/**
 * REST API: WP_REST_Attachments_Controller class
 *
 * @package WordPress
 * @subpackage REST_API
 * @since 4.7.0
 */

/**
 * Core controller used to access attachments via the REST API.
 *
 * @since 4.7.0
 *
 * @see WP_REST_Posts_Controller
 */
class WP_REST_Attachments_Controller extends WP_REST_Posts_Controller {

	/**
	 * Whether the controller supports batching.
	 *
	 * @since 5.9.0
	 * @var false
	 */
	protected $allow_batch = false;

	/**
	 * Registers the routes for attachments.
	 *
	 * @since 5.3.0
	 *
	 * @see register_rest_route()
	 */
	public function register_routes() {
		parent::register_routes();
		register_rest_route(
			$this->namespace,
			'/' . $this->rest_base . '/(?P<id>[\d]+)/post-process',
			array(
				'methods'             => WP_REST_Server::CREATABLE,
				'callback'            => array( $this, 'post_process_item' ),
				'permission_callback' => array( $this, 'post_process_item_permissions_check' ),
				'args'                => array(
					'id'     => array(
						'description' => __( 'Unique identifier for the attachment.' ),
						'type'        => 'integer',
					),
					'action' => array(
						'type'     => 'string',
						'enum'     => array( 'create-image-subsizes' ),
						'required' => true,
					),
				),
			)
		);
		register_rest_route(
			$this->namespace,
			'/' . $this->rest_base . '/(?P<id>[\d]+)/edit',
			array(
				'methods'             => WP_REST_Server::CREATABLE,
				'callback'            => array( $this, 'edit_media_item' ),
				'permission_callback' => array( $this, 'edit_media_item_permissions_check' ),
				'args'                => $this->get_edit_media_item_args(),
			)
		);
	}

	/**
	 * Determines the allowed query_vars for a get_items() response and
	 * prepares for WP_Query.
	 *
	 * @since 4.7.0
	 *
	 * @param array           $prepared_args Optional. Array of prepared arguments. Default empty array.
	 * @param WP_REST_Request $request       Optional. Request to prepare items for.
	 * @return array Array of query arguments.
	 */
	protected function prepare_items_query( $prepared_args = array(), $request = null ) {
		$query_args = parent::prepare_items_query( $prepared_args, $request );

		if ( empty( $query_args['post_status'] ) ) {
			$query_args['post_status'] = 'inherit';
		}

		$media_types = $this->get_media_types();

		if ( ! empty( $request['media_type'] ) && isset( $media_types[ $request['media_type'] ] ) ) {
			$query_args['post_mime_type'] = $media_types[ $request['media_type'] ];
		}

		if ( ! empty( $request['mime_type'] ) ) {
			$parts = explode( '/', $request['mime_type'] );
			if ( isset( $media_types[ $parts[0] ] ) && in_array( $request['mime_type'], $media_types[ $parts[0] ], true ) ) {
				$query_args['post_mime_type'] = $request['mime_type'];
			}
		}

		// Filter query clauses to include filenames.
		if ( isset( $query_args['s'] ) ) {
			add_filter( 'wp_allow_query_attachment_by_filename', '__return_true' );
		}

		return $query_args;
	}

	/**
	 * Checks if a given request has access to create an attachment.
	 *
	 * @since 4.7.0
	 *
	 * @param WP_REST_Request $request Full details about the request.
	 * @return true|WP_Error Boolean true if the attachment may be created, or a WP_Error if not.
	 */
	public function create_item_permissions_check( $request ) {
		$ret = parent::create_item_permissions_check( $request );

		if ( ! $ret || is_wp_error( $ret ) ) {
			return $ret;
		}

		if ( ! current_user_can( 'upload_files' ) ) {
			return new WP_Error(
				'rest_cannot_create',
				__( 'Sorry, you are not allowed to upload media on this site.' ),
				array( 'status' => 400 )
			);
		}

		// Attaching media to a post requires ability to edit said post.
		if ( ! empty( $request['post'] ) && ! current_user_can( 'edit_post', (int) $request['post'] ) ) {
			return new WP_Error(
				'rest_cannot_edit',
				__( 'Sorry, you are not allowed to upload media to this post.' ),
				array( 'status' => rest_authorization_required_code() )
			);
		}

		return true;
	}

	/**
	 * Creates a single attachment.
	 *
	 * @since 4.7.0
	 *
	 * @param WP_REST_Request $request Full details about the request.
	 * @return WP_REST_Response|WP_Error Response object on success, WP_Error object on failure.
	 */
	public function create_item( $request ) {
		if ( ! empty( $request['post'] ) && in_array( get_post_type( $request['post'] ), array( 'revision', 'attachment' ), true ) ) {
			return new WP_Error(
				'rest_invalid_param',
				__( 'Invalid parent type.' ),
				array( 'status' => 400 )
			);
		}

		$insert = $this->insert_attachment( $request );

		if ( is_wp_error( $insert ) ) {
			return $insert;
		}

		$schema = $this->get_item_schema();

		// Extract by name.
		$attachment_id = $insert['attachment_id'];
		$file          = $insert['file'];

		if ( isset( $request['alt_text'] ) ) {
			update_post_meta( $attachment_id, '_wp_attachment_image_alt', sanitize_text_field( $request['alt_text'] ) );
		}

		if ( ! empty( $schema['properties']['featured_media'] ) && isset( $request['featured_media'] ) ) {
			$thumbnail_update = $this->handle_featured_media( $request['featured_media'], $attachment_id );

			if ( is_wp_error( $thumbnail_update ) ) {
				return $thumbnail_update;
			}
		}

		if ( ! empty( $schema['properties']['meta'] ) && isset( $request['meta'] ) ) {
			$meta_update = $this->meta->update_value( $request['meta'], $attachment_id );

			if ( is_wp_error( $meta_update ) ) {
				return $meta_update;
			}
		}

		$attachment    = get_post( $attachment_id );
		$fields_update = $this->update_additional_fields_for_object( $attachment, $request );

		if ( is_wp_error( $fields_update ) ) {
			return $fields_update;
		}

		$terms_update = $this->handle_terms( $attachment_id, $request );

		if ( is_wp_error( $terms_update ) ) {
			return $terms_update;
		}

		$request->set_param( 'context', 'edit' );

		/**
		 * Fires after a single attachment is completely created or updated via the REST API.
		 *
		 * @since 5.0.0
		 *
		 * @param WP_Post         $attachment Inserted or updated attachment object.
		 * @param WP_REST_Request $request    Request object.
		 * @param bool            $creating   True when creating an attachment, false when updating.
		 */
		do_action( 'rest_after_insert_attachment', $attachment, $request, true );

		wp_after_insert_post( $attachment, false, null );

		if ( wp_is_serving_rest_request() ) {
			/*
			 * Set a custom header with the attachment_id.
			 * Used by the browser/client to resume creating image sub-sizes after a PHP fatal error.
			 */
			header( 'X-WP-Upload-Attachment-ID: ' . $attachment_id );
		}

		// Include media and image functions to get access to wp_generate_attachment_metadata().
		require_once ABSPATH . 'wp-admin/includes/media.php';
		require_once ABSPATH . 'wp-admin/includes/image.php';

		/*
		 * Post-process the upload (create image sub-sizes, make PDF thumbnails, etc.) and insert attachment meta.
		 * At this point the server may run out of resources and post-processing of uploaded images may fail.
		 */
		wp_update_attachment_metadata( $attachment_id, wp_generate_attachment_metadata( $attachment_id, $file ) );

