From 687b4b0f338ce3549cf0fe3aa91fb7b286e50ef9 Mon Sep 17 00:00:00 2001
From: Vincent Nivoliers <vincent.nivoliers@univ-lyon1.fr>
Date: Mon, 18 Nov 2019 12:14:24 +0100
Subject: [PATCH] debut de presentation
---
Code/hull.cpp | 95 +-
Presentation/Figures/hull.pdf | Bin 0 -> 7992 bytes
Presentation/Figures/hull.svg | 1695 +++++++++++++++++++++
Presentation/Figures/hull_aligned.pdf | Bin 0 -> 1538 bytes
Presentation/Figures/hull_aligned.svg | 17 +
Presentation/Figures/hull_sort.pdf | Bin 0 -> 8516 bytes
Presentation/Figures/increment_hull_1.pdf | Bin 0 -> 9126 bytes
Presentation/Figures/increment_hull_2.pdf | Bin 0 -> 9055 bytes
Presentation/Figures/increment_hull_3.pdf | Bin 0 -> 9009 bytes
Presentation/Figures/partial_hull.pdf | Bin 0 -> 8884 bytes
Presentation/beamer_preamble.tex | 183 +++
Presentation/beamerthemeNivoliev.sty | 65 +
Presentation/presentation.tex | 83 +
Presentation/ucblalgo.sty | 92 ++
14 files changed, 2191 insertions(+), 39 deletions(-)
create mode 100644 Presentation/Figures/hull.pdf
create mode 100644 Presentation/Figures/hull.svg
create mode 100644 Presentation/Figures/hull_aligned.pdf
create mode 100644 Presentation/Figures/hull_aligned.svg
create mode 100644 Presentation/Figures/hull_sort.pdf
create mode 100644 Presentation/Figures/increment_hull_1.pdf
create mode 100644 Presentation/Figures/increment_hull_2.pdf
create mode 100644 Presentation/Figures/increment_hull_3.pdf
create mode 100644 Presentation/Figures/partial_hull.pdf
create mode 100644 Presentation/beamer_preamble.tex
create mode 100644 Presentation/beamerthemeNivoliev.sty
create mode 100644 Presentation/presentation.tex
create mode 100644 Presentation/ucblalgo.sty
diff --git a/Code/hull.cpp b/Code/hull.cpp
index 9a467ff..25249b6 100644
--- a/Code/hull.cpp
+++ b/Code/hull.cpp
@@ -10,6 +10,8 @@
#include <sstream>
#include <cmath>
+//{{{ struct vec
+
struct vec {
vec(float x, float y) : x(x), y(y) {}
float x ;
@@ -36,33 +38,23 @@ struct vec {
}
} ;
-using rational = boost::multiprecision::cpp_rational ;
+//}}}
-template<typename number = rational>
int orient(const vec& v0, const vec& v1) {
- number v0x = v0.x ;
- number v0y = v0.y ;
- number v1x = v1.x ;
- number v1y = v1.y ;
+ //determinant
+ float d = v0.x*v1.y - v0.y*v1.x ;
- number d = v0x*v1y - v0y*v1x ;
+ //encode as sign
if(d > 0) return 1 ;
if(d < 0) return -1 ;
- std::cout << "zero case" << std::endl ;
- //return 0 ;
- if(v1y > 0) return 1 ;
- if(v1y < 0) return -1 ;
- if(v1x > 0) return -1 ;
- if(v1x < 0) return 1 ;
- if(v0y > 0) return -1 ;
- if(v0y < 0) return 1 ;
- if(v0x > 0) return 1 ;
- if(v0y < 0) return -1 ;
- return 1 ;
+ return 0 ;
}
struct vec_compare {
+ //functor given leftmost point for sort
vec_compare(const vec& origin) : origin(origin) {}
+
+ //comparison
