geometry synopses

geometry.scad

@@ -18,6 +18,7 @@
 // Usage:
 //   pt = is_point_on_line(point, line, [bounded], [eps]);
 // Topics: Geometry, Points, Segments
+// Synopsis: Determine if a point is on a line, ray or segment. 
 // Description:
 //   Determine if the point is on the line segment, ray or segment defined by the two between two points.
 //   Returns true if yes, and false if not.  If bounded is set to true it specifies a segment, with
@@ -141,6 +142,7 @@ function _point_left_of_line2d(point, line, eps=EPSILON) =
 // Function: is_collinear()
 // Usage:
 //   bool = is_collinear(a, [b, c], [eps]);
+// Synopsis: Determine if a points are collinear.
 // Topics: Geometry, Points, Collinearity
 // Description:
 //   Returns true if the points `a`, `b` and `c` are co-linear or if the list of points `a` is collinear.
@@ -163,6 +165,7 @@ function is_collinear(a, b, c, eps=EPSILON) =
 // Usage:
 //   dist = point_line_distance(line, pt, [bounded]);
 // Topics: Geometry, Points, Lines, Distance
+// Synopsis: Find shortest distance from point to a line, segment or ray.
 // Description:
 //   Finds the shortest distance from the point `pt` to the specified line, segment or ray.
 //   The bounded parameter specifies the whether the endpoints give a ray or segment.
@@ -188,8 +191,9 @@ function point_line_distance(pt, line, bounded=false) =
 //   dist = segment_distance(seg1, seg2, [eps]);
 // Topics: Geometry, Segments, Distance
 // See Also: convex_collision(), convex_distance()
+// Synopsis: Find smallest distance between two line semgnets.
 // Description:
-//   Returns the closest distance of the two given line segments.
+//   Returns the smallest distance of the points on two given line segments.
 // Arguments:
 //   seg1 = The list of two points representing the first line segment to check the distance of.
 //   seg2 = The list of two points representing the second line segment to check the distance of.
@@ -209,6 +213,7 @@ function segment_distance(seg1, seg2,eps=EPSILON) =
 // Topics: Geometry, Lines
 // Description:
 //   Returns the 2D normal vector to the given 2D line. This is otherwise known as the perpendicular vector counter-clockwise to the given ray.
+// Synopsis: Return normal vector to given line. 
 // Arguments:
 //   p1 = First point on 2D line.
 //   p2 = Second point on 2D line.
@@ -252,6 +257,7 @@ function _general_line_intersection(s1,s2,eps=EPSILON) =
 // Function: line_intersection()
 // Usage:
 //    pt = line_intersection(line1, line2, [bounded1], [bounded2], [bounded=], [eps=]);
+// Synopsis: Compute intersection of two lines, segments or rays.
 // Description:
 //    Returns the intersection point of any two 2D lines, segments or rays.  Returns undef
 //    if they do not intersect.  You specify a line by giving two distinct points on the
@@ -313,6 +319,7 @@ function line_intersection(line1, line2, bounded1, bounded2, bounded, eps=EPSILO
 // Usage:
 //   pt = line_closest_point(line, pt, [bounded]);
 // Topics: Geometry, Lines, Distance
+// Synopsis: Find point on given line, segment or ray that is closest to a given point. 
 // Description:
 //   Returns the point on the given line, segment or ray that is closest to the given point `pt`.
 //   The inputs `line` and `pt` args should be of the same dimension.  The parameter bounded indicates
@@ -396,9 +403,10 @@ function line_closest_point(line, pt, bounded=false) =
 // Function: line_from_points()
 // Usage:
 //   line = line_from_points(points, [fast], [eps]);
+// Synopsis: Given a list of collinear points, return the line they define. 
 // Topics: Geometry, Lines, Points
 // Description:
-//   Given a list of 2 or more collinear points, returns a line containing them.
+//   Given a list of 2 or more collinear points, returns two points defining a line containing them.
