import type { SineCoefficient, TangentCoefficient } from "./geometry";
import type { Coord } from "@khanacademy/perseus-core";
export type AbsoluteValueCoefficient = [m: number, h: number, v: number];
export type NamedSineCoefficient = {
    amplitude: number;
    angularFrequency: number;
    phase: number;
    verticalOffset: number;
};
export type NamedTangentCoefficient = {
    amplitude: number;
    angularFrequency: number;
    phase: number;
    verticalOffset: number;
};
export declare function getSinusoidCoefficients(coords: ReadonlyArray<Coord>): SineCoefficient;
/** Coefficients for f(x) = a·ln(b·x + c). */
export type LogarithmCoefficient = {
    /** Vertical scale factor. */
    a: number;
    /** Horizontal scale factor. */
    b: number;
    /** Horizontal shift (determines vertical asymptote at x = −c/b). */
    c: number;
};
/** Coefficients for f(x) = a·eᵇˣ + c. */
export type ExponentialCoefficient = {
    /** Vertical scale factor (amplitude). */
    a: number;
    /** Growth/decay rate (exponent coefficient). */
    b: number;
    /** Vertical shift (horizontal asymptote y-value). */
    c: number;
};
/**
 * Returns the coefficients {a, b, c} for f(x) = a·eᵇˣ + c given two points
 * on the curve and a horizontal asymptote line.
 *
 * Returns undefined if the inputs are geometrically invalid (same x, a point
 * on the asymptote, or points on opposite sides of the asymptote).
 */
export declare function getExponentialCoefficients(coords: ReadonlyArray<Coord>, asymptote: number): ExponentialCoefficient | undefined;
/**
 * Returns the coefficients {a, b, c} for f(x) = a·ln(b·x + c) given two
 * points on the curve and the x-value of the vertical asymptote.
 *
 * Uses the inverse exponential approach: flip each coordinate (x, y) → (y, x),
 * compute exponential coefficients from the flipped points, then invert.
 *
 * Returns undefined if the inputs are geometrically invalid (same y, a point
 * on the asymptote, or points on opposite sides of the asymptote).
 */
export declare function getLogarithmCoefficients(coords: ReadonlyArray<Coord>, asymptote: number): LogarithmCoefficient | undefined;
export declare function getTangentCoefficients(coords: ReadonlyArray<Coord>): TangentCoefficient;
export type QuadraticCoefficient = [number, number, number];
export declare function getQuadraticCoefficients(coords: ReadonlyArray<Coord>): QuadraticCoefficient;
/**
 * Compute the coefficients [m, h, v] for f(x) = m * |x - h| + v from two
 * control points: p1 (vertex) and p2 (a point on one arm).
 */
export declare function getAbsoluteValueCoefficients(coords: ReadonlyArray<Coord>): AbsoluteValueCoefficient;