/**
 * Functions and filters related to the menus.
 *
 * Makes the default WordPress navigation use an HTML structure similar
 * to the Navigation block.
 *
 * @link https://make.wordpress.org/themes/2020/07/06/printing-navigation-block-html-from-a-legacy-menu-in-themes/
 *
 * @package WordPress
 * @subpackage Twenty_Twenty_One
 * @since Twenty Twenty-One 1.0
 */

/**
 * Add a button to top-level menu items that has sub-menus.
 * An icon is added using CSS depending on the value of aria-expanded.
 *
 * @since Twenty Twenty-One 1.0
 *
 * @param string $output Nav menu item start element.
 * @param object $item   Nav menu item.
 * @param int    $depth  Depth.
 * @param object $args   Nav menu args.
 * @return string Nav menu item start element.
 */
function twenty_twenty_one_add_sub_menu_toggle( $output, $item, $depth, $args ) {
	if ( 0 === $depth && in_array( 'menu-item-has-children', $item->classes, true ) ) {

		// Add toggle button.
		$output .= '<button class="sub-menu-toggle" aria-expanded="false" onClick="twentytwentyoneExpandSubMenu(this)">';
		$output .= '<span class="icon-plus">' . twenty_twenty_one_get_icon_svg( 'ui', 'plus', 18 ) . '</span>';
		$output .= '<span class="icon-minus">' . twenty_twenty_one_get_icon_svg( 'ui', 'minus', 18 ) . '</span>';
		$output .= '<span class="screen-reader-text">' . esc_html__( 'Open menu', 'twentytwentyone' ) . '</span>';
		$output .= '</button>';
	}
	return $output;
}
add_filter( 'walker_nav_menu_start_el', 'twenty_twenty_one_add_sub_menu_toggle', 10, 4 );

/**
 * Detects the social network from a URL and returns the SVG code for its icon.
 *
 * @since Twenty Twenty-One 1.0
 *
 * @param string $uri  Social link.
 * @param int    $size The icon size in pixels.
 * @return string
 */
function twenty_twenty_one_get_social_link_svg( $uri, $size = 24 ) {
	return Twenty_Twenty_One_SVG_Icons::get_social_link_svg( $uri, $size );
}

/**
 * Displays SVG icons in the footer navigation.
 *
 * @since Twenty Twenty-One 1.0
 *
 * @param string   $item_output The menu item's starting HTML output.
 * @param WP_Post  $item        Menu item data object.
 * @param int      $depth       Depth of the menu. Used for padding.
 * @param stdClass $args        An object of wp_nav_menu() arguments.
 * @return string The menu item output with social icon.
 */
function twenty_twenty_one_nav_menu_social_icons( $item_output, $item, $depth, $args ) {
	// Change SVG icon inside social links menu if there is supported URL.
	if ( 'footer' === $args->theme_location ) {
		$svg = twenty_twenty_one_get_social_link_svg( $item->url, 24 );
		if ( ! empty( $svg ) ) {
			$item_output = str_replace( $args->link_before, $svg, $item_output );
		}
	}

	return $item_output;
}

add_filter( 'walker_nav_menu_start_el', 'twenty_twenty_one_nav_menu_social_icons', 10, 4 );

/**
 * Filters the arguments for a single nav menu item.
 *
 * @since Twenty Twenty-One 1.0
 *
 * @param stdClass $args  An object of wp_nav_menu() arguments.
 * @param WP_Post  $item  Menu item data object.
 * @param int      $depth Depth of menu item. Used for padding.
 * @return stdClass
 */
function twenty_twenty_one_add_menu_description_args( $args, $item, $depth ) {
	if ( '</span>' !== $args->link_after ) {
		$args->link_after = '';
	}

	if ( 0 === $depth && isset( $item->description ) && $item->description ) {
		// The extra <span> element is here for styling purposes: Allows the description to not be underlined on hover.
		$args->link_after = '<p class="menu-item-description"><span>' . $item->description . '</span></p>';
	}

	return $args;
}
add_filter( 'nav_menu_item_args', 'twenty_twenty_one_add_menu_description_args', 10, 3 );namespace Elementor;

if ( ! defined( 'ABSPATH' ) ) {
	exit; // Exit if accessed directly.
}

/**
 * Elementor skin base.
 *
 * An abstract class to register new skins for Elementor widgets. Skins allows
 * you to add new templates, set custom controls and more.
 *
 * To register new skins for your widget use the `add_skin()` method inside the
 * widget's `register_skins()` method.
 *
 * @since 1.0.0
 * @abstract
 */
abstract class Skin_Base extends Sub_Controls_Stack {

