version 1.25 (427 KB) by
David Legland

Geometry library for matlab. Performs geometric computations on points, lines, circles, polygons...

**Editor's Note:** This file was selected as MATLAB Central Pick of the Week

Geometry library to handle and visualize geometric primitives such as points, lines, circles and ellipses, polylines and polygons...

The goal is to provide a low-level library for manipulating geometrical primitives, making easier the development of more complex geometric algorithms.

The library proposes functions to:

* create various shapes (points, circles, lines, ellipses, polylines, polygons) using an intuitive syntax. Ex: createCircle(p1, p2, p3) to create a circle through 3 points, create parallel and perpendicular lines

* compute intersections between 2 lines, between a line and a circle

* work on polylines and polygons: compute centroid and area, expand, clip with half-plane...

* measure distances (between points, a point and a line, a point and a group of points), angle (of a line, between 3 points), or test geometry (point on a line, on a circle).

* manipulate planar transformations. Ex: P2 = transformPoint(P1, createRotation(CENTER, THETA));

* draw shapes easily. Ex: drawCircle([50 50], 25), drawLine([X0 Y0 DX DY]). Some clipping is performed for infinite shapes such as lines or rays.

Additional help is provided in geom/Contents.m file, as well as summary files like 'points2d.m' or 'lines2d.m'.

Note: the project has merged with the geom3d library (FeX 24484), and is now hosted on GitHub: https://github.com/mattools/matGeom

David Legland (2021). geom2d (https://www.mathworks.com/matlabcentral/fileexchange/7844-geom2d), MATLAB Central File Exchange. Retrieved .

Created with
R2019a

Compatible with any release

**Inspired by:**
Minimum Enclosing Circle, Curve intersections

**Inspired:**
Split Line Segments (Edges), Geometric and Topological Methods for Significance Testing in Wavelet Analysis, Cumulative Areawise Testing in Wavelet Analysis, Chord Length Distribution from Binary 2D Images, image ellipsoid 3D, imMinkowski, Generate random line segments without intersecting

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!Create scripts with code, output, and formatted text in a single executable document.

Ettore Pennestri'David Legland@Zhao chuan: I have had a look, and in fact the problem comes from the fact that first and last vertex of the polygon are the same. Removing last vertex should solve your issue. I have made a more detailed answer on GitHub.

Best,

David

zhao chuanHi David, I have obtained a wrong result when I use expandPolygon, the detail description is on https://github.com/mattools/matGeom/issues/111, could you have a look?

David LeglandHi Hubert,

Thanks you for the suggestion! I have fixed the file. New version is available on GitHub, and will be included in next version.

Best,

David

Hubert Schneegans*

%Previous version

%a = abs(atan2(v(2),v(1)) - atan2(u(2),u(1)));

%New version

a = abs(mod(atan2(v(2),v(1)),2*pi) - mod(atan2(u(2),u(1)),2*pi));

Hubert SchneegansHi David,

I had some trouble with your minimumCaliperDiameter.m function with some of my cloud of points.

It appeared the problem came because of angle evaluation of your vectorAngle.m function.

I changed it a bit just by adding mod() for your atan2() results:

%Previous version

%a = abs(mod(atan2(v(2),v(1)),2*pi) - mod(atan2(u(2),u(1)),2*pi));

%New version

a = abs(mod(atan2(v(2),v(1)),2*pi) - mod(atan2(u(2),u(1)),2*pi));

I hope it will not affect the proper functionning of your other functions but for my application, it's ok.

Thank you for your work!

David LeglandHi di,

this is strange indeed... I had a look but could not reproduce... I just fixed some deprecated call in this function; if you can open an issue with a sample of code showing the pbm, that would be great!

diDavid,

I don't quite understand.The radius on output of this function [imInscribedCircle] will be "inf" sometimes,even in the example you provided.How can it become infinite?

diDavid,

Thank you for reply and help, which is very useful to me.Have a good day.

David LeglandHi di,

I wrote such a function. It is part of the "MatImage" toolbox (https://github.com/mattools/matImage ).

Works for binary or label imags. You get get it from GitHub: https://github.com/mattools/matImage/blob/master/matImage/imMeasures/imInscribedCircle.m

diDavid,

I have a question that does this package or other packages include an algorithm for finding the maximum inscribed circle of label image or bw image ?

