/**
 * @fileoverview GaussianSH — the spherical-harmonics (view-dependent) color model for the native
 * 3DGS trainer. Closes the /critic #4 gap ("flat RGB, cannot fit view-dependent / specular color").
 *
 * Real 3DGS encodes each gaussian's color as SH coefficients (the inria default is degree 3). The
 * color seen from a view direction d is C(d) = 0.5 + Σ_k basis_k(d)·coeff_k — so the same gaussian
 * looks different from different angles (specular highlights, sheen). Flat RGB is exactly SH degree 0
 * with no directional terms, which can only reproduce the angular AVERAGE.
 *
 * This module is the gradient-checked SH color FUNCTION (forward + backward, degrees 0-2). It is the
 * piece a SH-aware runner uses as the per-view color: forward3D's flat `r,gr,bl` would be replaced by
 * `0.5 + evalSH(coeffs, viewdir)` per view, and the existing dL/d{r,gr,bl} chained back to dL/dcoeffs
 * (and dL/dviewdir → dL/dmean3d) via evalSHGrad. The model + its view-dependence are verified here;
 * threading it through the full 3D training loop is the documented integration step.
 */
/** Real-SH basis constants (match the inria 3DGS / gsplat convention). */
export declare const SH_C0 = 0.28209479177387814;
export declare const SH_C1 = 0.4886025119029199;
export declare const SH_C2: readonly [1.0925484305920792, -1.0925484305920792, 0.31539156525252005, -1.0925484305920792, 0.5462742152960396];
/** Number of SH coefficients per color channel for a given degree: (deg+1)^2. */
export declare function shCoeffCount(deg: number): number;
/** SH basis values at a (normalized) direction (x,y,z), length (deg+1)^2. */
export declare function shBasis(x: number, y: number, z: number, deg: number): number[];
/** Single-channel SH radiance Σ basis_k·coeff_k (the caller adds the 0.5 offset for final color). */
export declare function evalSH(coeffs: ArrayLike<number>, x: number, y: number, z: number, deg: number): number;
export interface SHGrad {
    /** dRadiance/dcoeff_k, length (deg+1)^2. */
    dCoeffs: number[];
    /** dRadiance/d(x,y,z) — the view-direction gradient (for the mean3d chain). */
    dDir: [number, number, number];
}
/**
 * Backward of evalSH. Given the upstream dRadiance (= dL/dcolor), returns dL/dcoeffs and dL/ddir.
 * Verified against central finite differences in GaussianSH.test.ts.
 */
export declare function evalSHGrad(coeffs: ArrayLike<number>, x: number, y: number, z: number, deg: number, dR: number): SHGrad;
/** Convenience: SH color (0.5 + radiance, clamped to [0,1]) for one channel at a view direction. */
export declare function shColor(coeffs: ArrayLike<number>, x: number, y: number, z: number, deg: number): number;
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