[kous500]

What and why

At an end of a segment whose handle is at its point, the curve has no direction (its derivative is zero), and //bc then laid the cross section along +x. CurveLayout stepped along the curve by adding 1 / fineness to t; that reached t = 1 only for some lengths, because of rounding. With a fineness of 1 it did for lengths such as 1 - 5, 8, 12 and 16: a straight curve along x from 0 to 4 with a selection three blocks wide got the blocks (4, 0) and (5, 0) at its end instead of (4, -1), (4, 0) and (4, 1). With the default fineness of 10 it did not reach t = 1 for any length from 1 to 300.

• BezierSegment.tangent: the direction of the curve, also where direction is zero. At an end without a handle, the curve leaves p0 towards p2, or arrives at p3 from p1, which is the direction just beside the end; when that is zero too, from p0 to p3.
• Steps of //bc: t is a whole step divided by the fineness, so the end of a segment is always a step when the fineness is whole, and it does not drift with rounding (by up to 1.6e-13 before). The direction is tangent, so the first step is at t = 0 instead of t = 0.00001.

How it was tested

• New tests: CurveLayoutTest lays a straight curve along x with one step per block and checks the blocks at its end; it fails on the code before this change. BezierSegmentTest checks tangent where there is a direction, at the ends of a straight segment, at an end without a handle, and for a segment at one place.
• ./gradlew build :curvebuilding-fabric:26.3:runGameTest checkCodeStyle --warning-mode all: the build and unit tests pass, with no Gradle, javac or Checkstyle warnings. The game tests pass on the six versions that build runs them on. After the last change, to the Javadoc of tangent, only the compilation and checkCodeStyle were run again.
• IntelliJ IDEA's inspections report no warnings in the changed files.
• //bc was checked in the game by the maintainer.
• Minecraft version: the versions of the game tests
• Server software / loader: Fabric (game tests)
• WorldEdit / FastAsyncWorldEdit version: the versions in the build

Notes

• With the default fineness, a segment whose length is a whole number now also gets a step at its end; it usually falls on the same block as the step before it.