Merge pull request #836 from revarbat/revarbat_dev

Fixed interior_fillet(). Refactored circle_* functions.

drawing.scad

@@ -710,7 +710,7 @@ function arc(n, r, angle, d, cp, points, corner, width, thickness, start, wedge=
         let( r = get_radius(r=r, d=d) )
         assert(is_finite(r) && r>0, "Must specify r= or d= when corner= is given.")
         let(
-            ci = circle_2tangents(corner[0], corner[1], corner[2], r=r, tangents=true),
+            ci = circle_2tangents(r, corner[0], corner[1], corner[2], tangents=true),
             cp = ci[0], nrm = ci[1], tp1 = ci[2], tp2 = ci[3],
             dir = det2([corner[1]-corner[0],corner[2]-corner[1]]) > 0,
             corner = dir? [tp1,tp2] : [tp2,tp1],

geometry.scad

@@ -861,14 +861,14 @@ function _is_point_above_plane(plane, point) =
 
 // Function: circle_line_intersection()
 // Usage:
-//   isect = circle_line_intersection(c, r|d=, line, [bounded], [eps=]);
+//   pts = circle_line_intersection(r|d=, cp, line, [bounded], [eps=]);
 // Topics: Geometry, Circles, Lines, Intersection
 // Description:
-//   Find intersection points between a 2d circle and a line, ray or segment specified by two points.
+//   Find intersection points between a 2D circle and a line, ray or segment specified by two points.
 //   By default the line is unbounded.  Returns the list of zero or more intersection points.
 // Arguments:
-//   c = Center of circle
 //   r = Radius of circle
+//   cp = Center of circle
 //   line = Two points defining the line
 //   bounded = False for unbounded line, true for a segment, or a vector [false,true] or [true,false] to specify a ray with the first or second end unbounded.  Default: false
 //   ---
@@ -879,14 +879,14 @@ function _is_point_above_plane(plane, point) =
 //   cp = [1,2]; r = 10;
 //   translate(cp) circle(r=r);
 //   color("black") stroke(line, endcaps="arrow2", width=0.5);
-//   isects = circle_line_intersection(c=cp, r=r, line=line);
+//   isects = circle_line_intersection(r=r, cp=cp, line=line);
 //   color("red") move_copies(isects) circle(d=1);
 // Example(2D): Tangent intersection returns one point.
 //   line = [[-10,12], [10,12]];
 //   cp = [1,2]; r = 10;
 //   translate(cp) circle(r=r);
 //   color("black") stroke(line, endcaps="arrow2", width=0.5);
-//   isects = circle_line_intersection(c=cp, r=r, line=line);
+//   isects = circle_line_intersection(r=r, cp=cp, line=line);
 //   color("#f44") move_copies(isects) circle(d=1);
 // Example(2D): A bounded ray might only intersect in one direction.
 //   line = [[-5,2], [5,7]];
@@ -895,30 +895,30 @@ function _is_point_above_plane(plane, point) =
 //   translate(cp) circle(r=r);
 //   color("gray") dashed_stroke(extended, width=0.2);
 //   color("black") stroke(line, endcap2="arrow2", width=0.5);
-//   isects = circle_line_intersection(c=cp, r=r, line=line, bounded=[true,false]);
+//   isects = circle_line_intersection(r=r, cp=cp, line=line, bounded=[true,false]);
 //   color("#f44") move_copies(isects) circle(d=1);
 // Example(2D): If they don't intersect at all, then an empty list is returned.
 //   line = [[-12,12], [12,8]];
 //   cp = [-5,-2]; r = 10;
 //   translate(cp) circle(r=r);
 //   color("black") stroke(line, endcaps="arrow2", width=0.5);
-//   isects = circle_line_intersection(c=cp, r=r, line=line);
+//   isects = circle_line_intersection(r=r, cp=cp, line=line);
 //   color("#f44") move_copies(isects) circle(d=1);
-function circle_line_intersection(c,r,line,bounded=false,d,eps=EPSILON) =
+function circle_line_intersection(r, cp, line, bounded=false, d, eps=EPSILON) =
   assert(_valid_line(line,2), "Invalid 2d line.")
-  assert(is_vector(c,2), "Circle center must be a 2-vector")
-  _circle_or_sphere_line_intersection(c,r,line,bounded,d,eps);
+  assert(is_vector(cp,2), "Circle center must be a 2-vector")
+  _circle_or_sphere_line_intersection(r, cp, line, bounded, d, eps);
 
 
 
