Adding the game engine and its related resources

COPYING

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+                    GNU GENERAL PUBLIC LICENSE
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+THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
+GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
+USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
+PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+  17. Interpretation of Sections 15 and 16.
+
+  If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+                     END OF TERMS AND CONDITIONS
+
+            How to Apply These Terms to Your New Programs
+
+  If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+  To do so, attach the following notices to the program.  It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+    <one line to give the program's name and a brief idea of what it does.>
+    Copyright (C) <year>  <name of author>
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+  If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+    <program>  Copyright (C) <year>  <name of author>
+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License.  Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+<http://www.gnu.org/licenses/>.
+
+  The GNU General Public License does not permit incorporating your program
+into proprietary programs.  If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library.  If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.  But first, please read
+<http://www.gnu.org/philosophy/why-not-lgpl.html>.

Makefile

@@ -0,0 +1,83 @@
+#  Makefile 
+#  Auteur : Farès BELHADJ
+#  Email  : amsi@up8.edu
+#  Date   : 16/11/2021
+# définition des commandes utilisées
+CC = gcc
+ECHO = echo
+RM = rm -f
+TAR = tar
+ZIP = zip
+MKDIR = mkdir
+CHMOD = chmod
+CP = rsync -R
+# déclaration des options du compilateur
+CFLAGS = -Wall -O3
+CPPFLAGS = -I.
+LDFLAGS = -lm
+# définition des fichiers et dossiers
+PACKNAME = sc_00_07
+PROGNAME = rasterizer
+VERSION = 0.1
+distdir = $(PACKNAME)_$(PROGNAME)-$(VERSION)
+HEADERS = rasterize.h
+SOURCES = window.c rasterize.c vtransform.c surface.c geometry.c
+MSVCSRC = $(patsubst %,<ClCompile Include=\"%\\\" \\/>,$(SOURCES))
+OBJ = $(SOURCES:.c=.o)
+DOXYFILE = documentation/Doxyfile
+VSCFILES = $(PROGNAME).vcxproj $(PROGNAME).sln
+EXTRAFILES = COPYING $(wildcard shaders/*.?s images/*) $(VSCFILES)
+DISTFILES = $(SOURCES) Makefile $(HEADERS) $(DOXYFILE) $(EXTRAFILES)
+# Traitements automatiques pour ajout de chemins et options (ne pas modifier)
+ifneq (,$(shell ls -d /usr/local/include 2>/dev/null | tail -n 1))
+	CPPFLAGS += -I/usr/local/include
+endif
+ifneq (,$(shell ls -d $(HOME)/local/include 2>/dev/null | tail -n 1))
+	CPPFLAGS += -I$(HOME)/local/include
+endif
+ifneq (,$(shell ls -d /usr/local/lib 2>/dev/null | tail -n 1))
+	LDFLAGS += -L/usr/local/lib
+endif
+ifneq (,$(shell ls -d $(HOME)/local/lib 2>/dev/null | tail -n 1))
+	LDFLAGS += -L$(HOME)/local/lib
+endif
+ifeq ($(shell uname),Darwin)
+	MACOSX_DEPLOYMENT_TARGET = 10.8
+        CFLAGS += -mmacosx-version-min=$(MACOSX_DEPLOYMENT_TARGET)
+        LDFLAGS += -framework OpenGL -mmacosx-version-min=$(MACOSX_DEPLOYMENT_TARGET)
+else
+        LDFLAGS += -lGL
+endif
+CPPFLAGS += $(shell sdl2-config --cflags)
+LDFLAGS  += -lGL4Dummies $(shell sdl2-config --libs)
+all: $(PROGNAME)
+$(PROGNAME): $(OBJ)
+	$(CC) $(OBJ) $(LDFLAGS) -o $(PROGNAME)
+%.o: %.c
+	$(CC) $(CPPFLAGS) $(CFLAGS) -c $< -o $@
+dist: distdir
+	$(CHMOD) -R a+r $(distdir)
+	$(TAR) zcvf $(distdir).tgz $(distdir)
+	$(RM) -r $(distdir)
+zip: distdir
+	$(CHMOD) -R a+r $(distdir)
+	$(ZIP) -r $(distdir).zip $(distdir)
+	$(RM) -r $(distdir)
+distdir: $(DISTFILES)
+	$(RM) -r $(distdir)
+	$(MKDIR) $(distdir)
+	$(CHMOD) 777 $(distdir)
+	$(CP) $(DISTFILES) $(distdir)
+doc: $(DOXYFILE)
+	cat $< | sed -e "s/PROJECT_NAME *=.*/PROJECT_NAME = $(PROGNAME)/" |\
+	  sed -e "s/PROJECT_NUMBER *=.*/PROJECT_NUMBER = $(VERSION)/" >> $<.new
+	mv -f $<.new $<
+	cd documentation && doxygen && cd ..
+msvc: $(VSCFILES)
+	@echo "Now these files ($?) already exist. If you wish to regenerate them, you should first delete them manually."  
+$(VSCFILES):
+	@echo "Generating $@ ..."
+	@cat ../../Windows/templates/gl4dSample$(suffix $@) | sed -e "s/INSERT_PROJECT_NAME/$(PROGNAME)/g" | sed -e "s/INSERT_TARGET_NAME/$(PROGNAME)/" | sed -e "s/INSERT_SOURCE_FILES/$(MSVCSRC)/" > $@
+clean:
+	@$(RM) -r $(PROGNAME) $(OBJ) *~ $(distdir).tgz $(distdir).zip gmon.out	\
+	  core.* documentation/*~ shaders/*~ documentation/html

geometry.c

@@ -0,0 +1,157 @@
+/*!\file geometry.h 
+ *
+ * \brief quelques surfaces basiques sous forme polygonale : un plan
+ * (quad), un cube et une sphere.
