joiners.scad

@@ -1220,155 +1220,4 @@ module rabbit_clip(type, length, width,  snap, thickness, depth, compression=0.1
 
 
 
-// Section: Splines
-
-// Module: hirth()
-// Usage:
-//   hirth(n, ir|id=, or|od=, tooth_angle, [cone_angle=], [chamfer=], [rounding=], [base=], [crop=], [anchor=], [spin=], [orient=]
-// Description:
-//   Create a Hirth face spline.  The Hirth face spline is a joint that locks together two cylinders using radially
-//   positioned triangular teeth on the ends of the cylinders.  If the joint is held together (e.g. with a screw) then
-//   the two parts will rotate (or not) together.  The two parts of the regular Hirth spline joint are identical.
-//   Each tooth is a triangle that grows larger with radius.  You specify a nominal tooth angle; the actual tooth
-//   angle will be slightly different.
-//   .
-//   You can also specify a cone_angle which raises or lowers the angle of the teeth.  When you do this you ened to
-//   mate splines with opposite angles such as -20 and +20.  The splines appear centered at the origin so that two
-//   splines will mate if their centers coincide.  Therefore `attach(CENTER,CENTER)` will produce two mating splines
-//   assuming that they are rotated correctly.  The bottom anchors will be at the bottom of the spline base.  The top
-//   anchors are at an arbitrary location and are not useful.  
-//   .
-//   By default the spline is created as a polygon with `2n` edges and the radius is the outer radius to the unchamfered corners.
-//   For large choices of `n` this will produce result that is close to circular.  For small `n` the result will be obviously polygonal.
-//   If you want a cylindrical result then set `crop=true`, which will intersect an oversized version of the joint with a suitable cylinder.
-//   Note that cropping makes the most difference when the tooth count is low.  
-//   .
-//   The teeth are chamfered proportionally based on the `chamfer` argument which specifies the fraction of the teeth tips
-//   to remove.  The teeth valleys are chamfered by half the specified value to ensure that there is room for the parts
-//   to mate.  The base is added based on the unchamfered dimensions of the joint, and the "teeth_bot" anchor is located
-//   based on the unchamfered dimensions.
-// Named Anchors:
-//   "teeth_bot" = center of the joint, aligned with the bottom of the (unchamfered) teeth, pointing DOWN.  
-//   "mate" = center of the joint, pointing UP, but with the correct spin so that the part will mate with a compatible parent joint.  
-// Arguments:
-//   n = number of teeth
-//   ir/id = inner radius or diameter
-//   or/od = outer radius or diameter
-//   tooth_angle = nominal tooth angle.  Default: 60
-//   cone_angle = raise or lower the angle of the teeth in the radial direction.  Default: 0
-//   chamfer = chamfer teeth by this fraction at tips and half this fraction at valleys.  Default: 0
-//   roudning = round the teeth by this fraction at the tips, and half this fraction at valleys.  Default: 0
-//   base = add base of this height to the bottom.  Default: 1
-//   crop = crop to a cylindrical shape.  Default: false
-//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
-//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
-//   orient = Vector to rotate top towards, after spin.  See [orient](attachments.scad#subsection-orient).  Default: `UP`
-// Example:  Basic uncropped hirth spline
-//   hirth(32,20,50);
-// Example: Raise cone angle
-//   hirth(32,20,50,cone_angle=30);
-// Example: Lower cone angle
-//   hirth(32,20,50,cone_angle=-30);
-// Example: Adding a large base
-//   hirth(20,20,50,base=20);
-// Example: Only 8 teeth, with chamfering
-//   hirth(8,20,50,tooth_angle=60,base=10,chamfer=.1);
-// Example: Only 8 teeth, cropped
-//   hirth(8,20,50,tooth_angle=60,base=10,chamfer=.1, crop=true);
-// Example: Only 8 teeth, with rounding
-//   hirth(8,20,50,tooth_angle=60,base=10,rounding=.1);
-// Example: Only 8 teeth, different tooth angle, cropping with $fn to crop cylinder aligned with teeth
-//   hirth(8,20,50,tooth_angle=90,base=10,rounding=.05,crop=true,$fn=48);
-// Example: Two identical parts joined together (with 1 unit offset to reveal the joint line).  With odd tooth count you can use the CENTER anchor for the child and the teeth line up correctly.  
