_edges(_edges("ALL",BACK), toplabel=["(edges=\"ALL\")", "except=BACK"]);
// _show_edges(_edges("Y",BACK), toplabel=["edges=\"Y\"","except=BACK"]);
// }
// Figure(3D,Big,NoScales,VPD=310): On the left `except` is a list to remove two edges. In the center we show a corner edge set defined by a numerical vector, and at the right we remove that same corner edge set with named direction vectors.
// xdistribute(52){
// _show_edges(_edges("ALL",[FRONT+RIGHT,FRONT+LEFT]),
// toplabel=["except=[FRONT+RIGHT,"," FRONT+LEFT]"]);
// _show_edges(_edges([1,-1,1]),toplabel=["edges=[1,-1,1]"]);
// _show_edges(_edges([TOP,BOT], TOP+RIGHT+FRONT),toplabel=["edges=[TOP,BOT]","except=TOP+RIGHT+FRONT"]);
// }
// SubSection: Specifying Corners
// Modules operating on corners use two arguments to describe the corner set they will use: The `corners` argument
// is a list of corner set descriptors to include in the corner set, and the `except` argument is a list of
// corner set descriptors to remove from the corner set.
// The default value for `corners` is `"ALL"`, the set of all corners.
// The default value for `except` is the empty set, meaning no corners are removed.
// If either argument is just a single corner set
// descriptor it can be passed directly rather than in a singleton list.
// Each corner set descriptor must be one of:
// - A vector pointing towards a corner, indicating that corner.
// - A vector pointing towards an edge indicating both corners at the ends of that edge.
// - A vector pointing towards a face, indicating all the corners of that face.
// - The string `"ALL"`, indicating all corners.
// - The string `"NONE"`, indicating no corners at all.
// - A length 8 vector where each entry corresponds to a corner and is 1 if the corner is included and 0 if it is excluded. The corner ordering is
// ```
// [X-Y-Z-, X+Y-Z-, X-Y+Z-, X+Y+Z-, X-Y-Z+, X+Y-Z+, X-Y+Z+, X+Y+Z+]
// ```
// You can specify corner descriptors directly by giving a vector, or you can use sums of the
// named direction vectors described above. Below we show all of the corner sets you can
// describe with sums of the direction vectors and then we show some examples of combining
// corner set descriptors.
// Figure(3D,Big,NoScales,VPD=300): Vectors pointing toward a corner select that corner.
// ydistribute(55) {
// xdistribute(35) {
// _show_corners(corners=FRONT+LEFT+TOP);
// _show_corners(corners=FRONT+RIGHT+TOP);
// _show_corners(corners=FRONT+LEFT+BOT);
// _show_corners(corners=FRONT+RIGHT+BOT);
// }
// xdistribute(35) {
// _show_corners(corners=TOP+LEFT+BACK);
// _show_corners(corners=TOP+RIGHT+BACK);
// _show_corners(corners=BOT+LEFT+BACK);
// _show_corners(corners=BOT+RIGHT+BACK);
// }
// }
// Figure(3D,Big,NoScales,VPD=340): Vectors pointing toward an edge select the corners and the ends of the edge.
// ydistribute(55) {
// xdistribute(35) {
// _show_corners(corners=BOT+RIGHT);
// _show_corners(corners=BOT+BACK);
// _show_corners(corners=BOT+LEFT);
// _show_corners(corners=BOT+FRONT);
// }
// xdistribute(35) {
// _show_corners(corners=FWD+RIGHT);
// _show_corners(corners=BACK+RIGHT);
// _show_corners(corners=BACK+LEFT);
// _show_corners(corners=FWD+LEFT);
// }
// xdistribute(35) {
// _show_corners(corners=TOP+RIGHT);
// _show_corners(corners=TOP+BACK);
// _show_corners(corners=TOP+LEFT);
// _show_corners(corners=TOP+FRONT);
// }
// }
// Figure(3D,Med,NoScales,VPD=225): Vectors pointing toward a face select the corners of the face.
// ydistribute(55) {
// xdistribute(35) {
// _show_corners(corners=LEFT);
// _show_corners(corners=FRONT);
// _show_corners(corners=RIGHT);
// }
// xdistribute(35) {
// _show_corners(corners=TOP);
// _show_corners(corners=BACK);
// _show_corners(corners=BOTTOM);
// }
// }
// Figure(3D,Med,NoScales,VPD=200): Corners by name
// xdistribute(35) {
// _show_corners(corners="ALL");
// _show_corners(corners="NONE");
// }
// Figure(3D,Big,NoScales,VPD=300): Next are some examples showing how you can combine corner descriptors to obtain different corner sets. You can specify corner sets numerically or by adding together named directions. The third example shows a list of two corner specifications, giving all the corners on the front face or the right face.
// xdistribute(52){
// _show_corners(_corners([1,-1,-1]),toplabel=["corners=[1,-1,-1]"]);
// _show_corners(_corners(BOT+RIGHT+FRONT),toplabel=["corners=BOT+RIGHT+FRONT"]);
// _show_corners(_corners([FRONT,RIGHT]), toplabel=["corners=[FRONT,RIGHT]"]);
// }
// Figure(3D,Big,NoScales,VPD=300): Corners for one edge, two edges, and all the edges except the two on one edge. Note that since the default is all edges, you only need to give the except argument in this case:
// xdistribute(52){
// _show_corners(_corners(FRONT+TOP), toplabel=["corners=FRONT+TOP"]);
// _show_corners(_corners([FRONT+TOP,BOT+BACK]), toplabel=["corners=[FRONT+TOP,"," BOT+BACK]"]);
// _show_corners(_corners("ALL",FRONT+TOP), toplabel=["(corners=\"ALL\")","except=FRONT+TOP"]);
// }
// Figure(3D,Med,NoScales,VPD=240): The first example shows a single corner removed from the top corners using a numerical vector. The second one shows removing a set of two corner descriptors from the implied set of all corners.
// xdistribute(58){
// _show_corners(_corners(TOP,[1,1,1]), toplabel=["corners=TOP","except=[1,1,1]"]);
// _show_corners(_corners("ALL",[FRONT+RIGHT+TOP,FRONT+LEFT+BOT]),
// toplabel=["except=[FRONT+RIGHT+TOP,"," FRONT+LEFT+BOT]"]);
// }
// Section: Attachment Positioning
@ -1972,5 +2233,422 @@ module frame_ref(s=15, opacity=1) {
}
////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////
///
/// Code after this is internal code for managing edge and corner sets and for displaying
/// edge and corners in the docs
///
module _edges_text3d(txt,size=3) {
if (is_list(txt)) {
for (i=idx(txt)) {
down((i-len(txt)/2+0.5)*size*1.5) {
_edges_text3d(txt[i], size=size);
}
}
} else {
xrot(90) color("#000")
linear_extrude(height=0.1) {
text(text=txt, size=size, halign="center", valign="center");
}
}
}
function _edges_vec_txt(x) = is_string(x)? str("\"", x, "\"") :
assert(is_string(x) || is_vector(x,3), str(x))
let(
lst = concat(
x.z>0? ["TOP"] : x.z<0? ["BOT"] : [],
x.y>0? ["BACK"] : x.y<0? ["FWD"] : [],
x.x>0? ["RIGHT"] : x.x<0? ["LEFT"] : []
),
out = [
for (i = idx(lst))
i>0? str("+",lst[i]) : lst[i]
]
) out;
function _edges_text(edges) =
is_string(edges) ? [str("\"",edges,"\"")] :
edges==EDGES_NONE ? ["EDGES_NONE"] :
edges==EDGES_ALL ? ["EDGES_ALL"] :
_is_edge_array(edges) ? [""] :
is_vector(edges,3) ? _edges_vec_txt(edges) :
is_list(edges) ? let(
lst = [for (x=edges) each _edges_text(x)],
out = [
for (i=idx(lst))
str(
(i==0? "[" : ""),
lst[i],
(i<len(lst)-1? "," : ""),
(i==len(lst)-1? "]" : "")
)
]
) out :
[""];
/// Internal Constant: EDGES_NONE
/// Topics: Edges
/// See Also: EDGES_ALL, edges()
/// Description:
/// The set of no edges.
