[graphics] Solving minor graphical issues & improving documentation

.gitignore

@@ -69,6 +69,10 @@ wheelhouse/
 
 # Graphics files
 examples/**/*.xml
+examples/**/*.bmp
+examples/**/*.png
+examples/**/*.jpg
+examples/**/*.svg
 *.ipe
 
 # Matlab files

doc/manual/manual/extensions/capd/capd.rst

@@ -11,6 +11,7 @@ To use CAPD with Codac, you first need to install the CAPD library. You can find
 
 Note that as CAPD is a C++ only library, the content present in this page is **only available in C++**.
 
+.. _subsec-extensions-capd-capd-install:
 
 Installing the ``codac-capd`` extension
 ---------------------------------------

doc/manual/manual/extensions/capd/peibos_capd.rst

@@ -31,7 +31,7 @@ The PEIBOS function takes at least six arguments :
 - The final time for the integration of the ODE.
 - A timestep to get intermediate states.
 - The inverse chart for the gnomonic atlas (an analytic function).
-- The list of symmetries for the gnomonic atlas. Note that each symmetry is represented as a hyperoctahedral symmetry, see :ref:`sec-actions-octasym`.
+- The list of symmetries for the gnomonic atlas. Note that each symmetry is represented as a hyperoctahedral symmetry, see :ref:`sec-tools-octasym`.
 - A resolution :math:`\epsilon`. The initial box :math:`\left[-1,1\right]^m` will initiallly be splitted in boxes with a diameter smaller than :math:`\epsilon`.
 - Eventually an offset vector can be specified if the initial set is not centered around the origin.
 - Eventually a flag can be set to True to get the verbose.

doc/manual/manual/functions/peibos/peibos.rst

@@ -13,6 +13,7 @@ Let us consider an initial set :math:`\mathbb{X}_0 \subset \mathbb{R}^n` with it
 Considering a function :math:`\mathbf{f}:\mathbb{R}^n \to \mathbb{R}^p`, :math:`n \leq p`, the PEIBOS tool allows to compute the set :math:`\mathbf{Y}=\left\{ \mathbf{f}(\mathbf{x}) \mid \mathbf{x} \in \partial \mathbb{X}_0 \right\}`.
 
 .. _subsec-functions-peibos-gnomonic-atals:
+
 Gnomonic atlas
 --------------
 
@@ -60,7 +61,7 @@ The PEIBOS function takes at least four arguments :
 
 - The studied analytic function.
 - The inverse chart for the gnomonic atlas (an analytic function).
-- The list of symmetries for the gnomonic atlas. Note that each symmetry is represented as a hyperoctahedral symmetry, see :ref:`sec-actions-octasym`.
+- The list of symmetries for the gnomonic atlas. Note that each symmetry is represented as a hyperoctahedral symmetry, see :ref:`sec-tools-octasym`.
 - A resolution :math:`\epsilon`. The initial box :math:`\left[-1,1\right]^m` will initiallly be splitted in boxes with a diameter smaller than :math:`\epsilon`.
 - Eventually an offset vector can be specified if the initial set is not centered around the origin.
 - Eventually a flag can be set to True to get the verbose.

doc/manual/manual/visualization/2d_example.rst

@@ -0,0 +1,26 @@
+.. _sec-graphics-2d-example:
+
+2D graphical example
+====================
+
+Below is an example covering a wide variety of drawing functions, colors, styles etc.
+
+.. tabs::
+
+  .. group-tab:: Python
+
+    .. literalinclude:: 2d_example_src/src.py
+      :language: py
+      :dedent: 0
+
+  .. group-tab:: C++
+
+    .. literalinclude:: 2d_example_src/src.cpp
+      :language: c++
+      :dedent: 0
+
+  .. group-tab:: Matlab
+
+    .. literalinclude:: 2d_example_src/src.m
+      :language: matlab
+      :dedent: 0

