[kous500]

What and why

BezierSegment.angle found the direction of the curve with an expanded polynomial in t, written out once for x and once for z, and turned it into an angle with atan and its own cases for the quadrants. This makes the math read like the formulas it comes from.

• Angle: Math.atan2(dx, dz) instead of atan(dx / dz) with cases for NaN and dz < 0. A zero vector still gives 0, as the Javadoc says; atan2 alone would give Math.PI or -Math.PI there when dz is -0.0. The Javadoc now gives the range, -Math.PI to Math.PI.
• Direction: the derivative divided by 3, the steps between the points (step0 to step2) weighted by the quadratic Bernstein polynomials, instead of the expanded polynomial.
• Names: the weights are named after their degree, cubic0 to cubic3 in point (bernstein0 to bernstein3 before) and quadratic0 to quadratic2 in angle.
• Vector operations: Vector3.multiply(double) lets point and angle add weighted vectors instead of writing each coordinate.

Behavior:

• point gives the same values: the products and the sums are made in the same order.
• angle differs only in the last bits, and for directions towards -x and -z, where it now gives -π to -π/2 instead of π to 3π/2. The only caller, CurveLayout, uses its cosine and sine, which differ by at most about 7e-16. Compared with the previous code on 10 million random segments, the angle differs by at most 9.1e-13 radians where the direction is longer than 0.001.
• When dz is -0.0, the previous code gave the opposite direction along x (-π/2 for +x); atan2 gives the right one. dz is -0.0 only when every term of it is.

How it was tested

• ./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.
• New tests: BezierSegmentTest checks the angle towards -x and -z (-3π/4), and Vector3Test checks multiply.
• IntelliJ IDEA's inspections report no warnings in the changed files.
• Not checked: //bc and the preview in the game, and the cost of the extra Vector3 objects in point, which the Fabric preview calls every frame.
• Minecraft version: the versions of the game tests
• Server software / loader: Fabric (game tests)
• WorldEdit / FastAsyncWorldEdit version: the versions in the build

Notes

• No changes for players or server owners beyond the rounding described above.