update RELEASE

README.md

@@ -104,7 +104,6 @@ Too many dependencies? Because OpenSCAD doesn't provide namespace management, I
 	- [sphere_spiral_extrude](https://openhome.cc/eGossip/OpenSCAD/lib-sphere_spiral_extrude.html)
 
 - Matrix
-	- [m_multiply](https://openhome.cc/eGossip/OpenSCAD/lib-m_multiply.html)
 	- [m_cumulate](https://openhome.cc/eGossip/OpenSCAD/lib-m_cumulate.html)	
 	- [m_translation](https://openhome.cc/eGossip/OpenSCAD/lib-m_translation.html)
 	- [m_rotation](https://openhome.cc/eGossip/OpenSCAD/lib-m_rotation.html)

RELEASE.md

@@ -1,3 +1,12 @@
+# v1.1.1
+- Bugfixes
+  - `m_rotation` returns an identity matrix if `a` is 0.
+  - The `path_pts` parameter of `path_extrude` accepts two or three points. 
+  - The `points` parameter of `along_with` accepts two or three points. 
+
+- Others
+  -  OpenSCAD has built-in matrix multiplication so `m_multiply` is not necessary.
+
 # v1.1
 - New matrix functions:
   - [m_multiply](https://openhome.cc/eGossip/OpenSCAD/lib-m_multiply.html)

docs/lib-arc_path.md

@@ -15,8 +15,8 @@ Creates an arc path. You can pass a 2 element vector to define the central angle
     include <hull_polyline2d.scad>;
     
     $fn = 24;
-    points = arc_path(radius = 20, angle = [45, 290], width = 2);
-    hull_polyline2d(points);
+    points = arc_path(radius = 20, angle = [45, 290]);
+    hull_polyline2d(points, width = 2);
 
 ![arc_path](images/lib-arc_path-1.JPG)
 
@@ -24,8 +24,8 @@ Creates an arc path. You can pass a 2 element vector to define the central angle
     include <hull_polyline2d.scad>;
     
     $fn = 24;
-    points = arc_path(radius = 20, angle = 135, width = 2);
-    hull_polyline2d(points);
+    points = arc_path(radius = 20, angle = 135);
+    hull_polyline2d(points, width = 2);
 
 ![arc_path](images/lib-arc_path-2.JPG)
 

docs/lib-m_mirror.md

@@ -1,23 +0,0 @@
-# m_mirror
-
-Generate a 4x4 transformation matrix which can pass into `multmatrix` to mirror the child element on a plane through the origin. 
-
-**Since:** 1.1
-
-## Parameters
-
-- `v` : The normal vector of a plane intersecting the origin through which to mirror the object.
-
-## Examples
-
-	include <m_mirror.scad>;
-
-	rotate([0, 0, 10]) 
-		cube([3, 2, 1]);
-		
-	multmatrix(m_mirror([1, 1, 0]))
-		rotate([0, 0, 10]) 
-			cube([3, 2, 1]);
-
-![m_mirror](images/lib-m_mirror-1.JPG)
-

docs/lib-shape_cyclicpolygon.md

@@ -6,6 +6,7 @@ Returns shape points of a regular cyclic polygon. They can be used with xxx_extr
 
 - `sides` : The radius of the circle.
 - `circle_r` : The radius of the circumcircle.
+- `corner_r` : The radius of the circle at a corner.
 - `$fa`, `$fs`, `$fn` : Check [the circle module](https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Using_the_2D_Subsystem#circle) for more details.
 
