Update readme.md with figures

README.md

@@ -1,22 +1,93 @@
 # MatGeom
-Matlab library geometric computing in 2D/3D.
+Matlab geometry processing library in 2D/3D.
 
-**MatGeom** is a library for geometric computing with Matlab in 2D and 3D. 
-It contains several hundreds of functions for the creation and manipulation 
-of 2D and 3D shapes such as point sets, lines, polygons, ellipses, 3D meshes, and other shapes.
+**MatGeom** is a library for geometry processing / geometric computing with Matlab in 2D and 3D. 
+MatGeom is a “function-based” library: it contains several hundreds of functions for the creation,
+the manipulation and the display of 2D and 3D shapes such as point sets, lines, ellipses, polygons, 
+3D polygonal meshes...
+
+The official homepage for the project is http://github.com/mattools/matGeom. 
+A [user manual](https://github.com/mattools/matGeom/releases/download/v1.2.5/matGeom-manual-1.2.5.pdf) is available.
+
+Starting from February 2022, the html pages of the functions (obtained with m2html) are available [here](https://mattools.github.io/matGeom/api/index.html).
 
 The MatGeom lirbary corresponds to the concatenation of the "[geom2d](https://fr.mathworks.com/matlabcentral/fileexchange/7844-geom2d)" 
 and "[geom3d](https://fr.mathworks.com/matlabcentral/fileexchange/24484-geom3d)" libraries
 that were distributed on the FileExchange. Distribution as a single library greatly facilitates 
 the interoperability of the functions.
 
-The official homepage for the project is http://github.com/mattools/matGeom. 
-A [user manual](https://github.com/mattools/matGeom/releases/download/v1.2.5/matGeom-manual-1.2.5.pdf) is available.
 
-Starting from February 2022, the html pages of the functions (obtained with m2html) are available [here](https://mattools.github.io/matGeom/api/index.html).
+## Quick overview
+
+
+Basic functionalities comprise creation of simple geometries such as points, lines, ellipses... 
+An example is provided in the following script.
+
+    % load data
+    data = load('fisheriris');
+    pts = data.meas(:, [3 1]);
+    % display
+    figure; axis equal; hold on; axis([0 8 3 9]);
+    drawPoint(pts, 'bx');
+    % Fit line
+    line = fitLine(pts);
+    drawLine(line, 'color', 'k', 'linewidth', 2);
+    % Draw oriented box
+    obox = orientedBox(pts);
+    drawOrientedBox(obox, 'color', 'k', 'linewidth', 1);
+    % identifiy species index
+    [labels, ~, inds]= unique(str.species);
+    % for ech species, compute equivalent ellipse and display with axes
+    colors = [1 0 0; 0 0.8 0; 0 0 1];
+    for i = 1:3
+        pts_i = pts(inds == i, :);
+        drawPoint(pts_i, 'marker', 'x', 'color', colors(i,:), 'linewidth', 2);
+        elli = equivalentEllipse(pts_i);
+        drawEllipse(elli, 'color', colors(i,:), 'linewidth', 2)
+        drawEllipseAxes(elli, 'color', colors(i,:), 'linewidth', 2)
+    end
+
+![Computation of equivalent ellipses, oriented box, and fitting line from set of points](https://github.com/mattools/matGeom/blob/master/doc/images/demo_geom2d_iris.png)
+
+It is possible to work with more complex shapes such as polygonal lines ("polylines") or polygons.
+Common operations comprise smoothing, simplification (retaining only a selection of vertices), 
+computation of convex hull or of intersections with other geometric primitives. 
+A summary of typical operations in presented in the following script.
+
+    % read polygon data as a numeric N-by-2 array
+    poly = load('leaf_poly.txt');
+
+    % display the polygon using basic color option
+    figure; axis equal; hold on; axis([0 600 0 400]);
+    drawPolygon(poly, 'k');
+
+    % Bounding box of the polygon
+    poly_bnd = boundingBox(poly);
+    drawBox(poly_bnd, 'k');
+
+    % computes convex hull of polygon vertices
+    poly_hull = convexHull(poly);
+    drawPolygon(poly_hull, 'LineWidth', 2, 'Color', 'k');
+
+    % applies smoothing to the original polygon.
+    poly_smooth = smoothPolygon(poly, 51);
+    drawPolygon(poly_smooth, 'color', 'b', 'linewidth', 2);
+
+    % Computes a simplified version of the polygon
+    poly_simpl = simplifyPolygon(poly, 20);
+    drawPolygon(poly_simpl, 'color', 'r', 'linewidth', 2);
+    drawVertices(poly_simpl, 'Color', 'k', 'Marker', 's', 'MarkerFaceColor', 'w');
+
+    % compute intersections with an arbitrary line
+    line = createLine([0 250], [600 350]);
+    drawLine(line, 'k');
+    inters = intersectLinePolygon(line, poly_simpl);
+    drawPoint(inters, 'Color', 'r', 'Marker', 'o', 'MarkerFaceColor', 'w', 'linewidth', 2);
+
+![Summary of polygon processing operations: smoothing, simplification, convex hull, intersection with lines.](https://github.com/mattools/matGeom/blob/master/doc/images/leafPoly_variousOps.png)
+
 
-Package organization
----
+## Package organization
 
 The library is organized into several modules: