omdNode

The abstract base class for all nodes in the mathematical expression tree. It provides the core functionality for tree structure (parent-child relationships), layout calculations, rendering, and provenance tracking. All specific mathematical elements (constants, variables, operators, functions, equations) extend this class.

Class Definition

export class omdNode extends omdMetaExpression

This class is not meant to be instantiated directly. Instead, you should use one of its concrete subclasses (e.g., omdConstantNode, omdBinaryExpressionNode).

Key Concepts

• AST (Abstract Syntax Tree): Each omdNode is typically created from a node in the math.js AST, providing a structured representation of the mathematical expression.
• Tree Structure: Nodes are organized in a hierarchical tree with parent and childList properties, enabling traversal and manipulation of the expression.
• Layout: The computeDimensions() and updateLayout() methods are fundamental for determining the size and position of a node and its children, ensuring correct visual rendering.
• Provenance: The provenance array on each node tracks its history. When a node is cloned (e.g., during a simplification step), the new node's provenance array will contain the ID of the original node, creating a traceable link back to its predecessor. This is crucial for features like step-by-step explanations and highlighting.

Public Properties

• id (number): A unique identifier for each node instance, automatically assigned upon creation.
• type (string): A string indicating the specific type of the OMD node (e.g., "omdConstantNode", "omdBinaryExpressionNode").
• parent (omdNode | null): A reference to the parent node in the expression tree. null for the root node.
• astNodeData (object): The original math.js AST node from which this omdNode was created. This preserves the raw parsed data.
• provenance (Array<number>): An array of IDs from which this node was derived. This forms a historical chain, linking a node back through transformations or simplifications.
• argumentNodeList (object): A map (or object) containing references to the node's structurally significant children (e.g., left, right for binary expressions, args for functions). This is used for recursive operations and provenance tracking.
• isExplainHighlighted (boolean): A flag indicating if the node is currently highlighted for explanation purposes. This acts as a lock, preventing other highlights from overriding it.
• x (number): The x-coordinate of the node's top-left corner relative to its parent.
• y (number): The y-coordinate of the node's top-left corner relative to its parent.
• width (number): The calculated width of the node's bounding box.
• height (number): The calculated height of the node's bounding box.
• fontSize (number): The base font size applied to this node and its children.
• svgElement (SVGElement): The root SVG element that represents this node visually.

Public Methods

initialize()

Initializes the node by recursively computing its dimensions and updating its layout. This method should be called after a node and its children have been fully constructed to ensure proper sizing and positioning.

clone()

Creates a deep, structural clone of the node. The new node will have a new id, and its provenance will link back to the original node's id, establishing a historical connection.

• Returns: omdNode - A new instance of the same type as the original, with all children also cloned.

replaceWith(newNode, options)

Replaces this node with a newNode in the expression tree. This updates all parent and child references and triggers a re-layout and re-rendering of the affected parts of the SVG.

• newNode (omdNode): The node to substitute in.
• options (object, optional): Configuration for the replacement.
  • updateLayout (boolean): If true (default), the layout of the entire tree will be recalculated upwards from the point of replacement.
• Returns: boolean - true if the replacement was successful.

simplify()

Asynchronously attempts to simplify the expression rooted at this node by invoking the central simplification engine (simplifyStep).

• Returns: Promise<object> - A promise that resolves to an object like { success, foldedCount, newRoot, message }. Throws an error if the simplifyStep function is not set.

toMathJSNode()

Converts the omdNode and its children back into a math.js-compatible AST object. This method must be implemented by all concrete subclasses.

• Returns: object - The math.js AST node.
• Throws: Error if not implemented by the subclass.

toString()

Converts the node into a human-readable string representation. It typically uses the toMathJSNode() method internally to leverage math.js's string conversion capabilities.

• Returns: string.

render()

Generates or retrieves the SVG representation of the node. This method calls renderSelf() if the SVG element has not been created yet.

• Returns: SVGElement - The root SVG element representing this node.

renderSelf()

Abstract method that must be implemented by subclasses. This method is responsible for creating the specific SVG elements and structure for the node's visual representation.

• Returns: SVGElement - The SVG element created for this node.
• Throws: Error if not implemented by the subclass.

setFontSize(size)

Sets the base font size for this node and recursively propagates the new font size to all its children.

• size (number): The font size in pixels.

moveTo(x, y)

Moves the node to a new absolute position (x, y) relative to its parent. It also recursively moves all children by the same delta.

• x (number): The new x-coordinate.
• y (number): The new y-coordinate.

show()

Makes the node and its SVG representation visible.

hide()

Hides the node and its SVG representation.

getDepth()

Calculates the depth of the node in the expression tree (0 for the root node).