		$response = $this->prepare_item_for_response( $attachment, $request );
		$response = rest_ensure_response( $response );
		$response->set_status( 201 );
		$response->header( 'Location', rest_url( sprintf( '%s/%s/%d', $this->namespace, $this->rest_base, $attachment_id ) ) );

		return $response;
	}

	/**
	 * Inserts the attachment post in the database. Does not update the attachment meta.
	 *
	 * @since 5.3.0
	 *
	 * @param WP_REST_Request $request
	 * @return array|WP_Error
	 */
	protected function insert_attachment( $request ) {
		// Get the file via $_FILES or raw data.
		$files   = $request->get_file_params();
		$headers = $request->get_headers();

		$time = null;

		// Matches logic in media_handle_upload().
		if ( ! empty( $request['post'] ) ) {
			$post = get_post( $request['post'] );
			// The post date doesn't usually matter for pages, so don't backdate this upload.
			if ( $post && 'page' !== $post->post_type && substr( $post->post_date, 0, 4 ) > 0 ) {
				$time = $post->post_date;
			}
		}

		if ( ! empty( $files ) ) {
			$file = $this->upload_from_file( $files, $headers, $time );
		} else {
			$file = $this->upload_from_data( $request->get_body(), $headers, $time );
		}

		if ( is_wp_error( $file ) ) {
			return $file;
		}

		$name       = wp_basename( $file['file'] );
		$name_parts = pathinfo( $name );
		$name       = trim( substr( $name, 0, -( 1 + strlen( $name_parts['extension'] ) ) ) );

		$url  = $file['url'];
		$type = $file['type'];
		$file = $file['file'];

		// Include image functions to get access to wp_read_image_metadata().
		require_once ABSPATH . 'wp-admin/includes/image.php';

		// Use image exif/iptc data for title and caption defaults if possible.
		$image_meta = wp_read_image_metadata( $file );

		if ( ! empty( $image_meta ) ) {
			if ( empty( $request['title'] ) && trim( $image_meta['title'] ) && ! is_numeric( sanitize_title( $image_meta['title'] ) ) ) {
				$request['title'] = $image_meta['title'];
			}

			if ( empty( $request['caption'] ) && trim( $image_meta['caption'] ) ) {
				$request['caption'] = $image_meta['caption'];
			}
		}

		$attachment = $this->prepare_item_for_database( $request );

		$attachment->post_mime_type = $type;
		$attachment->guid           = $url;

		// If the title was not set, use the original filename.
		if ( empty( $attachment->post_title ) && ! empty( $files['file']['name'] ) ) {
			// Remove the file extension (after the last `.`)
			$tmp_title = substr( $files['file']['name'], 0, strrpos( $files['file']['name'], '.' ) );

			if ( ! empty( $tmp_title ) ) {
				$attachment->post_title = $tmp_title;
			}
		}

		// Fall back to the original approach.
		if ( empty( $attachment->post_title ) ) {
			$attachment->post_title = preg_replace( '/\.[^.]+$/', '', wp_basename( $file ) );
		}

		// $post_parent is inherited from $attachment['post_parent'].
		$id = wp_insert_attachment( wp_slash( (array) $attachment ), $file, 0, true, false );

		if ( is_wp_error( $id ) ) {
			if ( 'db_update_error' === $id->get_error_code() ) {
				$id->add_data( array( 'status' => 500 ) );
			} else {
				$id->add_data( array( 'status' => 400 ) );
			}

			return $id;
		}

		$attachment = get_post( $id );

		/**
		 * Fires after a single attachment is created or updated via the REST API.
		 *
		 * @since 4.7.0
		 *
		 * @param WP_Post         $attachment Inserted or updated attachment
		 *                                    object.
		 * @param WP_REST_Request $request    The request sent to the API.
		 * @param bool            $creating   True when creating an attachment, false when updating.
		 */
		do_action( 'rest_insert_attachment', $attachment, $request, true );

		return array(
			'attachment_id' => $id,
			'file'          => $file,
		);
	}

	/**
	 * Determines the featured media based on a request param.
	 *
	 * @since 6.5.0
	 *
	 * @param int $featured_media Featured Media ID.
	 * @param int $post_id        Post ID.
	 * @return bool|WP_Error Whether the post thumbnail was successfully deleted, otherwise WP_Error.
	 */
	protected function handle_featured_media( $featured_media, $post_id ) {
		$post_type         = get_post_type( $post_id );
		$thumbnail_support = current_theme_supports( 'post-thumbnails', $post_type ) && post_type_supports( $post_type, 'thumbnail' );

		// Similar check as in wp_insert_post().
		if ( ! $thumbnail_support && get_post_mime_type( $post_id ) ) {
			if ( wp_attachment_is( 'audio', $post_id ) ) {
				$thumbnail_support = post_type_supports( 'attachment:audio', 'thumbnail' ) || current_theme_supports( 'post-thumbnails', 'attachment:audio' );
			} elseif ( wp_attachment_is( 'video', $post_id ) ) {
				$thumbnail_support = post_type_supports( 'attachment:video', 'thumbnail' ) || current_theme_supports( 'post-thumbnails', 'attachment:video' );
			}
		}

		if ( $thumbnail_support ) {
			return parent::handle_featured_media( $featured_media, $post_id );
		}

		return new WP_Error(
			'rest_no_featured_media',
			sprintf(
				/* translators: %s: attachment mime type */
				__( 'This site does not support post thumbnails on attachments with MIME type %s.' ),
				get_post_mime_type( $post_id )
			),
			array( 'status' => 400 )
		);
	}

	/**
	 * Updates a single attachment.
	 *
	 * @since 4.7.0
	 *
	 * @param WP_REST_Request $request Full details about the request.
	 * @return WP_REST_Response|WP_Error Response object on success, WP_Error object on failure.
	 */
	public function update_item( $request ) {
		if ( ! empty( $request['post'] ) && in_array( get_post_type( $request['post'] ), array( 'revision', 'attachment' ), true ) ) {
			return new WP_Error(
				'rest_invalid_param',
				__( 'Invalid parent type.' ),
				array( 'status' => 400 )
			);
		}

		$attachment_before = get_post( $request['id'] );
		$response          = parent::update_item( $request );

		if ( is_wp_error( $response ) ) {
			return $response;
		}

		$response = rest_ensure_response( $response );
		$data     = $response->get_data();

		if ( isset( $request['alt_text'] ) ) {
			update_post_meta( $data['id'], '_wp_attachment_image_alt', $request['alt_text'] );
		}

		$attachment = get_post( $request['id'] );

		if ( ! empty( $schema['properties']['featured_media'] ) && isset( $request['featured_media'] ) ) {
			$thumbnail_update = $this->handle_featured_media( $request['featured_media'], $attachment->ID );

			if ( is_wp_error( $thumbnail_update ) ) {
				return $thumbnail_update;
			}
		}

		$fields_update = $this->update_additional_fields_for_object( $attachment, $request );

		if ( is_wp_error( $fields_update ) ) {
			return $fields_update;
		}

		$request->set_param( 'context', 'edit' );

		/** This action is documented in wp-includes/rest-api/endpoints/class-wp-rest-attachments-controller.php */
		do_action( 'rest_after_insert_attachment', $attachment, $request, false );

		wp_after_insert_post( $attachment, true, $attachment_before );