-//   hirth(27,20,50, tooth_angle=60,base=2,chamfer=.05)
-//     up(1) attach(CENTER,CENTER)
-//       hirth(27,20,50, tooth_angle=60,base=2,chamfer=.05);
-// Example: Two conical parts joined together, with opposite cone angles for a correct joint.  With an even tooth count you must use the "mate" anchor for correct alignment of the teeth.
-//   hirth(26,20,50, tooth_angle=60,base=2,cone_angle=30,chamfer=.05)
-//     up(1) attach(CENTER,"mate")
-//       hirth(26,20,50, tooth_angle=60,base=2,cone_angle=-30, chamfer=.05);
-
-module hirth(n, ir, or, id, od, tooth_angle=60, cone_angle=0, chamfer, rounding, base=1, crop=false, orient,anchor,spin)
-{
-  ir = get_radius(r=ir,d=id);
-  or = get_radius(r=or,d=od);
-  dummy = assert(all_positive([ir]), "ir/id must be a positive value")
-          assert(all_positive([or]), "or/od must be a positive value")
-          assert(is_int(n) && n>1, "n must be an integer larger than 1")
-          assert(ir<or, "inside radius (ir/id) must be smaller than outside radius (or/od)")
-          assert(all_positive([tooth_angle]) && tooth_angle<360*(n-1)/2/n, str("tooth angle must be between 0 and ",360*(n-1)/2/n," for spline with ",n," teeth."))
-          assert(num_defined([chamfer,rounding]) <=1, "Cannot define both chamfer and rounding")
-          assert(is_undef(chamfer) || all_nonnegative([chamfer]) && chamfer<1/2, "chamfer must be a non-negative value smaller than 1/2")
-          assert(is_undef(rounding) || all_nonnegative([rounding]) && rounding<1/2, "rounding must be a non-negative value smaller than 1/2")
-          assert(all_positive([base]), "base must be a positive value") ;
-  tooth_height = sin(180/n) / tan(tooth_angle/2);     // Normalized tooth height
-  conic_ht = tan(cone_angle);                         // Normalized height change corresponding to the cone angle
-  ridge_angle = atan(tooth_height/2 + conic_ht);
-  valley_angle = atan(-tooth_height/2 + conic_ht);
-  angle = 180/n;    // Half the angle occupied by each tooth going around the circle
-  
-  factor = crop ? 3 : 1;   // Make it oversized when crop is true
-
-  profile = is_undef(rounding) || rounding==0 ?
-                let(
-                     chamfer=default(chamfer,0),
-                     vchamf = chamfer*(ridge_angle-valley_angle),
-                     pts = [
-                             [-angle*(1-chamfer/2), valley_angle+vchamf/2],
-                             [-angle*chamfer, ridge_angle-vchamf]
-                           ]
-                )
-                concat(pts, reverse(xflip(pts)))
-          : let( 
-                vround=rounding*(ridge_angle-valley_angle),
-                profpts = [
-                             [  -angle, valley_angle+vround/2],
-                             [  -angle*(1-rounding/2), valley_angle+vround/2],
-                             [  -angle*rounding, ridge_angle-vround],
-                             [  0, ridge_angle-vround]
-                          ],
-                // Using computed values for the joints lead to round-off error issues
-                joints = [(profpts[1]-profpts[0]).x, (profpts[3]-profpts[2]).x],
-                segs = max(16,segs(or*rounding)),
-                rpts = round_corners(profpts, joint=joints,closed=false,$fn=segs)
-            )
-            concat(rpts, reverse(xflip(select(rpts,1,-2))));
-
-
-  