 //   If `fast` is false and the points are coincident or non-collinear, then `undef` is returned.
 //   if `fast` is true, then the collinearity test is skipped and a line passing through 2 distinct arbitrary points is returned.
 // Arguments:
@@ -423,6 +431,7 @@ function line_from_points(points, fast=false, eps=EPSILON) =
 // Usage:
 //   bool = is_coplanar(points,[eps]);
 // Topics: Geometry, Coplanarity
+// Synopsis: Check if 3d points are coplanar and not collinear.  
 // Description:
 //   Returns true if the given 3D points are non-collinear and are on a plane.
 // Arguments:
@@ -444,6 +453,7 @@ function is_coplanar(points, eps=EPSILON) =
 //   plane = plane3pt(p1, p2, p3);
 //   plane = plane3pt([p1, p2, p3]);
 // Topics: Geometry, Planes
+// Synopsis: Return a plane from 3 points. 
 // Description:
 //   Generates the normalized cartesian equation of a plane from three 3d points.
 //   Returns [A,B,C,D] where Ax + By + Cz = D is the equation of a plane.
@@ -467,6 +477,7 @@ function plane3pt(p1, p2, p3) =
 // Usage:
 //   plane = plane3pt_indexed(points, i1, i2, i3);
 // Topics: Geometry, Planes
+// Synopsis: Given list of 3d points and 3 indices, return the plane they define.  
 // Description:
 //   Given a list of 3d points, and the indices of three of those points,
 //   generates the normalized cartesian equation of a plane that those points all
@@ -494,6 +505,7 @@ function plane3pt_indexed(points, i1, i2, i3) =
 // Function: plane_from_normal()
 // Usage:
 //   plane = plane_from_normal(normal, [pt])
+// Synopsis: Return plane defined by normal vector and a point. 
 // Topics: Geometry, Planes
 // Description:
 //   Returns a plane defined by a normal vector and a point.  If you omit `pt` you will get a plane
@@ -554,6 +566,7 @@ function _covariance_evec_eval(points) =
 // Function: plane_from_points()
 // Usage:
 //   plane = plane_from_points(points, [fast], [eps]);
+// Synopsis: Return plane defined by a set of coplanar 3d points, with arbitrary normal direction.
 // Topics: Geometry, Planes, Points
 // See Also: plane_from_polygon()
 // Description:
@@ -561,7 +574,8 @@ function _covariance_evec_eval(points) =
 //   that is [A,B,C,D] where Ax+By+Cz=D is the equation of the plane and norm([A,B,C])=1.
 //   If `fast` is false and the points in the list are collinear or not coplanar, then `undef` is returned.
 //   If `fast` is true, the polygon coplanarity check is skipped and a best fitting plane is returned.
-//   It differs from `plane_from_polygon` as the plane normal is independent of the point order. It is faster, though.
+//   The direction of the plane's normal is arbitrary and is not determined by the point order, unlike {{plane_from_polygon()}}.
+//   This function is faster than {{plane_from_polygon()}}.  
 // Arguments:
 //   points = The list of points to find the plane of.
 //   fast = If true, don't verify the point coplanarity.  Default: false
@@ -591,6 +605,7 @@ function plane_from_points(points, fast=false, eps=EPSILON) =
 // Function: plane_from_polygon()
 // Usage:
 //   plane = plane_from_polygon(points, [fast], [eps]);
+// Synopsis: Given a 3d planar polygon, returns directed plane.  
 // Topics: Geometry, Planes, Polygons
 // See Also: plane_from_points()
 // Description:
@@ -599,6 +614,8 @@ function plane_from_points(points, fast=false, eps=EPSILON) =
 //   If not all the points in the polygon are coplanar, then [] is returned.
 //   If `fast` is false and the points in the list are collinear or not coplanar, then `undef` is returned.
 //   if `fast` is true, then the coplanarity test is skipped and a plane passing through 3 non-collinear arbitrary points is returned.