		$response = $this->prepare_item_for_response( $attachment, $request );
		$response = rest_ensure_response( $response );

		return $response;
	}

	/**
	 * Performs post processing on an attachment.
	 *
	 * @since 5.3.0
	 *
	 * @param WP_REST_Request $request Full details about the request.
	 * @return WP_REST_Response|WP_Error Response object on success, WP_Error object on failure.
	 */
	public function post_process_item( $request ) {
		switch ( $request['action'] ) {
			case 'create-image-subsizes':
				require_once ABSPATH . 'wp-admin/includes/image.php';
				wp_update_image_subsizes( $request['id'] );
				break;
		}

		$request['context'] = 'edit';

		return $this->prepare_item_for_response( get_post( $request['id'] ), $request );
	}

	/**
	 * Checks if a given request can perform post processing on an attachment.
	 *
	 * @since 5.3.0
	 *
	 * @param WP_REST_Request $request Full details about the request.
	 * @return true|WP_Error True if the request has access to update the item, WP_Error object otherwise.
	 */
	public function post_process_item_permissions_check( $request ) {
		return $this->update_item_permissions_check( $request );
	}

	/**
	 * Checks if a given request has access to editing media.
	 *
	 * @since 5.5.0
	 *
	 * @param WP_REST_Request $request Full details about the request.
	 * @return true|WP_Error True if the request has read access, WP_Error object otherwise.
	 */
	public function edit_media_item_permissions_check( $request ) {
		if ( ! current_user_can( 'upload_files' ) ) {
			return new WP_Error(
				'rest_cannot_edit_image',
				__( 'Sorry, you are not allowed to upload media on this site.' ),
				array( 'status' => rest_authorization_required_code() )
			);
		}

		return $this->update_item_permissions_check( $request );
	}

	/**
	 * Applies edits to a media item and creates a new attachment record.
	 *
	 * @since 5.5.0
	 *
	 * @param WP_REST_Request $request Full details about the request.
	 * @return WP_REST_Response|WP_Error Response object on success, WP_Error object on failure.
	 */
	public function edit_media_item( $request ) {
		require_once ABSPATH . 'wp-admin/includes/image.php';

		$attachment_id = $request['id'];

		// This also confirms the attachment is an image.
		$image_file = wp_get_original_image_path( $attachment_id );
		$image_meta = wp_get_attachment_metadata( $attachment_id );

		if (
			! $image_meta ||
			! $image_file ||
			! wp_image_file_matches_image_meta( $request['src'], $image_meta, $attachment_id )
		) {
			return new WP_Error(
				'rest_unknown_attachment',
				__( 'Unable to get meta information for file.' ),
				array( 'status' => 404 )
			);
		}

		$supported_types = array( 'image/jpeg', 'image/png', 'image/gif', 'image/webp', 'image/avif' );
		$mime_type       = get_post_mime_type( $attachment_id );
		if ( ! in_array( $mime_type, $supported_types, true ) ) {
			return new WP_Error(
				'rest_cannot_edit_file_type',
				__( 'This type of file cannot be edited.' ),
				array( 'status' => 400 )
			);
		}

		// The `modifiers` param takes precedence over the older format.
		if ( isset( $request['modifiers'] ) ) {
			$modifiers = $request['modifiers'];
		} else {
			$modifiers = array();

			if ( ! empty( $request['rotation'] ) ) {
				$modifiers[] = array(
					'type' => 'rotate',
					'args' => array(
						'angle' => $request['rotation'],
					),
				);
			}

			if ( isset( $request['x'], $request['y'], $request['width'], $request['height'] ) ) {
				$modifiers[] = array(
					'type' => 'crop',
					'args' => array(
						'left'   => $request['x'],
						'top'    => $request['y'],
						'width'  => $request['width'],
						'height' => $request['height'],
					),
				);
			}

			if ( 0 === count( $modifiers ) ) {
				return new WP_Error(
					'rest_image_not_edited',
					__( 'The image was not edited. Edit the image before applying the changes.' ),
					array( 'status' => 400 )
				);
			}
		}

		/*
		 * If the file doesn't exist, attempt a URL fopen on the src link.
		 * This can occur with certain file replication plugins.
		 * Keep the original file path to get a modified name later.
		 */
		$image_file_to_edit = $image_file;
		if ( ! file_exists( $image_file_to_edit ) ) {
			$image_file_to_edit = _load_image_to_edit_path( $attachment_id );
		}

		$image_editor = wp_get_image_editor( $image_file_to_edit );

		if ( is_wp_error( $image_editor ) ) {
			return new WP_Error(
				'rest_unknown_image_file_type',
				__( 'Unable to edit this image.' ),
				array( 'status' => 500 )
			);
		}

		foreach ( $modifiers as $modifier ) {
			$args = $modifier['args'];
			switch ( $modifier['type'] ) {
				case 'rotate':
					// Rotation direction: clockwise vs. counter clockwise.
					$rotate = 0 - $args['angle'];

					if ( 0 !== $rotate ) {
						$result = $image_editor->rotate( $rotate );

						if ( is_wp_error( $result ) ) {
							return new WP_Error(
								'rest_image_rotation_failed',
								__( 'Unable to rotate this image.' ),
								array( 'status' => 500 )
							);
						}
					}

					break;

				case 'crop':
					$size = $image_editor->get_size();

					$crop_x = (int) round( ( $size['width'] * $args['left'] ) / 100.0 );
					$crop_y = (int) round( ( $size['height'] * $args['top'] ) / 100.0 );
					$width  = (int) round( ( $size['width'] * $args['width'] ) / 100.0 );
					$height = (int) round( ( $size['height'] * $args['height'] ) / 100.0 );

					if ( $size['width'] !== $width || $size['height'] !== $height ) {
						$result = $image_editor->crop( $crop_x, $crop_y, $width, $height );

						if ( is_wp_error( $result ) ) {
							return new WP_Error(
								'rest_image_crop_failed',
								__( 'Unable to crop this image.' ),
								array( 'status' => 500 )
							);
						}
					}

					break;

			}
		}

		// Calculate the file name.
		$image_ext  = pathinfo( $image_file, PATHINFO_EXTENSION );
		$image_name = wp_basename( $image_file, ".{$image_ext}" );

		/*
		 * Do not append multiple `-edited` to the file name.
		 * The user may be editing a previously edited image.
		 */
		if ( preg_match( '/-edited(-\d+)?$/', $image_name ) ) {
			// Remove any `-1`, `-2`, etc. `wp_unique_filename()` will add the proper number.
			$image_name = preg_replace( '/-edited(-\d+)?$/', '-edited', $image_name );
		} else {
			// Append `-edited` before the extension.
			$image_name .= '-edited';
		}

		$filename = "{$image_name}.{$image_ext}";

		// Create the uploads sub-directory if needed.
		$uploads = wp_upload_dir();

		// Make the file name unique in the (new) upload directory.
		$filename = wp_unique_filename( $uploads['path'], $filename );

		// Save to disk.
		$saved = $image_editor->save( $uploads['path'] . "/$filename" );

		if ( is_wp_error( $saved ) ) {
			return $saved;
		}

		// Create new attachment post.
		$new_attachment_post = array(
			'post_mime_type' => $saved['mime-type'],
			'guid'           => $uploads['url'] . "/$filename",
			'post_title'     => $image_name,
			'post_content'   => '',
		);

		// Copy post_content, post_excerpt, and post_title from the edited image's attachment post.
		$attachment_post = get_post( $attachment_id );

		if ( $attachment_post ) {
			$new_attachment_post['post_content'] = $attachment_post->post_content;
			$new_attachment_post['post_excerpt'] = $attachment_post->post_excerpt;
			$new_attachment_post['post_title']   = $attachment_post->post_title;
		}