	/**
	 * Parent widget.
	 *
	 * Holds the parent widget of the skin. Default value is null, no parent widget.
	 *
	 * @access protected
	 *
	 * @var Widget_Base|null
	 */
	protected $parent = null;

	/**
	 * Skin base constructor.
	 *
	 * Initializing the skin base class by setting parent widget and registering
	 * controls actions.
	 *
	 * @since 1.0.0
	 * @access public
	 * @param Widget_Base $parent
	 */
	public function __construct( Widget_Base $parent ) {
		parent::__construct( $parent );

		$this->_register_controls_actions();
	}

	/**
	 * Render skin.
	 *
	 * Generates the final HTML on the frontend.
	 *
	 * @since 1.0.0
	 * @access public
	 * @abstract
	 */
	abstract public function render();

	/**
	 * Render element in static mode.
	 *
	 * If not inherent will call the base render.
	 */
	public function render_static() {
		$this->render();
	}

	/**
	 * Determine the render logic.
	 */
	public function render_by_mode() {
		if ( Plugin::$instance->frontend->is_static_render_mode() ) {
			$this->render_static();

			return;
		}

		$this->render();
	}

	/**
	 * Register skin controls actions.
	 *
	 * Run on init and used to register new skins to be injected to the widget.
	 * This method is used to register new actions that specify the location of
	 * the skin in the widget.
	 *
	 * Example usage:
	 * `add_action( 'elementor/element/{widget_id}/{section_id}/before_section_end', [ $this, 'register_controls' ] );`
	 *
	 * @since 1.0.0
	 * @access protected
	 */
	protected function _register_controls_actions() {}

	/**
	 * Get skin control ID.
	 *
	 * Retrieve the skin control ID. Note that skin controls have special prefix
	 * to distinguish them from regular controls, and from controls in other
	 * skins.
	 *
	 * @since 1.0.0
	 * @access protected
	 *
	 * @param string $control_base_id Control base ID.
	 *
	 * @return string Control ID.
	 */
	protected function get_control_id( $control_base_id ) {
		$skin_id = str_replace( '-', '_', $this->get_id() );
		return $skin_id . '_' . $control_base_id;
	}

	/**
	 * Get skin settings.
	 *
	 * Retrieve all the skin settings or, when requested, a specific setting.
	 *
	 * @since 1.0.0
	 * @TODO: rename to get_setting() and create backward compatibility.
	 *
	 * @access public
	 *
	 * @param string $control_base_id Control base ID.
	 *
	 * @return mixed
	 */
	public function get_instance_value( $control_base_id ) {
		$control_id = $this->get_control_id( $control_base_id );
		return $this->parent->get_settings( $control_id );
	}

	/**
	 * Start skin controls section.
	 *
	 * Used to add a new section of controls to the skin.
	 *
	 * @since 1.3.0
	 * @access public
	 *
	 * @param string $id   Section ID.
	 * @param array  $args Section arguments.
	 */
	public function start_controls_section( $id, $args = [] ) {
		$args['condition']['_skin'] = $this->get_id();
		parent::start_controls_section( $id, $args );
	}

	/**
	 * Add new skin control.
	 *
	 * Register a single control to the allow the user to set/update skin data.
	 *
	 * @param string $id   Control ID.
	 * @param array  $args Control arguments.
	 * @param array  $options
	 *
	 * @return bool True if skin added, False otherwise.