-function _circle_or_sphere_line_intersection(c,r,line,bounded=false,d,eps=EPSILON) =
+function _circle_or_sphere_line_intersection(r, cp, line, bounded=false, d, eps=EPSILON) =
   let(r=get_radius(r=r,d=d,dflt=undef))
   assert(is_num(r) && r>0, "Radius must be positive")
   assert(is_bool(bounded) || is_bool_list(bounded,2), "Invalid bound condition")
   let(
       bounded = force_list(bounded,2),
-      closest = line_closest_point(line,c),
-      d = norm(closest-c)
+      closest = line_closest_point(line,cp),
+      d = norm(closest-cp)
   )
   d > r ? [] :
   let(
@@ -934,73 +934,74 @@ function _circle_or_sphere_line_intersection(c,r,line,bounded=false,d,eps=EPSILO
 
 // Function: circle_circle_intersection()
 // Usage:
-//   pts = circle_circle_tangents(c1, r1|d1=, c2, r2|d2=, [eps]);
+//   pts = circle_circle_intersection(r1|d1=, cp1, r2|d2=, cp2, [eps]);
 // Topics: Geometry, Circles
 // Description:
 //   Compute the intersection points of two circles.  Returns a list of the intersection points, which
 //   will contain two points in the general case, one point for tangent circles, or will be empty
 //   if the circles do not intersect.
 // Arguments:
-//   c1 = Center of the first circle.
 //   r1 = Radius of the first circle.
-//   c2 = Center of the second circle.
+//   cp1 = Centerpoint of the first circle.
 //   r2 = Radius of the second circle.
+//   cp2 = Centerpoint of the second circle.
 //   eps = Tolerance for detecting tangent circles.  Default: EPSILON
 //   ---
 //   d1 = Diameter of the first circle.
 //   d2 = Diameter of the second circle.
 // Example(2D,NoAxes): Circles intersect in two points. 
 //   $fn=32;
-//   c1 = [4,4];  r1 = 3;
-//   c2 = [7,7]; r2 = 2;
-//   pts = circle_circle_intersection(c1,r1,c2,r2);
-//   move(c1) stroke(circle(r=r1), width=0.2, closed=true);
-//   move(c2) stroke(circle(r=r2), width=0.2, closed=true);
-//   color("red")move_copies(pts) circle(r=.3);
+//   cp1 = [4,4];  r1 = 3;
+//   cp2 = [7,7];  r2 = 2;
+//   pts = circle_circle_intersection(r1, cp1, r2, cp2);
+//   move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
+//   move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
+//   color("red") move_copies(pts) circle(r=.3);
 // Example(2D,NoAxes): Circles are tangent, so one intersection point:
 //   $fn=32;
-//   c1 = [4,4];  r1 = 4;
-//   c2 = [4,10]; r2 = 2;
-//   pts = circle_circle_intersection(c1,r1,c2,r2);
-//   move(c1) stroke(circle(r=r1), width=0.2, closed=true);
-//   move(c2) stroke(circle(r=r2), width=0.2, closed=true);
-//   color("red")move_copies(pts) circle(r=.3);
+//   cp1 = [4,4];  r1 = 4;
+//   cp2 = [4,10]; r2 = 2;
+//   pts = circle_circle_intersection(r1, cp1, r2, cp2);
+//   move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
+//   move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
+//   color("red") move_copies(pts) circle(r=.3);
 // Example(2D,NoAxes): Another tangent example:
 //   $fn=32;
-//   c1 = [4,4];  r1 = 4;
-//   c2 = [5,5];  r2 = 4-sqrt(2);
-//   pts = circle_circle_intersection(c1,r1,c2,r2);
-//   move(c1) stroke(circle(r=r1), width=0.2, closed=true);
-//   move(c2) stroke(circle(r=r2), width=0.2, closed=true);
-//   color("red")move_copies(pts) circle(r=.3);
+//   cp1 = [4,4];  r1 = 4;
+//   cp2 = [5,5];  r2 = 4-sqrt(2);
+//   pts = circle_circle_intersection(r1, cp1, r2, cp2);
+//   move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
+//   move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
+//   color("red") move_copies(pts) circle(r=.3);
 // Example(2D,NoAxes): Circles do not intersect.  Returns empty list. 
 //   $fn=32;
-//   c1 = [3,4];  r1 = 2;
-//   c2 = [7,10]; r2 = 3;
-//   pts = circle_circle_intersection(c1,r1,c2,r2);
-//   move(c1) stroke(circle(r=r1), width=0.2, closed=true);
-//   move(c2) stroke(circle(r=r2), width=0.2, closed=true);
-//   color("red")move_copies(pts) circle(r=.2);     // pts is []
-function circle_circle_intersection(c1,r1,c2,r2,eps=EPSILON,d1,d2) =
-    assert( is_path([c1,c2],dim=2), "Invalid center point(s)." )
+//   cp1 = [3,4];  r1 = 2;
+//   cp2 = [7,10]; r2 = 3;
+//   pts = circle_circle_intersection(r1, cp1, r2, cp2);
+//   move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
+//   move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
+//   color("red") move_copies(pts) circle(r=.3);
+function circle_circle_intersection(r1, cp1, r2, cp2, eps=EPSILON, d1, d2) =
+    assert( is_path([cp1,cp2],dim=2), "Invalid center point(s)." )
     let(
         r1 = get_radius(r1=r1,d1=d1),
         r2 = get_radius(r1=r2,d1=d2),
-        d = norm(c2-c1),
-        a = (c2-c1)/d,
+        d = norm(cp2-cp1),
+        a = (cp2-cp1)/d,
         b = [-a.y,a.x],
         L = (r1^2-r2^2+d^2)/2/d,
         hsqr = r1^2-L^2
     )
-    approx(hsqr,0,eps) ? [L*a+c1]
+    approx(hsqr,0,eps) ? [L*a+cp1]
   : hsqr<0 ? []
   : let(h=sqrt(hsqr))
-    [L*a+h*b+c1, L*a-h*b+c1];
+    [L*a+h*b+cp1, L*a-h*b+cp1];
 
