Linear Elements

Overview

In .duc, a Linear Element (DucLinearElement with type: "line", or DucArrowElement with type: "arrow") represents vector paths.

Unlike conventional graphics formats that restrict paths to simple 2-point segments or raw SVG command strings (d="M... L... C..."), .duc structures linear geometry using relational data arrays. This allows a single element to represent straight lines, polylines, smooth Bezier curves, and complex networks of interconnected line webs.

Line Heads (DucHead)

Linear elements support visual head attachments at their start (startBinding.head) and end (endBinding.head) endpoints.

export type DucHead = {
  type: LineHead;
  blockId: string | null;
  size: number;
};

• Standard Enum Heads: Built-in geometric indicators.
• Custom Block Heads (blockId): References a master Block definition ID to render custom architectural or engineering symbols as line heads.
• Size Scaling (size): Proportional scaling factor for the head marker.

Line Head Reference Table

Element Binding

Linear elements can bind their endpoints (startBinding and endBinding) to target canvas elements (DucBindableElement).

export type DucPointBinding = {
  elementId: string;
  focus: number; // Border position offset (-1 to 1)
  gap: PrecisionValue; // Clearance distance from target border
  fixedPoint: FixedPoint | null; // Fixed normalized coordinates [x, y] inside bound element (0.0 to 1.0)
  point: {
    index: number;
    offset: number;
  } | null; // Point or segment offset when binding to a linear element
  head: DucHead | null;
};

• Target Association (elementId): Binds the endpoint to a target element ID.
• Border Focus (focus): Defines a fractional offset (-1 to 1) along the target element’s border where the line attaches.
• Clearance Gap (gap): Maintains a defined distance between the line head and the target element boundary.
• Fixed Position (fixedPoint): Defines normalized internal coordinates [x, y] (0.0 to 1.0) inside the target element. When set, it overrides focus to pin the endpoint to a fixed location.
• Linear Point Binding (point): Binds the endpoint to a specific vertex index and segment offset of another linear element.
• Dynamic Updates: When a target element moves, rotates, or scales, bound linear elements re-evaluate endpoint positions and update their geometry automatically.

How Linear Path Geometry is Constructed

Path geometry in .duc is composed of two relational arrays:

1. points: DucPoint[]: Array of discrete spatial vertices [Point 0, Point 1, Point 2, ...].
2. lines: DucLine[]: Array of line segment connections referencing point indices [startReference, endReference].

export type DucLine = [DucLineReference, DucLineReference];
 
export type DucLineReference = {
  index: number; // Index of the target point in the points array
  handle: DucPointPosition | null; // Bezier control handle (null for sharp straight connections)
};

Here is how different linear path geometries are constructed step-by-step:

Step 1: Constructing a Straight Line Segment

To construct a straight line segment between two vertices, define two points in points and connect their indices in lines with handle: null on both ends.

const straightLine: DucLinearElement = {
  type: "line",
  points: [
    { x: { value: 0 }, y: { value: 0 } },   // Point Index 0
    { x: { value: 100 }, y: { value: 0 } }  // Point Index 1
  ],
  lines: [
    [
      { index: 0, handle: null }, // Start at Point 0 (no outgoing handle)
      { index: 1, handle: null }  // End at Point 1 (no incoming handle)
    ]
  ],
  // ... base element properties
};

Step 2: Constructing Curved Bezier Paths (Single-Handle & Dual-Handle)

In .duc, Bezier control handles on a line segment are independent per endpoint. A line segment does not require handles on both ends.

Control handles define path curvature:

• start.handle (handleOut): Outgoing control handle extending from the start point toward the end point.
• end.handle (handleIn): Incoming control handle extending into the end point from the start point.

A. Single-Handle Bezier Segments (handle: null on one end)

A segment can have handle: null on one end and a populated control handle on the other:

1. start.handle = null and end.handle = { x, y }: The line leaves Point 0 cleanly without an outgoing handle, but curves into Point 1 via an incoming control handle (handleIn).
2. start.handle = { x, y } and end.handle = null: The line leaves Point 1 via an outgoing control handle (handleOut), but enters Point 2 cleanly as a sharp connection without an incoming handle.