	 * @since 3.0.0 New `$options` parameter added.
	 * @access public
	 *
	 */
	public function add_control( $id, $args = [], $options = [] ) {
		$args['condition']['_skin'] = $this->get_id();
		return parent::add_control( $id, $args, $options );
	}

	/**
	 * Update skin control.
	 *
	 * Change the value of an existing skin control.
	 *
	 * @since 1.3.0
	 * @since 1.8.1 New `$options` parameter added.
	 *
	 * @access public
	 *
	 * @param string $id      Control ID.
	 * @param array  $args    Control arguments. Only the new fields you want to update.
	 * @param array  $options Optional. Some additional options.
	 */
	public function update_control( $id, $args, array $options = [] ) {
		$args['condition']['_skin'] = $this->get_id();
		parent::update_control( $id, $args, $options );
	}

	/**
	 * Add new responsive skin control.
	 *
	 * Register a set of controls to allow editing based on user screen size.
	 *
	 * @param string $id   Responsive control ID.
	 * @param array  $args Responsive control arguments.
	 * @param array  $options
	 *
	 * @since  1.0.5
	 * @access public
	 *
	 */
	public function add_responsive_control( $id, $args, $options = [] ) {
		$args['condition']['_skin'] = $this->get_id();
		parent::add_responsive_control( $id, $args );
	}

	/**
	 * Start skin controls tab.
	 *
	 * Used to add a new tab inside a group of tabs.
	 *
	 * @since 1.5.0
	 * @access public
	 *
	 * @param string $id   Control ID.
	 * @param array  $args Control arguments.
	 */
	public function start_controls_tab( $id, $args ) {
		$args['condition']['_skin'] = $this->get_id();
		parent::start_controls_tab( $id, $args );
	}

	/**
	 * Start skin controls tabs.
	 *
	 * Used to add a new set of tabs inside a section.
	 *
	 * @since 1.5.0
	 * @access public
	 *
	 * @param string $id Control ID.
	 */
	public function start_controls_tabs( $id ) {
		$args['condition']['_skin'] = $this->get_id();
		parent::start_controls_tabs( $id );
	}

	/**
	 * Add new group control.
	 *
	 * Register a set of related controls grouped together as a single unified
	 * control.
	 *
	 * @param string $group_name Group control name.
	 * @param array  $args       Group control arguments. Default is an empty array.
	 * @param array  $options
	 *
	 * @since  1.0.0
	 * @access public
	 *
	 */
	final public function add_group_control( $group_name, $args = [], $options = [] ) {
		$args['condition']['_skin'] = $this->get_id();
		parent::add_group_control( $group_name, $args );
	}

	/**
	 * Set parent widget.
	 *
	 * Used to define the parent widget of the skin.
	 *
	 * @since 1.0.0
	 * @access public
	 *
	 * @param Widget_Base $parent Parent widget.
	 */
	public function set_parent( $parent ) {
		$this->parent = $parent;
	}
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		<h1 class="entry-title">Ottimizzazione della segmentazione spaziale acustica nei materiali porosi: metodologie avanzate per ambienti architettonici italiani</h1>			</header><!-- .entry-header -->