+//   The normal direction is determined by the order of the points and the right hand rule.  This is slower than {{plane_from_points()}},
+//   which returns an arbitrary normal.  
 // Arguments:
 //   poly = The planar 3D polygon to find the plane of.
 //   fast = If true, doesn't verify that all points in the polygon are coplanar.  Default: false
@@ -626,6 +643,7 @@ function plane_from_polygon(poly, fast=false, eps=EPSILON) =
 // Usage:
 //   vec = plane_normal(plane);
 // Topics: Geometry, Planes
+// Synopsis: Returns the normal vector to a plane. 
 // Description:
 //   Returns the unit length normal vector for the given plane.
 // Arguments:
@@ -639,6 +657,7 @@ function plane_normal(plane) =
 // Usage:
 //   d = plane_offset(plane);
 // Topics: Geometry, Planes
+// Synopsis: Returns the signed offset of the plane from the origin.  
 // Description:
 //   Returns coeficient D of the normalized plane equation `Ax+By+Cz=D`, or the scalar offset of the plane from the origin.
 //   This value may be negative.
@@ -681,6 +700,7 @@ function _normalize_plane(plane) =
 // Usage:
 //   pt = plane_line_intersection(plane, line, [bounded], [eps]);
 // Topics: Geometry, Planes, Lines, Intersection
+// Synopsis: Returns the intersection of a plane and 3d line, segment or ray.  
 // Description:
 //   Takes a line, and a plane [A,B,C,D] where the equation of that plane is `Ax+By+Cz=D`.
 //   If `line` intersects `plane` at one point, then that intersection point is returned.
@@ -711,6 +731,7 @@ function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) =
 //   line = plane_intersection(plane1, plane2)
 //   pt = plane_intersection(plane1, plane2, plane3)
 // Topics: Geometry, Planes, Intersection
+// Synopsis: Returns the intersection of two or three planes.  
 // Description:
 //   Compute the point which is the intersection of the three planes, or the line intersection of two planes.
 //   If you give three planes the intersection is returned as a point.  If you give two planes the intersection
@@ -745,6 +766,7 @@ function plane_intersection(plane1,plane2,plane3) =
 // Usage:
 //   angle = plane_line_angle(plane,line);
 // Topics: Geometry, Planes, Lines, Angle
+// Synopsis: Returns the angle between a plane and a 3d line. 
 // Description:
 //   Compute the angle between a plane [A, B, C, D] and a 3d line, specified as a pair of 3d points [p1,p2].
 //   The resulting angle is signed, with the sign positive if the vector p2-p1 lies above the plane, on
@@ -765,6 +787,7 @@ function plane_line_angle(plane, line) =
 // Usage:
 //   pts = plane_closest_point(plane, points);
 // Topics: Geometry, Planes, Projection
+// Synopsis: Returns the orthogonal projection of points onto a plane. 
 // Description:
 //   Given a plane definition `[A,B,C,D]`, where `Ax+By+Cz=D`, and a list of 2d or
 //   3d points, return the closest 3D orthogonal projection of the points on the plane.
@@ -800,6 +823,7 @@ function plane_closest_point(plane, points) =
 // Usage:
 //   dist = point_plane_distance(plane, point)
 // Topics: Geometry, Planes, Distance
+// Synopsis: Determine distance between a point and plane. 
 // Description:
 //   Given a plane as [A,B,C,D] where the cartesian equation for that plane
 //   is Ax+By+Cz=D, determines how far from that plane the given point is.
@@ -831,6 +855,7 @@ function _pointlist_greatest_distance(points,plane) =
 // Usage:
 //   bool = are_points_on_plane(points, plane, [eps]);
 // Topics: Geometry, Planes, Points
+// Synopsis: Determine if all of the listed points are on a plane. 
 // Description:
 //   Returns true if the given 3D points are on the given plane.