Thank you very much!

Bogdan UdreaDavid,

Thank you for a great library. I have been using both geom2d and geom3d for at least five years now.

I have just downloaded the newest versions and noticed isAxisHandle function is missing from the geom2d zip file but it is available in the respective toolbox.

Best,

BU

David Legland@joe hubbard: what do you mean? can you be more specific about the bug or problem you encounter?

joe hubbardVectors do not appear to be functioning properly

Md. Salim RazaDavid LeglandHi Kaleesh,

You can use the following code as a base example:

figure(1); clf; hold on;

drawEllipse([50 50 40 20 30]);

axis equal; axis([0 100 10 90])

This draws an ellipse centered in (50,50), with axis lengths equal to 40 and 20, and with an orientation of 30 degrees. You can obtain more info by typing "help drawEllipse".

Kaleesh BalaHi could you explain how the fuction drawEllipse(varargin) works ?

Where to enter the inputs etc?

Huihua ZHAOGreat stuff, does the job very well!

I have some problems making animation since all the draw* functions could not refresh data. I am able to use the method of deleting handles to achieve what I need.

Bottom line, great stuff!

Thank you very much.

David Legland@Burak: yes! It was originally developped for later versions of Matlab, and I try to keep it compatible most of matlab versions.

Burak PehlivanHi,

Does it work with R2013b?

Yaren ZhangDavid Legland@mazen hakeem: the module 'graphs' is currently not packaged with the "geom2d" toolbox. You can find the related function in the parent MatGeom project, hosted in the GitHub repository: https://github.com/mattools/matGeom . The "drawGraph" function can be found at https://github.com/mattools/matGeom/blob/master/matGeom/graphs/drawGraph.m

Best,

David

mazen hakeemhow can I find drawGraph function in geom2d?

David Legland@linken lee: I just submitted a new version that should fix the problem in clipEdge. (The problem was about checking if a point belong to an edge, but should be solved now).

@Xiadong: the vecnorm function in geom2d is obsolete for long time (since 2009 actually...), and have been replaced by the "vectorNorm" function.

Hope this helps.

XiaodongBug report: On Matlab 2017b pre-release and maybe also the coming official Matlab 2017b, the vecnorm function have name conflict with the builtin Matlab function. Could you rename them to avoid this conflict? Just to let you know that I found this problem while running 2017b pre-release. Thanks!

Nishath Ranasinghelinken leeI report a bug.

for function clipEdge, I run below

edge=[ 102.5260 -1.8235 91.5926 12.6135];

box=[0 100 0 100];

clipEdge(edge, box)

the result is 101.1450 0 91.5926 12.6135

NienkeDavid LeglandHi Jingjing,

the polyxpoly function requires the mapping toolbox, and hence adds a dependency. The interX function works usually fine, can you describe the failing cases?

Anyway, I have updated the intersectPolylines function to avoid the call to the interX function (simply by adapting the code of interX directly into intersectPolylines).

Regards,

Jingjing MengThank you for the awesome package.

However, I find a bug in the function-intersectPolylines-basically you use the local function P = InterX(L1,varargin).

You can just use embedded function polyxpoly and ignore this error function.

David LeglandHi Saunhita,

I have updated a modified version that contains the missing file.

Regards,

Saunhita SapreHello David,

First of all thank you for the awesome package. But isAxisHandle function is missing in the toolbox. Can you please upload it. TIA.

Saunhita SapreDavid LeglandHello Lockywolf,

It could be a problem of numerical accuracy, that can be quickly problematic with noisy data and/or result of GUI interactions.

I have tried to update the library to make it little bit more robust, in particular it is now possible to specify a 'tolerance' parameter to the polygonLoops function. This allows to tune the way vertices are detected similar, or how intersections at edges intersections are handled. Default is 1e-14, but using larger values (say 1e-12, or 1e-10) should provide better results.

Hope this helps? Otherwise feel free to open an issue on the MatGeom GitHub (ideally with running example...)

regards,

LockywolfHello, everyone. Firstly, this package is wonderful, honestly.

Secondly. There seems to be a bug in the polygonLoops code.

The code throws an exception when the polygon is very irregular with a lot of self-crossings.

