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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
%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.
% 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.
% 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 given by 2 points.
% 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.
% pointOnLine - Create a point on a line at a given position on the 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.
% 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 2005-2023 INRA - Cepia Software Platform
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