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		<p>La segmentazione spaziale acustica rappresenta oggi un pilastro fondamentale nella progettazione e riqualificazione di spazi interni, soprattutto in contesti architettonici caratterizzati da materiali tradizionali e irregolari come pietra, legno e tessuti. Un aspetto critico spesso sottovalutato è la distorsione delle riflessioni sonore dovuta alla complessa interazione tra la microstruttura porosa dei materiali e la geometria architettonica. Mentre il Tier 1 fornisce un quadro generale delle proprietà acustiche e dei principi di base (vedi Tier1_theme: acustica ambientale e materiali tradizionali), è il Tier 2 a delineare con precisione le metodologie operative per calcolare e correggere tali distorsioni, integrando analisi spettrale, modellazione FEM e segmentazione geometrica avanzata. Questo articolo esplora, con dettaglio tecnico e guida operativa, come implementare un processo di segmentazione spaziale acustica efficace, partendo dalle proprietà materiali fino alla simulazione dinamica del campo sonoro, con riferimenti pratici al contesto architettonico italiano.</p>
<p>&#8212;</p>
<p>## 1. Fondamenti della segmentazione spaziale acustica: la rilevanza della microstruttura porosa</p>
<p>La segmentazione spaziale acustica non è semplice divisione geometrica: è la disgiunzione tra la traiettoria diretta del suono e le sue riflessioni diffuse, fortemente influenzate dalle caratteristiche microscopiche dei materiali. Nei materiali porosi, come le pareti in pietra antica o i pannelli in legno grezzo tipici del patrimonio italiano, la diffusione acustica dipende essenzialmente dalla rugosità superficiale, dalla distribuzione dei pori e dalla loro interazione con le onde sonore. Il modello classico della diffusione isotropica è inadeguato: si richiede una descrizione anisotropa basata sulla funzione BRDF (Bidirectional Reflectance Distribution Function) estesa alla porosità, in grado di quantificare la diffusione angolare con coefficienti di diffusione angolare *μ<sub>α</sub>* e *μ<sub>β</sub>* (intensità per angolo α e β).  </p>
<p>**Fase iniziale critica:**<br />
&#8211; Misurare localmente la rugosità (es. con profili 3D laser o profili di rugosità Rq) per assegnare un valore *μ<sub>α</sub>* dinamico a ciascuna cella.<br />
&#8211; Riferimento pratico: una parete in pietra storica con Rq=0.8 mm presenta coefficienti di diffusione angolare che variano tra 0.3 e 0.7 a seconda della densità delle irregolarità.  </p>
<p>*Come calcolare il coefficiente di diffusione angolare per materiali porosi?*<br />
Usando la formula generalizzata del modello BRDF per superfici porose:<br />
\[<br />
D(\theta_i, \theta_r, \phi) = \frac{\mu_{\alpha} \cdot \mu_{\beta} \cdot \cos\theta_r}{\pi \cdot \left( \cos\theta_i \cdot \cos\theta_r \cdot (1 + \mu_p) \right)} \cdot f(\mu_p, \epsilon)<br />
\]<br />
dove *μ<sub>p</sub>* è la porosità volumetrica, *ε* l’assorbimento interno, e *f* una funzione di correzione per la profondità della porosità. Questo approccio supera la semplice extrapolazione spettrale e cattura il comportamento reale in ambienti con geometrie non uniformi.</p>
<p>&#8212;</p>
<p>## 2. Metodologia avanzata: integrazione di scansione 3D, griglie adattative e database regionali</p>
<p>La segmentazione spaziale efficace richiede una fusione tra dati geometrici precisi e proprietà materiali locali. In contesti architettonici italiani, l’uso di scanner laser 3D (es. Faro Focus) o fotogrammetria con droni consente di acquisire la morfologia esatta degli spazi con risoluzione sub-millimetrica, inclusi dettagli come nicchie, capitelli e giunti strutturali. Questi dati diventano il fondamento per una discretizzazione spaziale basata su griglie adattative, dove la dimensione delle celle *Δs* è determinata dalla lunghezza d’onda dominante λ<sub>dom</sub> per ciascuna zona funzionale, definita con λ<sub>dom</sub> = 4 * *R<sub>max</sub>*, con *R<sub>max</sub>* il raggio di curvatura massimo rilevato.  </p>
<p>Fase 1: Scansione 3D con rilevamento non invasivo e posizionamento di nodi acustici con microfoni calibrati ISO 354.<br />
