Fix Cylinder(h, 0, r) to support cone with apex at bottom (#1541)

* fix upside down cone using cylinder

* minor changes

* minor fixes

src/constructors.cpp

@@ -148,7 +148,8 @@ Manifold Manifold::Cube(vec3 size, bool center) {
  * form cones if both radii are specified.
  *
  * @param height Z-extent
- * @param radiusLow Radius of bottom circle. Must be positive.
+ * @param radiusLow Radius of bottom circle. Must be non-negative. If zero,
+ * radiusHigh must be positive and a cone with apex at the bottom is created.
  * @param radiusHigh Radius of top circle. Can equal zero. Default is equal to
  * radiusLow.
  * @param circularSegments How many line segments to use around the circle.
@@ -158,9 +159,20 @@ Manifold Manifold::Cube(vec3 size, bool center) {
  */
 Manifold Manifold::Cylinder(double height, double radiusLow, double radiusHigh,
                             int circularSegments, bool center) {
-  if (height <= 0.0 || radiusLow <= 0.0) {
+  if (height <= 0.0 || radiusLow < 0.0) {
     return Invalid();
   }
+  if (radiusLow == 0.0) {
+    if (radiusHigh <= 0.0) {
+      return Invalid();
+    }
+    // Cone with apex at bottom: create the centered apex-at-top version and
+    // mirror it
+    Manifold cone = Cylinder(height, radiusHigh, 0.0, circularSegments, true);
+    cone = cone.Mirror(vec3(0.0, 0.0, 1.0));
+    if (!center) cone = cone.Translate(vec3(0.0, 0.0, height / 2.0));
+    return cone.AsOriginal();
+  }
   const double scale = radiusHigh >= 0.0 ? radiusHigh / radiusLow : 1.0;
   const double radius = fmax(radiusLow, radiusHigh);
   const int n = circularSegments > 2 ? circularSegments

test/manifold_test.cpp

@@ -294,6 +294,30 @@ TEST(Manifold, Cylinder) {
   EXPECT_EQ(cylinder.NumTri(), 4 * n - 4);
 }
 
+TEST(Manifold, CylinderZeroRadiusLow) {
+  // cylinder(h, 0, r) should produce a cone with apex at z=0 and base at z=h.
+  // Use enough segments for accurate volume.
+  const int n = 256;
+  const double h = 5.0, r = 3.0;
+  Manifold coneApexBottom = Manifold::Cylinder(h, 0.0, r, n);
+  Manifold coneApexTop = Manifold::Cylinder(h, r, 0.0, n);
+
+  EXPECT_EQ(coneApexBottom.Status(), Manifold::Error::NoError);
+  EXPECT_FALSE(coneApexBottom.IsEmpty());
+
+  // Both cones must have equal total volume.
+  const double totalVol = coneApexTop.Volume();
+  EXPECT_NEAR(coneApexBottom.Volume(), totalVol, 1e-6);
+
+  // Differentiate orientation by intersecting with the bottom half (z in
+  // [0, h/2]). A sub-cone scaled by 1/2 in all dimensions has 1/8 the volume,
+  // so apex-at-bottom gives V/8 and apex-at-top gives 7*V/8.
+  Manifold slicer = Manifold::Cube(vec3(2 * r + 1, 2 * r + 1, h / 2))
+                        .Translate(vec3(-(r + 0.5), -(r + 0.5), 0.0));
+  EXPECT_NEAR((coneApexBottom ^ slicer).Volume(), totalVol / 8.0, 0.01);
+  EXPECT_NEAR((coneApexTop ^ slicer).Volume(), 7.0 * totalVol / 8.0, 0.01);
+}
+
 TEST(Manifold, Extrude) {
   Polygons polys = SquareHole();
   Manifold donut = Manifold::Extrude(polys, 1.0, 3);
@@ -813,6 +837,8 @@ TEST(Manifold, Invalid) {
   EXPECT_EQ(Manifold::Sphere(0).Status(), invalid);
   EXPECT_EQ(Manifold::Cylinder(0, 5).Status(), invalid);
   EXPECT_EQ(Manifold::Cylinder(2, -5).Status(), invalid);
+  EXPECT_EQ(Manifold::Cylinder(2, 0).Status(), invalid);
+  EXPECT_EQ(Manifold::Cylinder(2, 0, 0).Status(), invalid);
   EXPECT_EQ(Manifold::Cube(vec3(0.0)).Status(), invalid);
   EXPECT_EQ(Manifold::Cube({-1, 1, 1}).Status(), invalid);
   EXPECT_EQ(Manifold::Extrude(circ.ToPolygons(), 0.).Status(), invalid);