 
 // Function: circle_2tangents()
 // Usage:
-//   circ = circle_2tangents(pt1, pt2, pt3, r|d=, [tangents=]);
+//   circ = circle_2tangents(r|d=, pt1, pt2, pt3, [tangents=]);
+//   circ = circle_2tangents(r|d=, [PT1, PT2, PT3], [tangents=]);
 // Topics: Geometry, Circles, Tangents
 // Description:
 //   Given a pair of rays with a common origin, and a known circle radius/diameter, finds
@@ -1017,7 +1018,7 @@ function circle_circle_intersection(c1,r1,c2,r2,eps=EPSILON,d1,d2) =
 // Figure(3D,Med,NoAxes,VPD=130,VPT=[29,19,3],VPR=[55,0,25]):
 //   pts = [[45,10,-5], [10,5,10], [15,40,5]];
 //   rad = 15;
-//   circ = circle_2tangents(pt1=pts[0], pt2=pts[1], pt3=pts[2], r=rad, tangents=true);
+//   circ = circle_2tangents(r=rad, pt1=pts[0], pt2=pts[1], pt3=pts[2], tangents=true);
 //   cp = circ[0]; n = circ[1]; tp1 = circ[2]; tp2 = circ[3];
 //   color("yellow") stroke(pts, endcaps="arrow2");
 //   color("purple") move_copies([cp,tp1,tp2]) sphere(d=2, $fn=12);
@@ -1034,32 +1035,32 @@ function circle_circle_intersection(c1,r1,c2,r2,eps=EPSILON,d1,d2) =
 //       ["TanPt2", "brown", 2.0, [-5, 0, 2], tp2],
 //   ];
 //   for(l=labels)
-//       color(l[1]) move(l[4]+l[3]) rot($vpr)
+//       color(l[1]) move(l[4]+l[3]) rot([55,0,25])
 //           linear_extrude(height=0.1)
 //               text(text=l[0], size=l[2], halign="center", valign="center");
 //   color("green",0.5) move(cp) cyl(h=0.1, r=rad, orient=n, $fn=36);
 // Arguments:
+//   r = The radius of the circle to find.
 //   pt1 = A point that the first ray passes though.
 //   pt2 = The starting point of both rays.
 //   pt3 = A point that the second ray passes though.
-//   r = The radius of the circle to find.
 //   ---
 //   d = The diameter of the circle to find.
 //   tangents = If true, extended information about the tangent points is calculated and returned.  Default: false
 // Example(2D):
 //   pts = [[40,40], [10,10], [55,5]];  rad = 10;
-//   circ = circle_2tangents(pt1=pts[0], pt2=pts[1], pt3=pts[2], r=rad);
+//   circ = circle_2tangents(r=rad, pt1=pts[0], pt2=pts[1], pt3=pts[2]);
 //   stroke(pts, endcaps="arrow2");
 //   color("red") move(circ[0]) circle(r=rad);
 // Example(2D):
 //   pts = [[20,40], [10,10], [55,20]];  rad = 10;
-//   circ = circle_2tangents(pt1=pts[0], pt2=pts[1], pt3=pts[2], r=rad, tangents=true);
+//   circ = circle_2tangents(r=rad, pt1=pts[0], pt2=pts[1], pt3=pts[2], tangents=true);
 //   stroke(pts, endcaps="arrow2");
 //   color("red") move(circ[0]) circle(r=rad);
 //   color("blue") move_copies(select(circ,2,3)) circle(d=2);
 // Example(3D): Fit into 3D path corner.
 //   pts = [[45,5,10], [10,10,15], [30,40,30]];  rad = 10;
-//   circ = circle_2tangents(pt1=pts[0], pt2=pts[1], pt3=pts[2], r=rad);
+//   circ = circle_2tangents(rad, [pts[0], pts[1], pts[2]]);
 //   stroke(pts, endcaps="arrow2");
 //   color("red") move(circ[0]) cyl(h=10, r=rad, orient=circ[1]);
 // Example(3D):
@@ -1067,17 +1068,17 @@ function circle_circle_intersection(c1,r1,c2,r2,eps=EPSILON,d1,d2) =
 //   stroke(path, closed=true);
 //   for (i = [0:1:5]) {
 //       crn = select(path, i*2-1, i*2+1);
-//       ci = circle_2tangents(crn[0], crn[1], crn[2], r=5);
+//       ci = circle_2tangents(5, crn[0], crn[1], crn[2]);
 //       move(ci[0]) cyl(h=10,r=5,,orient=ci[1]);
 //   }
-function circle_2tangents(pt1, pt2, pt3, r, d, tangents=false) =
+function circle_2tangents(r, pt1, pt2, pt3, tangents=false, d) =
     let(r = get_radius(r=r, d=d, dflt=undef))
     assert(r!=undef, "Must specify either r or d.")
     assert( ( is_path(pt1) && len(pt1)==3 && is_undef(pt2) && is_undef(pt3))
             || (is_matrix([pt1,pt2,pt3]) && (len(pt1)==2 || len(pt1)==3) ),
             "Invalid input points." )
     is_undef(pt2)
-    ? circle_2tangents(pt1[0], pt1[1], pt1[2], r=r, tangents=tangents)
+    ? circle_2tangents(r, pt1[0], pt1[1], pt1[2], tangents=tangents)
     : is_collinear(pt1, pt2, pt3)? undef :
         let(
             v1 = unit(pt1 - pt2),
@@ -1100,7 +1101,7 @@ function circle_2tangents(pt1, pt2, pt3, r, d, tangents=false) =
 // Function: circle_3points()
 // Usage:
 //   circ = circle_3points(pt1, pt2, pt3);
-//   circ = circle_3points([pt1, pt2, pt3]);
+//   circ = circle_3points([PT1, PT2, PT3]);
 // Topics: Geometry, Circles
 // Description:
 //   Returns the [CENTERPOINT, RADIUS, NORMAL] of the circle that passes through three non-collinear
@@ -1109,8 +1110,8 @@ function circle_2tangents(pt1, pt2, pt3, r, d, tangents=false) =
 //   points are 2D, then the resulting centerpoint will be 2D, and the normal will be UP ([0,0,1]).
 //   If any of the points are 3D, then the resulting centerpoint will be 3D.  If the three points are
 //   collinear, then `[undef,undef,undef]` will be returned.  The normal will be a normalized 3D
-//   vector with a non-negative Z axis.
-//   Instead of 3 arguments, it is acceptable to input the 3 points in a list `pt1`, leaving `pt2`and `pt3` as undef.
+//   vector with a non-negative Z axis.  Instead of 3 arguments, it is acceptable to input the 3 points
+//   as a list given in `pt1`, leaving `pt2`and `pt3` as undef.
 // Arguments:
 //   pt1 = The first point.
 //   pt2 = The second point.
@@ -1186,7 +1187,7 @@ function circle_point_tangents(r, cp, pt, d) =
 