 // Arguments:
@@ -848,7 +873,7 @@ function are_points_on_plane(points, plane, eps=EPSILON) =
 /// Usage:
 ///   bool = _is_point_above_plane(plane, point);
 /// Topics: Geometry, Planes
-// Description:
+/// Description:
 ///   Given a plane as [A,B,C,D] where the cartesian equation for that plane
 ///   is Ax+By+Cz=D, determines if the given 3D point is on the side of that
 ///   plane that the normal points towards.  The normal of the plane is the
@@ -866,6 +891,7 @@ function _is_point_above_plane(plane, point) =
 // Function: circle_line_intersection()
 // Usage:
 //   pts = circle_line_intersection(r|d=, cp, line, [bounded], [eps=]);
+// Synopsis: Find the intersection points between a 2d circle and a line, ray or segment.
 // Topics: Geometry, Circles, Lines, Intersection
 // Description:
 //   Find intersection points between a 2D circle and a line, ray or segment specified by two points.
@@ -939,6 +965,7 @@ function _circle_or_sphere_line_intersection(r, cp, line, bounded=false, d, eps=
 // Function: circle_circle_intersection()
 // Usage:
 //   pts = circle_circle_intersection(r1|d1=, cp1, r2|d2=, cp2, [eps]);
+// Synopsis: Find the intersection points of two 2d circles.
 // Topics: Geometry, Circles
 // Description:
 //   Compute the intersection points of two circles.  Returns a list of the intersection points, which
@@ -1007,8 +1034,9 @@ function circle_circle_intersection(r1, cp1, r2, cp2, eps=EPSILON, d1, d2) =
 //   circ = circle_2tangents(r|d=, pt1, pt2, pt3, [tangents=]);
 //   circ = circle_2tangents(r|d=, [PT1, PT2, PT3], [tangents=]);
 // Topics: Geometry, Circles, Tangents
+// Synopsis: Given two 2d or 3d rays, find a circle tangent to both.  
 // Description:
-//   Given a pair of rays with a common origin, and a known circle radius/diameter, finds
+//   Given a pair of 2d or 3d rays with a common origin, and a known circle radius/diameter, finds
 //   the centerpoint for the circle of that size that touches both rays tangentally.
 //   Both rays start at `pt2`, one passing through `pt1`, and the other through `pt3`.
 //   .
@@ -1107,6 +1135,7 @@ function circle_2tangents(r, pt1, pt2, pt3, tangents=false, d) =
 //   circ = circle_3points(pt1, pt2, pt3);
 //   circ = circle_3points([PT1, PT2, PT3]);
 // Topics: Geometry, Circles
+// Synopsis: Find a circle passing through three 2d or 3d points. 
 // Description:
 //   Returns the [CENTERPOINT, RADIUS, NORMAL] of the circle that passes through three non-collinear
 //   points where NORMAL is the normal vector of the plane that the circle is on (UP or DOWN if the points are 2D).
@@ -1157,6 +1186,7 @@ function circle_3points(pt1, pt2, pt3) =
 // Usage:
 //   tangents = circle_point_tangents(r|d=, cp, pt);
 // Topics: Geometry, Circles, Tangents
+// Synopsis: Given a circle and point, find tangents to circle passing through the point.
 // Description:
 //   Given a 2d circle and a 2d point outside that circle, finds the 2d tangent point(s) on the circle for a
 //   line passing through the point.  Returns a list of zero or more 2D tangent points.
@@ -1193,6 +1223,7 @@ function circle_point_tangents(r, cp, pt, d) =
 // Usage:
 //   segs = circle_circle_tangents(r1|d1=, cp1, r2|d2=, cp2);
 // Topics: Geometry, Circles, Tangents
+// Synopsis: Find tangents to a pair of circles in 2d.  
 // Description:
 //   Computes 2d lines tangents to a pair of circles in 2d.  Returns a list of line endpoints [p1,p2] where
 //   p1 is the tangent point on circle 1 and p2 is the tangent point on circle 2.