bool operator()(const vec& p0, const vec& p1) {
int o = orient(p0-origin, p1-origin) ;
return o < 0 ;
@@ -70,6 +62,8 @@ struct vec_compare {
const vec& origin ;
} ;
+//{{{leftmost
+
size_t leftmost(const std::vector<vec>& points) {
size_t min = 0 ;
for(size_t i = 1; i < points.size(); ++i) {
@@ -80,18 +74,26 @@ size_t leftmost(const std::vector<vec>& points) {
return min ;
}
+//}}}
+
void compute_hull(std::vector<vec>& points, std::vector<vec>& hull) {
+ //leftmost point ahead
size_t l = leftmost(points) ;
std::swap(*points.begin(), *(points.begin() + l)) ;
+ //sort the rest by angle
std::sort(points.begin() + 1, points.end(), vec_compare(points[0])) ;
+ //add the first two points to the hull
hull.push_back(points[0]) ;
hull.push_back(points[1]) ;
+ //sweep the remaining points
for(size_t i = 2; i < points.size(); ++i) {
+ //check whether the last segment creates a wrong turn
const vec& p = points[i] ;
vec v1 = p - *(hull.end() - 1) ;
vec v2 = *(hull.end() - 1) - *(hull.end() - 2) ;
while(hull.size() > 1 && orient(v1, v2) < 0) {
+ //in case of wrong turn, rease the last point of the hull and iterate
hull.erase(hull.end() - 1) ;
v1 = p - *(hull.end() - 1) ;
v2 = p - *(hull.end() - 2) ;
@@ -100,6 +102,8 @@ void compute_hull(std::vector<vec>& points, std::vector<vec>& hull) {
}
}
+//{{{ generate svg
+
void svg_hull(const std::string& filename, const std::vector<vec>& points, const std::vector<vec>& hull) {
std::ofstream file(filename) ;
SvgPad svg(file, 1024, 1024) ;
@@ -118,12 +122,33 @@ void svg_hull(const std::string& filename, const std::vector<vec>& points, const
svg.close() ;
}
+void svg_sort(const std::string& filename, const std::vector<vec>& points) {
+ std::ofstream file(filename) ;
+ SvgPad svg(file, 1024, 1024) ;
+ svg.open() ;
+
+ float col0[3] = { 1., 0.9, 0.3 } ;
+ float col1[3] = { 0.35, 0.2, 0.4 } ;
+ for(size_t i = 1; i < points.size(); ++i) {
+ float b = ((float) i-1) / (points.size() - 1) ;
+ float a = 1-b ;
+ svg.stroke(a*col0[0] + b*col1[0], a*col0[1] + b*col1[1], a*col0[2] + b*col1[2]) ;
+ svg.line(points[0].x, points[0].y, points[i].x, points[i].y) ;
+ }
+
+ svg.close() ;
+}
+
+//}}}
+
int main() {
unsigned int size = 100 ;
+ //{{{ random test
{
+ //random numbers
std::random_device rd ;
std::mt19937 alea(rd()) ;
std::uniform_real_distribution<float> uniform_float(0, 1) ;
@@ -131,50 +156,42 @@ int main() {
std::vector<vec> points ;
for(unsigned int i = 0; i < size; ++i) {
+ //generate a uniform point in a ball
vec p(normal_float(alea), normal_float(alea)) ;
float n = sqrt(uniform_float(alea)) / 2 ;
p = p * (n / p.length()) + vec(0.5,0.5);
points.push_back(p) ;
}
+ //hull
std::vector<vec> hull ;
compute_hull(points, hull) ;
- svg_hull("/tmp/test_hull.svg", points, hull) ;
+ svg_hull("/tmp/hull_test.svg", points, hull) ;