/// Figure(3D):
/// _show_edges(edges="NONE");
EDGES_NONE = [[0,0,0,0], [0,0,0,0], [0,0,0,0]];
/// Internal Constant: EDGES_ALL
/// Topics: Edges
/// See Also: EDGES_NONE, edges()
/// Description:
/// The set of all edges.
/// Figure(3D):
/// _show_edges(edges="ALL");
EDGES_ALL = [[1,1,1,1], [1,1,1,1], [1,1,1,1]];
/// Internal Constant: EDGES_OFFSETS
/// Topics: Edges
/// See Also: EDGES_NONE, EDGES_ALL, edges()
/// Description:
/// The vectors pointing to the center of each edge of a unit sized cube.
/// Each item in an edge array will have a corresponding vector in this array.
EDGE_OFFSETS = [
[
[ 0,-1,-1],
[ 0, 1,-1],
[ 0,-1, 1],
[ 0, 1, 1]
], [
[-1, 0,-1],
[ 1, 0,-1],
[-1, 0, 1],
[ 1, 0, 1]
], [
[-1,-1, 0],
[ 1,-1, 0],
[-1, 1, 0],
[ 1, 1, 0]
]
];
/// Internal Function: _is_edge_array()
/// Topics: Edges, Type Checking
/// Usage:
/// bool = _is_edge_array(x);
/// Description:
/// Returns true if the given value has the form of an edge array.
/// Arguments:
/// x = The item to check the type of.
/// See Also: edges(), EDGES_NONE, EDGES_ALL
function _is_edge_array(x) = is_list(x) && is_vector(x[0]) && len(x)==3 && len(x[0])==4;
function _edge_set(v) =
_is_edge_array(v)? v : [
for (ax=[0:2]) [
for (b=[-1,1], a=[-1,1]) let(
v2=[[0,a,b],[a,0,b],[a,b,0]][ax]
) (
is_string(v)? (
v=="X"? (ax==0) : // Return all X axis aligned edges.
v=="Y"? (ax==1) : // Return all Y axis aligned edges.
v=="Z"? (ax==2) : // Return all Z axis aligned edges.
v=="ALL"? true : // Return all edges.
v=="NONE"? false : // Return no edges.
let(valid_values = ["X", "Y", "Z", "ALL", "NONE"])
assert(
in_list(v, valid_values),
str(v, " must be a vector, edge array, or one of ", valid_values)
) v
) :
let(nonz = sum(v_abs(v)))
nonz==2? (v==v2) : // Edge: return matching edge.
let(
matches = count_true([
for (i=[0:2]) v[i] && (v[i]==v2[i])
])
)
nonz==1? (matches==1) : // Face: return surrounding edges.
(matches==2) // Corner: return touching edges.
)? 1 : 0
]
];
/// Internal Function: _normalize_edges()
/// Topics: Edges
/// Usage:
/// edges = _normalize_edges(v);
/// Description:
/// Normalizes all values in an edge array to be `1`, if it was originally greater than `0`,
/// or `0`, if it was originally less than or equal to `0`.
/// See Also: edges(), EDGES_NONE, EDGES_ALL
function _normalize_edges(v) = [for (ax=v) [for (edge=ax) edge>0? 1 : 0]];
/// Internal Function: _edges()
/// Topics: Edges
/// Usage:
/// edgs = _edges(v);
/// edgs = _edges(v, except);
///
/// Description:
/// Takes a list of edge set descriptors, and returns a normalized edges array
/// that represents all those given edges.
/// Arguments:
/// v = The edge set to include.
/// except = The edge set to specifically exclude, even if they are in `v`.
///
/// See Also: EDGES_NONE, EDGES_ALL
///
function _edges(v, except=[]) =
v==[] ? EDGES_NONE :
(is_string(v) || is_vector(v) || _is_edge_array(v))? _edges([v], except=except) :
(is_string(except) || is_vector(except) || _is_edge_array(except))? _edges(v, except=[except]) :
except==[]? _normalize_edges(sum([for (x=v) _edge_set(x)])) :
_normalize_edges(
_normalize_edges(sum([for (x=v) _edge_set(x)])) -
sum([for (x=except) _edge_set(x)])
);
/// Internal Module: _show_edges()
/// Topics: Edges, Debugging
/// Usage:
/// _show_edges(edges, [size=], [text=], [txtsize=]);
/// Description:
/// Draws a semi-transparent cube with the given edges highlighted in red.
/// Arguments:
/// edges = The edges to highlight.
/// size = The scalar size of the cube.
/// text = The text to show on the front of the cube.
/// txtsize = The size of the text.
/// See Also: _edges(), EDGES_NONE, EDGES_ALL
/// Example:
/// _show_edges(size=30, edges=["X","Y"]);
module _show_edges(edges="ALL", size=20, text, txtsize=3,toplabel) {
edge_set = _edges(edges);
text = !is_undef(text) ? text : _edges_text(edges);
color("red") {
for (axis=[0:2], i=[0:3]) {
if (edge_set[axis][i] > 0) {
translate(EDGE_OFFSETS[axis][i]*size/2) {
if (axis==0) xcyl(h=size, d=2);
if (axis==1) ycyl(h=size, d=2);
if (axis==2) zcyl(h=size, d=2);
}
}
}
}
fwd(size/2) _edges_text3d(text, size=txtsize);
color("yellow",0.7) cuboid(size=size);
vpr = [55,0,25];
color("black")
if (is_def(toplabel))
for(h=idx(toplabel)) up(21+6*h)rot(vpr)atext(select(toplabel,-h-1),size=3.3,h=0.1,orient=UP,anchor=FRONT);
}
/// Internal Constant: CORNERS_NONE
/// Topics: Corners
/// Description:
/// The set of no corners.
/// Figure(3D):
/// _show_corners(corners="NONE");
/// See Also: CORNERS_ALL, corners()
CORNERS_NONE = [0,0,0,0,0,0,0,0]; // No corners.
/// Internal Constant: CORNERS_ALL
/// Topics: Corners
/// Description:
/// The set of all corners.
/// Figure(3D):
/// _show_corners(corners="ALL");
/// See Also: CORNERS_NONE, _corners()
CORNERS_ALL = [1,1,1,1,1,1,1,1];
/// Internal Constant: CORNER_OFFSETS
/// Topics: Corners
/// Description:
/// The vectors pointing to each corner of a unit sized cube.
/// Each item in a corner array will have a corresponding vector in this array.
/// See Also: CORNERS_NONE, CORNERS_ALL, _corners()
CORNER_OFFSETS = [
[-1,-1,-1], [ 1,-1,-1], [-1, 1,-1], [ 1, 1,-1],
[-1,-1, 1], [ 1,-1, 1], [-1, 1, 1], [ 1, 1, 1]
];
/// Internal Function: _is_corner_array()
/// Topics: Corners, Type Checking
/// Usage:
/// bool = _is_corner_array(x)
/// Description:
/// Returns true if the given value has the form of a corner array.