doc/manual/manual/visualization/2d_example_src/src.cpp

@@ -0,0 +1,124 @@
+#include <codac>
+#include <filesystem>
+#include <iostream>
+
+using namespace std;
+using namespace codac2;
+
+int main(){
+
+  // Graphics can be directly called without a Figure2D instanciation, using "DefaultFigure"
+
+  DefaultFigure::set_window_properties({600,600},{300,300});
+  DefaultFigure::draw_box({{2.2,2.5},{2.2,2.5}},{Color::black(),Color::yellow(0.5)});
+  DefaultFigure::draw_AUV({1,1,3.14/2},1.,{{Color::black(),Color::yellow()}, "-.."});
+  DefaultFigure::draw_motor_boat({0,0,0}, 1., {Color::black(),Color::yellow()});
+  DefaultFigure::draw_tank({2,1,3.14/2},1.,{{Color::black(),Color::yellow()},"vehicles","-."});
+  DefaultFigure::draw_pie({2,2},{1.5,2.5},{(3*3.14/4)-0.5,(3*3.14/4)+0.5},{Color::blue(),Color::cyan()});
+  DefaultFigure::draw_polyline({{2,-0.5},{4,0.5},{3,1.5},{4,2.5},{3,3}}, Color::red());
+  DefaultFigure::draw_polygon({{2,4.5},{4,4.5},{4.2,3.5},{3.5,3}}, {Color::none(),Color::green(0.5)});
+  DefaultFigure::draw_polyline({{-0.8,0},{0,1.5}}, 0.2, {Color::red(),Color::black(0.3)});
+
+  // Last argument corresponds to "StyleProperties" with one or two colors: edge color + (optional) fill color
+  // Predefined Color objects can be configured with a float parameter for opacity (1=opaque, 0=transparent)
+
+  // Custom figures can also be created:
+  std::shared_ptr<codac2::Figure2D> fig1 = std::make_shared<Figure2D>("My Figure 1",GraphicOutput::VIBES|GraphicOutput::IPE);
+
+  // Here, graphics will be rendered by two tools: both VIBES and IPE
+  // For VIBES, it requires the VIBes viewer to be launched prior to the execution
+  // For IPE, it generates a file named "My figure 1.xml" that can be edited with IPE, and converted to PDF
+
+  fig1->set_window_properties({50,50},{500,500}); // position, window size
+  fig1->set_axes(IntervalVector::constant(2,{-10,10})); // bounding box
+  fig1->draw_box({{-1,1},{-1,1}},{Color::green(),Color::red(0.2)}); // drawing a green box with red opacity values inside
+  fig1->draw_circle({1,1},0.5,Color({255,155,5})); // drawing a circle at (1,1) of radius 0.5 with a custom RGB color
+  fig1->draw_ring({1,1},{4,6},Color::red()); // drawing a ring at (1,1) of radius {4,6} with a predefined red color
+
+  std::shared_ptr<codac2::Figure2D> fig2 = std::make_shared<Figure2D>("My Figure 2",GraphicOutput::VIBES|GraphicOutput::IPE);  
+  fig2->set_axes(axis(0,{-1,5}), axis(1,{-1,5})); // (axis_id,{range_of_values_on_this_axis})
+  fig2->set_window_properties({250,250},{500,500});
+
+  // The previously declared figure "fig2" can now be used as a DefaultFigure
+  DefaultFigure::set(fig2);
+  DefaultFigure::draw_box({{2.2,2.5},{2.2,2.5}},{Color::black(),Color::green(0.8)});
+
+  DefaultFigure::set(fig1);
+  DefaultFigure::draw_box({{2.2,2.5},{2.2,2.5}},{Color::blue(),Color::cyan(0.8)});
+
+  fig2->draw_circle({2.,2.},0.5,{{Color::red(),Color::red(0.2)}, "z:1."}); // will alway be on top despite being "drawn" first
+
+  fig2->draw_AUV({1,1,3.14/2},2.,{{Color::black(),Color::yellow()}, "w:0.1", "vehicles"});
+  fig2->draw_tank({2,1,3.14/2},1.5,{{Color::black(),Color::yellow()},"vehicles","w:0.1"});
+  fig2->draw_motor_boat({0,0,0}, 1., {{Color::black(),Color::yellow()},"vehicles"});
+  fig2->draw_pie({2,2},{1.5,2.5},{(3*3.14/4)-0.5,(3*3.14/4)+0.5},{Color::blue(),Color::cyan()});
