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