commit 05c9fd91e0a6adcf45662530bc61c33a4c99f04b
parent 484547166d5cc6479b2677112e051998cb1036e8
Author: Georges Dupéron <jahvascriptmaniac+github@free.fr>
Date: Sun, 13 Nov 2011 19:00:39 +0100
Tous les diagrammes de perlin et craters, en haute qualité. Ça va faire mal.
Diffstat:
| M | présentation.tex | | | 308 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++---------- |
1 file changed, 271 insertions(+), 37 deletions(-)
diff --git a/présentation.tex b/présentation.tex
@@ -18,7 +18,7 @@
\usetheme{Frankfurt}
\usepackage{graphicx}
-% \title{FMIN313 Moteurs de jeux\\ Génération de terrains}
+\title{FMIN313 Moteurs de jeux\\ Génération de terrains}
\author{DUPÉRON Georges \and\texorpdfstring{\\}{} BONAVERO Yoann}
\institute{Université Montpellier II,\\Département informatique\\Master 2 IFPRU\\Encadrants~: F. Koriche et M. Moulis}
\date{Lundi 14 novembre 2011}
@@ -58,6 +58,11 @@
\xdef\noiseseed{\pgfmathresult}
\makeatletter
+\def\getcache#1{\csname cache,#1\endcsname}
+\def\setcache#1#2{\expandafter\xdef\csname cache,#1\endcsname{#2}}
+\def\clearcache#1{\expandafter\global\expandafter\let\csname cache,#1\endcsname\@undefined}
+\def\setintmacro#1#2{\pgfmathparse{int(#2)}\edef#1{\pgfmathresult}}
+%
\pgfmathdeclarefunction{lazyifthenelse}{3}{%
\ifx 1#1%
\pgfmathparse{#2}%
@@ -96,6 +101,18 @@
% Craters
sqdistance_(\dx,\dy)=\dx*\dx+\dy*\dy;
sqdistance(\x,\y,\cx,\cy)=sqdistance_(\x-\cx,\y-\cy);
+ % 2D Perlin
+ noise2D(\x,\y,\octave)=hash(\x,hash(\y,hash(\octave,\noiseseed)));
+ sampleLeftAbove2D(\x,\y,\periode,\octave)=noise2D(floor(\x/\periode), floor(\y/\periode) + 1, \octave);
+ sampleLeftBelow2D(\x,\y,\periode,\octave)=noise2D(floor(\x/\periode), floor(\y/\periode), \octave);
+ sampleRightAbove2D(\x,\y,\periode,\octave)=noise2D(floor(\x/\periode)+1, floor(\y/\periode) + 1, \octave);
+ sampleRightBelow2D(\x,\y,\periode,\octave)=noise2D(floor(\x/\periode)+1, floor(\y/\periode), \octave);
+ octave2DCosine(\x,\y,\octave,\periode,\amplitude)=\amplitude*cosineInterpolation(sampleDelta(\y,\periode),
+ cosineInterpolation(sampleDelta(\x,\periode), sampleLeftBelow2D(\x,\y,\periode,\octave), sampleRightBelow2D(\x,\y,\periode,\octave)),
+ cosineInterpolation(sampleDelta(\x,\periode), sampleLeftAbove2D(\x,\y,\periode,\octave), sampleRightAbove2D(\x,\y,\periode,\octave))
+ );
+ perlin2DCosine_(\x,\y,\octave,\periode,\octaves,\persistance,\amplitude)=lazyifthenelse(\octave >= \octaves, 0, "octave2DCosine(\x,\y,\octave,\periode,\amplitude) + perlin2DCosine_(\x,\y,\octave+1,\periode*0.5,\octaves,\persistance,\amplitude*\persistance)");
+ perlin2DCosine(\x,\y,\periode,\octaves,\persistance,\amplitude)=perlin2DCosine_(\x,\y,0,\periode,\octaves,\persistance,\amplitude);
}
}
\shorthandon{;?:}
@@ -206,21 +223,135 @@
\begin{frame}
\frametitle{Perlin noise (Variations)}
\begin{itemize}
- \item Cavernes, nuages, textures, terrains : bruit $n$D et voxels.