+ *
+ * \author Farès BELHADJ, amsi@up8.edu
+ * \date November, 2021. 
+*/
+#include "rasterize.h"
+#include <assert.h>
+#if defined(_MSC_VER)
+#  define _USE_MATH_DEFINES
+#endif
+#include <math.h>
+
+/*!\brief fabrique et renvoie une surface représentant un
+ * quadrilatère "debout" et à la profondeur 0. Il fait la hauteur et
+ * la largeur du cube unitaire (-1 à 1).*/
+surface_t * mk_quad(void) {
+  static const float
+    data[] = {
+	      -1.0f, -1.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f,  0.0f,
+	       1.0f, -1.0f, 0.0f, 0.0f, 0.0f, 1.0f, 1.0f,  0.0f,
+	      -1.0f,  1.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, -1.0f,
+	       1.0f,  1.0f, 0.0f, 0.0f, 0.0f, 1.0f, 1.0f, -1.0f
+  };
+  static const int order[] = { 0, 1, 2, 2, 1, 3 };
+  surface_t * s;
+  /* on met du jaune partout */
+  const vec4 color0 = { 1.0f, 1.0f, 0.0f, 1.0f }; 
+  triangle_t t[2];
+  int i, j, k, o;
+  for(i = 0, o = 0; i < 2; ++i)
+    for(j = 0; j < 3; ++j, ++o) {
+      k = order[o] * 8;
+      t[i].v[j].position = *(vec4 *)&(data[k]);
+      t[i].v[j].position.w = 1.0f;
+      t[i].v[j].normal   = *(vec3 *)&(data[k + 3]);
+      t[i].v[j].texCoord = *(vec2 *)&(data[k + 6]);
+      t[i].v[j].color0   = color0;
+    }
+  s = new_surface(t, 2, 1, 1);
+  snormals(s);
+  return s;
+}
+
+/*!\brief fabrique et renvoie une surface représentant un
+ * cube unitaire (de -1 à 1).*/
+surface_t * mk_cube(void) {
+  const float
+    data[] = {
+	      /* front */
+	      -1.0f, -1.0f, 1.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f,
+	      1.0f, -1.0f, 1.0f, 0.0f, 0.0f, 1.0f, 1.0f, 0.0f,
+	      -1.0f,  1.0f, 1.0f, 0.0f, 0.0f, 1.0f, 0.0f, 1.0f,
+	      1.0f,  1.0f, 1.0f, 0.0f, 0.0f, 1.0f, 1.0f, 1.0f,
+	      /* back */
+	      1.0f, -1.0f, -1.0f, 0.0f, 0.0f, -1.0f, 0.0f, 0.0f,
+	      -1.0f, -1.0f, -1.0f, 0.0f, 0.0f, -1.0f, 1.0f, 0.0f,
+	      1.0f,  1.0f, -1.0f, 0.0f, 0.0f, -1.0f, 0.0f, 1.0f,
+	      -1.0f,  1.0f, -1.0f, 0.0f, 0.0f, -1.0f, 1.0f, 1.0f,
+	      /* right */
+	      1.0f, -1.0f,  1.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f,
+	      1.0f, -1.0f, -1.0f, 1.0f, 0.0f, 0.0f, 1.0f, 0.0f,
+	      1.0f,  1.0f,  1.0f, 1.0f, 0.0f, 0.0f, 0.0f, 1.0f,
+	      1.0f,  1.0f, -1.0f, 1.0f, 0.0f, 0.0f, 1.0f, 1.0f,
+	      /* left */
+	      -1.0f, -1.0f, -1.0f, -1.0f, 0.0f, 0.0f, 0.0f, 0.0f,
+	      -1.0f, -1.0f,  1.0f, -1.0f, 0.0f, 0.0f, 1.0f, 0.0f,
+	      -1.0f,  1.0f, -1.0f, -1.0f, 0.0f, 0.0f, 0.0f, 1.0f,
+	      -1.0f,  1.0f,  1.0f, -1.0f, 0.0f, 0.0f, 1.0f, 1.0f,
+	      /* top */
+	      -1.0f, 1.0f,  1.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f,
+	      1.0f, 1.0f,  1.0f, 0.0f, 1.0f, 0.0f, 1.0f, 0.0f,
+	      -1.0f, 1.0f, -1.0f, 0.0f, 1.0f, 0.0f, 0.0f, 1.0f,
+	      1.0f, 1.0f, -1.0f, 0.0f, 1.0f, 0.0f, 1.0f, 1.0f,
+	      /* bottom */
+	      -1.0f, -1.0f, -1.0f, 0.0f, -1.0f, 0.0f, 0.0f, 0.0f,
+	      1.0f, -1.0f, -1.0f, 0.0f, -1.0f, 0.0f, 1.0f, 0.0f,
+	      -1.0f, -1.0f,  1.0f, 0.0f, -1.0f, 0.0f, 0.0f, 1.0f,
+	      1.0f, -1.0f,  1.0f, 0.0f, -1.0f, 0.0f, 1.0f, 1.0f
+  };
+  const int order[] = { 0, 1, 2, 2, 1, 3 };
+  surface_t * s;
+  /* on met du vert-clair partout */
+  const vec4 color0 = { 0.5f, 1.0f, 0.0f, 1.0f }; 
+  triangle_t t[12];
+  int i, j, k, o;
+  for(i = 0, o = 0; i < 12; ++i)
+    for(j = 0; j < 3; ++j, ++o) {
+      k = 8 * (order[o % 6] + 4 * (i / 2));
+      t[i].v[j].position = *(vec4 *)&(data[k]);
+      t[i].v[j].position.w = 1.0f;
+      t[i].v[j].normal   = *(vec3 *)&(data[k + 3]);
+      t[i].v[j].texCoord = *(vec2 *)&(data[k + 6]);
+      t[i].v[j].color0   = color0;
+    }
+  s = new_surface(t, 12, 1, 1);
+  snormals(s);
+  return s;
+}
+
+/*!\brief fabrique et renvoie une surface représentant une sphère
+ * centrée en zéro et de rayon 1. Elle est découpée en \a longitudes