 ## Examples

src/__private__/__m_multiply.scad

@@ -1,13 +0,0 @@
-function __m_multiply(ma, mb) = 
-    let(
-        c1 = [mb[0][0], mb[1][0], mb[2][0], mb[3][0]],
-        c2 = [mb[0][1], mb[1][1], mb[2][1], mb[3][1]],
-        c3 = [mb[0][2], mb[1][2], mb[2][2], mb[3][2]],
-        c4 = [mb[0][3], mb[1][3], mb[2][3], mb[3][3]]
-    )
-    [
-        [ma[0] * c1, ma[0] * c2, ma[0] * c3, ma[0] * c4],
-        [ma[1] * c1, ma[1] * c2, ma[1] * c3, ma[1] * c4],
-        [ma[2] * c1, ma[2] * c2, ma[2] * c3, ma[2] * c4],
-        [ma[3] * c1, ma[3] * c2, ma[3] * c3, ma[3] * c4]
-    ];

src/along_with.scad

@@ -7,11 +7,10 @@
 * @see https://openhome.cc/eGossip/OpenSCAD/lib-along_with.html
 *
 **/ 
-
+ 
 include <__private__/__angy_angz.scad>;
 include <__private__/__is_vector.scad>;
 include <__private__/__to3d.scad>;
-include <__private__/__m_multiply.scad>;
 
 // Becuase of improving the performance, this module requires m_rotation.scad which doesn't require in dotSCAD 1.0. 
 // For backward compatibility, I directly include m_rotation here.
@@ -35,6 +34,13 @@ module along_with(points, angles, twist = 0, scale = 1.0) {
 
     // get rotation matrice for sections
 
+    identity_matrix = [
+        [1, 0, 0, 0],
+        [0, 1, 0, 0],
+        [0, 0, 1, 0],
+        [0, 0, 0, 1]
+    ];    
+
     function local_ang_vects(j) = 
         j == 0 ? [] : local_ang_vects_sub(j);
     
@@ -53,12 +59,16 @@ module along_with(points, angles, twist = 0, scale = 1.0) {
             leng_rot_matrice_minus_one = leng_rot_matrice - 1,
             leng_rot_matrice_minus_two = leng_rot_matrice - 2
         )
-        i == leng_rot_matrice - 2 ? 
+        leng_rot_matrice == 0 ? [identity_matrix] : (
+            leng_rot_matrice == 1 ? [rot_matrice[0], identity_matrix] : (
+                i == leng_rot_matrice_minus_two ? 
                [
                    rot_matrice[leng_rot_matrice_minus_one], 
-                   __m_multiply(rot_matrice[leng_rot_matrice_minus_two], rot_matrice[leng_rot_matrice_minus_one])
+                   rot_matrice[leng_rot_matrice_minus_two] * rot_matrice[leng_rot_matrice_minus_one]
                ] 
-               : cumulated_rot_matrice_sub(i, rot_matrice);
+               : cumulated_rot_matrice_sub(i, rot_matrice)
+            )
+        );
 
     function cumulated_rot_matrice_sub(i, rot_matrice) = 
         let(
@@ -66,7 +76,7 @@ module along_with(points, angles, twist = 0, scale = 1.0) {
             curr_matrix = rot_matrice[i],
             prev_matrix = matrice[len(matrice) - 1]
         )
-        concat(matrice, [__m_multiply(curr_matrix, prev_matrix)]);
+        concat(matrice, [curr_matrix * prev_matrix]);
 
     // align modules
 

src/m_cumulate.scad

@@ -8,12 +8,10 @@
 *
 **/
 
-include <__private__/__m_multiply.scad>;
-
 function _m_cumulate(matrice, i) = 
     i == len(matrice) - 2 ?
-        __m_multiply(matrice[i], matrice[i + 1]) :
-        __m_multiply(matrice[i], _m_cumulate(matrice, i + 1));
+        matrice[i] * matrice[i + 1] :
+        matrice[i] * _m_cumulate(matrice, i + 1);
 
 function m_cumulate(matrice) = 
     len(matrice) == 1 ? matrice[0] : _m_cumulate(matrice, 0);

src/m_multiply.scad

@@ -1,13 +0,0 @@
-/**
-* m_multiply.scad
-*
-* @copyright Justin Lin, 2019
-* @license https://opensource.org/licenses/lgpl-3.0.html
-*
-* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_multiply.html
-*
-**/
-
-include <__private__/__m_multiply.scad>;
-
-function m_multiply(ma, mb) = __m_multiply(ma, mb);

