fix: Lay the cross section of //bc across the curve at its ends

curvebuilding-core/src/main/java/me/kous500/curvebuilding/commands/bc/CurveLayout.java

@@ -120,12 +120,11 @@ private static List<Sample> samples(BezierSegment segment, double fineness) {
         List<Sample> samples = new ArrayList<>();
         Vector3 before = segment.p0();
         double distance = 0;
-        for (double t = 0; t <= 1; t += 1.0 / fineness) {
-            // At 0 a handle can be at the point itself, where the curve has no direction yet
-            double at = t == 0 ? 0.00001 : t;
-            Vector3 point = segment.point(at);
+        for (int step = 0; step <= fineness; step++) {
+            double t = step / fineness;
+            Vector3 point = segment.point(t);
             distance += before.distance(point);
-            samples.add(new Sample(point, across(segment.direction(at)), distance));
+            samples.add(new Sample(point, across(segment.tangent(t)), distance));
             before = point;
         }
         return samples;

curvebuilding-core/src/main/java/me/kous500/curvebuilding/curve/BezierSegment.java

@@ -111,6 +111,25 @@ public Vector3 direction(double t) {
                 .add(step2.multiply(quadratic2));
     }
 
+    /**
+     * The direction that the curve goes at {@code t}, like {@link #direction}, but also where that is zero, as at an
+     * end whose handle is at its point. There the curve leaves {@code p0} towards {@code p2}, or arrives at {@code p3}
+     * from {@code p1}, as {@link #direction} does just beside it; when that is zero too, from {@code p0} to
+     * {@code p3}.
+     *
+     * @param t where on the segment, from 0 to 1
+     * @return the direction, not scaled to any length; zero when none of these tells it, as when all four positions
+     * are at one place
+     */
+    public Vector3 tangent(double t) {
+        Vector3 direction = direction(t);
+        if (direction.lengthSq() != 0) return direction;
+
+        Vector3 besideTheEnd = t < 0.5 ? p2.subtract(p0) : p3.subtract(p1);
+        if (besideTheEnd.lengthSq() != 0) return besideTheEnd;
+        return p3.subtract(p0);
+    }
+
     /**
      * The length of the curve, measured along {@code fineness} straight steps.
      *

curvebuilding-core/src/test/java/me/kous500/curvebuilding/commands/bc/CurveLayoutTest.java

@@ -85,6 +85,19 @@ void crossSectionIsLaidAcrossTheCurve() throws Exception {
         assertEquals(5 * 9, blocks.size());
     }
 
+    @Test
+    void crossSectionIsAcrossTheCurveAtItsEnd() throws Exception {
+        // With one step per block, the last step is at the end, where the segment has no handle
+        CurveLayout.Selection selection = new CurveLayout.Selection(1, 1, 3, Vector3.at(0, 0, 1));
+        BezierSegment line = straight(Vector3.at(0, 64, 0), Vector3.at(4, 64, 0));
+        CurveLayout layout = new CurveLayout(selection, NO_ARGUMENTS, NEVER_AIR, 0, 10000, 1);
+        layout.add(line);
+        NavigableMap<BlockVector3, BlockVector3> blocks = layout.blocks();
+
+        assertEquals(Set.of(0, 1, 2, 3, 4), xs(blocks));
+        assertEquals(5 * 3, blocks.size());
+    }
+
     @Test
     void crossSectionTurnsWithTheCurve() throws Exception {
         CurveLayout.Selection selection = new CurveLayout.Selection(1, 3, 3, Vector3.at(0, 1, 1));

curvebuilding-core/src/test/java/me/kous500/curvebuilding/curve/BezierSegmentTest.java

@@ -90,6 +90,36 @@ void endWithoutHandleHasNoDirection() {
         }
     }
 
+    @Nested
+    class Tangent {
+        @Test
+        void isTheDirectionWhereThereIsOne() {
+            assertVector(5, 0, 0, ARCH.tangent(0.5));
+            assertVector(0, 10, 0, ARCH.tangent(0));
+        }
+
+        @Test
+        void straightSegmentGoesFromEndToEndAtItsEnds() {
+            BezierSegment segment = straight(Vector3.at(0, 64, 0), Vector3.at(10, 64, 0));
+            assertVector(10, 0, 0, segment.tangent(0));
+            assertVector(10, 0, 0, segment.tangent(1));
+        }
+
+        @Test
+        void endWithoutHandleGoesTowardsTheOtherHandle() {
+            Vector3 start = Vector3.at(0, 64, 0);
+            BezierSegment segment = new BezierSegment(start, start, Vector3.at(0, 64, 10), Vector3.at(10, 64, 10));
+            assertVector(0, 0, 10, segment.tangent(0));
+            assertVector(10, 0, 0, segment.tangent(1));
+        }
+
+        @Test
+        void segmentAtOnePlaceHasNoDirection() {
+            Vector3 a = Vector3.at(3, 64, 3);
+            assertVector(0, 0, 0, new BezierSegment(a, a, a, a).tangent(0));
+        }
+    }
+
     @Nested
     class Length {
         @ParameterizedTest