kone.misc.planimetricsCalculation/com.lounres.kone.misc.planimetricsCalculation

Package-level declarations

Types

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data class Line<C>(val x: LabeledPolynomial<C>, val y: LabeledPolynomial<C>, val z: LabeledPolynomial<C>)
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class PlanimetricsCalculationContext<C, out A : Ring<C>>(val ring: A) : KoneContext
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data class Point<C>(val x: LabeledPolynomial<C>, val y: LabeledPolynomial<C>, val z: LabeledPolynomial<C>)
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data class Quadric<C>(val xx: LabeledPolynomial<C>, val yy: LabeledPolynomial<C>, val zz: LabeledPolynomial<C>, val xy: LabeledPolynomial<C>, val xz: LabeledPolynomial<C>, val yz: LabeledPolynomial<C>)
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Functions

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fun <CT> PlanimetricsCalculationContext<CT, *>.centroid(A: Point<CT>, B: Point<CT>, C: Point<CT>): Point<CT>

Constructs centroid of triangle ABC.

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fun <C> PlanimetricsCalculationContext<C, *>.circleByCenterAndPoint(O: Point<C>, A: Point<C>): Quadric<C>

Constructs circle (as Quadric) by its center and point on it.

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fun <C> PlanimetricsCalculationContext<C, *>.circleByDiameter(A: Point<C>, B: Point<C>): Quadric<C>

Constructs circle (as Quadric) by the given opposite points on it.

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fun <CT> PlanimetricsCalculationContext<CT, *>.circumcenter(A: Point<CT>, B: Point<CT>, C: Point<CT>): Point<CT>

Constructs circumcenter of triangle ABC.

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fun <CT> PlanimetricsCalculationContext<CT, *>.circumcircle(A: Point<CT>, B: Point<CT>, C: Point<CT>): Quadric<CT>

Constructs circumcircle of triangle ABC as Quadric.

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fun <CT> PlanimetricsCalculationContext<CT, *>.collinearityCondition(A: Point<CT>, B: Point<CT>, C: Point<CT>): LabeledPolynomial<CT>

Returns an expression which equality to zero is equivalent to collinearity of the points.

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fun <CT> PlanimetricsCalculationContext<CT, *>.collinearityTest(A: Point<CT>, B: Point<CT>, C: Point<CT>): Boolean

Tests if the points are collinear.

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fun <C> PlanimetricsCalculationContext<C, *>.concurrencyCondition(l: Line<C>, m: Line<C>, n: Line<C>): LabeledPolynomial<C>

Returns an expression which equality to zero is equivalent to concurrency of the lines.

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fun <C> PlanimetricsCalculationContext<C, *>.concurrencyTest(l: Line<C>, m: Line<C>, n: Line<C>): Boolean

Tests if the lines are

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fun <V> PlanimetricsCalculationContext<V, *>.divideSegmentInRatio(A: Point<V>, B: Point<V>, lambda: V): Point<V>

Constructs a point P on the line through A and B that divides segment \( AB \) in ratio lambda. It means that on the affine map that is considered generated by Point.x and Point.y coordinates a point P such that \(\overrightarrow{AP}/\overrightarrow{PB} = \lambda\), so P is returned.

fun <V> PlanimetricsCalculationContext<V, *>.divideSegmentInRatio(A: Point<V>, B: Point<V>, a: V, b: V): Point<V>

Constructs a point P on the line through A and B that divides segment \( AB \) in ratio \(a/b\). It means that on the affine map that is considered generated by Point.x and Point.y coordinates a point P such that \(\overrightarrow{AP}/\overrightarrow{PB} = a/b\), so P is returned.

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fun <CT> PlanimetricsCalculationContext<CT, *>.eulerCircle(A: Point<CT>, B: Point<CT>, C: Point<CT>): Quadric<CT>

Constructs Euler's circle of triangle ABC as Quadric.

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fun <CT> PlanimetricsCalculationContext<CT, *>.eulerLine(A: Point<CT>, B: Point<CT>, C: Point<CT>): Line<CT>

Constructs Euler line of triangle ABC.

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fun <C> PlanimetricsCalculationContext<C, *>.intersectionOf(l: Line<C>, m: Line<C>): Point<C>

Constructs intersection of the given lines l and m.

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fun <C> Line(columnVector: ColumnVector<LabeledPolynomial<C>>): Line<C>
fun <C> Line(rowVector: RowVector<LabeledPolynomial<C>>): Line<C>
fun <C> Line(x: C, y: C, z: C): Line<C>
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fun <C, A : Ring<C>> A.Line(name: String): Line<C>
fun <C> PlanimetricsCalculationContext<C, *>.Line(name: String): Line<C>
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fun <C> PlanimetricsCalculationContext<C, *>.lineThrough(P: Point<C>): ReadOnlyProperty<Any?, Line<C>>

fun <C> PlanimetricsCalculationContext<C, *>.lineThrough(A: Point<C>, B: Point<C>): Line<C>

Constructs line that goes through the given points A and B.

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fun <C> PlanimetricsCalculationContext<C, *>.lyingCondition(P: Point<C>, l: Line<C>): LabeledPolynomial<C>

Returns an expression which equality to zero is equivalent to condition of P lying on l.

fun <C> PlanimetricsCalculationContext<C, *>.lyingCondition(P: Point<C>, q: Quadric<C>): LabeledPolynomial<C>

Returns an expression which equality to zero is equivalent to condition of P lying on q.

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fun <C> PlanimetricsCalculationContext<C, *>.midpoint(A: Point<C>, B: Point<C>): Point<C>

Constructs a midpoint between A and B. The affine map is considered generated by Point.x and Point.y coordinates.

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fun <CT> PlanimetricsCalculationContext<CT, *>.orthocenter(A: Point<CT>, B: Point<CT>, C: Point<CT>): Point<CT>

Constructs orthocenter of triangle ABC.

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fun <C> PlanimetricsCalculationContext<C, *>.perpendicular(l: Line<C>, A: Point<C>): Line<C>

Constructs perpendicular in terms of affine map that is considered generated by Point.x and Point.y coordinates line to the given line l through the given point A.

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fun <C> Point(columnVector: ColumnVector<LabeledPolynomial<C>>): Point<C>
fun <C> Point(rowVector: RowVector<LabeledPolynomial<C>>): Point<C>
fun <C> Point(x: C, y: C, z: C): Point<C>
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fun <C, A : Ring<C>> A.Point(name: String): Point<C>
fun <C> PlanimetricsCalculationContext<C, *>.Point(name: String): Point<C>
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fun <C> PlanimetricsCalculationContext<C, *>.tangencyCondition(l: Line<C>, q: Quadric<C>): LabeledPolynomial<C>

Returns an expression which equality to zero is equivalent to condition of l being tangent to q.