- \item Ridged Perlin Noise.
- \item Midpoint displacement.
- \item Simplex noise : généralisation des triangles équilatéraux à $n$ dimensions, interpolation par rapport aux coins. $d^2$ au lieu de $2^d$.
- \item Bruit répétable 1D : points sur un cercle dans un espace 2D. Généralisation à $n$ dimensions : hypercercle $n$D dans un espace $2n$D.
+ \item<1-> Cavernes, nuages\only<2->{, textures, terrains : bruit $n$D et voxels.}
+ \only<1>{
+ \begin{figure}[h]
+ \centering
+ \begin{tikzpicture}[scale=0.025]
+ \xdef\twodperlinsize{128}
+ \xdef\maxvtwodperlin{0}
+ \xdef\minvtwodperlin{0}
+ \def\maxradius{32}
+ \def\ncircles{10}
+ \foreach \y in {1,2,...,\twodperlinsize}{
+ \message{Perlin 2D line \y/\twodperlinsize.}
+ \foreach \x in {1,2,...,\twodperlinsize}{
+ \pgfmathsetmacro{\v}{-perlin2DCosine(\x,\y,16,3,0.5,50}
+ \setcache{vtwodperlin,\x,\y}{\v}
+ \pgfmathparse{max(\maxvtwodperlin,\v)}
+ \xdef\maxvtwodperlin{\pgfmathresult}
+ \pgfmathparse{min(\minvtwodperlin,\v)}
+ \xdef\minvtwodperlin{\pgfmathresult}
+ }
+ }
+ \definecolor{gradientpoint0}{rgb}{0,0,1}
+ \definecolor{gradientpoint1}{rgb}{0,0.3,1}
+ \definecolor{gradientpoint2}{rgb}{0.3,0.3,1}
+ \definecolor{gradientpoint3}{rgb}{1,1,1}
+ \def\positions{{0,0.1,0.9,1}}
+ \foreach \y in {1,2,...,\twodperlinsize}{
+ \message{Gradient line \y/\twodperlinsize...}
+ \foreach \x in {1,2,...,\twodperlinsize}{
+ \pgfmathsetmacro{\v}{(\getcache{vtwodperlin,\x,\y}-\minvtwodperlin)/max(1,\maxvtwodperlin-\minvtwodperlin)}
+ \pgfmathsetmacro{\v}{max(0,min(1,\v))}
+ \foreach \pointb in {1,...,3}{
+ \pgfmathsetmacro{\posb}{\positions[\pointb]}
+ \pgfmathparse{\v <= \posb}
+ \ifnum 1=\pgfmathresult
+ \setintmacro{\pointa}{\pointb-1}
+ \pgfmathsetmacro{\posa}{\positions[\pointa]}
+ \pgfmathsetmacro{\mix}{100 - 100 * (\v-\posa) / (\posb-\posa)}
+ \xdef\colora{gradientpoint\pointa}
+ \xdef\colorb{gradientpoint\pointb}
+ \xdef\mix{\mix}
+ \breakforeach
+ \fi
+ }
+ \path[fill=\colora!\mix!\colorb] (\x,\y) rectangle ++(1.5,1.5);
+ }
+ }
+ \end{tikzpicture}
+ \end{figure}
+ }
+ \only<2>{
+ \begin{figure}[h]
+ \centering
+ \begin{tikzpicture}[scale=0.025]
+ \definecolor{gradientpoint0}{rgb}{0,0,0.5}
+ \definecolor{gradientpoint1}{rgb}{0.2,0.2,1}
+ \definecolor{gradientpoint2}{rgb}{0.9,0.6,0.1}