@@ -1318,6 +1349,7 @@ function _noncollinear_triple(points,error=true,eps=EPSILON) =
 // Usage:
 //   isect = sphere_line_intersection(r|d=, cp, line, [bounded], [eps=]);
 // Topics: Geometry, Spheres, Lines, Intersection
+// Synopsis: Find intersection between a sphere and line, ray or segment. 
 // Description:
 //   Find intersection points between a sphere and a line, ray or segment specified by two points.
 //   By default the line is unbounded.
@@ -1350,6 +1382,7 @@ function sphere_line_intersection(r, cp, line, bounded=false, d, eps=EPSILON) =
 // Usage:
 //   area = polygon_area(poly, [signed]);
 // Topics: Geometry, Polygons, Area
+// Synopsis: Calculate area of a 2d or 3d polygon. 
 // Description:
 //   Given a 2D or 3D simple planar polygon, returns the area of that polygon.
 //   If the polygon is non-planar the result is `undef.`  If the polygon is self-intersecting
@@ -1384,6 +1417,7 @@ function polygon_area(poly, signed=false) =
 // Usage:
 //   c = centroid(object, [eps]);
 // Topics: Geometry, Polygons, Centroid
+// Synopsis: Compute centroid of a 2d or 3d polygon or a VNF. 
 // Description:
 //   Given a simple 2D polygon, returns the 2D coordinates of the polygon's centroid.
 //   Given a simple 3D planar polygon, returns the 3D coordinates of the polygon's centroid.
@@ -1469,6 +1503,7 @@ function _polygon_centroid(poly, eps=EPSILON) =
 // Usage:
 //   vec = polygon_normal(poly);
 // Topics: Geometry, Polygons
+// Synopsis: Return normal to a polygon.  
 // Description:
 //   Given a 3D simple planar polygon, returns a unit normal vector for the polygon.  The vector
 //   is oriented so that if the normal points towards the viewer, the polygon winds in the clockwise
@@ -1497,6 +1532,7 @@ function polygon_normal(poly) =
 // Usage:
 //   bool = point_in_polygon(point, poly, [nonzero], [eps])
 // Topics: Geometry, Polygons
+// Synopsis: Checks if a 2d point is inside or on the boundary of a 2d polygon. 
 // Description:
 //   This function tests whether the given 2D point is inside, outside or on the boundary of
 //   the specified 2D polygon.  
@@ -1640,6 +1676,7 @@ function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
 // Usage:
 //   pt = polygon_line_intersection(poly, line, [bounded], [nonzero], [eps]);
 // Topics: Geometry, Polygons, Lines, Intersection
+// Synopsis: Find intersection between 2d or 3d polygon and a line, segment or ray.  
 // Description:
 //   Takes a possibly bounded line, and a 2D or 3D planar polygon, and finds their intersection.  Note the polygon is
 //   treated as its boundary and interior, so the intersection may include both points and line segments.  
@@ -1825,6 +1862,7 @@ function _merge_segments(insegs,outsegs, eps, i=1) =
 // Function: polygon_triangulate()
 // Usage:
 //   triangles = polygon_triangulate(poly, [ind], [error], [eps])
+// Synopsis: Divide a polygon into triangles. 
 // Description:
 //   Given a simple polygon in 2D or 3D, triangulates it and returns a list 
 //   of triples indexing into the polygon vertices. When the optional argument `ind` is 
@@ -2015,6 +2053,7 @@ function _none_inside(idxs,poly,p0,p1,p2,eps,i=0) =
 //   bool = is_polygon_clockwise(poly);
 // Topics: Geometry, Polygons, Clockwise
 // See Also: clockwise_polygon(), ccw_polygon(), reverse_polygon()
+// Synopsis: Determine if a 2d polygon winds clockwise.  
 // Description:
 //   Return true if the given 2D simple polygon is in clockwise order, false otherwise.
