/**
 * Layout geometry: a PURE function from expression trees to positioned,
 * id-keyed boxes and glyphs. No DOM, no font measurement — static metric
 * tables only. The UI package projects this onto SVG; hit testing is a
 * geometry query answered here.
 *
 * Design rules (the display decisions the AST deliberately does not encode):
 *  - Sum(a, Neg(b)) renders as binary subtraction "a − b". The minus sign is
 *    owned by the NEG node (so dragging the signed term grabs sign and all);
 *    the Sum only contributes "+" separators and spacing.
 *  - Negative literals (canonically Neg(Integer)) render as "−3".
 *  - Parentheses are owned by the PARENT that requires them: a Sum factor in
 *    a Product, a Sum under Neg, compound Pow bases, Neg factors.
 *  - Products juxtapose ("3x"); a "·" appears only where juxtaposition would
 *    glue digits to digits.
 *  - Fraction numerator/denominator lists render as centered rows above and
 *    below the bar; empty lists render an implicit "1".
 *  - Pow exponents are raised and scaled by SUP_SCALE.
 *
 * Geometry invariants (property-tested):
 *  - every tree node has exactly one box; child boxes nest inside parents;
 *  - sibling boxes never overlap;
 *  - glyphs stay inside their owner's box;
 *  - a subtree's internal geometry is context-independent up to translation
 *    and uniform scale (what makes id-keyed animation work);
 *  - hitTest returns the deepest box containing a point.
 */
import type { Node, NodeId } from "./expr.js";
export declare const METRICS: {
    readonly ASCENT: 0.78;
    readonly DESCENT: 0.22;
    readonly AXIS: 0.26;
    readonly DIGIT_W: 0.54;
    readonly LETTER_W: 0.54;
    readonly SIGN_W: 0.58;
    readonly DOT_W: 0.3;
    readonly PAREN_W: 0.34;
    readonly OP_PAD: 0.18;
    readonly EQ_PAD: 0.26;
    readonly MUL_GAP: 0.07;
    readonly NEG_GAP: 0.05;
    readonly EXP_GAP: 0.04;
    readonly SUP_SCALE: 0.7;
    readonly SUP_RAISE: 0.42;
    readonly FRAC_GAP: 0.12;
    readonly FRAC_PAD: 0.08;
    readonly BAR_TH: 0.06;
    readonly RADICAL_W: 0.5;
    readonly RAD_GAP: 0.1;
};
export interface LayoutRect {
    readonly x: number;
    readonly y: number;
    readonly width: number;
    readonly height: number;
}
export interface LayoutBox {
    readonly nodeId: NodeId;
    readonly kind: Node["kind"];
    readonly rect: LayoutRect;
    /** Absolute y of this node's baseline. */
    readonly baseline: number;
    /** Font scale relative to the root (1 = base size). */
    readonly scale: number;
    /** Tree depth from the layout root (root = 0); hitTest picks the max. */
    readonly depth: number;
}
export type PlacedGlyph = {
    readonly kind: "char";
    readonly char: string;
    readonly x: number;
    /** Absolute y of the glyph baseline. */
    readonly baseline: number;
    readonly scale: number;
    readonly width: number;
    readonly ascent: number;
    readonly descent: number;
    readonly owner: NodeId;
} | {
    readonly kind: "bar";
    readonly x: number;
    /** Absolute y of the bar's vertical center. */
    readonly y: number;
    readonly width: number;
    readonly thickness: number;
    readonly owner: NodeId;
};
export interface Layout {
    readonly rootId: NodeId;
    readonly width: number;
    readonly height: number;
    readonly boxes: ReadonlyMap<NodeId, LayoutBox>;
    readonly glyphs: readonly PlacedGlyph[];
}
export declare function layoutNode(root: Node): Layout;
/**
 * The deepest node whose box contains the point, or undefined. Sibling boxes
 * are disjoint (property-tested), so "deepest containing" is unambiguous: the
 * containing boxes always form a single ancestor chain.
 */
export declare function hitTest(layout: Layout, x: number, y: number): NodeId | undefined;
/** Convenience: the center of a node's box (a natural anchor for gestures). */
export declare function boxCenter(layout: Layout, id: NodeId): {
    x: number;
    y: number;
};
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