+ \definecolor{gradientpoint3}{rgb}{0.1,0.6,0.2}
+ \definecolor{gradientpoint4}{rgb}{0.6,0.3,0.05}
+ \definecolor{gradientpoint5}{rgb}{1,1,1}
+ \def\positions{{0,0.3,0.4,0.88,0.94,1}}
+ \foreach \y in {1,2,...,\twodperlinsize}{
+ \message{Gradient line \y/\twodperlinsize...}
+ \foreach \x in {1,2,...,\twodperlinsize}{
+ \pgfmathsetmacro{\v}{(\getcache{vtwodperlin,\x,\y}-\minvtwodperlin)/max(1,\maxvtwodperlin-\minvtwodperlin)}
+ \pgfmathsetmacro{\v}{max(0,min(1,\v))}
+ \foreach \pointb in {1,...,5}{
+ \pgfmathsetmacro{\posb}{\positions[\pointb]}
+ \pgfmathparse{\v <= \posb}
+ \ifnum 1=\pgfmathresult
+ \setintmacro{\pointa}{\pointb-1}
+ \pgfmathsetmacro{\posa}{\positions[\pointa]}
+ \pgfmathsetmacro{\mix}{100 - 100 * (\v-\posa) / (\posb-\posa)}
+ \xdef\colora{gradientpoint\pointa}
+ \xdef\colorb{gradientpoint\pointb}
+ \xdef\mix{\mix}
+ \breakforeach
+ \fi
+ }
+ \path[fill=\colora!\mix!\colorb] (\x,\y) rectangle ++(1.5,1.5);
+ }
+ }
+ \end{tikzpicture}
+ \end{figure}
+ }
+ \item<3-> Ridged Perlin Noise.
+ \only<3>{
+ \begin{figure}[h]
+ \centering
+ \begin{tikzpicture}[scale=0.025]
+ \definecolor{gradientpoint0}{rgb}{0,0,0.5}
+ \definecolor{gradientpoint1}{rgb}{0.2,0.2,1}
+ \definecolor{gradientpoint2}{rgb}{0.9,0.6,0.1}
+ \definecolor{gradientpoint3}{rgb}{0.1,0.6,0.2}
+ \definecolor{gradientpoint4}{rgb}{0.6,0.3,0.05}
+ \definecolor{gradientpoint5}{rgb}{1,1,1}
+ \def\positions{{0,0.3,0.4,0.88,0.94,1}}
+ \foreach \y in {1,2,...,\twodperlinsize}{
+ \message{Gradient line \y/\twodperlinsize...}
+ \foreach \x in {1,2,...,\twodperlinsize}{
+ \pgfmathsetmacro{\v}{(\getcache{vtwodperlin,\x,\y}-\minvtwodperlin)/max(1,\maxvtwodperlin-\minvtwodperlin)}
+ \pgfmathsetmacro{\v}{max(0,min(1,\v))}
+ \pgfmathsetmacro{\v}{abs(\v-0.5)*2}
+ \foreach \pointb in {1,...,5}{
+ \pgfmathsetmacro{\posb}{\positions[\pointb]}
+ \pgfmathparse{\v <= \posb}
+ \ifnum 1=\pgfmathresult
+ \setintmacro{\pointa}{\pointb-1}
+ \pgfmathsetmacro{\posa}{\positions[\pointa]}
+ \pgfmathsetmacro{\mix}{100 - 100 * (\v-\posa) / (\posb-\posa)}
+ \xdef\colora{gradientpoint\pointa}
+ \xdef\colorb{gradientpoint\pointb}
+ \xdef\mix{\mix}
+ \breakforeach
+ \fi
+ }
+ \path[fill=\colora!\mix!\colorb] (\x,\y) rectangle ++(1.5,1.5);
+ }
+ }
+ \end{tikzpicture}
+ \end{figure}
+ }
+ \item<4-> Midpoint displacement.