+ * longitudes et \a latitudes latitudes. */
+surface_t * mk_sphere(int longitudes, int latitudes) {
+  triangle_t * t;
+  vertex_t * data;
+  double phi, theta, r, y;
+  double c2MPI_Long = 2.0 * M_PI / longitudes;
+  double cMPI_Lat = M_PI / latitudes;
+  /* on met du vert-clair partout */
+  const vec4 color0 = { 0.5f, 1.0f, 0.0f, 1.0f }; 
+  int z, nz, x, nx, zw, nzw, k, n = 2 * longitudes * latitudes;
+  assert(n);
+  data = malloc((longitudes + 1) * (latitudes + 1) * sizeof *data);
+  assert(data);
+  t = malloc(n * sizeof *t);
+  assert(t);
+  for(z = 0, k = 0; z <= latitudes; ++z) {
+    theta  = -M_PI_2 + z * cMPI_Lat;
+    y = sin(theta);
+    r = cos(theta);
+    for(x = 0; x <= longitudes; ++x, ++k) {
+      phi = x * c2MPI_Long;
+      data[k].position.x = r * cos(phi);
+      data[k].position.y = y;
+      data[k].position.z = r * sin(phi);
+      data[k].position.w = 1.0f;
+      data[k].texCoord.x = phi / (2.0 * M_PI);
+      data[k].texCoord.y = (theta + M_PI_2) / M_PI;
+      data[k].color0     = color0;
+      /* gcc 7.5 et plus abusent : data[k].normal     = *(vec3 *)&(data[k].position); */
+      data[k].normal.x   = data[k].position.x;
+      data[k].normal.y   = data[k].position.y;
+      data[k].normal.z   = data[k].position.z;
+    }
+  }
+  for(z = 0, k = 0; z < latitudes; ++z) {
+    nz = z + 1;
+    zw = z * (longitudes + 1);
+    nzw = nz * (longitudes + 1);
+    for(x = 0; x < longitudes; ++x) {
+      nx = x + 1;
+      t[k].v[0] = data[zw  +  x];
+      t[k].v[1] = data[nzw +  x];
+      t[k].v[2] = data[zw  + nx];
+      tnormal(&t[k]);++k;
+      t[k].v[0] = data[zw  + nx];
+      t[k].v[1] = data[nzw +  x];
+      t[k].v[2] = data[nzw + nx];
+      tnormal(&t[k]);++k;
+    }
+  }
+  free(data);
+  return new_surface(t, n, 0, 1);
+}

rasterize.c

@@ -0,0 +1,455 @@
+/*!\file rasterize.c
+ * \brief ensemble de fonctions de rasterization "DIY". S'occupe
+ * principalement que du cas du triangle.
+ *
+ * CE CODE A EU COMME POINT DE DÉPART CE QUI A ÉTÉ FAIT
+ * EN COURS, IL EST COMPLÉTÉ PAR L'ENSEIGNANT POUR ÊTRE 
+ * FONCTIONNEL MAIS IL DES CHOSES À AMÉLIORER.
+ *
+ * \author Farès BELHADJ, amsi@up8.edu
+ * \date November 16, 2021.
+ */
+
+#include "rasterize.h"
+#include <assert.h>
+
+/* bloc de fonctions locales (static) */
+static inline void    fill_triangle(surface_t * s, triangle_t * t);
+static inline void    abscisses(surface_t * s, vertex_t * p0, vertex_t * p1, vertex_t * absc, int replace);
+static inline void    horizontal_line(surface_t * s, vertex_t * vG, vertex_t * vD);
+static inline void    shading_none(surface_t * s, GLuint * pcolor, vertex_t * v);
+static inline void    shading_only_tex(surface_t * s, GLuint * pcolor, vertex_t * v);
+static inline void    shading_only_color_CM(surface_t * s, GLuint * pcolor, vertex_t * v);
+static inline void    shading_only_color(surface_t * s, GLuint * pcolor, vertex_t * v);
+static inline void    shading_all_CM(surface_t * s, GLuint * pcolor, vertex_t * v);
+static inline void    shading_all(surface_t * s, GLuint * pcolor, vertex_t * v);
+static inline void    interpolate(vertex_t * r, vertex_t * a, vertex_t * b, float fa, float fb, int s, int e);
+static inline void    metainterpolate_none(vertex_t * r, vertex_t * a, vertex_t * b, float fa, float fb);
+static inline void    metainterpolate_only_tex(vertex_t * r, vertex_t * a, vertex_t * b, float fa, float fb);
+static inline void    metainterpolate_only_color(vertex_t * r, vertex_t * a, vertex_t * b, float fa, float fb);
+static inline void    metainterpolate_all(vertex_t * r, vertex_t * a, vertex_t * b, float fa, float fb);
+static inline GLuint  rgba(GLubyte r, GLubyte g, GLubyte b, GLubyte a);
+static inline GLubyte red(GLuint c);
+static inline GLubyte green(GLuint c);
+static inline GLubyte blue(GLuint c);