I am not particularly sure how to reproduce it, but essentially, works every time I try to kind of "paint a dot" with a imfreehand, close it and and feed the result into polygonLoops.

Anyway, thanks for your work.

David LeglandHi Scrat,

you can use the "distancePointPolygon" function, using circle centers as first argument (as N-by-2 array), and square vertices as second argument (as 4-by-2 array).

regards!

ScratHello,

suppose i have square and three circles inside the square. ist possible to measure the shortest distance from the centroid of each circle to the square perimeter.

if so then which are the functions i can use,

Thanks

David LeglandHi Thayes,

sorry for delay... I have no answer to you problem. I would have also used the polygonSelfIntersection function, I think additional processing is required, but not that easy to implement...

David LeglandHi Stratosphere,

you can compute intersection of the polygon with rays or lines at various angles. You can use createRay for creating the rays, and intersectRayPolygon function for computing the intersections.

StratosphereHello,

Is it possible to find intersection points on the polygon with equal angles to the center point? I mean that I want to choose a point N1 on the polygon and then find the following [N1,N2,...,N36] points on the polygon such that:

Angle between N1 and Center = Theta

Angle between N2 and Center = Theta + 10

Angle between N3 and Center = Theta + 20

Angle between N4 and Center = Theta + 30

...

Angle between N36 and Center = Theta + 350

Which functions can help me? Thanks.

Thayjes SrivasHi,

I have a question on how exactly we could reorder the points of a polygon such that all the self intersections are removed ? I have tried playing around with the polygonSelfIntersection and polygonLoops function but still not figured out how to reorder the points. Thanks

filippDavid LeglandHi Filipp,

the function "projPointOnPolygon" does not rely on any toolbox, so I do not understand the difference in speed. The underlying function is "distancePointEdge", that I tried to optimize using bsxfun. Do no work with large number of vertices? Have you tried to profile to identify where code is slow? (You can contact me by mail, this will be easier to exchange)

Regards, David

filippHi, I have a question on the projPointOnPolygon function. It is running extremely slow on one system with Matlab 2014b (no toolboxes installed), but works properly on another system with Matlab 2012 (most toolboxes installed). Is it using any toolboxes? Are there other reasons why it might be so slow (given that the first system even has more RAM)? Thank you!

EricKrisztian SzucherDavid Legland@Tao:

In the case you propose, the test line overlap one of the edges of the polygon. The function intersectLinePolygon does not handle such degenerate cases. You can avoid it by slightly shifting the test line for example.

TaoI probably met a bug in intersectLinePolygon.m

I call this function by:

line=[0 11.8760 1 0];

offsets= [-6.0960 11.8760;

-6.0960 11.6760;

-6.7870 11.6760;

-9.1180 11.8330;

-9.1180 11.8760;

-6.0960 11.8760];

intersect=intersectLinePolygon(line,offsets)

then I get: intersect =

-6.0960 11.8760

But it is supposed be: intersect =

-9.1180 11.8760

-6.0960 11.8760

For other situations ,it works well except this one.

Can you work it out?? My MATLAB version is : R2012a

David Legland@Jan:

I have updated a new version, with some updates on medialAxisConvex. It works on the few polygons I have tested. I hope it will fit your needs.

regards,

Jan BartonicekI tried to run demoMedialAxis and got this error:

??? Error using ==> vertcat

CAT arguments dimensions are not consistent.

Error in ==> medialAxisConvex at 123

events = [events; ir(1) i pint(1,:) ti(1); ir(2) i pint(2,:) ti(2)]; %#ok<AGROW>

There may be some problem with point adding. Do you know where?

Thank you

David Legland@bn dhouba:

an edge in geom2d should be understood as 'line segment'. Is defined by two extremities, and is restricted to the set of points between these two points. The functions working on 'line' objects considers infinite straigt lines. Hope this makes things clearer? regards,

bh dhouhaHi, i really apprciate this package it's really intresting. I just dont understand the exact meaning of edge here in the functions DrawEdge or intersecEdges , do you mean simply line? is it the same thing?

Sincerely

David LeglandHi William,

functions meshVolume and polygonArea depends on the face (or vertices) orientation. If all faces are oriented outwards, the volume will be positive. If all facets are orieted inwards, you will obtain the negative value of the volume. Just be careful to ensure faces orientation is consistent (use checkMeshAdjacentFaces for example)

WilliamI seem to get a negative volume using the meshVolume function...

