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Matrix2d.md

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Matrix2d Struct

Overview

The Matrix2d struct represents a 3x3 transformation matrix for 2D geometric transformations. It is used for translation, rotation, scaling, and mirroring operations in the XY plane.

Namespace

Autodesk.AutoCAD.Geometry

Key Properties

Property Type Description
Inverse Matrix2d Gets the inverse matrix
IsIdentity bool Checks if matrix is identity matrix
IsUniscaledOrtho bool Checks if matrix is orthogonal with uniform scaling

Static Factory Methods

Method Description
Identity Returns identity matrix (no transformation)
Displacement(Vector2d) Creates translation matrix
Rotation(double, Point2d) Creates rotation matrix around point
Scaling(double, Point2d) Creates uniform scaling matrix
Mirroring(Line2d) Creates mirror transformation across line
Mirroring(Point2d) Creates mirror transformation across point

Key Methods

Method Return Type Description
PreMultiplyBy(Matrix2d) Matrix2d Multiplies this matrix by another
PostMultiplyBy(Matrix2d) Matrix2d Multiplies another matrix by this
Transpose() Matrix2d Returns transposed matrix
Invert() Matrix2d Returns inverted matrix
IsEqualTo(Matrix2d) bool Checks equality

Code Examples

Example 1: Translation

// Move 10 units in X, 5 in Y
Vector2d displacement = new Vector2d(10, 5);
Matrix2d translation = Matrix2d.Displacement(displacement);

Point2d pt = new Point2d(0, 0);
Point2d moved = pt.TransformBy(translation);

ed.WriteMessage($"\nOriginal: ({pt.X}, {pt.Y})");
ed.WriteMessage($"\nMoved: ({moved.X}, {moved.Y})");

Example 2: Rotation

// Rotate 45° around origin
double angle = Math.PI / 4;
Point2d center = new Point2d(0, 0);
Matrix2d rotation = Matrix2d.Rotation(angle, center);

Point2d pt = new Point2d(10, 0);
Point2d rotated = pt.TransformBy(rotation);

ed.WriteMessage($"\nRotated 45°: ({rotated.X:F2}, {rotated.Y:F2})");

Example 3: Scaling

// Scale 2x from origin
Point2d scaleBase = new Point2d(0, 0);
Matrix2d scale = Matrix2d.Scaling(2.0, scaleBase);

Point2d pt = new Point2d(5, 5);
Point2d scaled = pt.TransformBy(scale);

ed.WriteMessage($"\nScaled: ({scaled.X}, {scaled.Y})"); // (10, 10)

Example 4: Combining Transformations

// Move, rotate, scale
Vector2d move = new Vector2d(10, 5);
Matrix2d translation = Matrix2d.Displacement(move);

Matrix2d rotation = Matrix2d.Rotation(Math.PI / 4, new Point2d(0, 0));
Matrix2d scale = Matrix2d.Scaling(2.0, new Point2d(0, 0));

// Combine: scale * rotate * translate
Matrix2d combined = translation.PreMultiplyBy(rotation).PreMultiplyBy(scale);

Point2d pt = new Point2d(5, 0);
Point2d transformed = pt.TransformBy(combined);

ed.WriteMessage($"\nTransformed: ({transformed.X:F2}, {transformed.Y:F2})");

Best Practices

  1. Use for 2D: Prefer Matrix2d over Matrix3d for planar transformations
  2. Transformation Order: Matrix multiplication order matters
  3. Combine Transformations: Combine multiple transformations for efficiency
  4. Inverse: Use Inverse to undo transformations

Related Classes

  • Matrix3d - 3D transformation matrix
  • Vector2d - 2D displacement vectors
  • Point2d - 2D points to transform
  • Line2d - 2D line for mirroring

References