Experimenting with coordinate systems

fcad/align.scad

@@ -0,0 +1,29 @@
+function fAlign(modelA, coordNameA, modelB, coordNameB) = (
+  let(coordA = fModelCoord(modelA, coordNameA),
+      coordB = fModelCoord(modelB, coordNameB),
+      translation = fCoordTranslation(coordA) - fCoordTranslation(coordB),
+      rotation = fCoordRotation(coordA) - fCoordRotation(coordB),
+      scale = fCoordScale(coordA) - fCoordScale(coordB))
+  fUnion(
+    modelA,
+    fTranslate(
+      fRotate(modelB, coordNameB, rotation),
+      translation
+    )
+  )
+);
+
+function fAttach(modelA, coordNameA, modelB, coordNameB) = (
+  let(coordA = fModelCoord(modelA, coordNameA),
+      coordB = fModelCoord(modelB, coordNameB),
+      translation = fCoordTranslation(coordA) - fCoordTranslation(coordB),
+      rotation = fCoordRotation(coordA) - (-1 * fCoordRotation(coordB)),
+      scale = fCoordScale(coordA) - fCoordScale(coordB))
+  fUnion(
+    modelA,
+    fTranslate(
+      fRotate(modelB, coordNameB, rotation),
+      translation
+    )
+  )
+);

fcad/coord.scad

@@ -35,3 +35,11 @@ function fCoordRotation(coord) = (
 function fCoordScale(coord) = (
   fMapLookup(fKeyScale, coord)
 );
+
+function fCoordInverse(coord) = (
+  fCoord(
+    translation=[0, 0, 0] - fCoordTranslation(coord),
+    rotation=[180, 180, 180] + fCoordRotation(coord),
+    scale=1 / fCoordScale(coord)
+  )
+);

fcad/cube.scad

@@ -13,8 +13,14 @@ function fCube(dims) = (
       [1, 3, 7, 5], // +z
     ],
     coords=[
-      [ "/x+,/y+,-z+", fCoord(translation=[x / 2, y / 2, 0]) ],
+      [ "-x-,/y-,/z-", fCoord(translation=[    0, y / 2, z / 2], rotation=[  0, -90,   0]) ],
-      [ "/x+,/y+,+z+", fCoord(translation=[x / 2, y / 2, z]) ],
+      [ "+x+,/y+,/z+", fCoord(translation=[    x, y / 2, z / 2], rotation=[  0,  90,   0]) ],
+
+      [ "/x-,-y-,/z-", fCoord(translation=[x / 2,     0, z / 2], rotation=[-90,   0,   0]) ],
+      [ "/x+,+y+,/z+", fCoord(translation=[x / 2,     y, z / 2], rotation=[ 90,   0,   0]) ],
+
+      [ "/x-,/y-,-z-", fCoord(translation=[x / 2, y / 2,     0], rotation=[180,   0, 180]) ],
+      [ "/x+,/y+,+z+", fCoord(translation=[x / 2, y / 2,     z], rotation=[  0,   0,   0]) ],
     ]
   )
 );

fcad/cylinder.scad

@@ -19,6 +19,9 @@ function fCylinder(h, r, r1=undef, r2=undef, sides=36) = (
       // sides
       [for (side = side_range)
         [for (vertex = [2, 3, 1, 0]) (side * 2 + vertex) % (sides * 2)]]
-    )
+    ),
+    coords=[
+      [ "start", fCoord() ],
+    ]
   )
 );

fcad/draw.scad

@@ -1,25 +1,3 @@
 module fDraw(model) {
   polyhedron(points=fModelPoints(model), faces=fModelFaces(model));
 }
-
-module fDrawN(model, scales) {
-  fDraw(model);
-  points = fModelPoints(model);
-  model_max = fMaxPoint(model);
-  translation =
-    [for (axis = [0 : 2])
-      scales[axis] * model_max[axis]];
-  translate(translation) children();
-}
-
-module fDrawX(model) {
-  fDrawN(model, [1, 0, 0]) children();
-}
-
-module fDrawY(model) {
-  fDrawN(model, [0, 1, 0]) children();
-}
-
-module fDrawZ(model) {
-  fDrawN(model, [0, 0, 1]) children();
-}