+ svg_sort("/tmp/hull_lines.svg", points) ;
}
- {
- unsigned int subdivisions = 30 ;
- float near = 127 ;
- float mid = 0.5 ;
- for(unsigned int ratio = 1; ratio < subdivisions; ++ratio) {
- std::vector<vec> points ;
- points.emplace_back(1, 0) ;
- points.emplace_back(0, 0) ;
- points.emplace_back(mid, 1) ;
- points.emplace_back(mid/near, 1./near) ;
- points.emplace_back(mid/near + (mid - 1./near) * ((float) ratio) / subdivisions, 1./near + (1 - 2./near) * ((float) ratio) / subdivisions) ;
-
- std::vector<vec> hull ;
- compute_hull(points, hull) ;
- std::stringstream fname ;
- fname << "/tmp/pbm_hull" << ratio << ".svg" ;
- svg_hull(fname.str(), points, hull) ;
- }
- }
+ //}}}
+
+ //{{{ wicked test
{
std::vector<vec> points ;
+ //aligned points
points.emplace_back(0, 0.5) ;
points.emplace_back(0, 1) ;
points.emplace_back(0, 0) ;
points.emplace_back(0, 0.8) ;
+ //make the hull non flat
points.emplace_back(1, 0.5) ;
+ //hull
std::vector<vec> hull ;
compute_hull(points, hull) ;
- svg_hull("/tmp/ordered.svg", points, hull) ;
+ svg_hull("/tmp/hull_aligned.svg", points, hull) ;
}
+ //}}}
+
return 0 ;
}
diff --git a/Presentation/Figures/hull.pdf b/Presentation/Figures/hull.pdf
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diff --git a/Presentation/beamer_preamble.tex b/Presentation/beamer_preamble.tex
new file mode 100644
index 0000000..b87fe3d
--- /dev/null
+++ b/Presentation/beamer_preamble.tex
@@ -0,0 +1,183 @@
+\documentclass[french,pdftex]{beamer}
+\usepackage[french]{babel}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage[rm={oldstyle=false}, sf={oldstyle=false}, tt={oldstyle=false}]{cfr-lm}
+\usetheme[compress]{Nivoliev}
+\usepackage{tabularx}
+\usepackage{hyperref}
+\usepackage{graphicx}
+\usepackage{tikz}
+\usepackage{amsmath, amssymb, amsfonts}
+\usepackage{mathrsfs}
+\usepackage{amsthm}
+\usepackage{verbatim}
+\usepackage{color}
+\usepackage{colortbl}
+\usepackage{multimedia}
+\usepackage{listings}
+\usepackage{multimedia}
+\usepackage{xparse}
+\usepackage{comment}
+\usepackage{animate}
+
+\setbeamersize{text margin left=0.5cm}
+\setbeamersize{text margin right=0.5cm}
+\definecolor{thcolor}{rgb}{0.8,0.3,0}
+\setbeamercolor{structure}{fg=thcolor}
+\setbeamertemplate{navigation symbols}{}
+\setbeamertemplate{enumerate items}[default]
+\setbeamercovered{transparent}
+
+\lstset{breakatwhitespace,
+basicstyle=\tiny\ttfamily,
+columns=fullflexible,
+keepspaces,
+breaklines,
+tabsize=3,
+showstringspaces=false,
+extendedchars=true}
+
+\setcounter{tocdepth}{1}
+
+\newcommand{\hl}[1]{\textcolor{structure}{#1}}
+\newcommand{\lighten}{\xglobal\blendcolors*{!20!white}\color{black}}
+\newcommand{\unlighten}{\xglobal\blendcolors{}\color{black}}
+
+\newcommand{\li}{\linewidth}
+
+%{fold} minipages
+
+\newcommand{\minip}[2]{
+ \begin{minipage}[c]{#1\linewidth}
