[kous500]

What and why

Some of the math of //bc and of the particle preview went through angles or wrote each coordinate out, which hid what it computes. This writes it with vector operations.

• Cross section of //bc: CurveLayout turned the direction of the curve into an angle with atan2 and back with cos(-angle) and sin(-angle) to lay the cross section across the curve. It now turns the direction a quarter turn on the xz plane (the way that takes +z to +x) and scales it to length 1. A curve that does not move on the xz plane still gets +x. Sample keeps this vector instead of the angle.
• BezierSegment.direction: gives the direction of the curve (the derivative divided by 3) as a vector. angle, whose only caller was CurveLayout, is removed.
• Cross of a handle: each line goes from a corner of the block towards its center, corner + (center - corner) * i / density, instead of 0.5 * x + (density * x + (-x * 2 + 1) * i) / density * 0.5 for each coordinate.
• Handle line: start + (handle - point) * t instead of each coordinate.
• Distances: BezierSegment.length and CurveLayout use Vector3.distance instead of writing the square root out; the result is the same to the bit.

How it was tested

• Where //bc places the blocks beside the curve was compared with the angle version on 20,000 random curves (68 million positions): 2 differ, both at exactly .5, where the rounding went the other way by about 1e-15.
• ./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.
• Tests: BezierSegmentTest checks direction (the ends go towards their handles, the weights at t = 0.5, and no direction at an end without a handle) instead of angle, and a new CurveLayoutTest checks that the cross section is laid across a curve along z, as the existing one does along x.
• IntelliJ IDEA's inspections report no warnings in the changed files.
• Not checked: //bc and the particle preview in the game.
• 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.