/// See Also: CORNERS_NONE, CORNERS_ALL, _corners()
function _is_corner_array(x) = is_vector(x) && len(x)==8 && all([for (xx=x) xx==1||xx==0]);
/// Internal Function: _normalize_corners()
/// Topics: Corners
/// Usage:
/// corns = _normalize_corners(v);
/// Description:
/// Normalizes all values in a corner array to be `1`, if it was originally greater than `0`,
/// or `0`, if it was originally less than or equal to `0`.
/// See Also: CORNERS_NONE, CORNERS_ALL, _corners()
function _normalize_corners(v) = [for (x=v) x>0? 1 : 0];
function _corner_set(v) =
_is_corner_array(v)? v : [
for (i=[0:7]) let(
v2 = CORNER_OFFSETS[i]
) (
is_string(v)? (
v=="ALL"? true : // Return all corners.
v=="NONE"? false : // Return no corners.
let(valid_values = ["ALL", "NONE"])
assert(
in_list(v, valid_values),
str(v, " must be a vector, corner array, or one of ", valid_values)
) v
) :
all([for (i=[0:2]) !v[i] || (v[i]==v2[i])])
)? 1 : 0
];
/// Function: _corners()
/// Topics: Corners
/// Usage:
/// corns = _corners(v);
/// corns = _corners(v, except);
/// Description:
/// Takes a list of corner set descriptors, and returns a normalized corners array
/// that represents all those given corners. If the `except` argument is given
/// a list of corner set descriptors, then all those corners will be removed
/// from the returned corners array. If either argument only has a single corner
/// set descriptor, you do not have to pass it in a list.
function _corners(v, except=[]) =
v==[] ? CORNERS_NONE :
(is_string(v) || is_vector(v) || _is_corner_array(v))? _corners([v], except=except) :
(is_string(except) || is_vector(except) || _is_corner_array(except))? _corners(v, except=[except]) :
except==[]? _normalize_corners(sum([for (x=v) _corner_set(x)])) :
let(
a = _normalize_corners(sum([for (x=v) _corner_set(x)])),
b = _normalize_corners(sum([for (x=except) _corner_set(x)]))
) _normalize_corners(a - b);
/// Internal Function: _corner_edges()
/// Topics: Corners
/// Description:
/// Returns [XCOUNT,YCOUNT,ZCOUNT] where each is the count of edges aligned with that
/// axis that are in the edge set and touch the given corner.
/// Arguments:
/// edges = Standard edges array.
/// v = Vector pointing to the corner to count edge intersections at.
/// See Also: CORNERS_NONE, CORNERS_ALL, _corners()
function _corner_edges(edges, v) =
let(u = (v+[1,1,1])/2) [edges[0][u.y+u.z*2], edges[1][u.x+u.z*2], edges[2][u.x+u.y*2]];
/// InternalFunction: _corner_edge_count()
/// Topics: Corners
/// Description:
/// Counts how many given edges intersect at a specific corner.
/// Arguments:
/// edges = Standard edges array.
/// v = Vector pointing to the corner to count edge intersections at.
/// See Also: CORNERS_NONE, CORNERS_ALL, _corners()
function _corner_edge_count(edges, v) =
let(u = (v+[1,1,1])/2) edges[0][u.y+u.z*2] + edges[1][u.x+u.z*2] + edges[2][u.x+u.y*2];
function _corners_text(corners) =
is_string(corners) ? [str("\"",corners,"\"")] :
corners==CORNERS_NONE ? ["CORNERS_NONE"] :
corners==CORNERS_ALL ? ["CORNERS_ALL"] :
_is_corner_array(corners) ? [""] :
is_vector(corners,3) ? _edges_vec_txt(corners) :
is_list(corners) ? let(
lst = [for (x=corners) each _corners_text(x)],
out = [
for (i=idx(lst))
str(
(i==0? "[" : ""),
lst[i],
(i<len(lst)-1? "," : ""),
(i==len(lst)-1? "]" : "")
)
]
) out :
[""];
/// Internal Module: _show_corners()
/// Topics: Corners, Debugging
/// Usage:
/// _show_corners(corners, [size=], [text=], [txtsize=]);
/// Description:
/// Draws a semi-transparent cube with the given corners highlighted in red.
/// Arguments:
/// corners = The corners to highlight.
/// size = The scalar size of the cube.
/// text = If given, overrides the text to be shown on the front of the cube.
/// txtsize = The size of the text.
/// See Also: CORNERS_NONE, CORNERS_ALL, corners()
/// Example:
/// _show_corners(corners=FWD+RIGHT, size=30);
module _show_corners(corners="ALL", size=20, text, txtsize=3,toplabel) {
corner_set = _corners(corners);
text = !is_undef(text) ? text : _corners_text(corners);
for (i=[0:7]) if (corner_set[i]>0)
translate(CORNER_OFFSETS[i]*size/2)
color("red") sphere(d=2, $fn=16);
fwd(size/2) _edges_text3d(text, size=txtsize);
color("yellow",0.7) cuboid(size=size);
vpr = [55,0,25];
color("black")
if (is_def(toplabel))
for(h=idx(toplabel)) up(21+6*h)rot(vpr)atext(select(toplabel,-h-1),size=3.3,h=.1,orient=UP,anchor=FRONT);
}
module _show_cube_faces(faces, size=20, toplabel,botlabel) {
color("red")
for(f=faces){
move(f*size/2) rot(from=UP,to=f)
cuboid([size,size,.1]);
}
vpr = [55,0,25];
color("black"){
if (is_def(toplabel))
for(h=idx(toplabel)) up(21+6*h)rot(vpr)atext(select(toplabel,-h-1),size=3.3,h=.1,orient=UP,anchor=FRONT);
if (is_def(botlabel))
for(h=idx(botlabel)) down(26+6*h)rot(vpr)atext(botlabel[h],size=3.3,h=.1,orient=UP,anchor=FRONT);
}
color("yellow",0.7) cuboid(size=size);
}
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap

2
comparisons.scad
View file

@ -350,7 +350,7 @@ function max_index(vals, all=false) =
// Description:
// Finds the first item in `list` that matches `val`, returning the index. Returns `undef` if there is no match.
// Arguments:
// val = The value to search for. If given a function literal of signature `function (x)`, uses that function to check list items. Returns true for a match.
// val = The value to search for.
// list = The list to search through.
// ---
// start = The index to start searching from. Default: 0

672
edges.scad
View file

@ -1,672 +0,0 @@
//////////////////////////////////////////////////////////////////////
// LibFile: edges.scad
// This file describes how to specify directions, face sets, edge sets and corner sets.
// Includes:
// include <BOSL2/std.scad>
//////////////////////////////////////////////////////////////////////
// Section: Specifying Directions
// You can use direction vectors to specify anchors for objects or to specify edges, faces, and
// corners of cubes. You can simply specify these direction vectors numerically, but another
// option is to use named constants for direction vectors. These constants define unit vectors
// for the six axis directions as shown below.
// Figure(3D,Big,VPD=6): Named constants for direction vectors. Some directions have more than one name.