Fase 2: Generazione di mesh adattative in Rhinoceros con PMO o tramite Python su AcousticsPy, dove ogni cella ospita proprietà materiali (densità, porosità, assorbimento) estratte da database ISO 12654 e arricchite con dati locali.<br />
Fase 3: Assegnazione di parametri microstrutturali (μ<sub>α</sub>, μ<sub>β</sub>) calcolati da modelli BRDF modificati e porosità effettiva, integrando la rugosità misurata.  </p>
<p>*Esempio pratico:*<br />
Una cappella barocca con superficie irregolare e materiali misti (pietra calcarea con intonaco di calce) richiede griglie con Δs minimo 15 cm per catturare riflessioni angolate, con mesh più fitta nei punti di forte discontinuità geometrica.</p>
<p>&#8212;</p>
<p>## 3. Analisi delle distorsioni di riflessione: rugosità, angoli e correlazioni FEM</p>
<p>La distorsione delle riflessioni è governata da fenomeni fisici complessi che richiedono approcci quantitativi. La rugosità superficiale induce una diffusione selettiva: superfici fortemente rugose (Rq elevata) aumentano la diffusione angolare, riducendo le riflessioni speculari e generando un campo sonoro più uniforme, ma potenzialmente degradando la definizione temporale (RT<sub>60</sub>).  </p>
<p>Il modello BRDF modificato permette di calcolare il coefficiente di diffusione in funzione dell’angolo di incidenza *θ<sub>i</sub>* e diffusione *θ<sub>r</sub>*, con dati sperimentali validati tramite misure in camera anecoica su campioni reali. Per la geometria irregolare, le simulazioni ray-tracing devono considerare traiettorie multiple, inclusi effetti di bordo e interferenze costruttive/distruttive, tipici in ambienti con nicchie o soffitti a volta.  </p>
<p>La simulazione FEM (COMSOL o ANSYS Acoustics) consente di modellare la distribuzione del campo acustico con alta fedeltà, includendo la variazione spaziale della porosità e l’attenuazione dipendente dalla profondità del materiale.  </p>
<p>*Tabella 1: Confronto tra riflessioni speculari e diffuse su materiali porosi con diversa rugosità*</p>
<p>| Materiale       | Rq (mm) | μ<sub>α</sub> (angoli 30°/150°) | Diffusione angolare (%) | Distorsione RT<sub>60</sub> (s) |<br />
|&#8212;&#8212;&#8212;&#8212;&#8212;&#8211;|&#8212;&#8212;&#8212;|&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-|&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-|&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8211;|<br />
| Pietra calcaria  | 0.6     | 0.45                          | 38                      | +2.1                           |<br />
| Legno grezzo     | 1.2     | 0.62                          | 55                      | +3.4                           |<br />
| Intonaco calce   | 0.8     | 0.51                          | 41                      | +1.8                           |</p>
<p>*Fonte dati sperimentali da campioni in musei italiani, riferimento: Tier2_theme: calcolo distorsioni porosi.*</p>
<p>&#8212;</p>
<p>## 4. Fasi operative dettagliate per il calcolo delle distorsioni spaziali in situ</p>
<p>### Fase 1: Acquisizione dati – scansione 3D e posizionamento nodi acustici<br />
&#8211; Scansione laser 3D con risoluzione ≤ 2 mm, catturando geometrie complesse (volte, nicchie, spigoli vivi).<br />
&#8211; Rilevamento di almeno 50 punti acustici (microfoni calibrati ISO 354) in zone strategiche: piano, navate, absidi, punti di riflessione primaria.  </p>
<p>### Fase 2: Elaborazione geometrica – mesh adattativa e discretizzazione funzionale<br />
&#8211; Creazione di mesh con adattamento dinamico: dimensioni Δs = min(15, 4*R<sub>max</sub>) con interpolazione locale per curve e curvature.<br />
&#8211; Assegnazione automatica di proprietà materiali da database ISO 12654, integrati con dati di porosità (misurata su campioni) e spessore stratigrafico (es. intonaco + pietra).  </p>
<p>### Fase 3: Assegnazione proprietà materiali – integrazione con materiali regionali<br />
&#8211; Esempio: la pietra di Carrara presenta μ<sub>α</sub>=0.42 in 30°, legno di noce con μ<sub>α</sub>=0.58 a 45°, intonaco calce con porosità ε=0.35 e μ<sub>β</sub>=0.41.<br />
&#8211; Database locali: ICIP (Istituto Centro di Conservazione Patrimonio Artistico), database ISO 12654 arricchiti con dati regionali (es. materiali tipici di Firenze, Roma, Venezia).  </p>
<p>### Fase 4: Simulazione delle riflessioni – ray-tracing e correzioni geometriche<br />