+ \item<5-> Simplex noise : généralisation des triangles équilatéraux à $n$ dimensions, interpolation par rapport aux coins. $d^2$ au lieu de $2^d$.
+ \item<6-> Bruit répétable 1D : points sur un cercle dans un espace 2D. Généralisation à $n$ dimensions : hypercercle $n$D dans un espace $2n$D.
{\tiny\url{http://www.gamedev.net/blog/33/entry-2138456-seamless-noise/}}
\end{itemize}
\end{frame}
-\makeatletter
-\def\getcache#1{\csname cache,#1\endcsname}
-\def\setcache#1#2{\expandafter\xdef\csname cache,#1\endcsname{#2}}
-\def\clearcache#1{\expandafter\global\expandafter\let\csname cache,#1\endcsname\@undefined}
-\def\setintmacro#1#2{\pgfmathparse{int(#2)}\edef#1{\pgfmathresult}}
-\makeatother
\subsection{Craters et Hills Algorithm}
\begin{frame}
\frametitle{Craters et Hills Algorithm}
@@ -233,13 +364,14 @@
\begin{figure}[h]
\centering
\begin{tikzpicture}[scale=0.025]
- \def\craterssize{128}
- \xdef\maxv{0}
+ \xdef\craterssize{128}
+ \xdef\maxvcraters{0}
+ \xdef\minvcraters{0}
\def\maxradius{32}
- \def\ncircles{50}
+ \def\ncircles{100}
\foreach \y in {1,2,...,\craterssize}{
\foreach \x in {1,2,...,\craterssize}{
- \setcache{v,\x,\y}{0}
+ \setcache{vcraters,\x,\y}{0}
}
}
\foreach \c in {1,...,\ncircles}{
@@ -255,27 +387,30 @@
\setintmacro{\x}{\circlex+\dx}
\pgfmathparse{(\x > 0) && (\x <= \craterssize)}
\ifnum 1=\pgfmathresult
- \xdef\oldv{\getcache{v,\x,\y}}
- \pgfmathparse{\oldv+max(0,\circler*\circler - (\dx*\dx + \dy*\dy))}
- \setcache{v,\x,\y}{\pgfmathresult}
- \pgfmathparse{max(\maxv,\pgfmathresult)}
- \xdef\maxv{\pgfmathresult}
+ \xdef\oldv{\getcache{vcraters,\x,\y}}
+ \pgfmathsetmacro{\v}{\oldv - max(0,\circler - ((\dx*\dx + \dy*\dy)/\circler))}
+ \setcache{vcraters,\x,\y}{\v}
+ \pgfmathparse{max(\maxvcraters,\v)}
+ \xdef\maxvcraters{\pgfmathresult}
+ \pgfmathparse{min(\minvcraters,\v)}
+ \xdef\minvcraters{\pgfmathresult}
\fi
}
\fi
}
}
+ \definecolor{gradientpoint0}{rgb}{0,0,0.5}
+ \definecolor{gradientpoint1}{rgb}{0.2,0.2,1}
+ \definecolor{gradientpoint2}{rgb}{0.9,0.6,0.1}
+ \definecolor{gradientpoint3}{rgb}{0.1,0.6,0.2}
+ \definecolor{gradientpoint4}{rgb}{0.6,0.3,0.05}
+ \definecolor{gradientpoint5}{rgb}{1,1,1}
+ \def\positions{{0,0.3,0.4,0.88,0.94,1}}
\foreach \y in {1,2,...,\craterssize}{
\message{Gradient line \y/\craterssize...}
\foreach \x in {1,2,...,\craterssize}{
- \pgfmathsetmacro{\v}{\getcache{v,\x,\y}/\maxv}
- \definecolor{gradientpoint0}{rgb}{0,0,0.5}
- \definecolor{gradientpoint1}{rgb}{0.2,0.2,1}