+ #2
+ \end{minipage}
+}
+
+\newcommand{\cminip}[2]{
+ \begin{minipage}[c]{#1\linewidth}
+ \begin{center}
+ #2
+ \end{center}
+ \end{minipage}
+}
+
+%{endfold}
+
+%{fold} blocks
+
+%\newsavebox{\blockbox}
+%\NewDocumentEnvironment{myblock}{O{} O{} m}%
+%{%
+% \sbox{\blockbox}\bgroup%
+%}
+%{%
+% \egroup
+% \begin{tikzpicture}%
+% \draw%
+% node[ drop shadow,%
+% rounded corners,%
+% draw, fill=white,%
+% inner sep = 3mm,%
+% #2%
+% ] (#1) {
+% \usebox{\blockbox}
+% } ;
+% \end{tikzpicture}%
+%}
+
+\NewDocumentEnvironment{myblock}{O{} O{} m}%
+{%
+ \begin{tikzpicture}%
+ \draw%
+ node[ drop shadow,%
+ rounded corners,%
+ draw, fill=white,%
+ inner sep = 3mm,%
+ #2%
+ ] (#1) \bgroup%
+ \begin{minipage}[c]{#3}%
+}
+{%
+ \end{minipage}%
+ \egroup
+ ;
+ \end{tikzpicture}%
+}
+
+\NewDocumentEnvironment{myoverlayblock}{O{} O{} m m}%
+{%
+ \begin{tikzpicture}[overlay]%
+ \draw #4%
+ node[ drop shadow,%
+ rounded corners,%
+ draw, fill=white,%
+ inner sep = 3mm,%
+ #2%
+ ]%
+ (#1)
+ \bgroup%
+ \begin{minipage}[c]{#3}%
+}
+{%
+ \end{minipage}%
+ \egroup ;%
+ \end{tikzpicture}%
+}
+
+%{endfold}
+
+%{fold} Tikz
+\everymath{\displaystyle}
+\tikzstyle{every picture}+=[remember picture]
+\usetikzlibrary{calc,fit,decorations.pathreplacing,decorations.pathmorphing,shadows}
+
+\tikzstyle{rounded boxed}=[thick, draw=black, fill=white, rounded corners]
+
+%blocks and arrows between them
+\newcommand{\pin}[2]{
+ \tikz[baseline]{
+ \node[anchor=base,inner sep=0pt, outer sep=0pt, minimum height=1em] (#1) {#2};
+ }
+}
+\newcommand{\back}[3]{
+ \tikz[baseline]{
+ \node[rectangle,rounded corners,anchor=base,fill=#2!10] (#1) {#3};
+ }
+}
+\newcommand{\backcol}[3]{
+ \tikz[baseline]{
+ \node[very thin,rectangle,rounded corners,anchor=base,fill=#2] (#1) {#3};
+ }
+}
+\newcommand{\arrow}[3]{
+ \tikz[overlay]{
+ \path[->] (#2) edge [#1] (#3);
+ }
+}
+
+\newcommand{\tikzmark}[1]{
+ \tikz[overlay,baseline=0pt]{
+ \node [anchor=base, inner sep = 0pt, outer sep = 0pt] (#1) {};
+ }
+}
+%{endfold}
+
+%{fold} listings
+
+\newcommand{\CodeSymbol}[1]{\textcolor{red}{#1}}
+
+\lstset{
+ showspaces=false,
+ showstringspaces=false,
+ basicstyle=\footnotesize,
+ numbersep=0pt,
+ keywordstyle=\color{structure!90!black},
+ belowskip=-0.8\baselineskip,
+ aboveskip=0pt,
+ escapechar=§
+}
+
+%{endfold}
+
+%\renewcommand\textbullet{\ensuremath{\bullet}}
diff --git a/Presentation/beamerthemeNivoliev.sty b/Presentation/beamerthemeNivoliev.sty
new file mode 100644
index 0000000..b52417f
--- /dev/null
+++ b/Presentation/beamerthemeNivoliev.sty
@@ -0,0 +1,65 @@
+% Copyright 2007 by Vincent Nivoliers
+%
+% This file may be distributed and/or modified
+%
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Public License.
+%
+% See the file doc/licenses/LICENSE for more details.