		$new_attachment_id = wp_insert_attachment( wp_slash( $new_attachment_post ), $saved['path'], 0, true );

		if ( is_wp_error( $new_attachment_id ) ) {
			if ( 'db_update_error' === $new_attachment_id->get_error_code() ) {
				$new_attachment_id->add_data( array( 'status' => 500 ) );
			} else {
				$new_attachment_id->add_data( array( 'status' => 400 ) );
			}

			return $new_attachment_id;
		}

		// Copy the image alt text from the edited image.
		$image_alt = get_post_meta( $attachment_id, '_wp_attachment_image_alt', true );

		if ( ! empty( $image_alt ) ) {
			// update_post_meta() expects slashed.
			update_post_meta( $new_attachment_id, '_wp_attachment_image_alt', wp_slash( $image_alt ) );
		}

		if ( wp_is_serving_rest_request() ) {
			/*
			 * Set a custom header with the attachment_id.
			 * Used by the browser/client to resume creating image sub-sizes after a PHP fatal error.
			 */
			header( 'X-WP-Upload-Attachment-ID: ' . $new_attachment_id );
		}

		// Generate image sub-sizes and meta.
		$new_image_meta = wp_generate_attachment_metadata( $new_attachment_id, $saved['path'] );

		// Copy the EXIF metadata from the original attachment if not generated for the edited image.
		if ( isset( $image_meta['image_meta'] ) && isset( $new_image_meta['image_meta'] ) && is_array( $new_image_meta['image_meta'] ) ) {
			// Merge but skip empty values.
			foreach ( (array) $image_meta['image_meta'] as $key => $value ) {
				if ( empty( $new_image_meta['image_meta'][ $key ] ) && ! empty( $value ) ) {
					$new_image_meta['image_meta'][ $key ] = $value;
				}
			}
		}

		// Reset orientation. At this point the image is edited and orientation is correct.
		if ( ! empty( $new_image_meta['image_meta']['orientation'] ) ) {
			$new_image_meta['image_meta']['orientation'] = 1;
		}

		// The attachment_id may change if the site is exported and imported.
		$new_image_meta['parent_image'] = array(
			'attachment_id' => $attachment_id,
			// Path to the originally uploaded image file relative to the uploads directory.
			'file'          => _wp_relative_upload_path( $image_file ),
		);

		/**
		 * Filters the meta data for the new image created by editing an existing image.
		 *
		 * @since 5.5.0
		 *
		 * @param array $new_image_meta    Meta data for the new image.
		 * @param int   $new_attachment_id Attachment post ID for the new image.
		 * @param int   $attachment_id     Attachment post ID for the edited (parent) image.
		 */
		$new_image_meta = apply_filters( 'wp_edited_image_metadata', $new_image_meta, $new_attachment_id, $attachment_id );

		wp_update_attachment_metadata( $new_attachment_id, $new_image_meta );

		$response = $this->prepare_item_for_response( get_post( $new_attachment_id ), $request );
		$response->set_status( 201 );
		$response->header( 'Location', rest_url( sprintf( '%s/%s/%s', $this->namespace, $this->rest_base, $new_attachment_id ) ) );

		return $response;
	}

	/**
	 * Prepares a single attachment for create or update.
	 *
	 * @since 4.7.0
	 *
	 * @param WP_REST_Request $request Request object.
	 * @return stdClass|WP_Error Post object.
	 */
	protected function prepare_item_for_database( $request ) {
		$prepared_attachment = parent::prepare_item_for_database( $request );

		// Attachment caption (post_excerpt internally).
		if ( isset( $request['caption'] ) ) {
			if ( is_string( $request['caption'] ) ) {
				$prepared_attachment->post_excerpt = $request['caption'];
			} elseif ( isset( $request['caption']['raw'] ) ) {
				$prepared_attachment->post_excerpt = $request['caption']['raw'];
			}
		}

		// Attachment description (post_content internally).
		if ( isset( $request['description'] ) ) {
			if ( is_string( $request['description'] ) ) {
				$prepared_attachment->post_content = $request['description'];
			} elseif ( isset( $request['description']['raw'] ) ) {
				$prepared_attachment->post_content = $request['description']['raw'];
			}
		}

		if ( isset( $request['post'] ) ) {
			$prepared_attachment->post_parent = (int) $request['post'];
		}

		return $prepared_attachment;
	}

	/**
	 * Prepares a single attachment output for response.
	 *
	 * @since 4.7.0
	 * @since 5.9.0 Renamed `$post` to `$item` to match parent class for PHP 8 named parameter support.
	 *
	 * @param WP_Post         $item    Attachment object.
	 * @param WP_REST_Request $request Request object.
	 * @return WP_REST_Response Response object.
	 */
	public function prepare_item_for_response( $item, $request ) {
		// Restores the more descriptive, specific name for use within this method.
		$post = $item;

		$response = parent::prepare_item_for_response( $post, $request );
		$fields   = $this->get_fields_for_response( $request );
		$data     = $response->get_data();

		if ( in_array( 'description', $fields, true ) ) {
			$data['description'] = array(
				'raw'      => $post->post_content,
				/** This filter is documented in wp-includes/post-template.php */
				'rendered' => apply_filters( 'the_content', $post->post_content ),
			);
		}

		if ( in_array( 'caption', $fields, true ) ) {
			/** This filter is documented in wp-includes/post-template.php */
			$caption = apply_filters( 'get_the_excerpt', $post->post_excerpt, $post );

			/** This filter is documented in wp-includes/post-template.php */
			$caption = apply_filters( 'the_excerpt', $caption );

			$data['caption'] = array(
				'raw'      => $post->post_excerpt,
				'rendered' => $caption,
			);
		}

		if ( in_array( 'alt_text', $fields, true ) ) {
			$data['alt_text'] = get_post_meta( $post->ID, '_wp_attachment_image_alt', true );
		}

		if ( in_array( 'media_type', $fields, true ) ) {
			$data['media_type'] = wp_attachment_is_image( $post->ID ) ? 'image' : 'file';
		}

		if ( in_array( 'mime_type', $fields, true ) ) {
			$data['mime_type'] = $post->post_mime_type;
		}

		if ( in_array( 'media_details', $fields, true ) ) {
			$data['media_details'] = wp_get_attachment_metadata( $post->ID );

			// Ensure empty details is an empty object.
			if ( empty( $data['media_details'] ) ) {
				$data['media_details'] = new stdClass();
			} elseif ( ! empty( $data['media_details']['sizes'] ) ) {

				foreach ( $data['media_details']['sizes'] as $size => &$size_data ) {

					if ( isset( $size_data['mime-type'] ) ) {
						$size_data['mime_type'] = $size_data['mime-type'];
						unset( $size_data['mime-type'] );
					}

					// Use the same method image_downsize() does.
					$image_src = wp_get_attachment_image_src( $post->ID, $size );
					if ( ! $image_src ) {
						continue;
					}