+  fig2->draw_polyline({{2,-0.5},{4,0.5},{3,1.5},{4,2.5},{3,3}}, {Color::red(),".."});
+  fig2->draw_polygon({{2,4.5},{4,4.5},{4.2,3.5},{3.5,3}}, {Color::none(),Color::green(0.5)});
+  fig2->draw_polyline({{-0.8,0},{0,1.5}}, 0.2, {Color::red(),Color::black(0.3)});
+  fig2->draw_ellipse({1,1},{0.5,2}, 0.2, {Color::blue(),Color::blue(0.3)});
+  fig2->draw_line({1,1},{3,3}, Color::blue());
+  fig2->draw_arrow({3,1},{2.2,2}, 0.2, {Color::red(),Color::black(0.3)});
+  fig2->draw_parallelepiped({{1.5,2.8},Matrix({{0.5,0.4},{0,0.2}})}, {{Color::red(),Color::green(0.5)}, "parallelepiped", "w:0.1"});
+
+  fig2->draw_zonotope({{4,1.5},
+		{{-0.2,-0.06,0.2,0.06,0.01,0.08,0},
+     {0.1,0.04,0.04,-0.04,-0.03,0.18,0}}},
+	{{Color::red(),Color::yellow(0.4)},"zonotope", "w:0.05"});
+
+  Parallelepiped p_3d ({1.2,3.5,2.2},Matrix({{0.5,0.4,0},{0,0.2,0.1},{0,0,0.3}}));
+  fig2->draw_zonotope(p_3d.proj({0,1}), {{Color::green(),Color::yellow(0.4)}, "zonotope"});
+
+  fig2->draw_text("Hello, World!",{-0.5,4.5},0.2, Color::blue());
+
+  std::filesystem::path p = __FILE__;
+  fig2->draw_raster(p.parent_path().string()+"/logo_codac.png", IntervalVector({{2.5,5},{-1,-0.4}}), StyleProperties("raster"));
+
+  fig2->draw_circle({0.5,0.5},0.5,{{Color::orange(),Color::orange(0.2)}, "z:-1."}); // will alway be in the bottom despite being "drawn" last
+
+  // Colors
+  // predefined colors without and with opacity
+  fig2->draw_point({2,2}, {Color::red(),Color::yellow(0.5)});
+  // HTML color without and with opacity
+  fig2->draw_box({{2.4,2.9},{2.4,2.9}},{Color("#da3907"),Color("#da390755")});
+  // HSV color without and with opacity
+  fig2->draw_box({{2.6,3.1},{2.6,3.1}},{Color({108,90,78},Model::HSV),Color({108,90,78,20},Model::HSV)});
+
+  Figure2D fig3 ("ColorMap figure",GraphicOutput::VIBES|GraphicOutput::IPE);
+  fig3.set_window_properties({800,250},{500,500});
+
+  ColorMap cmap_haxby = ColorMap::haxby();
+  ColorMap cmap_default = ColorMap::basic();
+  ColorMap cmap_blue_tube = ColorMap::blue_tube();
+  ColorMap cmap_red_tube = ColorMap::red_tube();
+  ColorMap cmap_rainbow = ColorMap::rainbow();
+
+  ColorMap custom_map;
+  custom_map[0] = Color({255,0,0});
+  custom_map[0.5] = Color({0,255,0});
+  custom_map[1] = Color({0,0,255});
+
+  double subdivisions = 40.;
+  fig3.set_axes(axis(0,{-1,subdivisions+1}), axis(1,{-1.25,0.05}));
+  for (double i=0.; i<=subdivisions; i+=1.0)
+  {
+    double ratio = i/subdivisions;
+    fig3.draw_box({{i,i+1},{-1./5.,0}},{Color::black(),cmap_default.color(ratio)});
+    fig3.draw_box({{i,i+1},{-2./5.,-1./5.}},{Color::black(),cmap_haxby.color(ratio)});
+    fig3.draw_box({{i,i+1},{-3./5.,-2./5.}},{Color::black(),cmap_rainbow.color(ratio)});
+    fig3.draw_box({{i,i+1},{-4./5.,-3./5.}},{Color::black(),cmap_blue_tube.color(ratio)});
+    fig3.draw_box({{i,i+1},{-5/5.,-4./5.}},{Color::black(),cmap_red_tube.color(ratio)});
+    fig3.draw_box({{i,i+1},{-6./5.,-5./5.}},{Color::black(),custom_map.color(ratio)});
+  }
+
+  Figure2D fig4 ("My Figure 4",GraphicOutput::VIBES);
+
+  fig4.set_window_properties({500,50},{500,500});
+  fig4.set_axes(axis(0,{-10,10}), axis(1,{-10,10}));
+
+  double a=0.8;
+  ScalarVar t;
+  // Fermat's spiral
+  AnalyticFunction f1 ({t},{a*sqrt(t)*cos(t),a*sqrt(t)*sin(t)});
+  AnalyticTraj traj4 ({0,100},f1);
+  fig4.draw_trajectory(traj4,{ColorMap::rainbow(), ".."});
+}

