Acad Geometry

Vectors

Vector2d / Vector3d (structs)

Vector3d v1 = new Vector3d(1.0, 0.0, 0.0);
Vector3d v2 = new Vector3d(0.0, 1.0, 0.0);
double angle = v1.GetAngleTo(v2);           // pi/2
Vector3d cross = v1.CrossProduct(v2);        // (0, 0, 1)
double dot = v1.DotProduct(v2);              // 0.0
Vector3d unit = new Vector3d(3, 4, 0).GetNormal();  // (0.6, 0.8, 0)
Vector3d perp = v1.GetPerpendicularVector(); // perpendicular in arbitrary direction
bool parallel = v1.IsParallelTo(v2);         // false

Transformations

Matrix3d / Matrix2d (structs)

// Rotate entity 45 degrees around a point
Point3d center = new Point3d(100, 100, 0);
Matrix3d rot = Matrix3d.Rotation(Math.PI / 4, Vector3d.ZAxis, center);
entity.TransformBy(rot);

// Mirror across a line (defined by two points)
Line3d mirrorLine = new Line3d(new Point3d(0, 0, 0), new Point3d(1, 1, 0));
Matrix3d mir = Matrix3d.Mirroring(mirrorLine);

// Scale from base point
Matrix3d scl = Matrix3d.Scaling(2.0, new Point3d(0, 0, 0));

// Compose transforms (apply scaling THEN rotation)
Matrix3d combined = rot * scl;  // right-to-left order
entity.TransformBy(combined);

// Move entity by displacement
Matrix3d move = Matrix3d.Displacement(new Vector3d(50, 100, 0));

Lines & Segments

Lines and Segments

// Find intersection of two lines
Line2d lineA = new Line2d(new Point2d(0, 0), new Point2d(10, 10));
Line2d lineB = new Line2d(new Point2d(0, 10), new Point2d(10, 0));
Point2d[] intersections = lineA.IntersectWith(lineB);
if (intersections != null && intersections.Length > 0)
    ed.WriteMessage("Intersection at: {0}\n", intersections[0]);

// Segment midpoint and length
LineSegment3d seg = new LineSegment3d(
    new Point3d(0, 0, 0), new Point3d(100, 0, 0));
Point3d mid = seg.MidPoint;    // (50, 0, 0)
double len = seg.Length;        // 100.0

Arcs & Circles

CircularArc2d / CircularArc3d

// Create arc through 3 points
CircularArc3d arc = new CircularArc3d(
    new Point3d(0, 0, 0),
    new Point3d(50, 50, 0),
    new Point3d(100, 0, 0));
double radius = arc.Radius;
Point3d center = arc.Center;

// Full circle
CircularArc2d circle = new CircularArc2d(
    new Point2d(100, 100), 50.0);

// Find arc-line intersections
Line3d testLine = new Line3d(center, Vector3d.XAxis);
Point3d[] hits = arc.IntersectWith(testLine);

Curves (Abstract Base)

CurveCurveIntersector2d / CurveCurveIntersector3d

For finding intersections between ANY two curves:

// 2D intersection
CurveCurveIntersector2d cci = new CurveCurveIntersector2d(curve1, curve2);
// Optional: with tolerance or restricted intervals
// new CurveCurveIntersector2d(curve1, curve2, Tolerance tolerance)
// new CurveCurveIntersector2d(curve1, curve2, Interval range1, Interval range2)

for (int i = 0; i < cci.NumberOfIntersectionPoints; i++)
{
    Point2d pt = cci.GetIntersectionPoint(i);
    double[] parms = cci.GetIntersectionParameters(i);  // [param1, param2]
    bool tangent = cci.IsTangential(i);
    bool transversal = cci.IsTransversal(i);
}

// Check for overlaps (collinear segments)
int overlapCount = cci.OverlapCount;   // property on 2d, method on 3d

Note: CurveCurveIntersector3d requires a Vector3d planeNormal parameter in all constructors (for projection direction).

Planes & Bounds

Extents2d / Extents3d (axis-aligned bounding boxes)

Namespace: Autodesk.AutoCAD.DatabaseServices (NOT Autodesk.AutoCAD.Geometry — easy to get wrong)

These are used very commonly:

// Extents3d is used by Entity.GeometricExtents
Extents3d ext = entity.GeometricExtents;
Point3d minPt = ext.MinPoint;
Point3d maxPt = ext.MaxPoint;

// Build extents from points
Extents3d bounds = new Extents3d();
bounds.AddPoint(new Point3d(0, 0, 0));
bounds.AddPoint(new Point3d(100, 200, 0));

// Merge extents
bounds.AddExtents(otherExtents);

Tolerance

// Global tolerance (used by default for all comparisons)
Tolerance defaultTol = Tolerance.Global;

// Custom tolerance for specific comparisons
Tolerance customTol = new Tolerance(1e-6, 1e-6);  // (equalVector, equalPoint)

// Use with comparison methods
bool equal = p1.IsEqualTo(p2, customTol);
bool parallel = v1.IsParallelTo(v2, customTol);

Properties: EqualPoint (double), EqualVector (double) - both get-only.

