/**
 * Trait brands for paths.
 *
 * Brands are phantom types — they exist only at the type level and carry no
 * runtime data. Refiners (`isContinuous`) and assertions (`asContinuous`) on
 * each path module attach these brands to the path's `Trait` parameter at the
 * type level.
 *
 * @since 2.0.0
 */
declare const ContinuousId: unique symbol;
/**
 * Brand for paths whose adjacent curves connect at their join points (G⁰
 * continuity). Calling `toPathData` on a `Continuous` path skips the
 * per-segment discontinuity check and emits a single `M` followed by drawing
 * commands.
 *
 * @since 2.0.0
 */
export type Continuous = {
    readonly [ContinuousId]: 'continuous';
};
declare const MonotonicXId: unique symbol;
/**
 * Brand for paths whose x-coordinate is monotonic as the path parameter
 * `u ∈ [0, 1]` advances. Implies every segment's x-polynomial is monotonic
 * and that adjacent segments' x-ranges don't overlap (so the path is
 * monotonic in x across the join, modulo a small floating-point tolerance).
 *
 * `Monotonic{X,Y}` is the brand `solveAt{X,Y}` requires.
 *
 * @since 2.0.0
 */
export type MonotonicX = {
    readonly [MonotonicXId]: 'monotonic-x';
};
declare const IncreasingXId: unique symbol;
/**
 * Brand for paths whose x-coordinate is non-decreasing as the path parameter
 * advances. Implies `MonotonicX`.
 *
 * @since 2.0.0
 */
export type IncreasingX = MonotonicX & {
    readonly [IncreasingXId]: 'increasing-x';
};
declare const DecreasingXId: unique symbol;
/**
 * Brand for paths whose x-coordinate is non-increasing as the path parameter
 * advances. Implies `MonotonicX`.
 *
 * @since 2.0.0
 */
export type DecreasingX = MonotonicX & {
    readonly [DecreasingXId]: 'decreasing-x';
};
declare const MonotonicYId: unique symbol;
/**
 * Brand for paths whose y-coordinate is monotonic as the path parameter
 * advances. The y analog of {@link MonotonicX}.
 *
 * @since 2.0.0
 */
export type MonotonicY = {
    readonly [MonotonicYId]: 'monotonic-y';
};
declare const IncreasingYId: unique symbol;
/**
 * Brand for paths whose y-coordinate is non-decreasing as the path parameter
 * advances. Implies `MonotonicY`.
 *
 * @since 2.0.0
 */
export type IncreasingY = MonotonicY & {
    readonly [IncreasingYId]: 'increasing-y';
};
declare const DecreasingYId: unique symbol;
/**
 * Brand for paths whose y-coordinate is non-increasing as the path parameter
 * advances. Implies `MonotonicY`.
 *
 * @since 2.0.0
 */
export type DecreasingY = MonotonicY & {
    readonly [DecreasingYId]: 'decreasing-y';
};
/**
 * Phantom property key used by path interfaces to hold their `Trait` type
 * parameter. The runtime object never has a value at this key.
 *
 * @since 2.0.0
 */
export declare const PathTraits: unique symbol;
export type PathTraits = typeof PathTraits;
export {};