Tous les diagrammes de perlin et craters, en haute qualité. Ça va faire mal.

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<1-> Cavernes, nuages\only<2->{, textures, terrains : bruit $n$D et voxels.}
-  \item Ridged Perlin Noise.
+    \only<1>{
-  \item Midpoint displacement.
+      \begin{figure}[h]
-  \item Simplex noise : généralisation des triangles équilatéraux à $n$ dimensions, interpolation par rapport aux coins. $d^2$ au lieu de $2^d$.
+        \centering
-  \item Bruit répétable 1D : points sur un cercle dans un espace 2D. Généralisation à $n$ dimensions : hypercercle $n$D dans un espace $2n$D.
+        \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\craterssize{128}
-            \xdef\maxv{0}
+            \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}}
+                  \xdef\oldv{\getcache{vcraters,\x,\y}}
-                  \pgfmathparse{\oldv+max(0,\circler*\circler - (\dx*\dx + \dy*\dy))}
+                  \pgfmathsetmacro{\v}{\oldv - max(0,\circler - ((\dx*\dx + \dy*\dy)/\circler))}
-                  \setcache{v,\x,\y}{\pgfmathresult}
+                  \setcache{vcraters,\x,\y}{\v}
-                  \pgfmathparse{max(\maxv,\pgfmathresult)}
+                  \pgfmathparse{max(\maxvcraters,\v)}
-                  \xdef\maxv{\pgfmathresult}
+                  \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}
+                \pgfmathsetmacro{\v}{(\getcache{vcraters,\x,\y}-\minvcraters)/max(1,\maxvcraters-\minvcraters)}
-                \definecolor{gradientpoint0}{rgb}{0,0,0.5}
+                \pgfmathsetmacro{\v}{max(0,min(1,\v))}
-                \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 \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);
+                \path[fill=\colora!\mix!\colorb] (\x,\y) rectangle ++(1.5,1.5);
-                \clearcache{v,\x,\y}
               }
             }
           \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
+  \item<4-> Hills Algorithm~: ajouter des cercles
-    \begin{itemize}
+      \only<4>{
-    \item Inverse de craters : on ajoute plein de cercles
+        \begin{figure}[h]
-    \end{itemize}
+          \centering
-  \item<5-> Stockage des cercles dans un arbre (BSP, Quadtree, arbre du LOD, \dots{}).
+          \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}