%CONTENTS GEOM2D Geometry 2D Toolbox.
% Version 1.24 07-Jun-2018.
%
% 	Library to handle and visualize geometric primitives such as points,
% 	lines, circles and ellipses, polygons...
%
%   The goal is to provide a low-level library for manipulating geometrical
%   primitives, making easier the development of more complex geometric
%   algorithms. 
%
%   Most functions works for planar shapes, but some ones have been
%   extended to 3D or to any dimension.
%
% Points
%   points2d                 - Description of functions operating on points.
%   midPoint                 - Middle point of two points or of an edge.
%   circumCenter             - Circumcenter of three points.
%   isCounterClockwise       - Compute the relative orientation of 3 points.
%   polarPoint               - Create a point from polar coordinates (rho + theta).
%   angle2Points             - Compute horizontal angle between 2 points.
%   angle3Points             - Compute oriented angle made by 3 points.
%   distancePoints           - Compute distance between two points.
%   transformPoint           - Apply an affine transform to a point or a point set.
%   drawPoint                - Draw the point on the axis.
%
% Point Sets
%   clipPoints               - Clip a set of points by a box.
%   centroid                 - Compute centroid (center of mass) of a set of points.
%   boundingBox              - Bounding box of a set of points.
%   principalAxes            - Principal axes of a set of ND points.
%   angleSort                - Sort points in the plane according to their angle to origin.
%   findClosestPoint         - Find index of closest point in an array.
%   minDistancePoints        - Minimal distance between several points.
%   mergeClosePoints         - Merge points that are closer than a given distance.
%   hausdorffDistance        - Hausdorff distance between two point sets.
%   nndist                   - Nearest-neighbor distances of each point in a set.
%
% Vectors
%   vectors2d                - Description of functions operating on plane vectors.
%   createVector             - Create a vector from two points.
%   vectorNorm               - Compute norm of a vector, or of a set of vectors.
%   vectorAngle              - Horizontal angle of a vector, or angle between 2 vectors.
%   normalizeVector          - Normalize a vector to have norm equal to 1.
%   isPerpendicular          - Check orthogonality of two vectors.
%   isParallel               - Check parallelism of two vectors.
%   transformVector          - Transform a vector with an affine transform.
%   rotateVector             - Rotate a vector by a given angle.
%
% Straight lines
%   lines2d                  - Description of functions operating on planar lines.
%   createLine               - Create a straight line from 2 points, or from other inputs.
%   fitLine                  - Fit a straight line to a set of points.
%   medianLine               - Create a median line between two points.
%   cartesianLine            - Create a straight line from cartesian equation coefficients.
%   orthogonalLine           - Create a line orthogonal to another one through a point.
%   parallelLine             - Create a line parallel to another one.
%   intersectLines           - Return all intersection points of N lines in 2D.
%   lineAngle                - Computes angle between two straight lines.
%   linePoint                - Coordinates of a point on a line from its position.
%   linePosition             - Position of a point on a line.
%   clipLine                 - Clip a line with a box.
%   reverseLine              - Return same line but with opposite orientation.
%   transformLine            - Transform a line with an affine transform.
%   lineToEdge               - Convert a straight line to a finite edge.
%   drawLine                 - Draw a straight line clipped by the current axis.
%
% Edges (line segments between 2 points)
%   edges2d                  - Description of functions operating on planar edges.
%   createEdge               - Create an edge between two points, or from a line.
%   edgeAngle                - Return angle of edge.
%   edgeLength               - Return length of an edge.
%   parallelEdge             - Edge parallel to another edge.
%   centeredEdgeToEdge       - Convert a centered edge to a two-points edge.
%   midPoint                 - Middle point of two points or of an edge.
%   edgePoint                - Extract a point from an edge.
%   edgePosition             - Return position of a point on an edge.
%   clipEdge                 - Clip an edge with a rectangular box.
%   reverseEdge              - Intervert the source and target vertices of edge.
%   intersectEdges           - Return all intersections between two set of edges.
%   intersectLineEdge        - Return intersection between a line and an edge.
%   transformEdge            - Transform an edge with an affine transform.
%   edgeToLine               - Convert an edge to a straight line.
%   edgeToPolyline           - Convert an edge to a polyline with a given number of segments.
%   drawEdge                 - Draw an edge defined by its two extremities.
%   drawCenteredEdge         - Draw an edge centered on a point.
%
% Rays
%   rays2d                   - Description of functions operating on planar rays.
%   createRay                - Create a ray (half-line), from various inputs.
%   bisector                 - Return the bisector of two lines, or 3 points.
%   clipRay                  - Clip a ray with a box.
%   drawRay                  - Draw a ray on the current axis.
%
% Relations between points and lines
%   distancePointEdge        - Minimum distance between a point and an edge.
%   distancePointLine        - Minimum distance between a point and a line.
%   projPointOnLine          - Project a point orthogonally onto a line.
%   isPointOnLine            - Test if a point belongs to a line.
%   isPointOnEdge            - Test if a point belongs to an edge.
%   isPointOnRay             - Test if a point belongs to a ray.
%   isLeftOriented           - Test if a point is on the left side of a line.
%
% Circles
%   circles2d                - Description of functions operating on circles.