I'm trying to calculate the volume of a bendy open ended cylinder, using the faces and vertices generated from an isosurface patch. Any thoughts?

David LeglandHi Jasper,

thanks for pointing out the bug! I have released a new version that should fix it. Tell me if there are still problems.

David

JdeenI believe I found a bug in the clipEdge function, however do not have the time to investigate what exactly the bug is. However, results can be different when calling clipEdge(allEdges, box) instead of clipEdge(oneEdge, box) for each box. Example variables where the error occurs can be found here: http://codepaste.net/sd1k8o

Edge in row number four is not correctly clipped when clipping all edges at once.

Fadi KahwashThis is a treasure for beginners in computational geometry.

Many Thanks,

Fadi

filippHi David,

thanks a lot for your suggestion. Using Delaunay triangulation sounds reasonable and I will definitely try that!

Regards,

filipp

David LeglandHi Filipp,

I think your problem is closely related to Hamiltonian path in graph theory. Maybe what you can try to do is create Delaunay triangulation of your points. This will produce a set of triangle, that you can convert to a set of edges that do not self-intersect. The set of edges form a graph, then you can find or write an algorithm that finds an Hamiltonian path that goes through each vertex once and only once. Hope this gives the idea...

By "sorting" vertices, I was meaning finding the order of indices that need to be considered. Maybe the term "ordering" would have been more appropriate. The idea is to keep the original array unchanged, and work only on vertex indices. But this is just technical consideration.

Regards,

David

filippHi David,

thanks for the patience :-) The second option would be the one that I am searching for: finding a path going through a set of (random) points without self-intersecting. I already tried a brute force method: choosing a random starting point, connecting points one-by-one, and going back when intersections are found. However, this is extremely costly and did not seem to be an elegant solution. So, what do you mean by sorting vertices of interest?

Regards,

filipp

David LeglandHi Filipp,

I am not sure to really understand your question... Do you want to draw the convex hull of a set of points? Or some kind of path going through a set of points without self-intersecting? In both cases, you first need to identify and/or sort vertices of interest before plotting them.

filippHi David,

thanks for your response. I've already tried these two functions, however, both allow for intersection. As a consequence, they do not result in a shape with a single circumferential contour but in a jumble of crossing lines. Do you have an alternative idea how to create closed contours from a number of random points?

Regards,

filipp

David LeglandHi filipp,

yes, you can use one of the "drawPolygon" or "fillPolygon" functions (in the "polygons" subpackage). Hope this helps ?

regards,

David

filippHi David,

I search for a way to display polygons without intersecting faces (i.e., shapes with one contour). Is this function available in your package or in matgeom? If not, do you have an idea to implement this?

Thanks!

Ralph TrimnellFinally, works good! Now for the real fun! Thanks, again, Ralph

Ralph TrimnellThanks, David,

Maybe I'm out of my depth here but geom looked ideal to create simulations of organic growth events as an addition to the jdk. Will it not work without Matlab?

Ralph

David LeglandHi Ralph,

There is no need to download java for using this contribution. What you get after download is a zip file that contains a set of '.m' files, in a small directory arborescence, that should be run with Matlab.

Hope this makes things clearer?

David

Ralph TrimnellRalph Trimnell

Could someone explain how to get Java to recognize geom I tried pasting the whole JAR into the jdk:no good! I put it's address in the system environment path: no good. Once extracted, it's no longer a Jar file,just has extention geom. There should be an easy way to do this. I'm using notepad on windows 8.1. Thanks

David LeglandHi Gary,

The "expansion" or "erosion" of the polygon depends on polygon orientation (counter-clockwise or clockwise) and on the sign of the distance. If polygon is CCW and distance is positive, the result will be expanded.

I have submitted a new version, that fixes some bugs. It seems to work better.

regards;

Gary KenwardThe function expandPolygon appears to have a number of problems.