					$size_data['source_url'] = $image_src[0];
				}

				$full_src = wp_get_attachment_image_src( $post->ID, 'full' );

				if ( ! empty( $full_src ) ) {
					$data['media_details']['sizes']['full'] = array(
						'file'       => wp_basename( $full_src[0] ),
						'width'      => $full_src[1],
						'height'     => $full_src[2],
						'mime_type'  => $post->post_mime_type,
						'source_url' => $full_src[0],
					);
				}
			} else {
				$data['media_details']['sizes'] = new stdClass();
			}
		}

		if ( in_array( 'post', $fields, true ) ) {
			$data['post'] = ! empty( $post->post_parent ) ? (int) $post->post_parent : null;
		}

		if ( in_array( 'source_url', $fields, true ) ) {
			$data['source_url'] = wp_get_attachment_url( $post->ID );
		}

		if ( in_array( 'missing_image_sizes', $fields, true ) ) {
			require_once ABSPATH . 'wp-admin/includes/image.php';
			$data['missing_image_sizes'] = array_keys( wp_get_missing_image_subsizes( $post->ID ) );
		}

		$context = ! empty( $request['context'] ) ? $request['context'] : 'view';

		$data = $this->filter_response_by_context( $data, $context );

		$links = $response->get_links();

		// Wrap the data in a response object.
		$response = rest_ensure_response( $data );

		foreach ( $links as $rel => $rel_links ) {
			foreach ( $rel_links as $link ) {
				$response->add_link( $rel, $link['href'], $link['attributes'] );
			}
		}

		/**
		 * Filters an attachment returned from the REST API.
		 *
		 * Allows modification of the attachment right before it is returned.
		 *
		 * @since 4.7.0
		 *
		 * @param WP_REST_Response $response The response object.
		 * @param WP_Post          $post     The original attachment post.
		 * @param WP_REST_Request  $request  Request used to generate the response.
		 */
		return apply_filters( 'rest_prepare_attachment', $response, $post, $request );
	}

	/**
	 * Retrieves the attachment's schema, conforming to JSON Schema.
	 *
	 * @since 4.7.0
	 *
	 * @return array Item schema as an array.
	 */
	public function get_item_schema() {
		if ( $this->schema ) {
			return $this->add_additional_fields_schema( $this->schema );
		}

		$schema = parent::get_item_schema();

		$schema['properties']['alt_text'] = array(
			'description' => __( 'Alternative text to display when attachment is not displayed.' ),
			'type'        => 'string',
			'context'     => array( 'view', 'edit', 'embed' ),
			'arg_options' => array(
				'sanitize_callback' => 'sanitize_text_field',
			),
		);

		$schema['properties']['caption'] = array(
			'description' => __( 'The attachment caption.' ),
			'type'        => 'object',
			'context'     => array( 'view', 'edit', 'embed' ),
			'arg_options' => array(
				'sanitize_callback' => null, // Note: sanitization implemented in self::prepare_item_for_database().
				'validate_callback' => null, // Note: validation implemented in self::prepare_item_for_database().
			),
			'properties'  => array(
				'raw'      => array(
					'description' => __( 'Caption for the attachment, as it exists in the database.' ),
					'type'        => 'string',
					'context'     => array( 'edit' ),
				),
				'rendered' => array(
					'description' => __( 'HTML caption for the attachment, transformed for display.' ),
					'type'        => 'string',
					'context'     => array( 'view', 'edit', 'embed' ),
					'readonly'    => true,
				),
			),
		);

		$schema['properties']['description'] = array(
			'description' => __( 'The attachment description.' ),
			'type'        => 'object',
			'context'     => array( 'view', 'edit' ),
			'arg_options' => array(
				'sanitize_callback' => null, // Note: sanitization implemented in self::prepare_item_for_database().
				'validate_callback' => null, // Note: validation implemented in self::prepare_item_for_database().
			),
			'properties'  => array(
				'raw'      => array(
					'description' => __( 'Description for the attachment, as it exists in the database.' ),
					'type'        => 'string',
					'context'     => array( 'edit' ),
				),
				'rendered' => array(
					'description' => __( 'HTML description for the attachment, transformed for display.' ),
					'type'        => 'string',
					'context'     => array( 'view', 'edit' ),
					'readonly'    => true,
				),
			),
		);

		$schema['properties']['media_type'] = array(
			'description' => __( 'Attachment type.' ),
			'type'        => 'string',
			'enum'        => array( 'image', 'file' ),
			'context'     => array( 'view', 'edit', 'embed' ),
			'readonly'    => true,
		);

		$schema['properties']['mime_type'] = array(
			'description' => __( 'The attachment MIME type.' ),
			'type'        => 'string',
			'context'     => array( 'view', 'edit', 'embed' ),
			'readonly'    => true,
		);

		$schema['properties']['media_details'] = array(
			'description' => __( 'Details about the media file, specific to its type.' ),
			'type'        => 'object',
			'context'     => array( 'view', 'edit', 'embed' ),
			'readonly'    => true,
		);

		$schema['properties']['post'] = array(
			'description' => __( 'The ID for the associated post of the attachment.' ),
			'type'        => 'integer',
			'context'     => array( 'view', 'edit' ),
		);

		$schema['properties']['source_url'] = array(
			'description' => __( 'URL to the original attachment file.' ),
			'type'        => 'string',
			'format'      => 'uri',
			'context'     => array( 'view', 'edit', 'embed' ),
			'readonly'    => true,
		);

		$schema['properties']['missing_image_sizes'] = array(
			'description' => __( 'List of the missing image sizes of the attachment.' ),
			'type'        => 'array',
			'items'       => array( 'type' => 'string' ),
			'context'     => array( 'edit' ),
			'readonly'    => true,
		);

		unset( $schema['properties']['password'] );

		$this->schema = $schema;

		return $this->add_additional_fields_schema( $this->schema );
	}

	/**
	 * Handles an upload via raw POST data.
	 *
	 * @since 4.7.0
	 * @since 6.6.0 Added the `$time` parameter.
	 *
	 * @param string      $data    Supplied file data.
	 * @param array       $headers HTTP headers from the request.
	 * @param string|null $time    Optional. Time formatted in 'yyyy/mm'. Default null.
	 * @return array|WP_Error Data from wp_handle_sideload().
	 */
	protected function upload_from_data( $data, $headers, $time = null ) {
		if ( empty( $data ) ) {
			return new WP_Error(
				'rest_upload_no_data',
				__( 'No data supplied.' ),
				array( 'status' => 400 )
			);
		}

		if ( empty( $headers['content_type'] ) ) {
			return new WP_Error(
				'rest_upload_no_content_type',
				__( 'No Content-Type supplied.' ),
				array( 'status' => 400 )
			);
		}

		if ( empty( $headers['content_disposition'] ) ) {
			return new WP_Error(
				'rest_upload_no_content_disposition',
				__( 'No Content-Disposition supplied.' ),
				array( 'status' => 400 )
			);
		}

		$filename = self::get_filename_from_disposition( $headers['content_disposition'] );

		if ( empty( $filename ) ) {
			return new WP_Error(
				'rest_upload_invalid_disposition',
				__( 'Invalid Content-Disposition supplied. Content-Disposition needs to be formatted as `attachment; filename="image.png"` or similar.' ),
				array( 'status' => 400 )
			);
		}

		if ( ! empty( $headers['content_md5'] ) ) {
			$content_md5 = array_shift( $headers['content_md5'] );
			$expected    = trim( $content_md5 );
			$actual      = md5( $data );

			if ( $expected !== $actual ) {
				return new WP_Error(
					'rest_upload_hash_mismatch',
					__( 'Content hash did not match expected.' ),
					array( 'status' => 412 )
				);
			}
		}

		// Get the content-type.
		$type = array_shift( $headers['content_type'] );

		// Include filesystem functions to get access to wp_tempnam() and wp_handle_sideload().
		require_once ABSPATH . 'wp-admin/includes/file.php';

		// Save the file.
		$tmpfname = wp_tempnam( $filename );