+
+\DeclareOptionBeamer{compress}{\beamer@compresstrue}
+\ProcessOptionsBeamer
+
+
+\mode<presentation>
+
+\setbeamercolor{section in head/foot}{use=structure,bg=structure.fg!25!bg}
+
+\useoutertheme[subsection=false]{miniframes}
+
+\useinnertheme[shadow=true]{rounded}
+
+\setbeamertemplate{frametitle}[default][center]
+
+\AtBeginDocument{%
+ {
+ \usebeamercolor{section in head/foot}
+ }
+
+ \pgfdeclareverticalshading{beamer@headfade}{\paperwidth}
+ {%
+ color(0cm)=(bg);
+ color(1cm)=(section in head/foot.bg)%
+ }
+
+ \pgfdeclareverticalshading{beamer@footfade}{\paperwidth}
+ {%
+ color(0cm)=(section in head/foot.bg);
+ color(2.5ex)=(bg)%
+ }
+
+ \setbeamercolor{section in head/foot}{bg=}
+}
+
+\addtoheadtemplate{\pgfuseshading{beamer@headfade}\vskip-1cm}{}
+
+\defbeamertemplate*{footline}{mytheme theme}
+{
+ \leavevmode%
+ \pgfuseshading{beamer@footfade}%
+ \vskip-3.5ex
+ \begin{beamercolorbox}[wd=\textwidth,ht=2.25ex,dp=1.25ex]{section in head/foot}%
+ \hspace{1em}
+ \insertshorttitle
+ \hfill
+ \insertauthor
+ \hfill
+ \insertframenumber{} $/$ \inserttotalframenumber
+ \hspace{1em}
+ \end{beamercolorbox}
+ \vskip0pt%
+}
+
+\beamertemplatedotitem
+
+\mode<all>
diff --git a/Presentation/presentation.tex b/Presentation/presentation.tex
new file mode 100644
index 0000000..d70438f
--- /dev/null
+++ b/Presentation/presentation.tex
@@ -0,0 +1,83 @@
+\input{beamer_preamble}
+
+\usepackage{ucblalgo}
+\setbeamercovered{invisible}
+
+\newcommand{\vor}[1]{\ensuremath{\mathrm{Vor}(#1)}}
+\newcommand{\site}{\mathbf{v}}
+\newcommand{\sites}{\mathbf{V}}
+\newcommand{\point}{\mathbf{p}}
+\newcommand{\R}{\mathbb{R}}
+
+\title{Robustesse des algorithmes géométriques : \\ prédicats, filtrage et perturbation}
+
+\author{Vincent Nivoliers}
+
+\begin{document}
+
+\frame{
+ \maketitle
+}
+
+
+\section{Enveloppe Convexe}
+
+\frame {
+ \frametitle{Enveloppe convexe}
+ \centering
+ \includegraphics[width=0.6\li]{Figures/hull.pdf}
+}
+
+\frame {
+ \frametitle{1 -- trier par angle}
+ \centering
+ \includegraphics[width=0.6\li]{Figures/hull_sort.pdf}
+}
+
+\frame {
+ \frametitle{2 -- balayage}
+ \centering
+ \only<1>{\includegraphics[width=0.6\li]{Figures/partial_hull.pdf}}%
+ \only<2>{\includegraphics[width=0.6\li]{Figures/increment_hull_1.pdf}}%
+ \only<3>{\includegraphics[width=0.6\li]{Figures/increment_hull_2.pdf}}%
+ \only<4>{\includegraphics[width=0.6\li]{Figures/increment_hull_3.pdf}}%
+ \only<5>{\includegraphics[width=0.6\li]{Figures/hull.pdf}}%
+}
+
+\frame {
+ \frametitle{Robustesse : alignements de points}
+ \centering
+ \includegraphics[width=0.6\li]{Figures/hull_aligned.pdf}
+}
+
+\frame {
+ \frametitle{Algorithme}
+ \centering
+ \begin{ucblalgo}
+ \SetKwData{pt}{p}
+ \SetKwData{hull}{enveloppe}
+ \Algorithme{
+ déterminer le point le plus à gauche \;
+ \only<1>{trier les points par angle \;}%
+ \only<2>{\hl{trier les points par angle} \;}
+ $\hull \leftarrow$ une nouvelle pile\;