src/m_rotation.scad

@@ -8,8 +8,6 @@
 *
 **/
 
-include <__private__/__m_multiply.scad>;
-
 function _q_rotation(a, v) = 
     let(
         half_a = a / 2,
@@ -77,11 +75,12 @@ function _to_avect(a) =
 
 function _xyz_rotation(a) =
     let(ang = _to_avect(a))
-    __m_multiply(
-        _m_zRotation(ang[2]), __m_multiply(
-            _m_yRotation(ang[1]), _m_xRotation(ang[0])
-        )
-    );
+    _m_zRotation(ang[2]) * _m_yRotation(ang[1]) * _m_xRotation(ang[0]);
 
 function m_rotation(a, v) = 
-    v == undef ? _xyz_rotation(a) : _q_rotation(a, v);
+    (a == 0 || a == [0, 0, 0] || a == [0] || a == [0, 0]) ? [
+        [1, 0, 0, 0],
+        [0, 1, 0, 0],
+        [0, 0, 1, 0],
+        [0, 0, 0, 1]
+    ] : (v == undef ? _xyz_rotation(a) : _q_rotation(a, v));

src/m_shearing.scad

@@ -8,7 +8,6 @@
 *
 **/
 
-include <__private__/__m_multiply.scad>;
 include <__private__/__m_shearing.scad>;
 
 function m_shearing(sx = [0, 0], sy = [0, 0], sz = [0, 0]) = __m_shearing(sx, sy, sz);

src/path_extrude.scad

@@ -11,7 +11,6 @@
 include <__private__/__is_vector.scad>;
 include <__private__/__to3d.scad>;
 include <__private__/__angy_angz.scad>;
-include <__private__/__m_multiply.scad>;
 
 // Becuase of improving the performance, this module requires m_rotation.scad which doesn't require in dotSCAD 1.0. 
 // For backward compatibility, I directly include m_rotation here.
@@ -70,13 +69,24 @@ module path_extrude(shape_pts, path_pts, triangles = "SOLID", twist = 0, scale =
     leng_rot_matrice_minus_one = leng_rot_matrice - 1;
     leng_rot_matrice_minus_two= leng_rot_matrice - 2;
 
+    identity_matrix = [
+        [1, 0, 0, 0],
+        [0, 1, 0, 0],
+        [0, 0, 1, 0],
+        [0, 0, 0, 1]
+    ];
+
     function cumulated_rot_matrice(i) = 
-        i == leng_rot_matrice - 2 ? 
-               [
-                   rot_matrice[leng_rot_matrice_minus_one], 
-                   __m_multiply(rot_matrice[leng_rot_matrice_minus_two], rot_matrice[leng_rot_matrice_minus_one])
-               ] 
-               : cumulated_rot_matrice_sub(i);
+        leng_rot_matrice == 0 ? [identity_matrix] : (
+             leng_rot_matrice == 1 ? [rot_matrice[0], identity_matrix] : 
+                (
+                    i == leng_rot_matrice_minus_two ? 
+                    [
+                        rot_matrice[leng_rot_matrice_minus_one], 
+                        rot_matrice[leng_rot_matrice_minus_two] * rot_matrice[leng_rot_matrice_minus_one]
+                    ] 
+                    : cumulated_rot_matrice_sub(i))
+        );
 
     function cumulated_rot_matrice_sub(i) = 
         let(
@@ -84,7 +94,7 @@ module path_extrude(shape_pts, path_pts, triangles = "SOLID", twist = 0, scale =
             curr_matrix = rot_matrice[i],
             prev_matrix = matrice[len(matrice) - 1]
         )
-        concat(matrice, [__m_multiply(curr_matrix, prev_matrix)]);
+        concat(matrice, [curr_matrix * prev_matrix]);
 
     cumu_rot_matrice = cumulated_rot_matrice(0);
 

src/shear.scad

@@ -8,7 +8,6 @@
 *
 **/
 
-include <__private__/__m_multiply.scad>;
 include <__private__/__m_shearing.scad>;
 
 module shear(sx = [0, 0], sy = [0, 0], sz = [0, 0]) {