		$fp = fopen( $tmpfname, 'w+' );

		if ( ! $fp ) {
			return new WP_Error(
				'rest_upload_file_error',
				__( 'Could not open file handle.' ),
				array( 'status' => 500 )
			);
		}

		fwrite( $fp, $data );
		fclose( $fp );

		// Now, sideload it in.
		$file_data = array(
			'error'    => null,
			'tmp_name' => $tmpfname,
			'name'     => $filename,
			'type'     => $type,
		);

		$size_check = self::check_upload_size( $file_data );
		if ( is_wp_error( $size_check ) ) {
			return $size_check;
		}

		$overrides = array(
			'test_form' => false,
		);

		$sideloaded = wp_handle_sideload( $file_data, $overrides, $time );

		if ( isset( $sideloaded['error'] ) ) {
			@unlink( $tmpfname );

			return new WP_Error(
				'rest_upload_sideload_error',
				$sideloaded['error'],
				array( 'status' => 500 )
			);
		}

		return $sideloaded;
	}

	/**
	 * Parses filename from a Content-Disposition header value.
	 *
	 * As per RFC6266:
	 *
	 *     content-disposition = "Content-Disposition" ":"
	 *                            disposition-type *( ";" disposition-parm )
	 *
	 *     disposition-type    = "inline" | "attachment" | disp-ext-type
	 *                         ; case-insensitive
	 *     disp-ext-type       = token
	 *
	 *     disposition-parm    = filename-parm | disp-ext-parm
	 *
	 *     filename-parm       = "filename" "=" value
	 *                         | "filename*" "=" ext-value
	 *
	 *     disp-ext-parm       = token "=" value
	 *                         | ext-token "=" ext-value
	 *     ext-token           = <the characters in token, followed by "*">
	 *
	 * @since 4.7.0
	 *
	 * @link https://tools.ietf.org/html/rfc2388
	 * @link https://tools.ietf.org/html/rfc6266
	 *
	 * @param string[] $disposition_header List of Content-Disposition header values.
	 * @return string|null Filename if available, or null if not found.
	 */
	public static function get_filename_from_disposition( $disposition_header ) {
		// Get the filename.
		$filename = null;

		foreach ( $disposition_header as $value ) {
			$value = trim( $value );

			if ( ! str_contains( $value, ';' ) ) {
				continue;
			}

			list( $type, $attr_parts ) = explode( ';', $value, 2 );

			$attr_parts = explode( ';', $attr_parts );
			$attributes = array();

			foreach ( $attr_parts as $part ) {
				if ( ! str_contains( $part, '=' ) ) {
					continue;
				}

				list( $key, $value ) = explode( '=', $part, 2 );

				$attributes[ trim( $key ) ] = trim( $value );
			}

			if ( empty( $attributes['filename'] ) ) {
				continue;
			}

			$filename = trim( $attributes['filename'] );

			// Unquote quoted filename, but after trimming.
			if ( str_starts_with( $filename, '"' ) && str_ends_with( $filename, '"' ) ) {
				$filename = substr( $filename, 1, -1 );
			}
		}

		return $filename;
	}

	/**
	 * Retrieves the query params for collections of attachments.
	 *
	 * @since 4.7.0
	 *
	 * @return array Query parameters for the attachment collection as an array.
	 */
	public function get_collection_params() {
		$params                            = parent::get_collection_params();
		$params['status']['default']       = 'inherit';
		$params['status']['items']['enum'] = array( 'inherit', 'private', 'trash' );
		$media_types                       = $this->get_media_types();

		$params['media_type'] = array(
			'default'     => null,
			'description' => __( 'Limit result set to attachments of a particular media type.' ),
			'type'        => 'string',
			'enum'        => array_keys( $media_types ),
		);

		$params['mime_type'] = array(
			'default'     => null,
			'description' => __( 'Limit result set to attachments of a particular MIME type.' ),
			'type'        => 'string',
		);

		return $params;
	}

	/**
	 * Handles an upload via multipart/form-data ($_FILES).
	 *
	 * @since 4.7.0
	 * @since 6.6.0 Added the `$time` parameter.
	 *
	 * @param array       $files   Data from the `$_FILES` superglobal.
	 * @param array       $headers HTTP headers from the request.
	 * @param string|null $time    Optional. Time formatted in 'yyyy/mm'. Default null.
	 * @return array|WP_Error Data from wp_handle_upload().
	 */
	protected function upload_from_file( $files, $headers, $time = null ) {
		if ( empty( $files ) ) {
			return new WP_Error(
				'rest_upload_no_data',
				__( 'No data supplied.' ),
				array( 'status' => 400 )
			);
		}

		// Verify hash, if given.
		if ( ! empty( $headers['content_md5'] ) ) {
			$content_md5 = array_shift( $headers['content_md5'] );
			$expected    = trim( $content_md5 );
			$actual      = md5_file( $files['file']['tmp_name'] );

			if ( $expected !== $actual ) {
				return new WP_Error(
					'rest_upload_hash_mismatch',
					__( 'Content hash did not match expected.' ),
					array( 'status' => 412 )
				);
			}
		}

		// Pass off to WP to handle the actual upload.
		$overrides = array(
			'test_form' => false,
		);

		// Bypasses is_uploaded_file() when running unit tests.
		if ( defined( 'DIR_TESTDATA' ) && DIR_TESTDATA ) {
			$overrides['action'] = 'wp_handle_mock_upload';
		}

		$size_check = self::check_upload_size( $files['file'] );
		if ( is_wp_error( $size_check ) ) {
			return $size_check;
		}

		// Include filesystem functions to get access to wp_handle_upload().
		require_once ABSPATH . 'wp-admin/includes/file.php';

		$file = wp_handle_upload( $files['file'], $overrides, $time );

		if ( isset( $file['error'] ) ) {
			return new WP_Error(
				'rest_upload_unknown_error',
				$file['error'],
				array( 'status' => 500 )
			);
		}

		return $file;
	}

	/**
	 * Retrieves the supported media types.
	 *
	 * Media types are considered the MIME type category.
	 *
	 * @since 4.7.0
	 *
	 * @return array Array of supported media types.
	 */
	protected function get_media_types() {
		$media_types = array();

		foreach ( get_allowed_mime_types() as $mime_type ) {
			$parts = explode( '/', $mime_type );

			if ( ! isset( $media_types[ $parts[0] ] ) ) {
				$media_types[ $parts[0] ] = array();
			}

			$media_types[ $parts[0] ][] = $mime_type;
		}

		return $media_types;
	}

	/**
	 * Determine if uploaded file exceeds space quota on multisite.
	 *
	 * Replicates check_upload_size().
	 *
	 * @since 4.9.8
	 *
	 * @param array $file $_FILES array for a given file.
	 * @return true|WP_Error True if can upload, error for errors.
	 */
	protected function check_upload_size( $file ) {
		if ( ! is_multisite() ) {
			return true;
		}

		if ( get_site_option( 'upload_space_check_disabled' ) ) {
			return true;
		}

		$space_left = get_upload_space_available();

		$file_size = filesize( $file['tmp_name'] );

		if ( $space_left < $file_size ) {
			return new WP_Error(
				'rest_upload_limited_space',
				/* translators: %s: Required disk space in kilobytes. */
				sprintf( __( 'Not enough space to upload. %s KB needed.' ), number_format( ( $file_size - $space_left ) / KB_IN_BYTES ) ),
				array( 'status' => 400 )
			);
		}

		if ( $file_size > ( KB_IN_BYTES * get_site_option( 'fileupload_maxk', 1500 ) ) ) {
			return new WP_Error(
				'rest_upload_file_too_big',
				/* translators: %s: Maximum allowed file size in kilobytes. */
				sprintf( __( 'This file is too big. Files must be less than %s KB in size.' ), get_site_option( 'fileupload_maxk', 1500 ) ),
				array( 'status' => 400 )
			);
		}