fcad/fcad.scad

@@ -1,10 +1,12 @@
+include <align.scad>;
 include <coord.scad>;
 include <cube.scad>;
 include <cylinder.scad>;
 include <draw.scad>;
 include <math.scad>;
 include <model.scad>;
-include <model_util.scad>;
+include <rotate.scad>;
 include <sphere.scad>;
 include <translate.scad>;
 include <types.scad>;
+include <union.scad>;

fcad/math.scad

@@ -6,4 +6,3 @@ function fCartesianProduct(vecs) = (
      for (val2 = fCartesianProduct(fVectorSlice(vecs, start=1)))
      concat(val1, val2)]
 );
-

fcad/model.scad

@@ -4,6 +4,13 @@
 ///   fKeyFaces "faces" fModelFaces(): [ [ pointIdx, ... ], ... ]
 ///   fKeyCoords "coords" fModelCoords(): [ [ name, coord ], ... ]
 
+/// OpenSCAD uses right-handed coordinates. We name directions on these axes:
+///   X: left (-), right (+)
+///   Y: back (-), front (+)
+///   Z: bottom (-), top (+)
+/// Coordinate systems that attach to surfaces should generally have the Z axis
+/// normal to the surface.
+///
 /// Standard model coords names:
 ///
 ///   [-/+] edge ("/" is midpoint)
@@ -39,15 +46,15 @@ function fModelFaces(model) = (
 );
 
 fCoordAliases = [
-  [ "bottom", "/x+,/y+,-z-" ],
+  [ "left",   "-x-,/y-,/z-" ],
+  [ "right",  "+x+,/y+,/z+" ],
+
+  [ "back",   "/x-,-y-,/z-" ],
+  [ "front",  "/x+,+y+,/z+" ],
+
+  [ "bottom", "/x-,/y-,-z-" ],
   [ "top",    "/x+,/y+,+z+" ],
 
-  [ "back",   "-x-,/y+,/z+" ],
-  [ "front",  "+x+,/y+,/z+" ],
-
-  [ "left",   "/x+,-y-,/z+" ],
-  [ "right",  "/x+,+y+,/z+" ],
-
   [ "center", "/x+,/y+,/z+" ],
 ];
 

fcad/model_util.scad

@@ -1,19 +0,0 @@
-function fMinPoint(model) = (
-  [for (axis = [0 : 2])
-   min([for (point = fModelPoints(model)) point[axis]])]
-);
-
-function fMaxPoint(model) = (
-  [for (axis = [0 : 2])
-   max([for (point = fModelPoints(model)) point[axis]])]
-);
-
-function fCenterPoint(model) = (
-  let(model_min = fMinPoint(model),
-      model_max = fMaxPoint(model),
-      model_size =
-        [for (axis = [0 : 2])
-         model_max[axis] - model_min[axis]])
-  [for (axis = [0 : 2])
-   model_min[axis] + (model_size[axis] / 2)]
-);

fcad/rotate.scad

@@ -0,0 +1,45 @@
+function fRotate(model, coordName, rotation) = (
+  // Shift the coordinate frame to the origin, rotate, then restore
+  let(coord = fModelCoord(model, coordName),
+      inverseCoord = fCoordInverse(coord),
+      zeroed = fTranslate(model, fCoordTranslation(inverseCoord)),
+      xMatrix = fRotationMatrixX(rotation[0]),
+      yMatrix = fRotationMatrixY(rotation[1]),
+      zMatrix = fRotationMatrixZ(rotation[2]))
+  fTranslate(
+    fModel(
+      points=
+        [for (point = fModelPoints(zeroed))
+         ([point] * xMatrix * yMatrix * zMatrix)[0]],
+      faces=fModelFaces(model),
+      coords=fModelCoords(model)
+    ),
+    fCoordTranslation(coord)
+  )
+);
+
+// These matrices are transposed because we apply them with post-multiplication
+// to work around OpenSCAD bugs.
+function fRotationMatrixX(theta) = (
+  [
+    [           1,           0,           0 ],
+    [           0,  cos(theta),  sin(theta) ],
+    [           0, -sin(theta),  cos(theta) ],
+  ]
+);
+
+function fRotationMatrixY(theta) = (
+  [
+    [  cos(theta),           0, -sin(theta) ],
+    [           0,           1,           0 ],
+    [  sin(theta),           0,  cos(theta) ],
+  ]
+);
+
+function fRotationMatrixZ(theta) = (
+  [
+    [  cos(theta),  sin(theta),           0 ],
+    [ -sin(theta),  cos(theta),           0 ],
+    [           0,           0,           1 ],
+  ]
+);