// $fn=12;
// stroke([[0,0,0],RIGHT], endcap2="arrow2", width=.05);
// color("black")right(.05)up(.05)move(RIGHT)atext("RIGHT",size=.1,h=.01,anchor=LEFT,orient=FRONT);
// stroke([[0,0,0],LEFT], endcap2="arrow2", width=.05);
// color("black")left(.05)up(.05)move(LEFT)atext("LEFT",size=.1,h=.01,anchor=RIGHT,orient=FRONT);
// stroke([[0,0,0],FRONT], endcap2="arrow2", width=.05);
// color("black")
// left(.1){
// up(.12)move(FRONT)atext("FRONT",size=.1,h=.01,anchor=RIGHT,orient=FRONT);
// move(FRONT)atext("FWD",size=.1,h=.01,anchor=RIGHT,orient=FRONT);
// down(.12)move(FRONT)atext("FORWARD",size=.1,h=.01,anchor=RIGHT,orient=FRONT);
// }
// stroke([[0,0,0],BACK], endcap2="arrow2", width=.05);
// right(.05)
// color("black")move(BACK)atext("BACK",size=.1,h=.01,anchor=LEFT,orient=FRONT);
// stroke([[0,0,0],DOWN], endcap2="arrow2", width=.05);
// color("black")
// right(.1){
// up(.12)move(BOT)atext("DOWN",size=.1,h=.01,anchor=LEFT,orient=FRONT);
// move(BOT)atext("BOTTOM",size=.1,h=.01,anchor=LEFT,orient=FRONT);
// down(.12)move(BOT)atext("BOT",size=.1,h=.01,anchor=LEFT,orient=FRONT);
// }
// stroke([[0,0,0],TOP], endcap2="arrow2", width=.05);
// color("black")left(.05){
// up(.12)move(TOP)atext("TOP",size=.1,h=.01,anchor=RIGHT,orient=FRONT);
// move(TOP)atext("UP",size=.1,h=.01,anchor=RIGHT,orient=FRONT);
// }
// Section: Specifying Faces
// Modules operating on faces accept a list of faces to describe the faces to operate on. Each
// face is given by a vector that points to that face. Attachments of cuboid objects onto their faces also
// work by choosing an attachment face with a single vector in the same manner.
// Figure(3D,Big,NoScales,VPD=275): The six faces of the cube. Some have faces have more than one name.
// ydistribute(50) {
// xdistribute(35){
// _show_cube_faces([BACK], botlabel=["BACK"]);
// _show_cube_faces([UP],botlabel=["TOP","UP"]);
// _show_cube_faces([RIGHT],botlabel=["RIGHT"]);
// }
// xdistribute(35){
// _show_cube_faces([FRONT],toplabel=["FRONT","FWD", "FORWARD"]);
// _show_cube_faces([DOWN],toplabel=["BOTTOM","BOT","DOWN"]);
// _show_cube_faces([LEFT],toplabel=["LEFT"]);
// }
// }
// Section: Specifying Edges
// Modules operating on edges use two arguments to describe the edge set they will use: The `edges` argument
// is a list of edge set descriptors to include in the edge set, and the `except` argument is a list of
// edge set descriptors to remove from the edge set.
// The default value for `edges` is `"ALL"`, the set of all edges.
// The default value for `except` is the empty set, meaning no edges are removed.
// If either argument is just a single edge set
// descriptor it can be passed directly rather than in a singleton list.
// Each edge set descriptor must be one of:
// - A vector pointing towards an edge, indicating that single edge.
// - A vector pointing towards a face, indicating all edges surrounding that face.
// - A vector pointing towards a corner, indicating all edges touching that corner.
// - The string `"X"`, indicating all X axis aligned edges.
// - The string `"Y"`, indicating all Y axis aligned edges.
// - The string `"Z"`, indicating all Z axis aligned edges.
// - The string `"ALL"`, indicating all edges.
// - The string `"NONE"`, indicating no edges at all.
// - A 3x4 array, where each entry corresponds to one of the 12 edges and is set to 1 if that edge is included and 0 if the edge is not. The edge ordering is:
// ```
// [
// [Y-Z-, Y+Z-, Y-Z+, Y+Z+],
// [X-Z-, X+Z-, X-Z+, X+Z+],
// [X-Y-, X+Y-, X-Y+, X+Y+]
// ]
// ```
// You can specify edge descriptors directly by giving a vector, or you can use sums of the
// named direction vectors described above. Below we show all of the edge sets you can
// describe with sums of the direction vectors, and then we show some examples of combining
// edge set descriptors.
// Figure(3D,Big,VPD=300,NoScales): Vectors pointing toward an edge select that single edge
// ydistribute(50) {
// xdistribute(30) {
// _show_edges(edges=BOT+RIGHT);
// _show_edges(edges=BOT+BACK);
// _show_edges(edges=BOT+LEFT);
// _show_edges(edges=BOT+FRONT);
// }
// xdistribute(30) {
// _show_edges(edges=FWD+RIGHT);
// _show_edges(edges=BACK+RIGHT);
// _show_edges(edges=BACK+LEFT);
// _show_edges(edges=FWD+LEFT);
// }
// xdistribute(30) {
// _show_edges(edges=TOP+RIGHT);
// _show_edges(edges=TOP+BACK);
// _show_edges(edges=TOP+LEFT);
// _show_edges(edges=TOP+FRONT);
// }
// }
// Figure(3D,Med,VPD=205,NoScales): Vectors pointing toward a face select all edges surrounding that face.
// ydistribute(50) {
// xdistribute(30) {
// _show_edges(edges=LEFT);
// _show_edges(edges=FRONT);
// _show_edges(edges=RIGHT);
// }
// xdistribute(30) {
// _show_edges(edges=TOP);
// _show_edges(edges=BACK);
// _show_edges(edges=BOTTOM);
// }
// }
// Figure(3D,Big,VPD=300,NoScales): Vectors pointing toward a corner select all edges surrounding that corner.
// ydistribute(50) {
// xdistribute(30) {
// _show_edges(edges=FRONT+LEFT+TOP);
// _show_edges(edges=FRONT+RIGHT+TOP);
// _show_edges(edges=FRONT+LEFT+BOT);
// _show_edges(edges=FRONT+RIGHT+BOT);
// }
// xdistribute(30) {
// _show_edges(edges=TOP+LEFT+BACK);
// _show_edges(edges=TOP+RIGHT+BACK);
// _show_edges(edges=BOT+LEFT+BACK);
// _show_edges(edges=BOT+RIGHT+BACK);
// }
// }
// Figure(3D,Med,VPD=205,NoScales): Named Edge Sets
// ydistribute(50) {
// xdistribute(30) {
// _show_edges(edges="X");
// _show_edges(edges="Y");
// _show_edges(edges="Z");
// }
// xdistribute(30) {
// _show_edges(edges="ALL");
// _show_edges(edges="NONE");
// }
// }
// Figure(3D,Big,VPD=310,NoScales): Next are some examples showing how you can combine edge descriptors to obtain different edge sets. You can specify the top front edge with a numerical vector or by combining the named direction vectors. If you combine them as a list you get all the edges around the front or top faces. Adding `except` removes an edge.
// xdistribute(43){
// _show_edges(_edges([0,-1,1]),toplabel=["edges=[0,-1,1]"]);
// _show_edges(_edges(TOP+FRONT),toplabel=["edges=TOP+FRONT"]);
// _show_edges(_edges([TOP,FRONT]),toplabel=["edges=[TOP,FRONT]"]);
// _show_edges(_edges([TOP,FRONT],TOP+FRONT),toplabel=["edges=[TOP,FRONT]","except=TOP+FRONT"]);
// }
// Figure(3D,Big,VPD=310,NoScales): Using `except=BACK` removes the four edges surrounding the back face if they are present in the edge set. In the first example only one edge needs to be removed. In the second example we remove two of the Z-aligned edges. The third example removes all four back edges from the default edge set of all edges. You can explicitly give `edges="ALL"` but it is not necessary, since this is the default. In the fourth example, the edge set of Y-aligned edges contains no back edges, so the `except` parameter has no effect.
// xdistribute(43){
// _show_edges(_edges(BOT,BACK), toplabel=["edges=BOT","except=BACK"]);
// _show_edges(_edges("Z",BACK), toplabel=["edges=\"Z\"", "except=BACK"]);
// _show_edges(_edges("ALL",BACK), toplabel=["(edges=\"ALL\")", "except=BACK"]);
// _show_edges(_edges("Y",BACK), toplabel=["edges=\"Y\"","except=BACK"]);
// }
// Figure(3D,Big,NoScales,VPD=310): On the left `except` is a list to remove two edges. In the center we show a corner edge set defined by a numerical vector, and at the right we remove that same corner edge set with named direction vectors.