 // Function: circle_circle_tangents()
 // Usage:
-//   segs = circle_circle_tangents(c1, r1|d1=, c2, r2|d2=);
+//   segs = circle_circle_tangents(r1|d1=, cp1, r2|d2=, cp2);
 // Topics: Geometry, Circles, Tangents
 // Description:
 //   Computes 2d lines tangents to a pair of circles in 2d.  Returns a list of line endpoints [p1,p2] where
@@ -1200,54 +1201,54 @@ function circle_point_tangents(r, cp, pt, d) =
 //   so the function returns the empty set.  When the circles are tangent a degenerate tangent line
 //   passes through the point of tangency of the two circles:  this degenerate line is NOT returned.
 // Arguments:
-//   c1 = Center of the first circle.
 //   r1 = Radius of the first circle.
-//   c2 = Center of the second circle.
+//   cp1 = Centerpoint of the first circle.
 //   r2 = Radius of the second circle.
+//   cp2 = Centerpoint of the second circle.
 //   ---
 //   d1 = Diameter of the first circle.
 //   d2 = Diameter of the second circle.
 // Example(2D,NoAxes): Four tangents, first in green, second in black, third in blue, last in red.
 //   $fn=32;
-//   c1 = [3,4];  r1 = 2;
-//   c2 = [7,10]; r2 = 3;
-//   pts = circle_circle_tangents(c1,r1,c2,r2);
-//   move(c1) stroke(circle(r=r1), width=0.2, closed=true);
-//   move(c2) stroke(circle(r=r2), width=0.2, closed=true);
+//   cp1 = [3,4];  r1 = 2;
+//   cp2 = [7,10]; r2 = 3;
+//   pts = circle_circle_tangents(r1, cp1, r2, cp2);
+//   move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
+//   move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
 //   colors = ["green","black","blue","red"];
 //   for(i=[0:len(pts)-1]) color(colors[i]) stroke(pts[i],width=0.2);
 // Example(2D,NoAxes): Circles overlap so only exterior tangents exist.
 //   $fn=32;
-//   c1 = [4,4];  r1 = 3;
-//   c2 = [7,7]; r2 = 2;
-//   pts = circle_circle_tangents(c1,r1,c2,r2);
-//   move(c1) stroke(circle(r=r1), width=0.2, closed=true);
-//   move(c2) stroke(circle(r=r2), width=0.2, closed=true);
+//   cp1 = [4,4];  r1 = 3;
+//   cp2 = [7,7];  r2 = 2;
+//   pts = circle_circle_tangents(r1, cp1, r2, cp2);
+//   move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
+//   move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
 //   colors = ["green","black","blue","red"];
 //   for(i=[0:len(pts)-1]) color(colors[i]) stroke(pts[i],width=0.2);
 // Example(2D,NoAxes): Circles are tangent.  Only exterior tangents are returned.  The degenerate internal tangent is not returned.
 //   $fn=32;
-//   c1 = [4,4];  r1 = 4;
-//   c2 = [4,10]; r2 = 2;
-//   pts = circle_circle_tangents(c1,r1,c2,r2);
-//   move(c1) stroke(circle(r=r1), width=0.2, closed=true);
-//   move(c2) stroke(circle(r=r2), width=0.2, closed=true);
+//   cp1 = [4,4];  r1 = 4;
+//   cp2 = [4,10]; r2 = 2;
+//   pts = circle_circle_tangents(r1, cp1, r2, cp2);
+//   move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
+//   move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
 //   colors = ["green","black","blue","red"];
 //   for(i=[0:1:len(pts)-1]) color(colors[i]) stroke(pts[i],width=0.2);
 // Example(2D,NoAxes): One circle is inside the other: no tangents exist.  If the interior circle is tangent the single degenerate tangent will not be returned.
 //   $fn=32;
-//   c1 = [4,4];  r1 = 4;
-//   c2 = [5,5];  r2 = 2;
-//   pts = circle_circle_tangents(c1,r1,c2,r2);
-//   move(c1) stroke(circle(r=r1), width=0.2, closed=true);
-//   move(c2) stroke(circle(r=r2), width=0.2, closed=true);
+//   cp1 = [4,4];  r1 = 4;
+//   cp2 = [5,5];  r2 = 2;
+//   pts = circle_circle_tangents(r1, cp1, r2, cp2);
+//   move(cp1) stroke(circle(r=r1), width=0.2, closed=true);
+//   move(cp2) stroke(circle(r=r2), width=0.2, closed=true);
 //   echo(pts);   // Returns []
-function circle_circle_tangents(c1,r1,c2,r2,d1,d2) =
-    assert( is_path([c1,c2],dim=2), "Invalid center point(s)." )
+function circle_circle_tangents(r1, cp1, r2, cp2, d1, d2) =
+    assert( is_path([cp1,cp2],dim=2), "Invalid center point(s)." )
     let(
         r1 = get_radius(r1=r1,d1=d1),
         r2 = get_radius(r1=r2,d1=d2),
-        Rvals = [r2-r1, r2-r1, -r2-r1, -r2-r1]/norm(c1-c2),
+        Rvals = [r2-r1, r2-r1, -r2-r1, -r2-r1]/norm(cp1-cp2),
         kvals = [-1,1,-1,1],
         ext = [1,1,-1,-1],
         N = 1-sqr(Rvals[2])>=0 ? 4 :
@@ -1256,13 +1257,13 @@ function circle_circle_tangents(c1,r1,c2,r2,d1,d2) =
             for(i=[0:1:N-1]) [
                 [Rvals[i], -kvals[i]*sqrt(1-sqr(Rvals[i]))],
                 [kvals[i]*sqrt(1-sqr(Rvals[i])), Rvals[i]]
-            ] * unit(c2-c1)
+            ] * unit(cp2-cp1)
         ]
     ) [
         for(i=[0:1:N-1]) let(
             pt = [
-                c1-r1*coef[i],
-                c2-ext[i]*r2*coef[i]
+                cp1-r1*coef[i],
+                cp2-ext[i]*r2*coef[i]
             ]
         ) if (pt[0]!=pt[1]) pt
     ];
@@ -1311,15 +1312,15 @@ function _noncollinear_triple(points,error=true,eps=EPSILON) =
 