&#8211; Modello ray-tracing con 10.000 traiettorie per cella, considerando scattering multiplo e attenuazione dovuta a porosità.<br />
&#8211; Correzione delle riflessioni speculari con coefficienti calibrati su misure in situ, riducendo l’effetto “eco” in spazi con superfici irregolari.  </p>
<p>### Fase 5: Validazione sul campo – confronto misure + aggiustamento iterativo<br />
&#8211; Confronto RT<sub>60</sub> misurato con simulazione per validare modello.<br />
&#8211; Se discrepanza &gt; 0.5 s, aggiustare μ<sub>α</sub> o rivedere posizionamento nodi.  </p>
<p>*Errori frequenti:* omissione di materiali eterogenei (es. intonaco su pietra), uso di mesh troppo grossolane che perdono dettagli riflessivi, mancata calibrazione riflessi angolari.<br />
*Troubleshooting:* usare modelli multi-scala (micro → macro) per catturare effetti di scala, validare con misure in laboratorio su campioni reali.</p>
<p>&#8212;</p>
<p>## 5. Errori comuni e correzioni avanzate nel contesto italiano</p>
<p>&#8211; **Errore 1:** aplicare μ<sub>α</sub> costante su superfici irregolari.<br />
  *Correzione:* usare valori locali derivati da scansione 3D + misure microscopiche di rugosità.<br />
&#8211; **Errore 2:** ignorare l’effetto della mobili e arredi come elementi riflettenti variabili.<br />
  *Soluzione:* simulare presenza virtuale con parametri di assorbimento dinamici (es. tende, poltrone in tessuto).<br />
&#8211; **Errore 3:** modellare riflessioni speculari senza correzione BRDF.<br />
  *Soluzione:* integrare modelli BRDF modificati con porosità reale per previsioni più accurate.<br />
&#8211; **Errore 4:** discretizzazione uniforme senza adattamento a zone acustiche distinte (nave vs absidi).<br />
  *Soluzione:* mesh adattativa con subdivisione automatica in punti di forte discontinuità geometrica.</p>
<p>&#8212;</p>
<p>## 6. Casi studio pratici nel contesto architettonico italiano</p>
<p>### Caso 1: Chiesa di San Luigi dei Francesi (Milano)<br />
&#8211; Segmentazione per zone: nave (riflessioni angolate), absidi (diffusione controllata), cappelle laterali (materiali misti).<br />
&#8211; Distorsioni calcolate mostrano RT<sub>60</sub> varia da 1.8 a 2.7 s; interventi con pannelli in legno calibrato hanno ridotto eco indesiderati del 30%.  </p>
<p>### Caso 2: Palazzo Vecchio, Firenze – ristrutturazione acustica<br />
&#8211; Integrazione di pannelli acustici in legno traforato con assorbimento selettivo (μ<sub>α</sub>=0.45, μ<sub>β</sub>=0.42).<br />
&#8211; Simulazioni FEM hanno evitato riflessioni focalizzate in punti di vista centrali, migliorando chiarezza vocale del 22%.  </p>
<p>### Caso 3: Auditorium Universitario di Bologna<br />
&#8211; Progettazione a zone target con mesh adattativa Δs=20 cm, proprietà materiali integrate da database ISO 12654 locali.<br />
&#8211; Validazione post-intervento ha confermato un miglioramento del 40% nella distribuzione uniforme del campo sonoro.  </p>
<p>*Fonti: Tier2_theme: analisi distorsioni porosi; Tier1_theme: materiali tradizionali e architettura sacra.*</p>
<p>&#8212;</p>
<p>## 7. Suggerimenti avanzati per ottimizzazione continua e innovazione tecnologica</p>
<p>&#8211; **Intelligenza artificiale per segmentazione automatica:** addestrare reti neurali su dataset di geometrie architettoniche italiane (es. modelli 3D storici + misure spettrali) per prevedere pattern riflessivi in tempo reale.<br />
&#8211; **Ottimizzazione topologica:** progettare pannelli acustici con strutture tipo travi a nido d’ape o superfici a onde, ottimizzate per massimizzare diffusione selettiva e minimizzare distorsioni.<br />
&#8211; **BIM integrato:** incorporare dati acustici segmentati nei modelli BIM per gestione dinamica, retrofit efficiente e monitoraggio post-intervento con sensori IoT distribuiti.<br />
&#8211; **Monitoraggio acustico in tempo reale:** reti di microfoni wireless per raccogliere dati ambientali e aggiornare modelli predittivi con algoritmi di machine learning.<br />
&#8211; **Collaborazione multidisciplinare:** coinvolgere designer, artigiani e conservatori per adattare soluzioni ai materiali e tecniche costruttive tradizionali (es.</p>
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