+static inline GLubyte alpha(GLuint c);
+static        void    pquit(void); 
+
+/*!\brief la texture courante à utiliser en cas de mapping de texture */
+static GLuint * _tex = NULL;
+/*!\brief la largeur de la texture courante à utiliser en cas de
+ * mapping de texture */
+static GLuint _texW = 0;
+/*!\brief la hauteur de la texture courante à utiliser en cas de
+ * mapping de texture */
+static GLuint _texH = 0;
+/*!\brief un buffer de depth pour faire le z-test */
+static float * _depth = NULL;
+/*!\brief flag pour savoir s'il faut ou non corriger l'interpolation
+ * par rapport à la profondeur en cas de projection en
+ * perspective */
+static int _perpective_correction = 0;
+
+/*!\brief transforme et rastérise l'ensemble des triangles de la
+ * surface. */
+void transform_n_rasterize(surface_t * s, float * model_view_matrix, float * projection_matrix) {
+  int i;
+  /* la première fois allouer le depth buffer */
+  if(_depth == NULL) {
+    _depth = calloc(gl4dpGetWidth() * gl4dpGetHeight(), sizeof *_depth);
+    assert(_depth);
+    atexit(pquit);
+  }
+  /* si projection_matrix[15] est à 1, c'est une projection orthogonale, pas
+   * besoin de correction de perspective */
+  _perpective_correction = projection_matrix[15] == 1.0f ? 0 : 1;
+  /* le viewport est fixe ; \todo peut devenir paramétrable ... */
+  float viewport[] = { 0.0f, 0.0f, (float)gl4dpGetWidth(), (float)gl4dpGetHeight() };
+  stransform(s, model_view_matrix, projection_matrix, viewport);
+  /* mettre en place la texture qui sera utilisée pour mapper la surface */
+  if(s->options & SO_USE_TEXTURE)
+    set_texture(s->tex_id);
+  for(i = 0; i < s->n; ++i) {
+    /* si le triangle est déclaré CULL (par exemple en backface), le rejeter */
+    if(s->t[i].state & PS_CULL ) continue;
+    /* on rejette aussi les triangles complètement out */
+    if(s->t[i].state & PS_TOTALLY_OUT) continue;
+    /* "hack" pas terrible permettant de rejeter les triangles
+     * partiellement out dont au moins un sommet est TOO_FAR (trop
+     * éloigné). Voir le fichier transformations.c pour voir comment
+     * améliorer ce traitement. */
+    if( s->t[i].state & PS_PARTIALLY_OUT &&
+	( (s->t[i].v[0].state & PS_TOO_FAR) ||
+	  (s->t[i].v[1].state & PS_TOO_FAR) ||
+	  (s->t[i].v[2].state & PS_TOO_FAR)    ) )
+      continue;
+    fill_triangle(s, &(s->t[i]));
+  }
+}
+
+/*!\brief effacer le buffer de profondeur (à chaque frame) pour
+ * réaliser le z-test */
+void clear_depth_map(void) {
+  if(_depth) {
+    memset(_depth, 0, gl4dpGetWidth() * gl4dpGetHeight() * sizeof *_depth);
+  }
+}
+
+/*!\brief met en place une texture pour être mappée sur la surface en cours */
+void set_texture(GLuint screen) {
+  GLuint old_id = gl4dpGetTextureId(); /* au cas où */
+  gl4dpSetScreen(screen);
+  _tex = gl4dpGetPixels();
+  _texW = gl4dpGetWidth();
+  _texH = gl4dpGetHeight();
+  if(old_id)
+    gl4dpSetScreen(old_id);
+}
+
+
+/*!\brief met à jour la fonction d'interpolation et de coloriage
+ * (shadingfunc) de la surface en fonction de ses options */
+void updatesfuncs(surface_t * s) {
+  int t;
+  if(s->options & SO_USE_TEXTURE) {
+    s->interpolatefunc = (t = s->options & SO_COLOR_MATERIAL) ? metainterpolate_all : metainterpolate_only_tex;
+    s->shadingfunc = (s->options & SO_USE_COLOR) ? (t ? shading_all_CM : shading_all) : shading_only_tex;
+  } else  {
+    s->interpolatefunc = (t = s->options & SO_COLOR_MATERIAL) ? metainterpolate_only_color : metainterpolate_none;
+    s->shadingfunc = (s->options & SO_USE_COLOR) ? (t ? shading_only_color_CM : shading_only_color) : shading_none;;
+  }
+}
+
+/*!\brief fonction principale de ce fichier, elle dessine un triangle
+ * rempli à l'écran en calculant l'ensemble des gradients
+ * (interpolations bilinaires des attributs du sommet).