 // Function: sphere_line_intersection()
 // Usage:
-//   isect = sphere_line_intersection(c,r|d=,line,[bounded],[eps=]);
+//   isect = sphere_line_intersection(r|d=, cp, line, [bounded], [eps=]);
 // Topics: Geometry, Spheres, Lines, Intersection
 // Description:
 //   Find intersection points between a sphere and a line, ray or segment specified by two points.
 //   By default the line is unbounded.
 // Arguments:
-//   c = center of sphere
-//   r = radius of sphere
-//   line = two points defining the line
+//   r = Radius of sphere
+//   cp = Centerpoint of sphere
+//   line = Two points defining the line
 //   bounded = false for unbounded line, true for a segment, or a vector [false,true] or [true,false] to specify a ray with the first or second end unbounded.  Default: false
 //   ---
 //   d = diameter of sphere
@@ -1327,14 +1328,14 @@ function _noncollinear_triple(points,error=true,eps=EPSILON) =
 // Example(3D):
 //   cp = [10,20,5];  r = 40;
 //   line = [[-50,-10,25], [70,0,40]];
-//   isects = sphere_line_intersection(c=cp, r=r, line=line);
+//   isects = sphere_line_intersection(r=r, cp=cp, line=line);
 //   color("cyan") stroke(line);
 //   move(cp) sphere(r=r, $fn=72);
 //   color("red") move_copies(isects) sphere(d=3, $fn=12);
-function sphere_line_intersection(c,r,line,bounded=false,d,eps=EPSILON) =
+function sphere_line_intersection(r, cp, line, bounded=false, d, eps=EPSILON) =
   assert(_valid_line(line,3), "Invalid 3d line.")
-  assert(is_vector(c,3), "Sphere center must be a 3-vector")
-  _circle_or_sphere_line_intersection(c,r,line,bounded,d,eps);
+  assert(is_vector(cp,3), "Sphere center must be a 3-vector")
+  _circle_or_sphere_line_intersection(r, cp, line, bounded, d, eps);
 
