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.
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.
lineFit - Fit a straight line to a set of points.
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 of 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.
isPointInEllipse - Check if a point is located inside a given ellipse.
ellipsePerimeter - Perimeter of an ellipse.
ellipseToPolygon - Convert an ellipse into a series of points.
drawEllipse - Draw an ellipse on the current axis.
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
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Author: David Legland
e-mail: david.legland@inrae.fr
Created: 2005-11-07
Copyright INRA - Cepia Software Platform.
Project homepage: http://github.com/mattools/matGeom
http://www.pfl-cepia.inra.fr/index.php?page=geom2d