 //   Results for complex (self-intersecting) polygon are indeterminate.
@@ -2040,6 +2079,7 @@ function is_polygon_clockwise(poly) =
 // Usage:
 //   newpoly = clockwise_polygon(poly);
 // Topics: Geometry, Polygons, Clockwise
+// Synopsis: Return clockwise version of a polygon. 
 // See Also: is_polygon_clockwise(), ccw_polygon(), reverse_polygon()
 // Description:
 //   Given a 2D polygon path, returns the clockwise winding version of that path.
@@ -2053,6 +2093,7 @@ function clockwise_polygon(poly) =
 // Function: ccw_polygon()
 // Usage:
 //   newpoly = ccw_polygon(poly);
+// Synopsis: Return counter-clockwise version of a polygon. 
 // See Also: is_polygon_clockwise(), clockwise_polygon(), reverse_polygon()
 // Topics: Geometry, Polygons, Clockwise
 // Description:
@@ -2067,6 +2108,7 @@ function ccw_polygon(poly) =
 // Function: reverse_polygon()
 // Usage:
 //   newpoly = reverse_polygon(poly)
+// Synopsis: Reverse winding direction of polygon. 
 // Topics: Geometry, Polygons, Clockwise
 // See Also: is_polygon_clockwise(), ccw_polygon(), clockwise_polygon()
 // Description:
@@ -2082,6 +2124,7 @@ function reverse_polygon(poly) =
 // Function: reindex_polygon()
 // Usage:
 //   newpoly = reindex_polygon(reference, poly);
+// Synopsis: Adjust point indexing of polygon to minimize pointwise distance to a reference polygon. 
 // Topics: Geometry, Polygons
 // Description:
 //   Rotates and possibly reverses the point order of a 2d or 3d polygon path to optimize its pairwise point
@@ -2137,13 +2180,14 @@ function reindex_polygon(reference, poly, return_error=false) =
 // Usage:
 //   newpoly = align_polygon(reference, poly, [angles], [cp], [tran], [return_ind]);
 // Topics: Geometry, Polygons
+// Synopsis: Find best alignment of a 2d polygon to a reference 2d polygon over a set of transformations.  
 // Description:
 //   Find the best alignment of a specified 2D polygon with a reference 2D polygon over a set of
 //   transformations.  You can specify a list or range of angles and a centerpoint or you can
 //   give a list of arbitrary 2d transformation matrices.  For each transformation or angle, the polygon is
 //   reindexed, which is a costly operation so if run time is a problem, use a smaller sampling of angles or
 //   transformations.  By default returns the rotated and reindexed polygon.  You can also request that
-//   the best angle or the index into the transformation list be returned.  When you specify an angle
+//   the best angle or the index into the transformation list be returned.  
 // Arguments:
 //   reference = reference polygon
 //   poly = polygon to rotate into alignment with the reference
@@ -2206,6 +2250,7 @@ function align_polygon(reference, poly, angles, cp, trans, return_ind=false) =
 // Description:
 //    Returns true if poly1 and poly2 are the same polongs
 //    within given epsilon tolerance.
+// Synopsis: Check if two polygons (not necessarily in the same point order) are equal.  
 // Arguments:
 //    poly1 = first polygon
 //    poly2 = second polygon
@@ -2258,6 +2303,7 @@ function ___is_polygon_in_list(poly, polys, i) =
 // Function: hull()
 // Usage:
 //   face_list_or_index_list = hull(points);
+// Synopsis: Convex hull of a list of 2d or 3d points.
 // Description:
 //   Takes a list of 2D or 3D points (but not both in the same list) and returns either the list of
 //   indexes into `points` that forms the 2D convex hull perimeter path, or the list of faces that
@@ -2278,6 +2324,7 @@ function hull(points) =
 // Module: hull_points()
 // Usage:
 //   hull_points(points, [fast]);
+// Synopsis: Convex hull of a list of 2d or 3d points.  