+ */
+inline void fill_triangle(surface_t * s, triangle_t * t) {
+  vertex_t * aG = NULL, * aD = NULL;
+  int bas, median, haut, n, signe, i, h = gl4dpGetHeight();
+  if(t->v[0].y < t->v[1].y) {
+    if(t->v[0].y < t->v[2].y) {
+      bas = 0;
+      if(t->v[1].y < t->v[2].y) {
+	median = 1;
+	haut = 2;
+      } else {
+	median = 2;
+	haut = 1;
+      }
+    } else {
+      bas = 2;
+      median = 0;
+      haut = 1;
+    }
+  } else { /* p0 au dessus de p1 */
+    if(t->v[1].y < t->v[2].y) {
+      bas = 1;
+      if(t->v[0].y < t->v[2].y) {
+	median = 0;
+	haut = 2;
+      } else {
+	median = 2;
+	haut = 0;
+      }
+    } else {
+      bas = 2;
+      median = 1;
+      haut = 0;
+    }
+  }
+  n = t->v[haut].y - t->v[bas].y + 1;
+  aG = malloc(n * sizeof *aG);
+  assert(aG);
+  aD = malloc(n * sizeof *aD);
+  assert(aD);
+  /* est-ce que Pm est à gauche (+) ou à droite (-) de la droite (Pb->Ph) ? */
+  /* idée TODO?, un produit vectoriel pourrait s'avérer mieux */
+  if(t->v[haut].x == t->v[bas].x || t->v[haut].y == t->v[bas].y) {
+    /* eq de la droite x = t->v[haut].x; ou y = t->v[haut].y; */
+    signe = (t->v[median].x > t->v[haut].x) ? -1 : 1;
+  } else {
+    /* eq ax + y + c = 0 */
+    float a, c, x;
+    a = (t->v[haut].y - t->v[bas].y) / (float)(t->v[bas].x - t->v[haut].x);
+    c = -a * t->v[haut].x - t->v[haut].y;
+    /* on trouve le x sur la droite au même y que le median et on compare */
+    x = -(c + t->v[median].y) / a;
+    signe = (t->v[median].x >= x) ? -1 : 1;
+  }
+  if(signe < 0) { /* aG reçoit Ph->Pb, et aD reçoit Ph->Pm puis Pm vers Pb */
+    abscisses(s, &(t->v[haut]), &(t->v[bas]), aG, 1);
+    abscisses(s, &(t->v[haut]), &(t->v[median]), aD, 1);
+    abscisses(s, &(t->v[median]), &(t->v[bas]), &aD[t->v[haut].y - t->v[median].y], 0);
+  } else { /* aG reçoit Ph->Pm puis Pm vers Pb, et aD reçoit Ph->Pb */
+    abscisses(s, &(t->v[haut]), &(t->v[bas]), aD, 1);
+    abscisses(s, &(t->v[haut]), &(t->v[median]), aG, 1);
+    abscisses(s, &(t->v[median]), &(t->v[bas]), &aG[t->v[haut].y - t->v[median].y], 0);
+  }
+  for(i = 0; i < n; ++i) {
+    if( aG[i].y >= 0 && aG[i].y < h &&
+	( (aG[i].z >= 0 && aG[i].z <= 1) || (aD[i].z >= 0 && aD[i].z <= 1) ) )
+      horizontal_line(s, &aG[i], &aD[i]);
+  }
+  free(aG);
+  free(aD);
+}
+
+/*!\brief utilise Br'65 pour determiner les abscisses des segments du
+ * triangle à remplir (par \a horizontal_line).
+ */
+inline void abscisses(surface_t * s, vertex_t * p0, vertex_t * p1, vertex_t * absc, int replace) {
+  int u = p1->x - p0->x, v = p1->y - p0->y, pasX = u < 0 ? -1 : 1, pasY = v < 0 ? -1 : 1;
+  float dmax = sqrtf(u * u + v * v), p;
+  u = abs(u); v = abs(v);
+  if(u > v) { // 1er octan
+    if(replace) {
+      int objX = (u + 1) * pasX;
+      int delta = u - 2 * v, incH = -2 * v, incO = 2 * u - 2 * v;
+      for (int x = 0, y = 0, k = 0; x != objX; x += pasX) {
+	absc[k].x = x + p0->x;
+	absc[k].y = y + p0->y;
+	p = sqrtf(x * x + y * y) / dmax;
+	s->interpolatefunc(&absc[k], p0, p1, 1.0f - p, p);
+	if(delta < 0) {
+	  ++k;
+	  y += pasY;
+	  delta += incO;
+	} else
+	  delta += incH;
+      }
+    } else {
+      int objX = (u + 1) * pasX;
+      int delta = u - 2 * v, incH = -2 * v, incO = 2 * u - 2 * v;
+      for (int x = 0, y = 0, k = 0, done = 0; x != objX; x += pasX) {
+	if(!done) {
+	  absc[k].x = x + p0->x;
+	  absc[k].y = y + p0->y;
+	  p = sqrtf(x * x + y * y) / dmax;
+	  s->interpolatefunc(&absc[k], p0, p1, 1.0f - p, p);
+	  done = 1;
+	}
+	if(delta < 0) {
+	  ++k;
+	  done = 0;
+	  y += pasY;
+	  delta += incO;
+	} else
+	  delta += incH;
+      }
+    }
+  } else { // 2eme octan
+    int objY = (v + 1) * pasY;
+    int delta = v - 2 * u, incH = -2 * u, incO = 2 * v - 2 * u;
+    for (int x = 0, y = 0, k = 0; y != objY; y += pasY) {
+      absc[k].x = x + p0->x;
+      absc[k].y = y + p0->y;
+      p = sqrtf(x * x + y * y) / dmax;
+      s->interpolatefunc(&absc[k], p0, p1, 1.0f - p, p);
+      ++k;
+      if(delta < 0) {
+	x += pasX;
+	delta += incO;
+      } else
+	delta += incH;
+    }
+  }
+}
+
+/*!\brief remplissage par droite horizontale entre deux abscisses */
+inline void horizontal_line(surface_t * s, vertex_t * vG, vertex_t * vD) {
+  int w = gl4dpGetWidth(), x, yw = vG->y * w;
+  GLuint * image = gl4dpGetPixels();
+  float dmax = vD->x - vG->x, p, deltap;
+  vertex_t v;
+  /* il reste d'autres optims possibles */
+  for(x = vG->x, p = 0.0f, deltap = 1.0f / dmax; x <= vD->x; ++x, p += deltap)