+ ajouter les deux premiers points à \hull \;
+ \PourCh{autre point \pt dans l'ordre}{
+ $\pt_0 \leftarrow $ dernier point de l'\hull \;
+ $\pt_1 \leftarrow $ avant dernier point de l'\hull \;
+ \Tq{
+ \only<1>{$(\pt_0\pt)$ tourne à gauche par rapport à $(\pt_1\pt)$}%
+ \only<2>{\hl{$(\pt_0\pt)$ tourne à gauche par rapport à $(\pt_1\pt)$}}
+ }{
+ retirer le sommet de l'\hull \;
+ $\pt_0 \leftarrow $ dernier point de l'\hull \;
+ $\pt_1 \leftarrow $ avant dernier point de l'\hull \;
+ }
+ ajouter \pt à l'\hull \;
+ }
+ \Retour{l'\hull} \;
+ }
+ \end{ucblalgo}
+}
+
+\end{document}
diff --git a/Presentation/ucblalgo.sty b/Presentation/ucblalgo.sty
new file mode 100644
index 0000000..e7353f6
--- /dev/null
+++ b/Presentation/ucblalgo.sty
@@ -0,0 +1,92 @@
+\ProvidesPackage{ucblalgo}
+\RequirePackage[vlined, french, nofillcomment]{algorithm2e}
+\RequirePackage{xstring}
+\RequirePackage{ifthen}
+
+%\SetFuncSty{textsf}%
+%\SetProcArgSty{textsf}%
+%\SetFuncArgSty{textsf}%
+%\SetArgSty{textrm}%
+\SetCommentSty{}%
+
+\SetKw{vrai}{vrai}
+\SetKw{faux}{faux}
+\SetKw{tableau}{tableau}
+
+\SetKwInput{donres}{données-résultat}
+\SetKwInput{donnee}{données}
+\SetKwInput{resultat}{résultat}
+\SetKwInput{variables}{variables}
+
+\SetKwFor{FonctionInner}{Fonction}{}{fin}
+\SetKwFor{ProcedureInner}{Procédure}{}{fin}
+
+\newcommand{\algoname}[1]{%
+ \StrBefore{#1}{(}%
+}
+
+\newcommand{\algoargs}[1]{%
+ (\StrBehind{#1}{(}%
+}
+
+\newcommand{\Fonction}[2]{
+ %\def\ucblalgoname{\algoname{#1}}%
+ %\def\ucblalgoargs{\algoargs{#1}}%
+ \SetKwFunction{#1}{#1}%
+ \FonctionInner{\expandafter\csname#1\endcsname{} \ifthenelse{\equal{#2}{}}{}{$\rightarrow$ #2}}
+}
+\newcommand{\ArgFonction}[3]{
+ \SetKwFunction{#1}{#1}%
+ \FonctionInner{\expandafter\csname#1\endcsname{#2} \ifthenelse{\equal{#3}{}}{}{$\rightarrow$ #3}}
+}
+\newcommand{\Procedure}[1]{
+ \SetKwFunction{#1}{#1}%
+ \ProcedureInner{\expandafter\csname#1\endcsname}
+}
+
+\newlength{\forewordlen}
+\newlength{\forewordantilen}
+
+\newenvironment{foreword}[1]{%
+ \settowidth{\forewordlen}{#1 : }%
+ \setlength{\forewordantilen}{\linewidth}%
+ \addtolength{\forewordantilen}{-\forewordlen}%
+ \begin{minipage}[t]{\forewordlen}%
+ #1 : %
+ \end{minipage}%
+ \begin{minipage}[t]{\forewordantilen}%
+}{%
+ \end{minipage}%
+}
+
+\newcommand{\precond}[1]{%
+ \begin{foreword}{précondition}%
+ \itshape{%
+ #1%
+ }%
+ \end{foreword}%
+}
+
+\newcommand{\postcond}[1]{%
+ \begin{foreword}{postcondition}%
+ \itshape{%
+ #1%
+ }%
+ \end{foreword}%
+}
+
+\newcommand{\incr}[1]{#1${+}{+}$}
+\newcommand{\decr}[1]{#1${-}{-}$}
+
+\newenvironment{ucblalgo}[1][H]{%
+ \renewcommand{\algorithmcfname}{Algorithme}%
+ \IncMargin{0em}%
+ \DontPrintSemicolon%
+ \begin{algorithm}[#1]%
+ \SetKwBlock{Algorithme}{Algorithme}{Fin}%
+}{%
+ \end{algorithm}%
+ \DecMargin{0em}%
+}
+
+\endinput
--
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