-  // project spherical coordinate point onto cylinder of radius r
-  cyl_proj = function (r,theta_phi) 
-     [for(pt=theta_phi)
-        let(xyz = spherical_to_xyz(1,pt[0], 90-pt[1]))
-        r * xyz / norm(point2d(xyz))];
-
-  bottom = min([tan(valley_angle)*ir,tan(valley_angle)*or])-base;
-  safebottom = min([tan(valley_angle)*ir/factor,tan(valley_angle)*or*factor])-base-(crop?1:0);
-
-  topinner = [for(ang=lerpn(0,360,n,endpoint=false))
-                                  each zrot(ang,cyl_proj(ir/factor,profile))];
-  topouter = [for(ang=lerpn(0,360,n,endpoint=false))
-                                  each zrot(ang,cyl_proj(factor*or,profile))];
-  botinner = [for(val=topinner) [val.x,val.y,safebottom]];
-  botouter = [for(val=topouter) [val.x,val.y,safebottom]];  
-  vert = [topouter, topinner, botinner, botouter];
-
-  anchors = [
-             named_anchor("teeth_bot", [0,0,bottom], DOWN),
-             named_anchor("mate", [0,0,0], UP, spin=n%2==0 ? 180/n : 0)
-            ];
-  
-  attachable(anchor=anchor,spin=spin,orient=orient, r=or, h=-2*bottom,anchors=anchors){
-      intersection(){
-        vnf_polyhedron(vnf_vertex_array(vert, reverse=true, col_wrap=true, row_wrap=true),convexity=min(10,n));
-        if (crop)
-           zmove(bottom)tube(or=or,ir=ir,height=4*or,anchor=BOT);
-      }
-    children();
-  }
-}
-
-
-
-
 // vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap

nurbs.scad

@@ -1,5 +1,5 @@
 /////////////////////////////////////////////////////////////////////
-// LibFile: nurbs.scad
+// LibFile: beziers.scad
 //   B-Splines and Non-uniform Rational B-Splines (NURBS) are a way to represent smooth curves and smoothly curving
 //   surfaces with a set of control points.  The curve or surface is defined by
 //   the control points and a set of "knot" points.  The NURBS can be "clamped" in which case the curve passes through
@@ -104,7 +104,7 @@ include<BOSL2/beziers.scad>
 // Example(2D,NoAxes): Same control points, degree 4, closed
 //   pts = [[5,0],[0,20],[33,43],[37,88],[60,62],[44,22],[77,44],[79,22],[44,3],[22,7]];
 //   debug_nurbs(pts,4,type="closed");
-// Example(2D,Med,NoAxes): Adding weights
+// Example(2D,NoAxes): Adding weights
 //   pts = [[5,0],[0,20],[33,43],[37,88],[60,62],[44,22],[77,44],[79,22],[44,3],[22,7]];
 //   weights = [1,1,1,3,1,1,3,1,1,1];
 //   debug_nurbs(pts,4,type="clamped",weights=weights);
@@ -145,7 +145,7 @@ include<BOSL2/beziers.scad>
 //   pts = [[5,0],[0,20],[33,43],[37,88],[60,62],[44,22],[77,44],[79,22],[44,3],[22,7]];
 //   knots = [0,1,3,13,13,13,19,21,27,28,33];
 //   debug_nurbs(pts,5,knots=knots,type="closed");
-// Example(2D,Med,NoAxes): Closed quintic spline with explicit knots and weights
+// Example(2D,NoAxes): Closed quintic spline with explicit knots and weights
 //   pts = [[5,0],[0,20],[33,43],[37,88],[60,62],[44,22],[77,44],[79,22],[44,3],[22,7]];
 //   weights = [1,2,3,4,5,6,7,6,5,4];
 //   knots = [0,1,3,13,13,13,19,21,27,28,33];
@@ -436,7 +436,7 @@ function is_nurbs_patch(x) =
 //   knots = a single list of pair of lists giving the knot vector in each of the two directions.  Default: uniform
 //   weights = a single list or pair of lists giving the weight at each control point in the patch.  Default: all 1
 //   type = a single string or pair of strings giving the NURBS type, where each entry is one of "clamped", "open" or "closed".  Default: "clamped"