// xdistribute(52){
// _show_edges(_edges("ALL",[FRONT+RIGHT,FRONT+LEFT]),
// toplabel=["except=[FRONT+RIGHT,"," FRONT+LEFT]"]);
// _show_edges(_edges([1,-1,1]),toplabel=["edges=[1,-1,1]"]);
// _show_edges(_edges([TOP,BOT], TOP+RIGHT+FRONT),toplabel=["edges=[TOP,BOT]","except=TOP+RIGHT+FRONT"]);
// }
// Section: Specifying Corners
// Modules operating on corners use two arguments to describe the corner set they will use: The `corners` argument
// is a list of corner set descriptors to include in the corner set, and the `except` argument is a list of
// corner set descriptors to remove from the corner set.
// The default value for `corners` is `"ALL"`, the set of all corners.
// The default value for `except` is the empty set, meaning no corners are removed.
// If either argument is just a single corner set
// descriptor it can be passed directly rather than in a singleton list.
// Each corner set descriptor must be one of:
// - A vector pointing towards a corner, indicating that corner.
// - A vector pointing towards an edge indicating both corners at the ends of that edge.
// - A vector pointing towards a face, indicating all the corners of that face.
// - The string `"ALL"`, indicating all corners.
// - The string `"NONE"`, indicating no corners at all.
// - A length 8 vector where each entry corresponds to a corner and is 1 if the corner is included and 0 if it is excluded. The corner ordering is
// ```
// [X-Y-Z-, X+Y-Z-, X-Y+Z-, X+Y+Z-, X-Y-Z+, X+Y-Z+, X-Y+Z+, X+Y+Z+]
// ```
// You can specify corner descriptors directly by giving a vector, or you can use sums of the
// named direction vectors described above. Below we show all of the corner sets you can
// describe with sums of the direction vectors and then we show some examples of combining
// corner set descriptors.
// Figure(3D,Big,NoScales,VPD=300): Vectors pointing toward a corner select that corner.
// ydistribute(55) {
// xdistribute(35) {
// _show_corners(corners=FRONT+LEFT+TOP);
// _show_corners(corners=FRONT+RIGHT+TOP);
// _show_corners(corners=FRONT+LEFT+BOT);
// _show_corners(corners=FRONT+RIGHT+BOT);
// }
// xdistribute(35) {
// _show_corners(corners=TOP+LEFT+BACK);
// _show_corners(corners=TOP+RIGHT+BACK);
// _show_corners(corners=BOT+LEFT+BACK);
// _show_corners(corners=BOT+RIGHT+BACK);
// }
// }
// Figure(3D,Big,NoScales,VPD=340): Vectors pointing toward an edge select the corners and the ends of the edge.
// ydistribute(55) {
// xdistribute(35) {
// _show_corners(corners=BOT+RIGHT);
// _show_corners(corners=BOT+BACK);
// _show_corners(corners=BOT+LEFT);
// _show_corners(corners=BOT+FRONT);
// }
// xdistribute(35) {
// _show_corners(corners=FWD+RIGHT);
// _show_corners(corners=BACK+RIGHT);
// _show_corners(corners=BACK+LEFT);
// _show_corners(corners=FWD+LEFT);
// }
// xdistribute(35) {
// _show_corners(corners=TOP+RIGHT);
// _show_corners(corners=TOP+BACK);
// _show_corners(corners=TOP+LEFT);
// _show_corners(corners=TOP+FRONT);
// }
// }
// Figure(3D,Med,NoScales,VPD=225): Vectors pointing toward a face select the corners of the face.
// ydistribute(55) {
// xdistribute(35) {
// _show_corners(corners=LEFT);
// _show_corners(corners=FRONT);
// _show_corners(corners=RIGHT);
// }
// xdistribute(35) {
// _show_corners(corners=TOP);
// _show_corners(corners=BACK);
// _show_corners(corners=BOTTOM);
// }
// }
// Figure(3D,Med,NoScales,VPD=200): Corners by name
// xdistribute(35) {
// _show_corners(corners="ALL");
// _show_corners(corners="NONE");
// }
// Figure(3D,Big,NoScales,VPD=300): Next are some examples showing how you can combine corner descriptors to obtain different corner sets. You can specify corner sets numerically or by adding together named directions. The third example shows a list of two corner specifications, giving all the corners on the front face or the right face.
// xdistribute(52){
// _show_corners(_corners([1,-1,-1]),toplabel=["corners=[1,-1,-1]"]);
// _show_corners(_corners(BOT+RIGHT+FRONT),toplabel=["corners=BOT+RIGHT+FRONT"]);
// _show_corners(_corners([FRONT,RIGHT]), toplabel=["corners=[FRONT,RIGHT]"]);
// }
// Figure(3D,Big,NoScales,VPD=300): Corners for one edge, two edges, and all the edges except the two on one edge. Note that since the default is all edges, you only need to give the except argument in this case:
// xdistribute(52){
// _show_corners(_corners(FRONT+TOP), toplabel=["corners=FRONT+TOP"]);
// _show_corners(_corners([FRONT+TOP,BOT+BACK]), toplabel=["corners=[FRONT+TOP,"," BOT+BACK]"]);
// _show_corners(_corners("ALL",FRONT+TOP), toplabel=["(corners=\"ALL\")","except=FRONT+TOP"]);
// }
// Figure(3D,Med,NoScales,VPD=240): The first example shows a single corner removed from the top corners using a numerical vector. The second one shows removing a set of two corner descriptors from the implied set of all corners.
// xdistribute(58){
// _show_corners(_corners(TOP,[1,1,1]), toplabel=["corners=TOP","except=[1,1,1]"]);
// _show_corners(_corners("ALL",[FRONT+RIGHT+TOP,FRONT+LEFT+BOT]),
// toplabel=["except=[FRONT+RIGHT+TOP,"," FRONT+LEFT+BOT]"]);
// }
module _edges_text3d(txt,size=3) {
if (is_list(txt)) {
for (i=idx(txt)) {
down((i-len(txt)/2+0.5)*size*1.5) {
_edges_text3d(txt[i], size=size);
}
}
} else {
xrot(90) color("#000")
linear_extrude(height=0.1) {
text(text=txt, size=size, halign="center", valign="center");
}
}
}
function _edges_vec_txt(x) = is_string(x)? str("\"", x, "\"") :
assert(is_string(x) || is_vector(x,3), str(x))
let(
lst = concat(
x.z>0? ["TOP"] : x.z<0? ["BOT"] : [],
x.y>0? ["BACK"] : x.y<0? ["FWD"] : [],
x.x>0? ["RIGHT"] : x.x<0? ["LEFT"] : []
),
out = [
for (i = idx(lst))
i>0? str("+",lst[i]) : lst[i]
]
) out;
function _edges_text(edges) =
is_string(edges) ? [str("\"",edges,"\"")] :
edges==EDGES_NONE ? ["EDGES_NONE"] :
edges==EDGES_ALL ? ["EDGES_ALL"] :
_is_edge_array(edges) ? [""] :
is_vector(edges,3) ? _edges_vec_txt(edges) :
is_list(edges) ? let(
lst = [for (x=edges) each _edges_text(x)],
out = [
for (i=idx(lst))
str(
(i==0? "[" : ""),
lst[i],
(i<len(lst)-1? "," : ""),
(i==len(lst)-1? "]" : "")
)
]
) out :
[""];
/// Internal Constant: EDGES_NONE
/// Topics: Edges
/// See Also: EDGES_ALL, edges()
/// Description:
/// The set of no edges.