doc/manual/manual/visualization/2d_example_src/src.m

@@ -0,0 +1,112 @@
+import py.codac4matlab.*
+
+% Graphics can be directly called without a Figure2D instanciation, using "DefaultFigure":
+
+DefaultFigure().set_window_properties(Vector({600,600}),Vector({300,300}));
+DefaultFigure().draw_box(IntervalVector({{2.2,2.5},{2.2,2.5}}),StyleProperties({Color().black(),Color().yellow(0.5)}));
+DefaultFigure().draw_AUV(Vector({1,1,3.14/2}),1.,StyleProperties({Color().black(),Color().yellow()},"-.."));
+DefaultFigure().draw_motor_boat(Vector({0,0,0}),1.,StyleProperties({Color().black(),Color().yellow()}));
+DefaultFigure().draw_tank(Vector({2,1,3.14/2}),1.,StyleProperties({Color().black(),Color().yellow()},"vehicles","-."));
+DefaultFigure().draw_pie(Vector({2,2}),Interval(1.5,2.5),Interval((3*3.14/4)-0.5,(3*3.14/4)+0.5),StyleProperties({Color().blue(),Color().cyan()}));
+DefaultFigure().draw_polyline({Vector({2,-0.5}),Vector({4,0.5}),Vector({3,1.5}),Vector({4,2.5}),Vector({3,3})},Color().red());
+DefaultFigure().draw_polygon(Polygon({Vector({2,4.5}),Vector({4,4.5}),Vector({4.2,3.5}),Vector({3.5,3})}),StyleProperties({Color().none(),Color().green(0.5)}));
+DefaultFigure().draw_polyline({Vector({-0.8,0}),Vector({0,1.5})},0.2,StyleProperties({Color().red(),Color().black(0.3)}));
+
+% Last argument corresponds to "StyleProperties" with one or two colors: edge color + (optional) fill color
+% Predefined Color objects can be configured with a float parameter for opacity (1=opaque, 0=transparent)
+
+% Custom figures can also be created:
+
+fig1 = Figure2D("My figure 1", GraphicOutput().VIBES.union(GraphicOutput().IPE));
+% Here, graphics will be rendered by two tools: both VIBES and IPE
+% For VIBES, it requires the VIBes viewer to be launched prior to the execution
+% For IPE, it generates a file named "My figure 1.xml" that can be edited with IPE, and converted to PDF
+
+fig1.set_window_properties(Vector({50,50}),Vector({500,500})); % position, window size
+fig1.set_axes(IntervalVector().constant(2,Interval(-10,10))); % bounding box
+fig1.draw_box(IntervalVector({{-1,1},{-1,1}}),StyleProperties({Color().green(),Color().red(0.2)})); % drawing a green box with red opacity values inside
+fig1.draw_circle(Vector({1,1}),0.5,Color({255,155,5})); % drawing a circle at (1,1) of radius 0.5 with a custom RGB color
+fig1.draw_ring(Vector({1,1}),Interval(4,6),Color().red()); % drawing a ring at (1,1) of radius [4,6] with a predefined red color
+
+fig2 = Figure2D("My figure 2", GraphicOutput().VIBES.union(GraphicOutput().IPE));