+    if(x >= 0 && x < w) {
+      s->interpolatefunc(&v, vG, vD, 1.0f - p, p);
+      if(v.z < 0 || v.z > 1 || v.z < _depth[yw + x]) { continue; }
+      s->shadingfunc(s, &image[yw + x], &v);
+      _depth[yw + x] = v.z;
+    }
+}
+/*!\brief aucune couleur n'est inscrite */
+inline void shading_none(surface_t * s, GLuint * pcolor, vertex_t * v) {
+  //vide pour l'instant, à prévoir le z-buffer
+}
+
+/*!\brief la couleur du pixel est tirée uniquement de la texture */
+inline void shading_only_tex(surface_t * s, GLuint * pcolor, vertex_t * v) {
+  int xt, yt, ct;
+  GLubyte r, g, b, a;
+  xt = (int)(v->texCoord.x * (_texW - EPSILON));
+  if(xt < 0) {
+    xt = xt % (-_texW);
+    while(xt < 0) xt += _texW;
+  } else
+    xt = xt % _texW;
+  yt = (int)(v->texCoord.y * (_texH - EPSILON));
+  if(yt < 0) {
+    yt = yt % (-_texH);
+    while(yt < 0) yt += _texH;
+  } else
+    yt = yt % _texH;
+  ct = yt * _texW + xt;
+  *pcolor = _tex[yt * _texW + xt];
+  r = (GLubyte)(  red(_tex[ct]) * v->li);
+  g = (GLubyte)(green(_tex[ct]) * v->li);
+  b = (GLubyte)( blue(_tex[ct]) * v->li);
+  a = (GLubyte) alpha(_tex[ct]);
+  *pcolor = rgba(r, g, b, a);
+}
+
+/*!\brief la couleur du pixel est tirée de la couleur interpolée */
+inline void shading_only_color_CM(surface_t * s, GLuint * pcolor, vertex_t * v) {
+  GLubyte r, g, b, a;
+  r = (GLubyte)(v->li * v->icolor.x * (255 + EPSILON));
+  g = (GLubyte)(v->li * v->icolor.y * (255 + EPSILON));
+  b = (GLubyte)(v->li * v->icolor.z * (255 + EPSILON));
+  a = (GLubyte)(v->icolor.w * (255 + EPSILON));
+  *pcolor = rgba(r, g, b, a);
+}
+
+/*!\brief la couleur du pixel est tirée de la couleur diffuse de la
+ * surface */
+inline void shading_only_color(surface_t * s, GLuint * pcolor, vertex_t * v) {
+  GLubyte r, g, b, a;
+  r = (GLubyte)(v->li * s->dcolor.x * (255 + EPSILON));
+  g = (GLubyte)(v->li * s->dcolor.y * (255 + EPSILON));
+  b = (GLubyte)(v->li * s->dcolor.z * (255 + EPSILON));
+  a = (GLubyte)(s->dcolor.w * (255 + EPSILON));
+  *pcolor = rgba(r, g, b, a);
+}
+
+/*!\brief la couleur du pixel est le produit de la couleur interpolée
+ * et de la texture */
+inline void shading_all_CM(surface_t * s, GLuint * pcolor, vertex_t * v) {
+  GLubyte r, g, b, a;
+  int xt, yt, ct;
+  xt = (int)(v->texCoord.x * (_texW - EPSILON));
+  if(xt < 0) {
+    xt = xt % (-_texW);
+    while(xt < 0) xt += _texW;
+  } else
+    xt = xt % _texW;
+  yt = (int)(v->texCoord.y * (_texH - EPSILON));
+  if(yt < 0) {
+    yt = yt % (-_texH);
+    while(yt < 0) yt += _texH;
+  } else
+    yt = yt % _texH;
+  ct = yt * _texW + xt;
+  r = (GLubyte)((  red(_tex[ct]) + EPSILON) * v->li * v->icolor.x);
+  g = (GLubyte)((green(_tex[ct]) + EPSILON) * v->li * v->icolor.y);
+  b = (GLubyte)(( blue(_tex[ct]) + EPSILON) * v->li * v->icolor.z);
+  a = (GLubyte)((alpha(_tex[ct]) + EPSILON) * v->icolor.w);
+  *pcolor = rgba(r, g, b, a);
+}
+
+/*!\brief la couleur du pixel est le produit de la couleur diffuse
+ * de la surface et de la texture */
+inline void shading_all(surface_t * s, GLuint * pcolor, vertex_t * v) {
+  GLubyte r, g, b, a;
+  int xt, yt, ct;
+  xt = (int)(v->texCoord.x * (_texW - EPSILON));
+  if(xt < 0) {
+    xt = xt % (-_texW);
+    while(xt < 0) xt += _texW;
+  } else
+    xt = xt % _texW;
+  yt = (int)(v->texCoord.y * (_texH - EPSILON));
+  if(yt < 0) {
+    yt = yt % (-_texH);
+    while(yt < 0) yt += _texH;
+  } else
+    yt = yt % _texH;
+  ct = yt * _texW + xt;
+  r = (GLubyte)((  red(_tex[ct]) + EPSILON) * v->li * s->dcolor.x);
+  g = (GLubyte)((green(_tex[ct]) + EPSILON) * v->li * s->dcolor.y);
+  b = (GLubyte)(( blue(_tex[ct]) + EPSILON) * v->li * s->dcolor.z);
+  a = (GLubyte)((alpha(_tex[ct]) + EPSILON) * s->dcolor.w);
+  *pcolor = rgba(r, g, b, a);
+}
+
+/*!\brief interpolation de plusieurs floattants (entre \a s et \a e)
+ * de la structure vertex_t en utilisant \a a et \a b, les
+ * facteurs \a fa et \a fb, le tout dans \a r 
+ * \todo un pointeur de fonction pour éviter un test s'il faut
+ * un _perpective_correction != 0 ??? */
+inline void interpolate(vertex_t * r, vertex_t * a, vertex_t * b, float fa, float fb, int s, int e) {
+  int i;
+  float * pr = (float *)&(r->texCoord);
+  float * pa = (float *)&(a->texCoord);
+  float * pb = (float *)&(b->texCoord);
+  /* Correction de l'interpolation par rapport à la perspective, le z
+   * joue un rôle dans les distances, il est nécessaire de le
+   * réintégrer en modifiant les facteurs de proportion.