UCS / OCS / WCS Coordinate Conversion

AutoCAD uses three coordinate systems:

• WCS — World Coordinate System (absolute, fixed)
• UCS — User Coordinate System (current user-defined system)
• OCS — Object Coordinate System (per-entity, e.g. a 2D polyline's plane)

// WCS point → current UCS point
Matrix3d ucsMatrix = ed.CurrentUserCoordinateSystem;
Point3d wcsPoint = new Point3d(100, 200, 0);
Point3d ucsPoint = wcsPoint.TransformBy(ucsMatrix.Inverse());

// UCS point → WCS point
Point3d backToWcs = ucsPoint.TransformBy(ucsMatrix);

// WCS → OCS (entity's local plane, e.g. for a 2D polyline)
// Use WorldToPlane with the entity's Normal vector
Vector3d normal = polyline.Normal;  // e.g. Vector3d.ZAxis for XY-plane poly
Matrix3d wcsToOcs = Matrix3d.WorldToPlane(normal);
Point3d ocsPoint = wcsPoint.TransformBy(wcsToOcs);

// OCS → WCS
Matrix3d ocsToWcs = Matrix3d.PlaneToWorld(normal);
Point3d wcsFromOcs = ocsPoint.TransformBy(ocsToWcs);

// Align coordinate systems (e.g. block transform from one CS to another)
Matrix3d alignXform = Matrix3d.AlignCoordinateSystem(
    Point3d.Origin,      // fromOrigin
    Vector3d.XAxis,      // fromXAxis
    Vector3d.YAxis,      // fromYAxis
    Vector3d.ZAxis,      // fromZAxis
    targetOrigin,        // toOrigin
    targetXAxis,         // toXAxis
    targetYAxis,         // toYAxis
    targetZAxis          // toZAxis
);

Common Geometry Recipes

// Offset a point along a direction by distance
Point3d OffsetPoint(Point3d pt, Vector3d dir, double dist)
{
    return pt + dir.GetNormal() * dist;
}

// Find intersection of two 2D lines
Point2d? IntersectLines(Point2d a1, Point2d a2, Point2d b1, Point2d b2)
{
    Line2d lineA = new Line2d(a1, a2);
    Line2d lineB = new Line2d(b1, b2);
    Point2d[] pts = lineA.IntersectWith(lineB);
    return pts?.Length > 0 ? pts[0] : (Point2d?)null;
}

// Project point onto a line
Point3d ProjectPointToLine(Point3d pt, Line3d line)
{
    PointOnCurve3d poc = line.GetClosestPointTo(pt);
    return poc.Point;
}

// Distance from point to line
double PointToLineDistance(Point3d pt, Line3d line)
{
    return line.GetDistanceTo(pt);
}

// Angle between two vectors (with reference for sign)
double SignedAngle(Vector3d from, Vector3d to, Vector3d refAxis)
{
    return from.GetAngleTo(to, refAxis);
}

// Check if point is on a curve within tolerance
bool IsPointOnCurve(Curve3d curve, Point3d pt)
{
    return curve.IsOn(pt);
}

Gotchas

• Point2d uses GetDistanceTo() but Point3d uses DistanceTo() (no "Get" prefix) - easy source of compile errors
• Vector3d.GetAngleTo(Vector3d) always returns 0 to pi. Use the 3-parameter overload GetAngleTo(Vector3d, Vector3d referenceVector) for signed angles (0 to 2pi)
• GetNormal() throws ZeroVectorException on zero-length vectors; check IsZeroLength() first or use GetNormal(Tolerance) which returns a zero vector instead
• Point2d/Point3d are structs (value types) - they are copied on assignment, not referenced
• Matrix multiplication is right-to-left: rot * scale applies scale first, then rotation
• Curve.GetLength() takes parameter values, not station values; get the interval first with GetInterval()
• All angle parameters are in radians, not degrees
• Line2d/Line3d are infinite lines; use LineSegment2d/LineSegment3d for bounded segments
• CircularArc2d/3d.IntersectWith() returns null (not empty array) when there are no intersections - always null-check
• CurveCurveIntersector3d requires a planeNormal parameter (for projection) - use Vector3d.ZAxis for XY-plane intersections
• CurveCurveIntersector2d.OverlapCount is a property (no parens); CurveCurveIntersector3d.OverlapCount() is a method (requires parens) - mixing them up causes compile errors
• 2D Polyline vertices are stored in OCS (Object Coordinate System), not WCS. Use Matrix3d.WorldToPlane(polyline.Normal) to convert WCS points to OCS before comparing or inserting vertices
• Extents2d and Extents3d are in Autodesk.AutoCAD.DatabaseServices, not Autodesk.AutoCAD.Geometry - add the correct using directive
• Tolerance overloads exist for almost every comparison method - use them when default global tolerance is too tight or too loose

Related Skills

• acad-polylines — polyline vertices, bulge arcs, and OCS vertex coordinate conversion