 
 

joiners.scad

@@ -963,7 +963,7 @@ module rabbit_clip(type, length, width,  snap, thickness, depth, compression=0.1
     scaled_len = length - 0.5 * (earwidth * snap + point_length * length) / sqrt(sqr(snap)+sqr(length/2));
     bottom_pt = [0,max(scaled_len*0.15+thickness, 2*thickness)];
     ctr = [width/2,scaled_len] + line_normal([width/2-snap, scaled_len/2], [width/2, scaled_len]) * earwidth/2;
-    inside_pt = circle_circle_tangents(bottom_pt, 0, ctr, earwidth/2)[0][1];
+    inside_pt = circle_circle_tangents(0, bottom_pt, earwidth/2, ctr)[0][1];
     sidepath =[
                [width/2,0],
                [width/2-snap,scaled_len/2],

rounding.scad

@@ -3281,7 +3281,7 @@ function _fix_angle_list(list,ind=0, result=[]) =
 function _cyl_line_intersection(R, line, ref) =
    let(
        line2d = path2d(line),
-       cisect = circle_line_intersection([0,0], r=R, line= line2d)
+       cisect = circle_line_intersection(r=R, cp=[0,0], line=line2d)
    )
    len(cisect)<2 ? [] :
    let(
@@ -3300,7 +3300,7 @@ function _cyl_line_intersection(R, line, ref) =
 
 function _sphere_line_isect_best(R, line, ref) =
    let(
-        pts = sphere_line_intersection([0,0,0],abs(R), line=line)
+        pts = sphere_line_intersection(abs(R), [0,0,0], line=line)
    )
    len(pts)<2 ? [] :
    let(  