- \definecolor{gradientpoint2}{rgb}{0.9,0.6,0.1}
- \definecolor{gradientpoint3}{rgb}{0.1,0.6,0.2}
- \definecolor{gradientpoint4}{rgb}{0.6,0.3,0.05}
- \definecolor{gradientpoint5}{rgb}{1,1,1}
- \def\positions{{0,0.3,0.4,0.88,0.94,1}}
+ \pgfmathsetmacro{\v}{(\getcache{vcraters,\x,\y}-\minvcraters)/max(1,\maxvcraters-\minvcraters)}
+ \pgfmathsetmacro{\v}{max(0,min(1,\v))}
\foreach \pointb in {1,...,5}{
\pgfmathsetmacro{\posb}{\positions[\pointb]}
\pgfmathparse{\v < \posb}
@@ -289,8 +424,7 @@
\breakforeach
\fi
}
- \path[fill=\colora!\mix!\colorb] (\x,\y) rectangle ++(1.2,1.2);
- \clearcache{v,\x,\y}
+ \path[fill=\colora!\mix!\colorb] (\x,\y) rectangle ++(1.5,1.5);
}
}
\end{tikzpicture}
@@ -298,14 +432,114 @@
}
\item<3-> Sur un terrain existant
\only<3>{
- % TODO
+ \begin{figure}[h]
+ \centering
+ \begin{tikzpicture}[scale=0.025]
+ \xdef\cratersperlinsize{\twodperlinsize}
+ \xdef\maxvcratersperlin{\maxvtwodperlin}
+ \xdef\minvcratersperlin{\minvtwodperlin}
+ \def\maxradius{32}
+ \def\ncircles{20}
+ \foreach \y in {1,2,...,\cratersperlinsize}{
+ \foreach \x in {1,2,...,\cratersperlinsize}{
+ \setcache{vcratersperlin,\x,\y}{\getcache{vtwodperlin,\x,\y}}
+ }
+ }
+ \foreach \c in {1,...,\ncircles}{
+ \setintmacro{\circlex}{noise1D(\c,0)*\cratersperlinsize}
+ \setintmacro{\circley}{noise1D(\c,1)*\cratersperlinsize}
+ \setintmacro{\circler}{noise1D(\c,2)*\maxradius}
+ \message{Circle number \c/\ncircles, center (\circlex, \circley), radius \circler}
+ \foreach \dy in {-\circler,...,\circler}{
+ \setintmacro{\y}{\circley+\dy}
+ \pgfmathparse{(\y > 0) && (\y <= \cratersperlinsize)}
+ \ifnum 1=\pgfmathresult
+ \foreach \dx in {-\circler,...,\circler}{
+ \setintmacro{\x}{\circlex+\dx}
+ \pgfmathparse{(\x > 0) && (\x <= \cratersperlinsize)}
+ \ifnum 1=\pgfmathresult
+ \xdef\oldv{\getcache{vcratersperlin,\x,\y}}
+ \pgfmathparse{\oldv - max(0,\circler - ((\dx*\dx + \dy*\dy)/\circler))}
+ \setcache{vcratersperlin,\x,\y}{\pgfmathresult}
+ \pgfmathparse{max(\maxvcratersperlin,\pgfmathresult)}
+ \xdef\maxvcratersperlin{\pgfmathresult}
+ \pgfmathparse{min(\minvcratersperlin,\pgfmathresult)}
+ \xdef\minvcratersperlin{\pgfmathresult}
+ \fi
+ }
+ \fi
+ }
+ }
+ \definecolor{gradientpoint0}{rgb}{0,0,0.5}
+ \definecolor{gradientpoint1}{rgb}{0.2,0.2,1}
+ \definecolor{gradientpoint2}{rgb}{0.9,0.6,0.1}
+ \definecolor{gradientpoint3}{rgb}{0.1,0.6,0.2}
+ \definecolor{gradientpoint4}{rgb}{0.6,0.3,0.05}
+ \definecolor{gradientpoint5}{rgb}{1,1,1}