%   createCircle             - Create a circle from 2 or 3 points.
%   createDirectedCircle     - Create a directed circle.
%   intersectCircles         - Intersection points of two circles.
%   intersectLineCircle      - Intersection point(s) of a line and a circle.
%   circleToPolygon          - Convert a circle into a series of points.
%   circleArcToPolyline      - Convert a circle arc into a series of points.
%   isPointInCircle          - Test if a point is located inside a given circle.
%   isPointOnCircle          - Test if a point is located on a given circle.
%   enclosingCircle          - Find the minimum circle enclosing a set of points.
%   circumCircle             - Circumscribed circle of three points.
%   radicalAxis              - Compute the radical axis (or radical line) of 2 circles.
%   drawCircle               - Draw a circle on the current axis.
%   drawCircleArc            - Draw a circle arc on the current axis.
%
% Ellipses and Parabola
%   ellipses2d               - Description of functions operating on ellipses.
%   equivalentEllipse        - Equivalent ellipse of a set of points.
%   fitEllipse               - Fit an ellipse to a set of 2D points.
%   transformEllipse         - Apply an affine transformation to an ellipse.
%   createEllipse            - Create an ellipse, from various input types.
%   distancePointEllipse     - Distance from a point to an ellipse.
%   projPointOnEllipse       - Project a point orthogonally onto an ellipse.
%   isPointInEllipse         - Check if a point is located inside a given ellipse.
%   ellipseArea              - Area of an ellipse.
%   ellipsePerimeter         - Perimeter of an ellipse.
%   ellipseToPolygon         - Convert an ellipse into a series of points.
%   ellipsePoint             - Coordinates of a point on an ellipse from parametric equation.
%   ellipseCartesianCoefficients - Cartesian coefficients of an ellipse.
%   drawEllipse              - Draw an ellipse on the current axis.
%   drawEllipseAxes          - Draw the main axes of an ellipse as line segments.
%   drawEllipseArc           - Draw an ellipse arc on the current axis.
%   drawParabola             - Draw a parabola on the current axis.
%
% Geometric transforms
%   transforms2d             - Description of functions operating on transforms.
%   createTranslation        - Create the 3*3 matrix of a translation.
%   createRotation           - Create the 3*3 matrix of a rotation.
%   createRotation90         - Matrix of a rotation for 90 degrees multiples.
%   createScaling            - Create the 3*3 matrix of a scaling in 2 dimensions.
%   createHomothecy          - Create the the 3x3 matrix of an homothetic transform.
%   createBasisTransform     - Compute matrix for transforming a basis into another basis.
%   createLineReflection     - Create the the 3x3 matrix of a line reflection.
%   principalAxesTransform   - Align a set of points along its principal axes.
%   fitAffineTransform2d     - Compute the affine transform that best register two point sets.
%   registerICP              - Fit affine transform by Iterative Closest Point algorithm.
%   polynomialTransform2d    - Apply a polynomial transform to a set of points.
%   fitPolynomialTransform2d - Coefficients of polynomial transform between two point sets.
%
% Angles
%   angles2d                 - Description of functions for manipulating angles.
%   normalizeAngle           - Normalize an angle value within a 2*PI interval.
%   angleAbsDiff             - Absolute difference between two angles.
%   angleDiff                - Difference between two angles.
%
% Boxes
%   boxes2d                  - Description of functions operating on bounding boxes.
%   intersectBoxes           - Intersection of two bounding boxes.
%   mergeBoxes               - Merge two boxes, by computing their greatest extent.
%   randomPointInBox         - Generate random point within a box.
%   boxToRect                - Convert box data to rectangle data.
%   boxToPolygon             - Convert a bounding box to a square polygon.
%   drawBox                  - Draw a box defined by coordinate extents.
%
% Triangles
%   isPointInTriangle        - Test if a point is located inside a triangle.
%   triangleArea             - Signed area of a triangle.
%
% Rectangles
%   rectToPolygon            - Convert a rectangle into a polygon (set of vertices).
%   rectToBox                - Convert rectangle data to box data.
%   drawRect                 - Draw rectangle on the current axis.
%   orientedBox              - Minimum-width oriented bounding box of a set of points.
%   orientedBoxToPolygon     - Convert an oriented box to a polygon (set of vertices).
%   drawOrientedBox          - Draw centered oriented rectangle.
%
% Splines
%   cubicBezierToPolyline    - Compute equivalent polyline from bezier curve control.
%   drawBezierCurve          - Draw a cubic bezier curve defined by 4 control points.
%
% Various drawing functions
%   drawVector               - Draw vector at a given position.
%   drawArrow                - Draw an arrow on the current axis.
%   drawLabels               - Draw labels at specified positions.
%   drawGrid                 - Draw a grid defined by vertex positions along each axis.
%   drawShape                - Draw various types of shapes (circles, polygons...).
%
% Other shapes
%   squareGrid               - Generate equally spaces points in plane.
%   hexagonalGrid            - Generate hexagonal grid of points in the plane.
%   triangleGrid             - Generate triangular grid of points in the plane.
%   crackPattern             - Create a (bounded) crack pattern tessellation.
%   crackPattern2            - Create a (bounded) crack pattern tessellation.
%
%
%   Credits:
%   * function 'enclosingCircle' rewritten from a file from Yazan Ahed
%       (yash78@gmail.com), available on Matlab File Exchange

% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-11-07
% Copyright 2005-2024 INRA - Cepia Software Platform

% deprecated
%   pointOnLine              - Create a point on a line at a given position on the line.

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