• Returns: number - The depth of the node.

findParentOfType(type)

Traverses up the tree to find the nearest parent node of a specific type.

• type (string): The type property of the node to search for (e.g., "omdEquationNode").
• Returns: omdNode | null - The found parent node or null if not found.

validateProvenance(nodeMap)

Validates the provenance integrity of this node and all its descendants. It checks for duplicate IDs, invalid references, and self-references in the provenance arrays.

• nodeMap (Map, optional): An optional map of all known nodes in the system, used for cross-referencing provenance IDs.
• Returns: Array<object> - An array of validation issues found, each describing the type of issue, the node involved, and relevant IDs.

setHighlight(highlightOn, color)

Applies or removes a highlight from the node's background. If isExplainHighlighted is true, this method will not override the existing explanation highlight.

• highlightOn (boolean): true to highlight, false to remove.
• color (string, optional): The color of the highlight. Defaults to omdColor.highlightColor.

lowlight()

Reduces the opacity of the node's background. Similar to setHighlight, it respects the isExplainHighlighted lock.

setFillColor(color)

Sets the fill color of the node's background rectangle. This method also respects the isExplainHighlighted lock.

Abstract Methods (to be implemented by subclasses)

• computeDimensions(): Calculates the width and height of the node based on its content and children. Provides a default empty implementation.
• updateLayout(): Positions the node's children relative to itself. Provides a default empty implementation.
• getAlignmentBaseline(): Returns the vertical y-coordinate within the node's bounding box that should be used for alignment with its siblings. By default, this is the vertical center (this.height / 2).
• isConstant(): Determines if the node represents a constant numerical value. Returns false by default.
• getValue(): Retrieves the numerical value of a constant node. Throws an error if the node is not constant.
• getRationalValue(): Retrieves the rational value of a constant node as a numerator/denominator pair. Throws an error if the node is not a constant rational expression.

Internal Methods

• _syncProvenanceFrom(originalNode): Recursively walks a cloned node tree and sets the provenance of each node to point back to the corresponding node in the original tree. This is a crucial part of maintaining the provenance chain during cloning operations.
• replaceNodeInParent(newNode): Helper method used by replaceWith to update specific references to this node within its parent's argumentNodeList and other properties.
• updateSvg(newNode): Helper method used by replaceWith to perform the actual DOM manipulation (replacing SVG elements).
• updateLayoutUpwards(): Traverses up the tree from this node's parent to re-calculate dimensions and layouts for all ancestors, ensuring the entire affected tree is correctly rendered after a change.
• _validateStepsProvenance(issues): Helper for validateProvenance to check provenance within steps.
• _findOrphanedNodes(issues): Helper for validateProvenance to find nodes in the nodeMap that are no longer part of the active tree.
• _collectAllProvenanceIds(newNodeMap): Collects all provenance IDs from nodes in a given map.
• _collectNodeProvenanceIds(node, referencedIds, processedNodes): Recursively collects provenance IDs for a single node.
• _preserveReferencedNodes(referencedIds, newNodeMap): Ensures that historical nodes referenced in provenance chains are kept in the nodeMap.
• _preserveNodeAndContext(id, newNodeMap, processedIds): Preserves a historical node and its relevant parent/sibling context.
• _preserveParentContext(node, newNodeMap): Preserves the parent nodes of a historical node.
• _preserveSiblingContext(node, newNodeMap): Preserves the sibling nodes of a historical node.

Example

// omdNode is an abstract class - use concrete subclasses
import { omdConstantNode } from './omdConstantNode.js';
import { omdBinaryExpressionNode } from './omdBinaryExpressionNode.js';
import { omdDisplay } from '../display/omdDisplay.js';

// Create a simple expression tree
const two = new omdConstantNode({ value: 2 });
const x = new omdVariableNode({ name: 'x' });
const twoX = new omdBinaryExpressionNode({
    type: 'OperatorNode', op: '*', fn: 'multiply',
    args: [two.astNodeData, x.astNodeData],
    implicit: true
});

// Initialize the root node (this will recursively initialize children)
twoX.initialize();

// Render it using omdDisplay
const container = document.getElementById('math-container');
const display = new omdDisplay(container);
display.render(twoX);

console.log(twoX.toString()); // Output: 2x

See Also

• omdLeafNode - The base class for nodes with no children (constants, variables, operators).
• omdBinaryExpressionNode - For nodes with two children (e.g., addition, subtraction, multiplication).
• omdFunctionNode - For function calls (e.g., sin(x)).
• omdEquationNode - For representing mathematical equations.