-// Example(3D,NoScale): Computing points on a patch using ranges
+// Example(NoScale): Computing points on a patch using ranges
 //   patch = [
 //       [[-50, 50,  0], [-16, 50,  20], [ 16, 50,  20], [50, 50,  0]],
 //       [[-50, 16, 20], [-16, 16,  40], [ 16, 16,  40], [50, 16, 20]],
@@ -445,7 +445,7 @@ function is_nurbs_patch(x) =
 //   ];
 //   pts = nurbs_patch_points(patch, 3, u=[0:.1:1], v=[0:.3:1]);
 //   move_copies(flatten(pts)) sphere(r=2,$fn=16);
-// Example(3D,NoScale): Computing points using splinesteps
+// Example(NoScale): Computing points using splinesteps
 //   patch = [
 //       [[-50, 50,  0], [-16, 50,  20], [ 16, 50,  20], [50, 50,  0]],
 //       [[-50, 16, 20], [-16, 16,  40], [ 16, 16,  40], [50, 16, 20]],
@@ -515,7 +515,7 @@ function nurbs_patch_points(patch, degree, splinesteps, u, v, weights, type=["cl
 //   weights = a single list or pair of lists giving the weight at each control point in the.  Default: all 1
 //   type = a single string or pair of strings giving the NURBS type, where each entry is one of "clamped", "open" or "closed".  Default: "clamped"
 //   style = {{vnf_vertex_array ()}} style to use for triangulating the surface.  Default: "default"
-// Example(3D): Quadratic B-spline surface
+// Example: Quadratic B-spline surface
 //   patch = [
 //       [[-50, 50,  0], [-16, 50,  20], [ 16, 50,  20], [50, 50,  0]],
 //       [[-50, 16, 20], [-16, 16,  40], [ 16, 16,  40], [50, 16, 20]],
@@ -524,7 +524,7 @@ function nurbs_patch_points(patch, degree, splinesteps, u, v, weights, type=["cl
 //   ];
 //   vnf = nurbs_vnf(patch, 2);
 //   vnf_polyhedron(vnf);
-// Example(3D): Cubic B-spline surface
+// Example: Cubic B-spline surface
 //   patch = [
 //       [[-50, 50,  0], [-16, 50,  20], [ 16, 50,  20], [50, 50,  0]],
 //       [[-50, 16, 20], [-16, 16,  40], [ 16, 16,  40], [50, 16, 20]],
@@ -533,7 +533,7 @@ function nurbs_patch_points(patch, degree, splinesteps, u, v, weights, type=["cl
 //   ];
 //   vnf = nurbs_vnf(patch, 3);
 //   vnf_polyhedron(vnf); 
-// Example(3D): Cubic B-spline surface, closed in one direction
+// Example: Cubic B-spline surface, closed in one direction
 //   patch = [
 //       [[-50, 50,  0], [-16, 50,  20], [ 16, 50,  20], [50, 50,  0]],
 //       [[-50, 16, 20], [-16, 16,  40], [ 16, 16,  40], [50, 16, 20]],
@@ -542,7 +542,7 @@ function nurbs_patch_points(patch, degree, splinesteps, u, v, weights, type=["cl
 //   ];
 //   vnf = nurbs_vnf(patch, 3, type=["closed","clamped"]);
 //   vnf_polyhedron(vnf); 
-// Example(3D): B-spline surface cubic in one direction, quadratic in the other
+// Example: B-spline surface cubic in one direction, quadratic in the other
 //   patch = [
 //       [[-50, 50,  0], [-16, 50,  20], [ 16, 50,  20], [50, 50,  0]],
 //       [[-50, 16, 20], [-16, 16,  40], [ 16, 16,  40], [50, 16, 20]],
@@ -551,7 +551,7 @@ function nurbs_patch_points(patch, degree, splinesteps, u, v, weights, type=["cl
 //   ];
 //   vnf = nurbs_vnf(patch, [3,2],type=["closed","clamped"]);
 //   vnf_polyhedron(vnf); 
-// Example(3D): The sphere can be represented using NURBS
+// Example: The sphere can be represented using NURBS
 //   patch = [
 //             [[0,0,1], [0,0,1], [0,0,1],  [0,0,1],  [0,0,1],    [0,0,1],  [0,0,1]],
 //             [[2,0,1], [2,4,1], [-2,4,1], [-2,0,1], [-2,-4,1],  [2,-4,1], [2,0,1]],