shapes2d.scad

@@ -254,7 +254,7 @@ function circle(r, d, points, corner, anchor=CENTER, spin=0) =
                 assert(is_undef(points), "Cannot specify points= when corner= is given.")
                 let(
                     r = get_radius(r=r, d=d, dflt=1),
-                    c = circle_2tangents(pt1=corner[0], pt2=corner[1], pt3=corner[2], r=r)
+                    c = circle_2tangents(r=r, pt1=corner[0], pt2=corner[1], pt3=corner[2])
                 )
                 assert(c!=undef, "Corner path cannot be collinear.")
                 let( cp = c[0] )
@@ -283,7 +283,7 @@ module circle(r, d, points, corner, anchor=CENTER, spin=0) {
         }
     } else if (is_path(corner)) {
         r = get_radius(r=r, d=d, dflt=1);
-        c = circle_2tangents(pt1=corner[0], pt2=corner[1], pt3=corner[2], r=r);
+        c = circle_2tangents(r=r, pt1=corner[0], pt2=corner[1], pt3=corner[2]);
         check = assert(c != undef && c[0] != undef, "Points must not be collinear.");
         cp = c[0];
         translate(cp) {
@@ -1298,7 +1298,7 @@ function egg(length, r1, r2, R, d1, d2, D, anchor=CENTER, spin=0) =
         c1 = [-length/2+r1,0],
         c2 = [length/2-r2,0],
         Rmin = (r1+r2+norm(c1-c2))/2,
-        Mlist = circle_circle_intersection(c1,R-r1,c2,R-r2),
+        Mlist = circle_circle_intersection(R-r1, c1, R-r2, c2),
         arcparms = reverse([for(M=Mlist) [M, c1+r1*unit(c1-M), c2+r2*unit(c2-M)]]),
         path = concat(
                       arc(r=r2, cp=c2, points=[[length/2,0],arcparms[0][2]],endpoint=false),

shapes3d.scad

@@ -1223,7 +1223,7 @@ module cyl(
                         ) [p1,p2]
                     ) : !is_undef(fil2)? (
                         let(
-                            cn = circle_2tangents([r2-fil2,l/2], [r2,l/2], [r1,-l/2], r=abs(fil2)),
+                            cn = circle_2tangents(abs(fil2), [r2-fil2,l/2], [r2,l/2], [r1,-l/2]),
                             ang = fil2<0? phi : phi-180,
                             steps = ceil(abs(ang)/360*segs(abs(fil2))),
                             step = ang/steps,
@@ -1238,7 +1238,7 @@ module cyl(
                         ) [p1,p2]
                     ) : !is_undef(fil1)? (
                         let(
-                            cn = circle_2tangents([r1-fil1,-l/2], [r1,-l/2], [r2,l/2], r=abs(fil1)),
+                            cn = circle_2tangents(abs(fil1), [r1-fil1,-l/2], [r1,-l/2], [r2,l/2]),
                             ang = fil1<0? 180-phi : -phi,
                             steps = ceil(abs(ang)/360*segs(abs(fil1))),
                             step = ang/steps,
@@ -2706,19 +2706,21 @@ module path_text(path, text, font, size, thickness, lettersize, offset=0, revers
 //
 // Example:
 //   union() {
-//       translate([0,2,-4])
-//           cube([20, 4, 24], anchor=BOTTOM);
-//       translate([0,-10,-4])
-//           cube([20, 20, 4], anchor=BOTTOM);
-//       color("green")
-//           interior_fillet(
-//               l=20, r=10,
-//               spin=180, orient=RIGHT
-//           );
+//     translate([0,2,-4])
+//       cube([20, 4, 24], anchor=BOTTOM);
+//     translate([0,-10,-4])
+//       cube([20, 20, 4], anchor=BOTTOM);
+//     color("green")
+//       interior_fillet(
+//         l=20, r=10,
+//         spin=180, orient=RIGHT
+//       );
 //   }
 //
-// Example:
-//   interior_fillet(l=40, r=10, spin=-90);
+// Examples:
+//   interior_fillet(l=10, r=20, ang=60);
+//   interior_fillet(l=10, r=20, ang=90);
+//   interior_fillet(l=10, r=20, ang=120);
 //
 // Example: Using with Attachments
 //   cube(50,center=true) {
@@ -2727,19 +2729,22 @@ module path_text(path, text, font, size, thickness, lettersize, offset=0, revers
 //     position(BOT+FRONT)
 //       interior_fillet(l=50, r=10, spin=180, orient=RIGHT);
 //   }
-module interior_fillet(l=1.0, r, ang=90, overlap=0.01, d, anchor=FRONT+LEFT, spin=0, orient=UP) {
+module interior_fillet(l=1.0, r, ang=90, overlap=0.01, d, anchor=CENTER, spin=0, orient=UP) {
     r = get_radius(r=r, d=d, dflt=1);
-    dy = r/tan(ang/2);
-    steps = ceil(segs(r)*ang/360);
-    step = ang/steps;
-    attachable(anchor,spin,orient, size=[r,r,l]) {
+    steps = ceil(segs(r)*(180-ang)/360);
+    arc = arc(n=steps+1, r=r, corner=[polar_to_xy(r,ang),[0,0],[r,0]]);
+    maxx = last(arc).x;
+    maxy = arc[0].y;
+    path = [
+        [maxx, -overlap],
+        polar_to_xy(overlap, 180+ang/2),
+        arc[0] + polar_to_xy(overlap, 90+ang),
+        each arc
+    ];
+    attachable(anchor,spin,orient, size=[2*maxx,2*maxy,l]) {
         if (l > 0) {
             linear_extrude(height=l, convexity=4, center=true) {
-                path = concat(
-                    [[0,0]],
-                    [for (i=[0:1:steps]) let(a=270-i*step) r*[cos(a),sin(a)]+[dy,r]]
-                );
-                translate(-[r,r]/2) polygon(path);
+                polygon(path);
             }
         }
         children();