/// Figure(3D):
/// _show_edges(edges="NONE");
EDGES_NONE = [[0,0,0,0], [0,0,0,0], [0,0,0,0]];
/// Internal Constant: EDGES_ALL
/// Topics: Edges
/// See Also: EDGES_NONE, edges()
/// Description:
/// The set of all edges.
/// Figure(3D):
/// _show_edges(edges="ALL");
EDGES_ALL = [[1,1,1,1], [1,1,1,1], [1,1,1,1]];
/// Internal Constant: EDGES_OFFSETS
/// Topics: Edges
/// See Also: EDGES_NONE, EDGES_ALL, edges()
/// Description:
/// The vectors pointing to the center of each edge of a unit sized cube.
/// Each item in an edge array will have a corresponding vector in this array.
EDGE_OFFSETS = [
[
[ 0,-1,-1],
[ 0, 1,-1],
[ 0,-1, 1],
[ 0, 1, 1]
], [
[-1, 0,-1],
[ 1, 0,-1],
[-1, 0, 1],
[ 1, 0, 1]
], [
[-1,-1, 0],
[ 1,-1, 0],
[-1, 1, 0],
[ 1, 1, 0]
]
];
/// Internal Function: _is_edge_array()
/// Topics: Edges, Type Checking
/// Usage:
/// bool = _is_edge_array(x);
/// Description:
/// Returns true if the given value has the form of an edge array.
/// Arguments:
/// x = The item to check the type of.
/// See Also: edges(), EDGES_NONE, EDGES_ALL
function _is_edge_array(x) = is_list(x) && is_vector(x[0]) && len(x)==3 && len(x[0])==4;
function _edge_set(v) =
_is_edge_array(v)? v : [
for (ax=[0:2]) [
for (b=[-1,1], a=[-1,1]) let(
v2=[[0,a,b],[a,0,b],[a,b,0]][ax]
) (
is_string(v)? (
v=="X"? (ax==0) : // Return all X axis aligned edges.
v=="Y"? (ax==1) : // Return all Y axis aligned edges.
v=="Z"? (ax==2) : // Return all Z axis aligned edges.
v=="ALL"? true : // Return all edges.
v=="NONE"? false : // Return no edges.
let(valid_values = ["X", "Y", "Z", "ALL", "NONE"])
assert(
in_list(v, valid_values),
str(v, " must be a vector, edge array, or one of ", valid_values)
) v
) :
let(nonz = sum(v_abs(v)))
nonz==2? (v==v2) : // Edge: return matching edge.
let(
matches = count_true([
for (i=[0:2]) v[i] && (v[i]==v2[i])
])
)
nonz==1? (matches==1) : // Face: return surrounding edges.
(matches==2) // Corner: return touching edges.
)? 1 : 0
]
];
/// Internal Function: _normalize_edges()
/// Topics: Edges
/// Usage:
/// edges = _normalize_edges(v);
/// Description:
/// Normalizes all values in an edge array to be `1`, if it was originally greater than `0`,
/// or `0`, if it was originally less than or equal to `0`.
/// See Also: edges(), EDGES_NONE, EDGES_ALL
function _normalize_edges(v) = [for (ax=v) [for (edge=ax) edge>0? 1 : 0]];
/// Internal Function: _edges()
/// Topics: Edges
/// Usage:
/// edgs = _edges(v);
/// edgs = _edges(v, except);
///
/// Description:
/// Takes a list of edge set descriptors, and returns a normalized edges array
/// that represents all those given edges.
/// Arguments:
/// v = The edge set to include.
/// except = The edge set to specifically exclude, even if they are in `v`.
///
/// See Also: EDGES_NONE, EDGES_ALL
///
function _edges(v, except=[]) =
v==[] ? EDGES_NONE :
(is_string(v) || is_vector(v) || _is_edge_array(v))? _edges([v], except=except) :
(is_string(except) || is_vector(except) || _is_edge_array(except))? _edges(v, except=[except]) :
except==[]? _normalize_edges(sum([for (x=v) _edge_set(x)])) :
_normalize_edges(
_normalize_edges(sum([for (x=v) _edge_set(x)])) -
sum([for (x=except) _edge_set(x)])
);
/// Internal Module: _show_edges()
/// Topics: Edges, Debugging
/// Usage:
/// _show_edges(edges, [size=], [text=], [txtsize=]);
/// Description:
/// Draws a semi-transparent cube with the given edges highlighted in red.
/// Arguments:
/// edges = The edges to highlight.
/// size = The scalar size of the cube.
/// text = The text to show on the front of the cube.
/// txtsize = The size of the text.
/// See Also: _edges(), EDGES_NONE, EDGES_ALL
/// Example:
/// _show_edges(size=30, edges=["X","Y"]);
module _show_edges(edges="ALL", size=20, text, txtsize=3,toplabel) {
edge_set = _edges(edges);
text = !is_undef(text) ? text : _edges_text(edges);
color("red") {
for (axis=[0:2], i=[0:3]) {
if (edge_set[axis][i] > 0) {
translate(EDGE_OFFSETS[axis][i]*size/2) {
if (axis==0) xcyl(h=size, d=2);
if (axis==1) ycyl(h=size, d=2);
if (axis==2) zcyl(h=size, d=2);
}
}
}
}
fwd(size/2) _edges_text3d(text, size=txtsize);
color("yellow",0.7) cuboid(size=size);
vpr = [55,0,25];
color("black")
if (is_def(toplabel))
for(h=idx(toplabel)) up(21+6*h)rot(vpr)atext(select(toplabel,-h-1),size=3.3,h=0.1,orient=UP,anchor=FRONT);
}
/// Internal Constant: CORNERS_NONE
/// Topics: Corners
/// Description:
/// The set of no corners.
/// Figure(3D):
/// _show_corners(corners="NONE");
/// See Also: CORNERS_ALL, corners()
CORNERS_NONE = [0,0,0,0,0,0,0,0]; // No corners.
/// Internal Constant: CORNERS_ALL
/// Topics: Corners
/// Description:
/// The set of all corners.
/// Figure(3D):
/// _show_corners(corners="ALL");
/// See Also: CORNERS_NONE, _corners()
CORNERS_ALL = [1,1,1,1,1,1,1,1];
/// Internal Constant: CORNER_OFFSETS
/// Topics: Corners
/// Description:
/// The vectors pointing to each corner of a unit sized cube.
/// Each item in a corner array will have a corresponding vector in this array.
/// See Also: CORNERS_NONE, CORNERS_ALL, _corners()
CORNER_OFFSETS = [
[-1,-1,-1], [ 1,-1,-1], [-1, 1,-1], [ 1, 1,-1],
[-1,-1, 1], [ 1,-1, 1], [-1, 1, 1], [ 1, 1, 1]
];
/// Internal Function: _is_corner_array()
/// Topics: Corners, Type Checking
/// Usage:
/// bool = _is_corner_array(x)
/// Description:
/// Returns true if the given value has the form of a corner array.
/// See Also: CORNERS_NONE, CORNERS_ALL, _corners()
function _is_corner_array(x) = is_vector(x) && len(x)==8 && all([for (xx=x) xx==1||xx==0]);
/// Internal Function: _normalize_corners()
/// Topics: Corners
/// Usage:
/// corns = _normalize_corners(v);
/// Description:
/// Normalizes all values in a corner array to be `1`, if it was originally greater than `0`,
/// or `0`, if it was originally less than or equal to `0`.