The following shrinks the polygon rather then expand it:

Sq1 = [-10.28,-15.39;-17.28,-4.611;-11.89,-1.110;-4.890,-11.89]

Sq1 = [ Sq1; Sq1(1,:) ];

Sq1e = cell2mat ( expandPolygon ( Sq1, 1 ) );

And, the following generates an error within the function:

Sq = [ [-10, -5]; [-10, 5]; [-5, 5]; [ -5, -5] ];

Sq1 = (Sq * [ cos(33*pi/180) -sin(33*pi/180); sin(33*pi/180) cos(33*pi/180)]' ) * 9/7 - 3;

Sq1 = [ Sq1; Sq1(1,:) ];

Sq1e = cell2mat ( expandPolygon ( Sq1, 1 ) );

The error message is:

Attempted to access poly(0,:); index must be a

positive integer or logical.

Error in distancePointPolygon (line 19)

if sum(poly(end, :)==poly(1,:))~=2

Error in distancePolygons (line 19)

dist2 = min(distancePointPolygon(poly2, poly1));

Error in expandPolygon (line 63)

distLoop(i) = distancePolygons(loops{i}, poly);

Boris SchauerteExactly what I was looking for. Well documented and easy to use. Thanks!

J.R.! Menzingernice work.

MarcReally nice works... Thanks

David LeglandHi sumitha,

basic format for representing lines is [x0 y0 dx dy], where (w0,y0) refers to origin point, and (dx,dy) to direction vector. You can create a line orthogonal to direction THETA with:

line1 = [x0 Y0 -sin(THETA) cos(THETA)];

drawLine(line1);

Regards.

sumithaHi,can u please suggest me which one of these i can use to draw a line orthogonal to the given orientation(in radian)or else can u plz give me an idea how i can proceed with the same.

David LeglandHi Benjamin, the clipping of polygon is not an easy problem. There are efficient algorithms, and their inclusion is planned, but I still haven't found time to write them down. It seems the mapping toolbox provides facilities for this, maybe you can check it.

Regards, David

Benjamin SanderseHi David, thanks for the great work. I have been using your clipPolygon successfully for clipping convex polygons, but now I also need it for non-convex polygons... are you planning to include this in a future release?

SHAFIQULVery nice and essential coding thanks for sharing.

marriam nayyeranyone please help me

David Legland@Frank: yes, there was a stupid bug in this function. I have submitted an enhanced version that fixes it.

Regards, David

Frank GommerHi, looks like a nice little toolbox!

I just tried your function "intersectLineCircle.m". Unfortunately, it seems that the code does not give the right answers for tangential lines (Returns 'nan') and lines which are not intersecting at all (gives a wrong intersection point).

Here is the data I used:

c1 = [0 0 0.5]

l1 = [0.5 0 0 1] %tangential

l1 = [-1 0 0 1] %non touching

pts = intersectLineCircle(l1, c1)

Cheers,

Frank

Juan Pablo Carbajalgeom2d is a first class complement to the geometry tools provided.

David: You should add a 2D alpha shape routine. I am testing this one at the moment, but leaves lots of room for improvement. http://www.mathworks.com/matlabcentral/fileexchange/6760-ashape-a-pedestrian-alpha-shape-extractor

David LeglandHi Chris,

intersection of circle with line/circle is not implemented for the moment, juste because I did not need it yet... But I will try to implement it in a future release.

Regards.

Chris TIANHi, this is very useful for me? I just wonder why didn't i find the function for obtaining intersections between a line and a circle? Thanks.

BenWell done, David!

Reto ZinggOK, I think this should work, circumventing eps. Again, looking at center points instead of end-points. This time the center points of segments. It still needed some fail-safe code when multiple edge segments show up inside box due to finite precission. The code should also maintain 'direction' of the edges, as your previous code.

Here the conplete code for clipEdge:

% process data input

if size(box, 1)==1

box = box([1 3 2 4]);

end

% get limits of window

xmin = box(1);

ymin = box(2);

xmax = box(3);

ymax = box(4);

% convert window limits into lines

lineX0 = [xmin ymin xmax-xmin 0];

lineX1 = [xmin ymax xmax-xmin 0];

lineY0 = [xmin ymin 0 ymax-ymin];

lineY1 = [xmax ymin 0 ymax-ymin];

edge2 = zeros(size(edge));

for i=1:size(edge,1)

% current edge

iedge = edge(i, :);