 // Description:
 //   If given a list of 2D points, creates a 2D convex hull polygon that encloses all those points.
 //   If given a list of 3D points, creates a 3D polyhedron that encloses all the points.  This should
@@ -2339,6 +2386,7 @@ function _is_cw(a,b,c,all) =
 //   Takes a list of arbitrary 2D points, and finds the convex hull polygon to enclose them.
 //   Returns a path as a list of indices into `points`. 
 //   When all==true, returns extra points that are on edges of the hull.
+// Synopsis: Convex hull of a list of 2d points. 
 // Arguments:
 //   points = list of 2d points to get the hull of.
 //   all = when true, includes all points on the edges of the convex hull. Default: false.
@@ -2397,6 +2445,7 @@ function _hull_collinear(points) =
 // Function: hull3d_faces()
 // Usage:
 //   faces = hull3d_faces(points)
+// Synopsis: Convex hull of a list of 3d points. 
 // Description:
 //   Takes a list of arbitrary 3D points, and finds the convex hull polyhedron to enclose
 //   them.  Returns a list of triangular faces, where each face is a list of indexes into the given `points`
@@ -2508,6 +2557,7 @@ function _find_first_noncoplanar(plane, points, i=0) =
 // Function: is_polygon_convex()
 // Usage:
 //   bool = is_polygon_convex(poly, [eps]);
+// Synopsis: Check if a polygon is convex. 
 // Topics: Geometry, Convexity, Test
 // Description:
 //   Returns true if the given 2D or 3D polygon is convex.
@@ -2553,6 +2603,7 @@ function is_polygon_convex(poly,eps=EPSILON) =
 // Function: convex_distance()
 // Usage:
 //   dist = convex_distance(points1, points2,eps);
+// Synopsis: Compute distance between convex hull of two point lists. 
 // Topics: Geometry, Convexity, Distance
 // See also: 
 //   convex_collision(), hull()
@@ -2615,8 +2666,9 @@ function _GJK_distance(points1, points2, eps=EPSILON, lbd, d, simplex=[]) =
 // Topics: Geometry, Convexity, Collision, Intersection
 // See also: 
 //   convex_distance(), hull()
+// Synopsis: Check whether the convex hulls of two point lists intersect. 
 // Description:
-//   Returns `true` if the convex hull of `points1` intercepts the convex hull of `points2`
+//   Returns `true` if the convex hull of `points1` intersects the convex hull of `points2`
 //   otherwise, `false`.
 //   All the points in the lists should have the same dimension, either 2D or 3D.
 //   This function is tipically faster than `convex_distance` to find a non-collision.
@@ -2762,6 +2814,7 @@ function _support_diff(p1,p2,d) =
 // Function: rot_decode()
 // Usage:
 //   info = rot_decode(rotation,[long]); // Returns: [angle,axis,cp,translation]
+// Synopsis: Extract axis and rotation angle from a rotation matrix. 
 // Topics: Affine, Matrices, Transforms
 // Description:
 //   Given an input 3D rigid transformation operator (one composed of just rotations and translations) represented

shapes3d.scad

@@ -2912,7 +2912,7 @@ function onion(r, ang=45, cap_h, d, anchor=CENTER, spin=0, orient=UP) =
 //   text3d("Fogmobar", h=2, anchor=CENTER, atype="ycenter");
 //   text3d("Fogmobar", h=2, anchor=RIGHT);
 //   text3d("Fogmobar", h=2, anchor=RIGHT+BOT, atype="ycenter");
-module text3d(text, h, size=10, font="Helvetica", spacing=1.0, direction="ltr", language="em", script="latin",
+module text3d(text, h, size=10, font="Helvetica", spacing=1.0, direction="ltr", language="en", script="latin",
               height, thickness, atype, center=false,
               anchor, spin=0, orient=UP) {
     no_children($children);