+   * lien utile : https://www.scratchapixel.com/lessons/3d-basic-rendering/rasterization-practical-implementation/perspective-correct-interpolation-vertex-attributes 
+   */
+  if(_perpective_correction) {
+    float z = 1.0f / (fa / a->zmod + fb / b->zmod);
+    if(e == 8) { /* attention il faut que cet indice colle avec la position de la proriété z à partir de l'adresse texCoord */
+      pr[e] = fa * pa[e] + fb * pb[e];
+      e = 7;
+    }
+    fa = z * fa / a->zmod; fb = z * fb / b->zmod;
+  }
+  for(i = s; i <= e; ++i)
+    pr[i] = fa * pa[i] + fb * pb[i];
+}
+
+/*!\brief meta-fonction pour appeler \a interpolate, demande
+ * uniquement l'interpolation des z */
+inline void metainterpolate_none(vertex_t * r, vertex_t * a, vertex_t * b, float fa, float fb) {
+  interpolate(r, a, b, fa, fb, 6, 8);
+}
+
+/*!\brief meta-fonction pour appeler \a interpolate, demande
+ * uniquement l'interpolation des coord. de texture et les z */
+inline void metainterpolate_only_tex(vertex_t * r, vertex_t * a, vertex_t * b, float fa, float fb) {
+  interpolate(r, a, b, fa, fb, 0, 1);
+  interpolate(r, a, b, fa, fb, 6, 8);
+}
+
+/*!\brief meta-fonction pour appeler \a interpolate, demande
+ * uniquement l'interpolation des couleurs et les z */
+inline void metainterpolate_only_color(vertex_t * r, vertex_t * a, vertex_t * b, float fa, float fb) {
+  interpolate(r, a, b, fa, fb, 2, 8);
+}
+
+/*!\brief meta-fonction pour appeler \a interpolate, demande
+ * l'interpolation de l'ensemble des attributs */
+inline void metainterpolate_all(vertex_t * r, vertex_t * a, vertex_t * b, float fa, float fb) {
+  interpolate(r, a, b, fa, fb, 0, 8);
+}
+
+GLuint rgba(GLubyte r, GLubyte g, GLubyte b, GLubyte a) {
+  return RGBA(r, g, b, a);
+}
+
+GLubyte red(GLuint c) {
+  return RED(c);
+}
+
+GLubyte green(GLuint c) {
+  return GREEN(c);
+}
+
+GLubyte blue(GLuint c) {
+  return BLUE(c);
+}
+
+GLubyte alpha(GLuint c) {
+  return ALPHA(c);
+}
+
+
+/*!\brief au moment de quitter le programme désallouer la mémoire
+ * utilisée pour _depth */
+void pquit(void) {
+  if(_depth) {
+    free(_depth);
+    _depth = NULL;
+  }
+}

rasterize.h

@@ -0,0 +1,162 @@
+/*!\file rasterize.h 
+ *
+ * \brief structures de données et protos de fonctions externes pour
+ * réaliser un moteur de rendu DIY par rastérisation.
+ *
+ * \author Farès BELHADJ, amsi@up8.edu
+ * \date November 17, 2021. 
+*/
+
+#ifndef RASTERIZE_H_SEEN
+#  define RASTERIZE_H_SEEN
+
+#  include <GL4D/gl4dp.h>
+#  include <GL4D/gl4dm.h>
+
+#include <float.h>
+#define EPSILON ((double)FLT_EPSILON)
+
+#  ifdef __cplusplus
+extern "C" {
+#  endif
+  
+  typedef enum pstate_t pstate_t;
+  typedef enum soptions_t soptions_t;
+  typedef struct vec4 vec4;
+  typedef struct vec3 vec3;
+  typedef struct vec2 vec2;
+  typedef struct vertex_t vertex_t;
+  typedef struct triangle_t triangle_t;
+  typedef struct surface_t surface_t;
+
+  /*!\brief états pour les sommets ou les triangles */
+  enum pstate_t {
+		 PS_NONE = 0,
+		 PS_TOTALLY_OUT = 1,
+		 PS_PARTIALLY_OUT = 2,
+		 PS_CULL = 4, /* si en BACKFACE et que
+				 SO_CULL_BACKFACES est actif */
+		 PS_TOO_FAR = 8,
+		 PS_OUT_LEFT = 16,
+		 PS_OUT_RIGHT = 32,
+		 PS_OUT_BOTTOM = 64,
+		 PS_OUT_TOP = 128,
+		 PS_OUT_NEAR = 256,
+		 PS_OUT_FAR = 512
+  };
+
+  /*!\brief options pour les surfaces */
+  enum soptions_t {
+		   SO_NONE = 0, /* la surface n'a pas de rendu
+				   "couleur" */
+		   SO_USE_TEXTURE = 1, /* utiliser la texture pour
+					  colorer (multiplication si
+					  SO_USE_COLOR est actif) */
+		   SO_USE_COLOR = 2, /* utiliser la couleur de la
+					surface ou des sommets pour
+					colorer (multiplication si
+					SO_USE_TEXTURE est actif) */
+		   SO_COLOR_MATERIAL = 4, /* utiliser la couleur aux
+					     sommets si actif
+					     (nécessite aussi
+					     l'activation de
+					     SO_USE_COLOR) */
+		   SO_CULL_BACKFACES = 8, /* active le fait de cacher
+					     les faces arrières */
+		   SO_USE_LIGHTING = 16, /* active le calcul d'ombre
+					    propre (Gouraud sur
+					    diffus) */
+		   SO_DEFAULT = SO_CULL_BACKFACES | SO_USE_COLOR /* comportement
+								    par
+								    défaut */
+  };
+
+  struct vec4 {
+    float x /* r */, y/* g */, z /* b */, w /* a */;
+  };
+
+  struct vec2 {