+ \def\positions{{0,0.3,0.4,0.88,0.94,1}}
+ \foreach \y in {1,2,...,\cratersperlinsize}{
+ \message{Gradient line \y/\cratersperlinsize...}
+ \foreach \x in {1,2,...,\cratersperlinsize}{
+ \pgfmathsetmacro{\v}{(\getcache{vcratersperlin,\x,\y}-\minvcratersperlin)/max(1,\maxvcratersperlin-\minvcratersperlin)}
+ \pgfmathsetmacro{\v}{max(0,min(1,\v))}
+ \foreach \pointb in {1,...,5}{
+ \pgfmathsetmacro{\posb}{\positions[\pointb]}
+ \pgfmathparse{\v <= \posb}
+ \ifnum 1=\pgfmathresult
+ \setintmacro{\pointa}{\pointb-1}
+ \pgfmathsetmacro{\posa}{\positions[\pointa]}
+ \pgfmathsetmacro{\mix}{100 - 100 * (\v-\posa) / (\posb-\posa)}
+ \xdef\colora{gradientpoint\pointa}
+ \xdef\colorb{gradientpoint\pointb}
+ \xdef\mix{\mix}
+ \breakforeach
+ \fi
+ }
+ \path[fill=\colora!\mix!\colorb] (\x,\y) rectangle ++(1.5,1.5);
+ }
+ }
+ \end{tikzpicture}
+ \end{figure}
}
\end{itemize}
- \item<4-> Hills Algorithm
- \begin{itemize}
- \item Inverse de craters : on ajoute plein de cercles
- \end{itemize}
- \item<5-> Stockage des cercles dans un arbre (BSP, Quadtree, arbre du LOD, \dots{}).
+ \item<4-> Hills Algorithm~: ajouter des cercles
+ \only<4>{
+ \begin{figure}[h]
+ \centering
+ \begin{tikzpicture}[scale=0.025]
+ \definecolor{gradientpoint0}{rgb}{0,0,0.5}
+ \definecolor{gradientpoint1}{rgb}{0.2,0.2,1}
+ \definecolor{gradientpoint2}{rgb}{0.9,0.6,0.1}
+ \definecolor{gradientpoint3}{rgb}{0.1,0.6,0.2}
+ \definecolor{gradientpoint4}{rgb}{0.6,0.3,0.05}
+ \definecolor{gradientpoint5}{rgb}{1,1,1}
+ \def\positions{{0,0.3,0.4,0.88,0.94,1}}
+ \foreach \y in {1,2,...,\craterssize}{
+ \message{Gradient line \y/\craterssize...}
+ \foreach \x in {1,2,...,\craterssize}{
+ \pgfmathsetmacro{\v}{(\getcache{vcraters,\x,\y}-\minvcraters)/max(1,\maxvcraters-\minvcraters)}
+ \pgfmathsetmacro{\v}{max(0,min(1,\v))}
+ \pgfmathsetmacro{\v}{1-\v}
+ \foreach \pointb in {1,...,5}{
+ \pgfmathsetmacro{\posb}{\positions[\pointb]}
+ \pgfmathparse{\v < \posb}
+ \ifnum 1=\pgfmathresult
+ \setintmacro{\pointa}{\pointb-1}
+ \pgfmathsetmacro{\posa}{\positions[\pointa]}
+ \pgfmathsetmacro{\mix}{100 - 100 * (\v-\posa) / (\posb-\posa)}
+ \xdef\colora{gradientpoint\pointa}
+ \xdef\colorb{gradientpoint\pointb}
+ \xdef\mix{\mix}
+ \breakforeach
+ \fi
+ }
+ \path[fill=\colora!\mix!\colorb] (\x,\y) rectangle ++(1.5,1.5);
+ }
+ }
+ \end{tikzpicture}
+ \end{figure}
+ }
+ \item<5-> Stockage des cercles dans un arbre (BSP, Quadtree, LOD, \dots{}).
\end{itemize}
\end{frame}