tests/test_geometry.scad

@@ -424,15 +424,15 @@ module test_line_closest_point() {
 
 module test_circle_2tangents() {
 //** missing tests with arg tangent=true
-    assert(approx(circle_2tangents([10,10],[0,0],[10,-10],r=10/sqrt(2))[0],[10,0]));
-    assert(approx(circle_2tangents([-10,10],[0,0],[-10,-10],r=10/sqrt(2))[0],[-10,0]));
-    assert(approx(circle_2tangents([-10,10],[0,0],[10,10],r=10/sqrt(2))[0],[0,10]));
-    assert(approx(circle_2tangents([-10,-10],[0,0],[10,-10],r=10/sqrt(2))[0],[0,-10]));
-    assert(approx(circle_2tangents([0,10],[0,0],[10,0],r=10)[0],[10,10]));
-    assert(approx(circle_2tangents([10,0],[0,0],[0,-10],r=10)[0],[10,-10]));
-    assert(approx(circle_2tangents([0,-10],[0,0],[-10,0],r=10)[0],[-10,-10]));
-    assert(approx(circle_2tangents([-10,0],[0,0],[0,10],r=10)[0],[-10,10]));
-    assert_approx(circle_2tangents(polar_to_xy(10,60),[0,0],[10,0],r=10)[0],polar_to_xy(20,30));
+    assert(approx(circle_2tangents(10/sqrt(2),[10,10],[0,0],[10,-10])[0], [10,0]));
+    assert(approx(circle_2tangents(10/sqrt(2),[-10,10],[0,0],[-10,-10])[0], [-10,0]));
+    assert(approx(circle_2tangents(10/sqrt(2),[-10,10],[0,0],[10,10])[0], [0,10]));
+    assert(approx(circle_2tangents(10/sqrt(2),[-10,-10],[0,0],[10,-10])[0], [0,-10]));
+    assert(approx(circle_2tangents(10,[0,10],[0,0],[10,0])[0], [10,10]));
+    assert(approx(circle_2tangents(10,[10,0],[0,0],[0,-10])[0], [10,-10]));
+    assert(approx(circle_2tangents(10,[0,-10],[0,0],[-10,0])[0], [-10,-10]));
+    assert(approx(circle_2tangents(10,[-10,0],[0,0],[0,10])[0], [-10,10]));
+    assert_approx(circle_2tangents(10,polar_to_xy(10,60),[0,0],[10,0])[0], polar_to_xy(20,30));
 }
 *test_circle_2tangents();
 

walls.scad

@@ -183,10 +183,10 @@ module thinning_wall(h=50, l=100, thick=5, ang=30, braces=false, strut, wall, an
     wall = is_num(wall)? wall : thick/2;
 
     bevel_h = strut + (thick-wall)/2/tan(ang);
-    cp1 = circle_2tangents([0,0,+h/2], [l2/2,0,+h/2], [l1/2,0,-h/2], r=strut)[0];
-    cp2 = circle_2tangents([0,0,+h/2], [l2/2,0,+h/2], [l1/2,0,-h/2], r=bevel_h)[0];
-    cp3 = circle_2tangents([0,0,-h/2], [l1/2,0,-h/2], [l2/2,0,+h/2], r=bevel_h)[0];
-    cp4 = circle_2tangents([0,0,-h/2], [l1/2,0,-h/2], [l2/2,0,+h/2], r=strut)[0];
+    cp1 = circle_2tangents(strut, [0,0,+h/2], [l2/2,0,+h/2], [l1/2,0,-h/2])[0];
+    cp2 = circle_2tangents(bevel_h, [0,0,+h/2], [l2/2,0,+h/2], [l1/2,0,-h/2])[0];
+    cp3 = circle_2tangents(bevel_h, [0,0,-h/2], [l1/2,0,-h/2], [l2/2,0,+h/2])[0];
+    cp4 = circle_2tangents(strut, [0,0,-h/2], [l1/2,0,-h/2], [l2/2,0,+h/2])[0];
 
     z1 = h/2;
     z2 = cp1.z;