+fig2.set_axes(axis(1,Interval(-1,5)), axis(2,Interval(-1,5))); % (axis_id,[range_of_values_on_this_axis])
+fig2.set_window_properties(Vector({250,250}),Vector({500,500}));
+
+% The previously declared figure "fig2" can now be used as a DefaultFigure
+DefaultFigure().set(fig2);
+DefaultFigure().draw_box(IntervalVector({{2.2,2.5},{2.2,2.5}}),StyleProperties({Color().black(),Color().green(0.8)}));
+
+DefaultFigure().set(fig1);
+DefaultFigure().draw_box(IntervalVector({{2.2,2.5},{2.2,2.5}}),StyleProperties({Color().blue(),Color().cyan(0.8)}));
+
+fig2.draw_circle(Vector({2,2}),0.5,StyleProperties({Color().red(),Color().red(0.2)},"z:1.")); % will alway be on top despite being "drawn" first
+
+fig2.draw_AUV(Vector({1,1,3.14/2}),2.,StyleProperties({Color().black(),Color().yellow()},"w:0.1","vehicles"));
+fig2.draw_tank(Vector({2,1,3.14/2}),1.5,StyleProperties({Color().black(),Color().yellow()},"vehicles","w:0.1"));
+fig2.draw_motor_boat(Vector({0,0,0}),1.,StyleProperties({Color().black(),Color().yellow()},"vehicles"));
+fig2.draw_pie(Vector({2,2}),Interval(1.5,2.5),Interval((3*3.14/4)-0.5,(3*3.14/4)+0.5),StyleProperties({Color().blue(),Color().cyan()}));
+fig2.draw_polyline({Vector({2,-0.5}),Vector({4,0.5}),Vector({3,1.5}),Vector({4,2.5}),Vector({3,3})},StyleProperties(Color().red(),".."));
+fig2.draw_polygon(Polygon({Vector({2,4.5}),Vector({4,4.5}),Vector({4.2,3.5}),Vector({3.5,3})}),StyleProperties({Color().none(),Color().green(0.5)}));
+fig2.draw_polyline({Vector({-0.8,0}),Vector({0,1.5})},0.2,StyleProperties({Color().red(),Color().black(0.3)}));
+fig2.draw_ellipse(Vector({1,1}),Vector({0.5,2.}),0.2,StyleProperties({Color().blue(),Color().blue(0.3)}));
+fig2.draw_line(Vector({1,1}),Vector({3,3}),Color().blue());
+fig2.draw_arrow(Vector({3,1}),Vector({2.2,2}),0.2,StyleProperties({Color().red(),Color().black(0.3)}));
+fig2.draw_parallelepiped(Parallelepiped(Vector({1.5,2.8}),Matrix({{0.5,0.4},{0,0.2}})),StyleProperties({Color().red(),Color().green(0.5)},"parallelepiped","w:0.1"));
+
+fig2.draw_zonotope(Zonotope(Vector({4,1.5}),Matrix({{-0.2,-0.06,0.2,0.06,0.01,0.08,0}, ...
+                                                    {0.1,0.04,0.04,-0.04,-0.03,0.18,0}})),StyleProperties({Color().red(),Color().yellow(0.4)},"zonotope","w:0.05"));
+
+p_3d = Parallelepiped(Vector({1.2,3.5,2.2}),Matrix({{0.5,0.4,0},{0,0.2,0.1},{0,0,0.3}}));
+fig2.draw_zonotope(p_3d.proj({1,2}),StyleProperties({Color().green(),Color().yellow(0.4)},"zonotope"));
+
+fig2.draw_text("Hello, World!",Vector({-0.5,4.5}),0.2, Color().blue());
+