% compute intersection points with each line of bounding window

px0 = intersectLineEdge(lineX0, iedge);

px1 = intersectLineEdge(lineX1, iedge);

py0 = intersectLineEdge(lineY0, iedge);

py1 = intersectLineEdge(lineY1, iedge);

% create array of points

points = [px0; px1; py0; py1; iedge(1:2); iedge(3:4)];

% and remove infinite points (edges parallel to box edges)

points = points(all(isfinite(points),2), :);

% sort points by x then y

points = sortrows(points);

% get center positions between points

centerPoints=(points(2:end,:)+points(1:end-1,:))/2;

% find the centerPoints (if any) inside window

ins = find( centerPoints(:,1)>=xmin & centerPoints(:,2)>=ymin & ...

centerPoints(:,1)<=xmax & centerPoints(:,2)<=ymax);

% if multiple segments inside box, which can happen due to finite resolution, only take the longest segment

if length(ins)>1

dv=points(ins+1,:)-points(ins,:); % delta vectors of the segments

len=hypot(dv(:,1), dv(:,2)); % lengths of segments

[a,I]=max(len); % find index of longest segment

ins=ins(I);

end

if length(ins)==1 % if one of the center points is inside box, then the according edge segment is indide box

if edge(i,1)>edge(i,3) || (edge(i,1)==edge(i,3) && edge(i,2)>edge(i,4)) % restore same direction of edge

edge2(i, :) = [points(ins+1,:) points(ins,:)];

else

edge2(i, :) = [points(ins,:) points(ins+1,:)];

end

end

end

Reto ZinggArgh, never mind. My solution has div by 0 problem. The whole eps stuff is really a pain in the ...

Reto Zinggturns out my suggestion above introduces a problem with negative numbers. The code below should work correctly:

% ins = find( points(:,1)-xmin>=-eps & points(:,2)-ymin>=-eps & ...

% points(:,1)-xmax<=eps & points(:,2)-ymax<=eps);

ins = find( (points(:,1)/xmin-1)*sign(xmin)>=-eps & (points(:,2)/ymin-1)*sign(ymin)>=-eps & ...

(points(:,1)/xmax-1)*sign(xmax)<=eps & (points(:,2)/ymax-1)*sign(ymax)<=eps);

Reto ZinggAlso in clipEdge() you should change the limit check. See code below. Change commented out to suggested.

cheers,

Reto

% ins = find( points(:,1)-xmin>=-eps & points(:,2)-ymin>=-eps & ...

% points(:,1)-xmax<=eps & points(:,2)-ymax<=eps);

ins = find( points(:,1)/xmin-1>=-eps & points(:,2)/ymin-1>=-eps & ...

points(:,1)/xmax-1<=eps & points(:,2)/ymax-1<=eps);

Reto ZinggBonjour,

again some trouble with large numbers and limit checking. This time in isPointOnEdge, which is used for intersectLineEdge, which in turn is used in clipEdges.

isPointOnEdge will not work correctly for coordinates with large numbers, as you apply a fixed tolerance. However, the numerical tolerance of matlab is relative to the number itself.

I normalized the point and edge x and y elements to the point x and y respectively. Like that you will deal with numbers in the range of 1 and your tolerance check will work.

See the code below. Note that I also dumped the Np==Ne check, as it didn't do anything.

Regards, Reto

% extract computation tolerance

tol = 1e-14;

if ~isempty(varargin)

tol = varargin{1};

end

% number of edges and of points

Np = size(point, 1);

Ne = size(edge, 1);

% adapt size of inputs

x0 = repmat(edge(:,1)', Np, 1);

y0 = repmat(edge(:,2)', Np, 1);

dx = repmat(edge(:,3)', Np, 1)-x0;

dy = repmat(edge(:,4)', Np, 1)-y0;

xp = repmat(point(:,1), 1, Ne);

yp = repmat(point(:,2), 1, Ne);

% normalize x, y to xp, yp

x0 = x0/xp;

y0 = y0/yp;

dx = dx/xp;

dy = dy/yp;

xp = 1;

yp = 1;

% test if point is located on supporting line

b1 = abs((xp-x0).*dy - (yp-y0).*dx)./hypot(dx, dy)<tol;

% check if point is located between edge bounds

% use different tests depending on line angle

ind = abs(dx)>abs(dy);

t = zeros(max(Np, Ne), 1);

t(ind) = (xp(ind)-x0(ind))./dx(ind);

t(~ind) = (yp(~ind)-y0(~ind))./dy(~ind);

b = t>-tol & t-1<tol & b1;

David LeglandHi,

this is a good idea, much more convenient than dealing with eps. I will implement it soon.

thanks for advices !