B. Complete Curved Path Example with Mixed Handles

Here is a 4-point closed path demonstrating mixed single-handle and dual-handle Bezier segments:

const bezierPath: DucLinearElement = {
  type: "line",
  points: [
    { x: { value: 0 }, y: { value: 0 } },                      // Point 0
    { x: { value: -35 }, y: { value: 80 }, mirroring: 12 },    // Point 1 (Symmetric Mirroring)
    { x: { value: 10 }, y: { value: 130 } },                    // Point 2
    { x: { value: 50 }, y: { value: 95 }, mirroring: 12 }      // Point 3 (Symmetric Mirroring)
  ],
  lines: [
    // Segment 0: Point 0 -> Point 1
    // Point 0 has handle = null; Point 1 has an incoming handle (handleIn)
    [
      { index: 0, handle: null },
      { index: 1, handle: { x: { value: -25 }, y: { value: 60 } } }
    ],
 
    // Segment 1: Point 1 -> Point 2
    // Point 1 has an outgoing handle (handleOut); Point 2 has handle = null
    [
      { index: 1, handle: { x: { value: -20 }, y: { value: 95 } } },
      { index: 2, handle: null }
    ],
 
    // Segment 2: Point 2 -> Point 3
    // Point 2 has handle = null; Point 3 has an incoming handle (handleIn)
    [
      { index: 2, handle: null },
      { index: 3, handle: { x: { value: 35 }, y: { value: 140 } } }
    ],
 
    // Segment 3: Point 3 -> Point 0 (Closing Loop)
    // Point 3 has an outgoing handle (handleOut); Point 0 has handle = null
    [
      { index: 3, handle: { x: { value: 60 }, y: { value: 45 } } },
      { index: 0, handle: null }
    ]
  ]
};

Bezier Mirroring Modes (mirroring)

When a point connects two curved segments, mirroring controls handle symmetry during edits:

• NONE (10): Handles move independently, creating sharp corners or asymmetrical curves.
• ANGLE (11): Handles mirror rotation angle, while handle lengths vary independently.
• ANGLE_LENGTH (12): Handles mirror both rotation angle and length symmetrically, producing smooth continuous curves.

Step 3: Constructing a Polyline or Closed Shape

Multiple line segments can be chained together across sequential point indices to construct a polyline or closed loop:

const closedTriangle: DucLinearElement = {
  type: "line",
  points: [
    { x: { value: 0 }, y: { value: 0 } },   // Point Index 0
    { x: { value: 100 }, y: { value: 0 } }, // Point Index 1
    { x: { value: 50 }, y: { value: 80 } }  // Point Index 2
  ],
  lines: [
    [{ index: 0, handle: null }, { index: 1, handle: null }], // Segment 0: Point 0 -> Point 1
    [{ index: 1, handle: null }, { index: 2, handle: null }], // Segment 1: Point 1 -> Point 2
    [{ index: 2, handle: null }, { index: 0, handle: null }]  // Segment 2: Point 2 -> Point 0 (Closed Loop)
  ],
  // ... base element properties
};

Step 4: Constructing a Complex Web or Network

Unlike SVG paths that must follow a single continuous sequence of points, .duc allows multiple lines in the lines array to reference the exact same point index.

This enables a single Linear Element to represent a T-junction, star network, or interconnected web of lines:

const tJunctionNetwork: DucLinearElement = {
  type: "line",
  points: [
    { x: { value: 50 }, y: { value: 50 } },  // Point Index 0 (Center Junction)
    { x: { value: 50 }, y: { value: 0 } },   // Point Index 1 (North Node)
    { x: { value: 100 }, y: { value: 50 } }, // Point Index 2 (East Node)
    { x: { value: 50 }, y: { value: 100 } }  // Point Index 3 (South Node)
  ],
  lines: [
    [{ index: 0, handle: null }, { index: 1, handle: null }], // Branch 1: Center -> North
    [{ index: 0, handle: null }, { index: 2, handle: null }], // Branch 2: Center -> East
    [{ index: 0, handle: null }, { index: 3, handle: null }]  // Branch 3: Center -> South
  ],
  // ... base element properties
};

Additional Path Properties

• pathOverrides (DucPath[]): Overrides background and stroke properties for specific sub-paths within a line network.
• wipeoutBelow: Boolean flag on DucLinearElement that masks out underlying canvas content beneath the stroke path.