+fig2.draw_raster("logo_codac.png", IntervalVector({{2.5,5},{-1,-0.4}}),StyleProperties("raster"));
+
+fig2.draw_circle(Vector({0.5,0.5}),0.5,StyleProperties({Color().orange(),Color().orange(0.2)},"z:-1.")); % will alway be in the bottom despite being "drawn" last
+
+% Colors
+% predefined colors without and with opacity
+fig2.draw_point(Vector({2,2}), StyleProperties({Color().red(),Color().yellow(0.5)}));
+% HTML color without and with opacity
+fig2.draw_box(IntervalVector({{2.4,2.9},{2.4,2.9}}),StyleProperties({Color("#da3907"),Color("#da390755")}));
+% HSV color without and with opacity
+fig2.draw_box(IntervalVector({{2.6,3.1},{2.6,3.1}}),StyleProperties({Color({108,90,78},Model().HSV),Color({108,90,78,20},Model().HSV)}));
+
+fig3 = Figure2D("ColorMap figure", GraphicOutput().VIBES.union(GraphicOutput().IPE));
+fig3.set_window_properties(Vector({800,250}),Vector({500,500}));
+
+cmap_haxby = ColorMap().haxby();
+cmap_default = ColorMap().basic();
+cmap_blue_tube = ColorMap().blue_tube();
+cmap_red_tube = ColorMap().red_tube();
+cmap_rainbow = ColorMap().rainbow();
+
+custom_map = ColorMap(Model().RGB);
+custom_map.set_item(0,Color({255,0,0}));
+custom_map.set_item(0.5,Color({0,255,0}));
+custom_map.set_item(1,Color({0,0,255}));
+
+subdivisions = 40;
+fig3.set_axes(axis(1,Interval(-1,subdivisions+1)), axis(2,Interval(-1.25,0.05)));
+
+for i = 0:(subdivisions)
+    ratio = i / subdivisions;
+    fig3.draw_box(IntervalVector({{i,i+1},{-1./5.,0}}),StyleProperties({Color().black(),cmap_default.color(ratio)}));
+    fig3.draw_box(IntervalVector({{i,i+1},{-2./5.,-1./5.}}),StyleProperties({Color().black(),cmap_haxby.color(ratio)}));
+    fig3.draw_box(IntervalVector({{i,i+1},{-3./5.,-2./5.}}),StyleProperties({Color().black(),cmap_rainbow.color(ratio)}));
+    fig3.draw_box(IntervalVector({{i,i+1},{-4./5.,-3./5.}}),StyleProperties({Color().black(),cmap_blue_tube.color(ratio)}));
+    fig3.draw_box(IntervalVector({{i,i+1},{-5./5.,-4./5.}}),StyleProperties({Color().black(),cmap_red_tube.color(ratio)}));
+    fig3.draw_box(IntervalVector({{i,i+1},{-6./5.,-5./5.}}),StyleProperties({Color().black(),custom_map.color(ratio)}));
+end
+
+fig4 = Figure2D("My Figure 4", GraphicOutput().VIBES);
+fig4.set_window_properties(Vector({500,50}),Vector({500,500}));
+fig4.set_axes(axis(1,Interval(-10,10)), axis(2,Interval(-10,10)));
+
+a= 0.8;
+t = ScalarVar();
+% Fermat's spiral
+f1 = AnalyticFunction({t},vec(a*sqrt(t)*cos(t),a*sqrt(t)*sin(t)));
+traj4 = AnalyticTraj(Interval(0,100),f1);
+fig4.draw_trajectory(traj4, StyleGradientProperties(ColorMap().rainbow(), ".."));