/// See Also: CORNERS_NONE, CORNERS_ALL, _corners()
function _normalize_corners(v) = [for (x=v) x>0? 1 : 0];
function _corner_set(v) =
_is_corner_array(v)? v : [
for (i=[0:7]) let(
v2 = CORNER_OFFSETS[i]
) (
is_string(v)? (
v=="ALL"? true : // Return all corners.
v=="NONE"? false : // Return no corners.
let(valid_values = ["ALL", "NONE"])
assert(
in_list(v, valid_values),
str(v, " must be a vector, corner array, or one of ", valid_values)
) v
) :
all([for (i=[0:2]) !v[i] || (v[i]==v2[i])])
)? 1 : 0
];
/// Function: _corners()
/// Topics: Corners
/// Usage:
/// corns = _corners(v);
/// corns = _corners(v, except);
/// Description:
/// Takes a list of corner set descriptors, and returns a normalized corners array
/// that represents all those given corners. If the `except` argument is given
/// a list of corner set descriptors, then all those corners will be removed
/// from the returned corners array. If either argument only has a single corner
/// set descriptor, you do not have to pass it in a list.
function _corners(v, except=[]) =
v==[] ? CORNERS_NONE :
(is_string(v) || is_vector(v) || _is_corner_array(v))? _corners([v], except=except) :
(is_string(except) || is_vector(except) || _is_corner_array(except))? _corners(v, except=[except]) :
except==[]? _normalize_corners(sum([for (x=v) _corner_set(x)])) :
let(
a = _normalize_corners(sum([for (x=v) _corner_set(x)])),
b = _normalize_corners(sum([for (x=except) _corner_set(x)]))
) _normalize_corners(a - b);
/// Internal Function: _corner_edges()
/// Topics: Corners
/// Description:
/// Returns [XCOUNT,YCOUNT,ZCOUNT] where each is the count of edges aligned with that
/// axis that are in the edge set and touch the given corner.
/// Arguments:
/// edges = Standard edges array.
/// v = Vector pointing to the corner to count edge intersections at.
/// See Also: CORNERS_NONE, CORNERS_ALL, _corners()
function _corner_edges(edges, v) =
let(u = (v+[1,1,1])/2) [edges[0][u.y+u.z*2], edges[1][u.x+u.z*2], edges[2][u.x+u.y*2]];
/// InternalFunction: _corner_edge_count()
/// Topics: Corners
/// Description:
/// Counts how many given edges intersect at a specific corner.
/// Arguments:
/// edges = Standard edges array.
/// v = Vector pointing to the corner to count edge intersections at.
/// See Also: CORNERS_NONE, CORNERS_ALL, _corners()
function _corner_edge_count(edges, v) =
let(u = (v+[1,1,1])/2) edges[0][u.y+u.z*2] + edges[1][u.x+u.z*2] + edges[2][u.x+u.y*2];
function _corners_text(corners) =
is_string(corners) ? [str("\"",corners,"\"")] :
corners==CORNERS_NONE ? ["CORNERS_NONE"] :
corners==CORNERS_ALL ? ["CORNERS_ALL"] :
_is_corner_array(corners) ? [""] :
is_vector(corners,3) ? _edges_vec_txt(corners) :
is_list(corners) ? let(
lst = [for (x=corners) each _corners_text(x)],
out = [
for (i=idx(lst))
str(
(i==0? "[" : ""),
lst[i],
(i<len(lst)-1? "," : ""),
(i==len(lst)-1? "]" : "")
)
]
) out :
[""];
/// Internal Module: _show_corners()
/// Topics: Corners, Debugging
/// Usage:
/// _show_corners(corners, [size=], [text=], [txtsize=]);
/// Description:
/// Draws a semi-transparent cube with the given corners highlighted in red.
/// Arguments:
/// corners = The corners to highlight.
/// size = The scalar size of the cube.
/// text = If given, overrides the text to be shown on the front of the cube.
/// txtsize = The size of the text.
/// See Also: CORNERS_NONE, CORNERS_ALL, corners()
/// Example:
/// _show_corners(corners=FWD+RIGHT, size=30);
module _show_corners(corners="ALL", size=20, text, txtsize=3,toplabel) {
corner_set = _corners(corners);
text = !is_undef(text) ? text : _corners_text(corners);
for (i=[0:7]) if (corner_set[i]>0)
translate(CORNER_OFFSETS[i]*size/2)
color("red") sphere(d=2, $fn=16);
fwd(size/2) _edges_text3d(text, size=txtsize);
color("yellow",0.7) cuboid(size=size);
vpr = [55,0,25];
color("black")
if (is_def(toplabel))
for(h=idx(toplabel)) up(21+6*h)rot(vpr)atext(select(toplabel,-h-1),size=3.3,h=.1,orient=UP,anchor=FRONT);
}
module _show_cube_faces(faces, size=20, toplabel,botlabel) {
color("red")
for(f=faces){
move(f*size/2) rot(from=UP,to=f)
cuboid([size,size,.1]);
}
vpr = [55,0,25];
color("black"){
if (is_def(toplabel))
for(h=idx(toplabel)) up(21+6*h)rot(vpr)atext(select(toplabel,-h-1),size=3.3,h=.1,orient=UP,anchor=FRONT);
if (is_def(botlabel))
for(h=idx(botlabel)) down(26+6*h)rot(vpr)atext(botlabel[h],size=3.3,h=.1,orient=UP,anchor=FRONT);
}
color("yellow",0.7) cuboid(size=size);
}
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap

26
skin.scad
View file

@ -1257,55 +1257,55 @@ function _smooth(data,len,closed=false,angle=false) =
// long = resample the "long way" around the rotation, a boolean or list of booleans. Default: false
// turns = add extra turns. If a scalar adds the turns to every rotation, or give a vector. Default: 0
// closed = if true then the rotation list is treated as closed. Default: false
// Example: Resampling the arc from a compound rotation with translations thrown in.
// Example(3D): Resampling the arc from a compound rotation with translations thrown in.
