Polygons & Collections (2D)

List<Point2D> Extensions

List<Point2D> has extension functions for coordinate extraction, bounding-box queries, arc-length, centroid, and parametric functions. These are available on any List<Point2D>, including the points property of Curve2D, Polygon2D, LinearSpline, and CubicSpline.

Extension	Type	Description
xPoints	List<Double>	x-coordinates
yPoints	List<Double>	y-coordinates
length	Double	Arc length (sum of segment lengths)
centroid	Point2D	Arithmetic mean of all points
minX, maxX	Double	x-axis bounds
minY, maxY	Double	y-axis bounds

val curve = Curve2D(Point2D(0.0, 0.0), Point2D(1.0, 1.0), Point2D(2.0, 0.0))

println(curve.points.length)      // arc length
println(curve.points.centroid)    // mean point
println(curve.points.minX)        // 0.0

Range checks

curve.points.inXRange(1.5)   // true if 1.5 is within [minX, maxX]
curve.points.inYRange(2.0)   // false if 2.0 is outside [minY, maxY]

Parametric functions from the point list

Extract Function2D objects by interpolating the point list:

val xFn: Function2D = curve.points.xParametricFunction()
val yFn: Function2D = curve.points.yParametricFunction()

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Curve2D

An open, ordered sequence of Point2D values. Supports concatenation and arithmetic transforms.

import plane.Curve2D
import plane.elements.Point2D

val c1 = Curve2D(Point2D(0.0, 0.0), Point2D(1.0, 1.0))
val c2 = Curve2D(Point2D(1.0, 1.0), Point2D(2.0, 0.0))

val combined: Curve2D = c1.concat(c2)

Arithmetic

val c = Curve2D(Point2D(0.0, 0.0), Point2D(1.0, 1.0))

// Translate all points by a vector
val shifted = c + Point2D(1.0, 0.0)

// Scale all points
val scaled = c * 3.0

Rotation

import units.Angle

val rotated = c.rotate(Angle.Degrees(45.0))
val rotatedAround = c.rotate(Point2D(1.0, 0.0), Angle.Degrees(90.0))

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Polygon2D

A closed polygon. The first point is implicitly repeated to close the shape.

import plane.Polygon2D
import plane.elements.Point2D

val triangle = Polygon2D(listOf(
    Point2D(0.0, 0.0),
    Point2D(2.0, 0.0),
    Point2D(1.0, 2.0)
))

println(triangle.area)   // computed via the shoelace formula

Closed point list

// Returns points with the first point appended at the end
triangle.pointsClosedPolygon   // List<Point2D> of size n+1

Rotation

import units.Angle

val rotated = triangle.rotate(Angle.Degrees(90.0))
val rotatedAround = triangle.rotate(Point2D(1.0, 1.0), Angle.Degrees(45.0))

Visualization

// requires geomez-visualization
triangle.plot()

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ConvexPolygon2D

A subtype of Polygon2D that represents a convex polygon. Typically obtained via the convex-hull utility:

import utils.convexHull
import plane.elements.Point2D

val points = listOf(
    Point2D(0.0, 0.0),
    Point2D(1.0, 2.0),
    Point2D(2.0, 1.0),
    Point2D(0.5, 0.5),   // interior point — excluded from hull
    Point2D(3.0, 0.0)
)

val (convexPolygon, hullIndices) = convexHull(points)
// convexPolygon: ConvexPolygon2D
// hullIndices: List<Int> — indices of the hull vertices in the original list