From 3112240dd9b8b7c922fdeabb0473bb09c5d33204 Mon Sep 17 00:00:00 2001
From: dakkar <dakkar@thenautilus.net>
Date: Fri, 21 Feb 2020 13:13:44 +0000
Subject: reworked to be more reliable

more elaborate shapes should now be possible
---
 ambiguous-cylinders.scad | 111 +++++++++++++++++++++++++----------------------
 1 file changed, 58 insertions(+), 53 deletions(-)

(limited to 'ambiguous-cylinders.scad')

diff --git a/ambiguous-cylinders.scad b/ambiguous-cylinders.scad
index c65352c..21ec446 100644
--- a/ambiguous-cylinders.scad
+++ b/ambiguous-cylinders.scad
@@ -34,65 +34,66 @@ module view_cylinder(shift=100/3,height=200,thin=0.1) {
 }
 
 /*
-  given two objects:
+  given a 2D object:
 
-  * build they view cylinders
+  * build the view cylinder at an angle
 
-  * rotate them so the two "observers" are opposite each other on the
-    Y axis, lookin toward the origin with a downward `angle`
+    * this means rotating the object, extruding, then rotating the
+      result the other way:
 
-  * intersect them
+               /    /
+              /    /
+             /____/
 
-  the result approximates the set of points that would look like the
-  first object to the first observers, and like the second object to
-  the second observer
+  * cut away half the cylinder
 
-  (`size` should be higher than the diameter of the largest child,
-  otherwise the shapes may get cut)
+    * because otherwise, in intersect_view_cylinders, we would get 4
+      arcs (two close to the XZ plane, two close to the XY plane), but
+      we only want 2 (the XY ones)
 */
 
-module intersect_view_cylinders(angle=45,size=100,thin=0.1) {
+module clipped_angled_view_cylinder(angle=60,side=1,size=100,thin=0.1) {
      shift=size/3;
      height=size*2;
 
      intersection() {
-          rotate([0,angle,0]) view_cylinder(shift,height,thin) children(0);
-          rotate([0,-angle,0]) view_cylinder(shift,height,thin) children(1);
+          rotate([angle,0,0])
+               view_cylinder(shift,height,thin)
+               rotate([-angle,0,0]) children(0);
+          rotate([angle,0,0])
+               translate([0,-side*size/2,0])
+               cube([size,size,size],center=true);
      }
-};
+}
 
 /*
-  `intersect_view_cylinders` produces a slightly ugly shape, with two
-  half-curves for each half-object; to see the problem, render this:
+  given two objects:
 
-intersect_view_cylinders() {
-     circle(d=14);
-     rotate([0,0,45]) square(size=10,center=true);
-}
+  * build their view cylinders, rotated so the two "observers" are
+    opposite each other on the Y axis, lookin toward the origin with a
+    downward `angle`
 
-  therefore, we render it twice, cutting the "wrong half" out each
-  time. This gives us the curve we want at the top of our ambiguous
-  cylinder
-*/
+  * intersect half of them at a time (see above, and Sugihara's paper,
+    for the reason)
 
+  the result approximates the set of points that would look like the
+  first object to the first observers, and like the second object to
+  the second observer
 
-module clip_intersect_view(angle=45,size=100,thin=0.1) {
-     bound=size*2;
-     skip=0;
+  (`size` should be higher than the diameter of the largest child,
+  otherwise the shapes may get cut)
+*/
 
-     intersection() {
-          intersect_view_cylinders(angle,size,thin) {
-               children(0);
-               children(1);
-          }
-          translate([0,-size/2,0]) rotate([0,-90-angle,0]) cube([size,size,size]);
-     }
-     intersection() {
-          intersect_view_cylinders(angle,size,thin) {
-               children(0);
-               children(1);
+module intersect_view_cylinders(angle=60,size=100,thin=0.1) {
+     union() {
+          intersection() {
+               clipped_angled_view_cylinder(angle,1,size,thin) children(0);
+               clipped_angled_view_cylinder(-angle,1,size,thin) children(1);
+               }
+          intersection() {
+               clipped_angled_view_cylinder(angle,-1,size,thin) children(0);
+               clipped_angled_view_cylinder(-angle,-1,size,thin) children(1);
           }
-          translate([0,-size/2,0]) rotate([0,90-angle,0]) cube([size,size,size]);
      }
 };
 
@@ -104,9 +105,9 @@ module clip_intersect_view(angle=45,size=100,thin=0.1) {
   (`thick` determines the thickness of the wall, `height` its height)
  */
 
-module ambiguous_cylinder(angle=45,size=100,thin=0.1,thick=1,height=10) {
+module ambiguous_cylinder(angle=60,size=100,thin=0.1,thick=1,height=10) {
      minkowski() {
-          clip_intersect_view(angle,size,thin) {
+          intersect_view_cylinders(angle,size,thin) {
                children(0);
                children(1);
           }
@@ -118,9 +119,6 @@ module ambiguous_cylinder(angle=45,size=100,thin=0.1,thick=1,height=10) {
   Some examples:
  */
 
-/*
-  Arrow that always points right
-  */
 module arrow(length=10) {
      scale([length/10,length/10,length/10])
           polygon([ [-5, 0], [-4.5, 1], [ 2, 1], [ 2.5, 3], [ 5, 0],
@@ -133,16 +131,23 @@ module fat_arrow(length=10) {
                     [ 0.5,-4], [-1,-1.5], [-4,-1.5] ]);
 }
 
-ambiguous_cylinder() {
-     rotate([0,0,90]) arrow(30);
-     rotate([0,0,-90]) arrow(30);
+module arrow_always_right() {
+     ambiguous_cylinder() {
+          arrow(30);
+          rotate([0,0,180]) arrow(30);
+     }
 }
 
-/*
-  circle / diamond
- */
+module fat_arrow_always_right() {
+     ambiguous_cylinder() {
+          fat_arrow(30);
+          rotate([0,0,180]) fat_arrow(30);
+     }
+}
 
-translate([0,50,0]) ambiguous_cylinder() {
-     circle(d=14);
-     rotate([0,0,45]) square(size=10,center=true);
+module circle_diamond() {
+     ambiguous_cylinder() {
+          circle(d=14);
+          rotate([0,0,45]) square(size=10,center=true);
+     }
 }
-- 
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