// tran = rot_resample([ident(4), back(5)*up(4)*xrot(-10)*zrot(-20)*yrot(117,cp=[10,0,0])], N=25);
// sweep(circle(r=1,$fn=3), tran);
// Example: Applying a scale factor
// Example(3D): Applying a scale factor
// tran = rot_resample([ident(4), back(5)*up(4)*xrot(-10)*zrot(-20)*yrot(117,cp=[10,0,0])], N=25, scale=2);
// sweep(circle(r=1,$fn=3), tran);
// Example: Applying twist
// Example(3D): Applying twist
// tran = rot_resample([ident(4), back(5)*up(4)*xrot(-10)*zrot(-20)*yrot(117,cp=[10,0,0])], N=25, twist=60);
// sweep(circle(r=1,$fn=3), tran);
// Example: Going the long way
// Example(3D): Going the long way
// tran = rot_resample([ident(4), back(5)*up(4)*xrot(-10)*zrot(-20)*yrot(117,cp=[10,0,0])], N=25, long=true);
// sweep(circle(r=1,$fn=3), tran);
// Example: Getting transformations from turtle3d
// Example(3D): Getting transformations from turtle3d
// include<BOSL2/turtle3d.scad>
// tran=turtle3d(["arcsteps",1,"up", 10, "arczrot", 10,170],transforms=true);
// sweep(circle(r=1,$fn=3),rot_resample(tran, N=40));
// Example: If you specify a larger angle in turtle you need to use the long argument
// Example(3D): If you specify a larger angle in turtle you need to use the long argument
// include<BOSL2/turtle3d.scad>
// tran=turtle3d(["arcsteps",1,"up", 10, "arczrot", 10,270],transforms=true);
// sweep(circle(r=1,$fn=3),rot_resample(tran, N=40,long=true));
// Example: And if the angle is over 360 you need to add turns to get the right result. Note long is false when the remaining angle after subtracting full turns is below 180:
// Example(3D): And if the angle is over 360 you need to add turns to get the right result. Note long is false when the remaining angle after subtracting full turns is below 180:
// include<BOSL2/turtle3d.scad>
// tran=turtle3d(["arcsteps",1,"up", 10, "arczrot", 10,90+360],transforms=true);
// sweep(circle(r=1,$fn=3),rot_resample(tran, N=40,long=false,turns=1));
// Example: Here the remaining angle is 270, so long must be set to true
// Example(3D): Here the remaining angle is 270, so long must be set to true
// include<BOSL2/turtle3d.scad>
// tran=turtle3d(["arcsteps",1,"up", 10, "arczrot", 10,270+360],transforms=true);
// sweep(circle(r=1,$fn=3),rot_resample(tran, N=40,long=true,turns=1));
// Example: Note the visible line at the scale transition
// Example(3D): Note the visible line at the scale transition
// include<BOSL2/turtle3d.scad>
// tran = turtle3d(["arcsteps",1,"arcup", 10, 90, "arcdown", 10, 90], transforms=true);
// rtran = rot_resample(tran,200,scale=[1,6]);
// sweep(circle(1,$fn=32),rtran);
// Example: Observe how using a large smoothlen value eases that transition
// Example(3D): Observe how using a large smoothlen value eases that transition
// include<BOSL2/turtle3d.scad>
// tran = turtle3d(["arcsteps",1,"arcup", 10, 90, "arcdown", 10, 90], transforms=true);
// rtran = rot_resample(tran,200,scale=[1,6],smoothlen=17);
// sweep(circle(1,$fn=32),rtran);
// Example: A similar issues can arise with twist, where a "line" is visible at the transition
// Example(3D): A similar issues can arise with twist, where a "line" is visible at the transition
// include<BOSL2/turtle3d.scad>
// tran = turtle3d(["arcsteps", 1, "arcup", 10, 90, "move", 10], transforms=true,state=[1,-.5,0]);
// rtran = rot_resample(tran,100,twist=[0,60],smoothlen=1);
// sweep(subdivide_path(rect([3,3]),40),rtran);
// Example: Here's the smoothed twist transition
// Example(3D): Here's the smoothed twist transition
// include<BOSL2/turtle3d.scad>
// tran = turtle3d(["arcsteps", 1, "arcup", 10, 90, "move", 10], transforms=true,state=[1,-.5,0]);
// rtran = rot_resample(tran,100,twist=[0,60],smoothlen=17);
// sweep(subdivide_path(rect([3,3]),40),rtran);
// Example: toothed belt based on list-comprehension-demos example. This version has a smoothed twist transition. Try changing smoothlen to 1 to see the more abrupt transition that occurs without smoothing.
// Example(3D): toothed belt based on list-comprehension-demos example. This version has a smoothed twist transition. Try changing smoothlen to 1 to see the more abrupt transition that occurs without smoothing.
// include<BOSL2/turtle3d.scad>
// r_small = 19; // radius of small curve
// r_large = 46; // radius of large curve

1
std.scad
View file

@ -20,7 +20,6 @@ include <drawing.scad>
include <masks3d.scad>
include <masks2d.scad>
include <paths.scad>
include <edges.scad>
include <lists.scad>
include <comparisons.scad>
include <math.scad>

65
tests/test_geometry.scad
View file

@ -798,21 +798,56 @@ module test_reindex_polygon() {
module test_align_polygon() {
/*
pentagon = subdivide_path(pentagon(side=2),10);
hexagon = subdivide_path(hexagon(side=2.7),10);
aligned = [[2.7,0],[2.025,-1.16913429511],[1.35,-2.33826859022],
[-1.35,-2.33826859022],[-2.025,-1.16913429511],[-2.7,0],
[-2.025,1.16913429511],[-1.35,2.33826859022],[1.35,2.33826859022],
[2.025,1.16913429511]];
assert_approx(align_polygon(pentagon,hexagon,[0:10:359]), aligned);
aligned2 = [[1.37638192047,0],[1.37638192047,-1],[0.425325404176,-1.30901699437],
[-0.525731112119,-1.61803398875],[-1.11351636441,-0.809016994375],
[-1.7013016167,0],[-1.11351636441,0.809016994375],
[-0.525731112119,1.61803398875],[0.425325404176,1.30901699437],
[1.37638192047,1]];
assert_approx(align_polygon(hexagon,pentagon,[0:10:359]), aligned2);
*/
ellipse = yscale(3,circle(r=10, $fn=32));
tri = move([-50/3,-9],
subdivide_path([[0,0], [50,0], [0,27]], 32));
aligned = align_polygon(ellipse,tri, [0:5:180]);
assert_approx(aligned,
[[8.6933324366, 2.32937140592], [9.77174512453,
-1.69531953695], [10.8501578125, -5.72001047982],
[11.9285705004, -9.74470142269], [13.0069831883,
-13.7693923656], [9.28126928691, -14.7676943967],
[5.55555538551, -15.7659964278], [1.82984148411,
-16.7642984589], [-1.89587241729, -17.76260049],
[-5.62158631869, -18.7609025211], [-9.34730022009,
-19.7592045522], [-13.0730141215, -20.7575065833],
[-12.0623183481, -16.5048600039], [-11.0516225746,
-12.2522134245], [-10.0409268012, -7.99956684512],
[-9.03023102775, -3.74692026572], [-8.01953525431,
0.505726313678], [-7.00883948087, 4.75837289308],
[-5.99814370744, 9.01101947248], [-4.987447934,
13.2636660519], [-3.97675216056, 17.5163126313],
[-2.96605638713, 21.7689592107], [-1.95536061369,
26.0216057901], [-0.944664840253, 30.2742523695],
[0.0660309331843, 34.5268989489], [1.14444362111,
30.502208006], [2.22285630904, 26.4775170631],
[3.30126899697, 22.4528261203], [4.37968168489,
18.4281351774], [5.45809437282, 14.4034442345],
[6.53650706075, 10.3787532917], [7.61491974867,
6.35406234879]]);
ellipse2 = yscale(2,circle(r=10, $fn=32));
tri2 = subdivide_path([[0,0], [27,0], [-7,50]], 32);
T = [for(x=[-10:0], y=[-30:-15]) move([x,y])];
aligned2 = align_polygon(ellipse2,tri2, trans=T);
assert_approx(aligned2,
[[10.5384615385, -3.61538461538], [13.1538461538,
-7.46153846154], [15.7692307692, -11.3076923077],
[18.3846153846, -15.1538461538], [21, -19],
[17.1428571429, -19], [13.2857142857, -19],
[9.42857142857, -19], [5.57142857143, -19],
[1.71428571429, -19], [-2.14285714286, -19], [-6, -19],
[-6.58333333333, -14.8333333333], [-7.16666666667,
-10.6666666667], [-7.75, -6.5], [-8.33333333333,
-2.33333333333], [-8.91666666667, 1.83333333333], [-9.5,
6], [-10.0833333333, 10.1666666667], [-10.6666666667,
14.3333333333], [-11.25, 18.5], [-11.8333333333,
22.6666666667], [-12.4166666667, 26.8333333333], [-13,
31], [-10.3846153846, 27.1538461538], [-7.76923076923,
23.3076923077], [-5.15384615385, 19.4615384615],
[-2.53846153846, 15.6153846154], [0.0769230769231,
11.7692307692], [2.69230769231, 7.92307692308],
[5.30769230769, 4.07692307692], [7.92307692308,
0.230769230769]]);
}
*test_align_polygon();