Reto ZinggHi David,

your new limit check assumes that the direction vector of the line has a similar scale as the bounding box, which is not necessarely true. The direction vector often has a magnitude of 1, while the bounding box can be numerically very large.

Here is an idea and the thinking behind it:

You are checking the endpoints of the edge to be within the bounding box. Naturally, the end points are always on the bounding box, so you run into numerical precission issues. So why not check if the center of the edge is within the box? This way you are away from the limit lines with the exception of horizontal and vertical lines. In those two cases you should not have any numerical issues, as they are at right angles.

So, I would re-write the limit check as follows and drop eps completely:

% check if edge center is within bounds

edgeCenterX=sum(edge(i,[1,3]))/2;

xMinOk = xmin <= edgeCenterX;

xMaxOk = edgeCenterX <= xmax;

edgeCenterY=sum(edge(i,[2,4]))/2;

yMinOk = ymin <= edgeCenterY;

yMaxOk = edgeCenterY <= ymax;

It works for me.

David LeglandHi Reto,

thank you for your numerous and constructive remarks. I have published a new version that take into account your corrections. I will try to propagate modification to other drawing functions.

For limit check, I have used a different strategy, but it seems to work with large bouding boxes as well. Tell me if there are still problems.

Reto ZinggAlso consider re-writing adding the precision to the limit check as follows:

xOk = xmin*(1-eps)-min(edge(:,[1,3]), [], 2)<0 & max(edge(:,[1,3]), [], 2)-xmax*(1+eps)<0;

yOk = ymin*(1-eps)-min(edge(:,[2,4]), [], 2)<0 & max(edge(:,[2,4]), [], 2)-ymax*(1+eps)<0;

This will take into consideration the scale of the limiting box. With the original code you run into precission issues when the box has large numbers (I'm working with numbers in the 1e9 range). Like this the precision is relative rather than absolute.

Reto ZinggYet an other bug. This library is a good start, but definitely not ready fro prime time.

in clipLine() there is incorrect indexing. Fix is below. Consider using this fixed function in drawLine() (see bug in drawLine() above).

% check bounds of result edge in each direction

% incorrect indices, indexing a edge, not a box

% xOk = xmin-min(edge(:,1:2), [], 2)<eps & max(edge(:,1:2), [],2)-xmax<eps;

% yOk = ymin-min(edge(:,3:4), [], 2)<eps & max(edge(:,3:4), [],2)-ymax<eps;

% this is correct indexing

xOk = xmin-min(edge(:,[1,3]), [], 2)<eps & max(edge(:,[1,3]), [], 2)-xmax<eps;

yOk = ymin-min(edge(:,[2,4]), [], 2)<eps & max(edge(:,[2,4]), [], 2)-ymax<eps;

Reto Zinggoops, now my correction of the correction replaced the original correction. You can tell I'm a novice to this system...

So, here again the complete suggested correction to drawLine().

The original code will draw horizontal lines even though they are outside the axis. It will also draw lines in the quadrant to the right and below the axis.

% sort points along the x coordinate, and draw a line between

% the two in the middle

points = sortrows([px1 ; px2 ; py1 ; py2], 1);

if isfinite(points(3,1)) % if not horizontal or vertical

points=points(2:3,:);

else % else horizontal or vertical

points=points(1:2,:);

end

if points(1,1)>=xmin && points(2,1)<=xmax &&...

points(1,2)>=ymin && points(2,2)<=ymax

h(i)=line(points(1:2, 1), points(1:2, 2));

if ~isempty(varargin)

set(h(i), varargin{:});

end

else

h(i)=-1;

end

Reto ZinggSorry, correction to the correction:

if points(1,1)>=xmin && points(2,1)<=xmax &&...

points(1,2)>=ymin && points(2,2)<=ymax

Reto ZinggThere is a bug in intersectEdges(). Change lines 143 and 144 from

x0(out) = NaN;

x0(out) = NaN;

to

x0(i(out)) = NaN;

y0(i(out)) = NaN;

otherwise indexing is incorrect and you get false results.