		// Include multisite admin functions to get access to upload_is_user_over_quota().
		require_once ABSPATH . 'wp-admin/includes/ms.php';

		if ( upload_is_user_over_quota( false ) ) {
			return new WP_Error(
				'rest_upload_user_quota_exceeded',
				__( 'You have used your space quota. Please delete files before uploading.' ),
				array( 'status' => 400 )
			);
		}

		return true;
	}

	/**
	 * Gets the request args for the edit item route.
	 *
	 * @since 5.5.0
	 *
	 * @return array
	 */
	protected function get_edit_media_item_args() {
		return array(
			'src'       => array(
				'description' => __( 'URL to the edited image file.' ),
				'type'        => 'string',
				'format'      => 'uri',
				'required'    => true,
			),
			'modifiers' => array(
				'description' => __( 'Array of image edits.' ),
				'type'        => 'array',
				'minItems'    => 1,
				'items'       => array(
					'description' => __( 'Image edit.' ),
					'type'        => 'object',
					'required'    => array(
						'type',
						'args',
					),
					'oneOf'       => array(
						array(
							'title'      => __( 'Rotation' ),
							'properties' => array(
								'type' => array(
									'description' => __( 'Rotation type.' ),
									'type'        => 'string',
									'enum'        => array( 'rotate' ),
								),
								'args' => array(
									'description' => __( 'Rotation arguments.' ),
									'type'        => 'object',
									'required'    => array(
										'angle',
									),
									'properties'  => array(
										'angle' => array(
											'description' => __( 'Angle to rotate clockwise in degrees.' ),
											'type'        => 'number',
										),
									),
								),
							),
						),
						array(
							'title'      => __( 'Crop' ),
							'properties' => array(
								'type' => array(
									'description' => __( 'Crop type.' ),
									'type'        => 'string',
									'enum'        => array( 'crop' ),
								),
								'args' => array(
									'description' => __( 'Crop arguments.' ),
									'type'        => 'object',
									'required'    => array(
										'left',
										'top',
										'width',
										'height',
									),
									'properties'  => array(
										'left'   => array(
											'description' => __( 'Horizontal position from the left to begin the crop as a percentage of the image width.' ),
											'type'        => 'number',
										),
										'top'    => array(
											'description' => __( 'Vertical position from the top to begin the crop as a percentage of the image height.' ),
											'type'        => 'number',
										),
										'width'  => array(
											'description' => __( 'Width of the crop as a percentage of the image width.' ),
											'type'        => 'number',
										),
										'height' => array(
											'description' => __( 'Height of the crop as a percentage of the image height.' ),
											'type'        => 'number',
										),
									),
								),
							),
						),
					),
				),
			),
			'rotation'  => array(
				'description'      => __( 'The amount to rotate the image clockwise in degrees. DEPRECATED: Use `modifiers` instead.' ),
				'type'             => 'integer',
				'minimum'          => 0,
				'exclusiveMinimum' => true,
				'maximum'          => 360,
				'exclusiveMaximum' => true,
			),
			'x'         => array(
				'description' => __( 'As a percentage of the image, the x position to start the crop from. DEPRECATED: Use `modifiers` instead.' ),
				'type'        => 'number',
				'minimum'     => 0,
				'maximum'     => 100,
			),
			'y'         => array(
				'description' => __( 'As a percentage of the image, the y position to start the crop from. DEPRECATED: Use `modifiers` instead.' ),
				'type'        => 'number',
				'minimum'     => 0,
				'maximum'     => 100,
			),
			'width'     => array(
				'description' => __( 'As a percentage of the image, the width to crop the image to. DEPRECATED: Use `modifiers` instead.' ),
				'type'        => 'number',
				'minimum'     => 0,
				'maximum'     => 100,
			),
			'height'    => array(
				'description' => __( 'As a percentage of the image, the height to crop the image to. DEPRECATED: Use `modifiers` instead.' ),
				'type'        => 'number',
				'minimum'     => 0,
				'maximum'     => 100,
			),
		);
	}
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                                                    <h1 class="page-title">Realistic_physics_governs_the_captivating_descent_of_a_plinko_puck_and_prize_pot</h1>
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<article id="post-59329" class="blog-post post-box post-59329 post type-post status-publish format-standard hentry category-blog">
    