fcad/translate.scad

@@ -2,49 +2,8 @@ function fTranslate(model, translation) = (
   fModel(
     points=
       [for (point = fModelPoints(model))
-        [for (axis = [0 : 2])
+       point + translation],
-         point[axis] + translation[axis]]
+    faces=fModelFaces(model),
-      ],
+    coords=fModelCoords(model)
-    faces=fModelFaces(model)
   )
 );
-
-function fZeroN(model, scales) = (
-  let(model_min = fMinPoint(model),
-      translation =
-        [for (axis = [0 : 2])
-         scales[axis] * model_min[axis]])
-  fTranslate(model, translation)
-);
-
-function fZeroX(model) = (
-  fZeroN(model, [-1, 0, 0])
-);
-
-function fZeroY(model) = (
-  fZeroN(model, [0, -1, 0])
-);
-
-function fZeroZ(model) = (
-  fZeroN(model, [0, 0, -1])
-);
-
-function fCenterN(model, scales) = (
-  let(model_center = fCenterPoint(model),
-      translation =
-        [for (axis = [0 : 2])
-        scales[axis] * model_center[axis]])
-  fTranslate(model, translation)
-);
-
-function fCenterX(model) = (
-  fCenterN(model, [-1, 0, 0])
-);
-
-function fCenterY(model) = (
-  fCenterN(model, [0, -1, 0])
-);
-
-function fCenterZ(model) = (
-  fCenterN(model, [0, 0, -1])
-);

fcad/union.scad

@@ -0,0 +1,10 @@
+function fUnion(modelA, modelB) = (
+  let(numPointsA = len(fModelPoints(modelA)))
+  fModel(
+    points=concat(fModelPoints(modelA), fModelPoints(modelB)),
+    faces=concat(fModelFaces(modelA),
+                 [for (face = fModelFaces(modelB))
+                  [for (point = face) point + numPointsA]])
+  )
+  // TODO: how should we handle coords here?
+);

test.scad

@@ -1,5 +1,21 @@
 use <fcad/fcad.scad>;
 
-fDrawX(fCylinder(10, r1=5, r2=2))
+module testAxes(translation=[0, 0, 0], rotation=[0, 0, 0]) {
-fDrawX(fSphere(10))
+  color("red") fDraw(fTranslate(fRotate(fRotate(fCylinder(h=100, r=1), "start", [0, 90, 0]), "start", rotation), translation));
-fDrawX(fCube(10));
+  color("green") fDraw(fTranslate(fRotate(fRotate(fCylinder(h=100, r=1), "start", [-90, 0, 0]), "start", rotation), translation));
+  color("blue") fDraw(fTranslate(fRotate(fRotate(fCylinder(h=100, r=1), "start", [0, 0, 0]), "start", rotation), translation));
+}
+
+testAxes(translation=[0, 0, 200], rotation=[0, 0, 0]);
+testAxes(translation=[200, 0, 0], rotation=[0, 180, ]);
+testAxes(translation=[0, 0, -200], rotation=[180, 0, 0]);
+testAxes(translation=[-200, 0, 0], rotation=[0, -90, 0]);
+testAxes(translation=[0, 200, 0], rotation=[-90, 0, 0]);
+testAxes(translation=[0, -200, 0], rotation=[90, 0, 0]);
+
+
+//result = fAttach(fCube(10), "top", fCube(5), "bottom5");
+//result = fRotate(fCube(5), "front", [0, 360, 360]);
+
+//echo(result);
+//#fDraw(result);