David Legland@Matthew:

I have submitted a new version, that fixes the bug in the 'centroid' function, as well as many others.

regards

MatthewMinor (but fatal) bug found in centroid.m for calculating mass-weighted centroid of 2d object.

Change line 69 of the file from:

center = mean(pts.*repmat(mass, 1, 3));

to

center = mean(pts.*repmat(mass, 1, 2));

Or it will error with a subscript assignment dimension mismatch...pts is a 2-column matrix, not a 3-column matrix.

Juan Pablo CarbajalDavid LeglandHi Aleksandar,

at the moment there is no additional argument for drawRect function.

To specify the figure to draw in, the best is to use figure(...) before calling drawRect, eventually using hold on to avoid clearing previous image.

To change rectangle color or width, you can use the handle returned by the function:

hr = drawRect([x0 y0 w h]);

set(hr, 'color', 'r', 'linewidth', 4);

AleksandarI need help with function drawRect.

Can this function have more arguments? (Like: image on which to put rectangle,rectangle color ...)

I have this part of code

picture = double(imread('test2.jpg'));

im = drawRect(...

picture,...

round((vj(pos, 2) - 1) * sF + 1),...

round((vj(pos, 2) + velicinaLica(1) - 1) * sF + 1),...

round((vj(pos, 3) - 1) * sF + 1),...

round((vj(pos, 3) + velicinaLica(2) - 1) * sF + 1),...

[1 0 0]...

);

David Leglandoops, sorry for badly corrected bug...

A new version has been submitted, with suggested corrections. There are also some new functions for polygons and polylines (see for example "help polygons2d" or "help polylines2d")

Bala KrishnamoorthyI tested some of the other functions. Quite useful indeed! Thanks.

Bala KrishnamoorthyThe file intersectLinePolygon.m still contains 'pi' in place of 'intersects'. The HISTORY says it has been replaced, but it has NOT been replaced yet. I downloaded the zip file on July 22, 2009.

Also, here is a clearer (and of course equivalent way) to do the update:

intersects = [];

for i=1:length(edges)

p0 = intersectLines(line, createLine(edges(i,1:2), edges(i,3:4)));

if isPointOnEdge(p0, edges(i,:))

intersects = [intersects; p0];

end

end

Nathan ThernThis library and its companion, geom3d, are shining jewels - indispensable for doing non-trivial calculations on objects in 2d and 3d space.

By the way, leave all the files in the geom2d directory and add the directory to your path. Then you can type "help geom2d" or "doc geom2d" and get properly linked help text in the command window or the help window. The Contents.m file is the proper "MATLAB way" of providing documentation.

David LeglandHi,

I've submitted a new version, which fixes the bug in intersectEdges, and adds new functions for manipulating polylines (intersections, distance to point...). Please do not hesitate to report bugs (direct email preferred).

The 'pi' variable (cf. alexia's comment) was not supposed to cause problem, as it is located inside of a function. The goal of the library is mainly to hide computational details into functions with explicit names, without having to read the inner code. However, the variable 'pi' was renamed in a more appropriate (and hopefully explicit) name.

regards, David

GregI've tried the function intersectEdges but found that some cases are mishanlded etc.

alexia lavadensHi, what a bad name for a variable/function "pi", I mean:

"pi=intersectLinePolygon(line, points)"

I had a headache trying to discover what was wrong with this file (because in theory it should work), it was part of a very large project I was working in.

Finally I discovered the "pi" issue, "pi" is present in the code, but I also had to work with pi=3.1415..., and this cr*p of matlab got confused. Oh Mathematica !, I have such good memories...

Certainly is not so clever call a variable/function "pi" in a geometry script. Besides, as peter said is very badly commented (found errors), so don't trust to much with this one.

alexia lavadensNilimb Misalvery helpful in implementing more complicated geometry algorithms

Matthew DavidsondrawLabels doesn't actually draw any labels...

Peter GurkTried circleaspolygon and rectaspolygon but both were not self contained, badly explained. The package seems to be promising but far from plug and play.

Stephen McNeillVery handy functions for geometric analysis