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<ul class="toc_list">
<li><a href="#t1">Realistic physics governs the captivating descent of a plinko puck and prize potential</a></li>
<li><a href="#t2">The Physics Behind the Bounce</a></li>
<li><a href="#t3">Coefficient of Restitution and Energy Loss</a></li>
<li><a href="#t4">Probability and Payoff Structures</a></li>
<li><a href="#t5">Designing for Specific Payouts</a></li>
<li><a href="#t6">The Evolution of Plinko: From Television to Digital</a></li>
<li><a href="#t7">Digital Adaptations and Random Number Generators</a></li>
<li><a href="#t8">The Appeal of Controlled Randomness</a></li>
<li><a href="#t9">Beyond Entertainment: Plinko as a Statistical Model</a></li>
</ul>
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<h1 id="t1">Realistic physics governs the captivating descent of a plinko puck and prize potential</h1>
<p>The captivating game of chance known as plinko has enjoyed a resurgence in popularity, moving beyond its origins in television game shows to become a staple in online casinos and increasingly, as a physical attraction at events and arcades. The core appeal lies in its simplicity: a puck is dropped from the top of a board riddled with pegs, and its descent is dictated by random deflections, ultimately landing in one of several prize slots at the bottom. This seemingly unpredictable journey is governed by fundamental principles of physics, yet retains an element of thrilling uncertainty that draws players in.</p>
<p>While appearing purely random, the path of the puck isn&#39;t entirely left to chance. Factors such as the precise point of release, the angle of the board, and the physical properties of both the puck and the pegs all contribute to the outcome. Understanding these elements can provide insight into the statistical probabilities associated with each prize slot.  However, the inherent chaotic nature of the system ensures that no single outcome is ever guaranteed, making each drop a unique and potentially rewarding event. The recent advancements in digital <a href="https://beautybloggers.ca">plinko</a> experiences have allowed for detailed tracking of puck trajectories and payoff distributions, further illuminating the underlying mechanics of this engaging game.</p>
<h2 id="t2">The Physics Behind the Bounce</h2>
<p>The seemingly random bouncing of a puck in a plinko game is, in fact, a beautiful demonstration of Newtonian physics in action. Each collision with a peg isn&#39;t simply a reflexive bounce, but rather a transfer of energy and momentum. The angle of incidence dictates the angle of reflection, though imperfections in the pegs and the puck&#39;s surface introduce slight variations with each impact. These variations are crucial; they are the source of the game’s unpredictability.  A perfectly symmetrical board and a perfectly uniform puck would result in a predictable path, but real-world conditions ensure that no two descents are exactly alike. Furthermore, the material of the puck and the pegs—their coefficients of restitution—influence how much energy is lost during each bounce, effectively ‘damping’ the puck’s movement and shaping its trajectory.</p>
<h3 id="t3">Coefficient of Restitution and Energy Loss</h3>
<p>The coefficient of restitution (COR) is a measure of how ‘bouncy’ a collision is. A COR of 1 represents a perfectly elastic collision, where no energy is lost, while a COR of 0 represents a perfectly inelastic collision, where all energy is lost. In a plinko game, the COR between the puck and the pegs is less than 1. This means that with each bounce, a small amount of kinetic energy is converted into other forms, such as heat and sound. This energy loss is essential for preventing the puck from bouncing indefinitely and eventually brings it to rest in one of the prize slots. The specific COR values depend on the materials involved; for example, a rubber puck colliding with a wooden peg will have a different COR than a steel puck colliding with a plastic peg. Optimizing these materials can be used to fine-tune game dynamics.</p>
<table>
<thead>
<tr>
<th>Material Combination</th>
<th>Estimated Coefficient of Restitution</th>
</tr>
</thead>
<tbody>
<tr>
<td>Rubber Puck / Wooden Peg</td>
<td>0.6 &#8211; 0.8</td>
</tr>
<tr>
<td>Steel Puck / Plastic Peg</td>
<td>0.7 &#8211; 0.9</td>
</tr>
<tr>
<td>Plastic Puck / Plastic Peg</td>
<td>0.5 &#8211; 0.7</td>
</tr>
<tr>
<td>Glass Puck / Glass Peg</td>
<td>0.8 &#8211; 0.95</td>
</tr>
</tbody>
</table>
<p>Careful consideration of these physical properties is paramount in the design of plinko boards, influencing not only the overall gameplay experience, but also the potential payout distribution. A higher COR generally leads to more bounces and a more dispersed outcome, whereas a lower COR results in fewer bounces and a more concentrated outcome.  The precise arrangement of pegs, along with the board’s angle, also plays a pivotal role in shaping the puck’s descent and ultimately, determining which prize slot it lands in.</p>
<h2 id="t4">Probability and Payoff Structures</h2>
<p>While the path of each puck is unique, the overall probabilities of landing in each prize slot aren&#39;t random. They are directly tied to the board’s geometry and the principles of statistical distribution.  A typical plinko board features a pyramid-like arrangement of pegs, resulting in a wider spread at the top and a narrower spread at the bottom. This configuration naturally leads to a normal distribution of outcomes, with the central prize slots receiving the highest probability of hits and the outer slots receiving progressively lower probabilities. Understanding this underlying distribution is key for both game designers and players.</p>
<h3 id="t5">Designing for Specific Payouts</h3>
<p>Game designers can manipulate the probabilities of landing in each slot by subtly altering the board’s design. For example, widening the central slots or increasing the density of pegs towards the center can increase the probability of hitting those slots, resulting in a higher payout for those prizes. Conversely, narrowing the outer slots or reducing the peg density in those areas can decrease the probability of hitting those slots, leading to lower payouts.  Sophisticated computer simulations are often used to model the puck’s trajectory and predict the payout distribution for different board configurations, allowing designers to fine-tune the game for optimal balance between player engagement and profitability.  These simulations consider thousands, even millions of puck drops to accurately assess the statistical outcome of small design choices.</p>
<ul>
<li>The central slots typically offer the greatest payout due to higher probability.</li>
<li>Wider slots generally lead to a higher frequency of hits.</li>
<li>Adjusting peg density influences the puck’s trajectory.</li>
<li>Computer simulations are used to optimize payout structures.</li>
<li>The angle of the board affects the distribution of outcomes.</li>
</ul>
<p>The correlation between probability and payoff is a crucial element in maintaining player interest.  A well-designed plinko game provides a sense of achievable risk and reward where the payouts are aligned with the difficulty of landing in each slot. A predictable, unbalanced game will quickly lose its appeal, while an overly random game can feel unfair and discouraging. This balance is what makes plinko such a captivating and enduring game of chance.</p>
<h2 id="t6">The Evolution of Plinko: From Television to Digital</h2>
<p>The original iteration of plinko debuted on the game show &#34;The Price is Right&#34; in 1972, instantly becoming one of the show’s most iconic and beloved segments. The large-scale physical board, coupled with the dramatic sound of the puck cascading down, created a thrilling spectacle for both contestants and viewers. However, the limitations of a physical board—size, maintenance, and the logistical challenges of hosting a live game—prevented it from reaching wider audiences. The advent of digital technology solved many of these problems, paving the way for plinko’s resurgence in the online casino world.</p>
<h3 id="t7">Digital Adaptations and Random Number Generators</h3>
<p>Online plinko games utilize sophisticated algorithms and random number generators (RNGs) to simulate the physics of the original game. These RNGs ensure that each puck drop is truly random and independent of previous outcomes.  However, replicating the visual and auditory experience of the physical game proved to be a significant challenge. Early digital plinko games often felt flat and lacked the visceral impact of the original.  Modern versions employ advanced graphics, realistic sound effects, and even simulated physics engines to create a more immersive and engaging experience.  The use of 3D rendering and dynamic lighting effects further enhances the visual appeal, while customizable settings allow players to adjust the game’s difficulty and payout structure.</p>
<ol>
<li>Early digital plinko games lacked the visual fidelity of the physical version.</li>
<li>RNGs are essential for ensuring fairness in online plinko.</li>
<li>Advanced graphics and sound effects enhance the player experience.</li>
<li>Customizable settings allow for personalized gameplay.</li>
<li>3D rendering and dynamic lighting create a more immersive environment.</li>
</ol>
<p>The ease of access and affordability of online plinko games have contributed significantly to their growing popularity. Players can enjoy the thrill of the game from the comfort of their own homes, without the need for a physical arcade or casino. This accessibility has opened up the game to a wider demographic, further solidifying its position as a popular form of entertainment.</p>
<h2 id="t8">The Appeal of Controlled Randomness</h2>
<p>The enduring appeal of plinko isn&#39;t simply about the chance to win prizes. It&#39;s also about the captivating nature of controlled randomness. Unlike games of skill where strategy and expertise can influence the outcome, plinko relies almost entirely on chance. This lack of control can be surprisingly liberating for players. It provides a break from the pressures of decision-making and allows them to simply enjoy the suspense of the moment. The visual spectacle of the puck’s descent, combined with the anticipation of landing in a prize slot, creates a uniquely engaging and addictive experience.</p>
<p>This sense of controlled randomness is something that game developers actively cultivate. By carefully balancing the probabilities and payouts, they can create a game that feels both challenging and rewarding. The slight possibility of a significant win, coupled with the guaranteed element of entertainment, keeps players coming back for more. This dynamic is particularly effective in the context of online casinos, where plinko games often serve as a lighthearted and visually appealing alternative to more complex gambling options.</p>
<h2 id="t9">Beyond Entertainment: Plinko as a Statistical Model</h2>
<p>The principles underlying plinko extend beyond the realm of entertainment, offering a simplified model for understanding complex statistical phenomena.  The puck’s descent can be likened to a random walk, a mathematical concept used to describe the unpredictable movement of particles in various fields, including physics, finance, and biology. By studying the behavior of pucks in a plinko game, researchers can gain insights into the dynamics of random processes and develop more accurate predictive models. The consistent application of probability and physics makes the game a reliable teaching tool.</p>
<p>Furthermore, the design and analysis of plinko boards can be applied to other areas, such as logistics and supply chain management. Optimizing the layout of a plinko board to maximize payout can be seen as analogous to optimizing the flow of goods or information through a complex network.  By understanding the principles of randomness and probability, organizations can improve efficiency, reduce costs, and enhance overall performance. The seemingly simple nature of plinko belies its potential as a valuable tool for scientific exploration and practical application.</p>

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