+    float x /* s */, y /* t */;
+  };
+
+  struct vec3 {
+    float x /* r */, y/* g */, z/* b */;
+  };
+
+  /*!\brief le sommet et l'ensemble de ses attributs */
+  struct vertex_t {
+    vec4 position;
+    vec4 color0;
+    /* début des données à partir desquelles on peut interpoler en masse */
+    vec2 texCoord; /* coordonnée de texture */
+    vec4 icolor;   /* couleur à interpoler */
+    float li;      /* intensité de lumière (lambertien) */
+    float zmod;    /* z après modelview, sert à corriger
+		      l'interpolation par rapport à une projection en
+		      perspective */
+    float z;       /* ce z représente la depth */
+    /* fin des données à partir desquelles on peut interpoler */
+    vec3 normal; /* interpolez les normales si vous implémentez Phong */
+    int x, y;
+    enum pstate_t state;
+  };
+
+  /*!\brief le triangle */
+  struct triangle_t {
+    vertex_t v[3];
+    vec3 normal;  
+    enum pstate_t state;
+  };
+
+  /*!\brief la surface englobe plusieurs triangles et des options
+   * telles que le type de rendu, la couleur diffuse ou la texture.
+   */
+  struct surface_t {
+    int n;
+    triangle_t * t;
+    GLuint tex_id;
+    vec4 dcolor; /* couleur diffuse, ajoutez une couleur ambiante et
+		    spéculaire si vous souhaitez compléter le
+		    modèle */
+    soptions_t options; /* paramétrage du rendu de la surface */
+    void (*interpolatefunc)(vertex_t *, vertex_t *, vertex_t *, float, float);
+    void (*shadingfunc)(surface_t *, GLuint *, vertex_t *);
+  };
+  
+  /* dans rasterize.c */
+  extern void transform_n_rasterize(surface_t * s, float * model_view_matrix, float * projection_matrix);
+  extern void clear_depth_map(void);
+  extern void set_texture(GLuint screen);
+  extern void updatesfuncs(surface_t * s);
+
+  /* dans vtranform.c */
+  extern vertex_t vtransform(surface_t * s, vertex_t v, float * model_view_matrix, float * ti_model_view_matrix, float * projection_matrix, float * viewport);
+  extern void     stransform(surface_t * s, float * model_view_matrix, float * projection_matrix, float * viewport);
+  extern void     mult_matrix(float * res, float * m);
+  extern void     translate(float * m, float tx, float ty, float tz);
+  extern void     rotate(float * m, float angle, float x, float y, float z);
+  extern void     scale(float * m, float sx, float sy, float sz);
+  extern void     lookAt(float * m, float eyeX, float eyeY, float eyeZ, float centerX, float centerY, float centerZ, float upX, float upY, float upZ);
+  
+  /* dans surface.c */
+  extern void        tnormal(triangle_t * t);
+  extern void        snormals(surface_t * s);
+  extern void        tnormals2vertices(surface_t * s);
+  extern void        set_texture_id(surface_t * s, GLuint tex_id);
+  extern void        set_diffuse_color(surface_t * s, vec4 dcolor);
+  extern void        enable_surface_option(surface_t * s, soptions_t option);
+  extern void        disable_surface_option(surface_t * s, soptions_t option);
+  extern surface_t * new_surface(triangle_t * t, int n, int duplicateTriangles, int hasNormals);
+  extern void        free_surface(surface_t * s);
+  extern GLuint      get_texture_from_BMP(const char * filename);
+
+  /* dans geometry.c */
+  extern surface_t * mk_quad(void);  
+  extern surface_t * mk_cube(void);
+  extern surface_t * mk_sphere(int longitudes, int latitudes);
+#  ifdef __cplusplus
+}
+#  endif
+
+
+#endif

surface.c

@@ -0,0 +1,126 @@
+/*!\file surface.c
+ *
+ * \brief gestion de surfaces et autres éléments de la scène :
+ * lumière(s) (TODO), options, textures ...
+ *
+ * \author Farès BELHADJ, amsi@up8.edu
+ * \date November 17, 2021.
+*/
+
+#include "rasterize.h"
+#include <assert.h>
+
+/*!\brief calcule le vecteur normal à un triangle */
+void tnormal(triangle_t * t) {
+  vec3 u = {
+	    t->v[1].position.x - t->v[0].position.x,
+	    t->v[1].position.y - t->v[0].position.y,
+	    t->v[1].position.z - t->v[0].position.z
+  };
+  vec3 v = {
+	    t->v[2].position.x - t->v[0].position.x,
+	    t->v[2].position.y - t->v[0].position.y,
+	    t->v[2].position.z - t->v[0].position.z
+  };
+  MVEC3CROSS((float *)&(t->normal), (float *)&u, (float *)&v);
+  MVEC3NORMALIZE((float *)&(t->normal));
+}
+
+/*!\brief calcule les vecteurs normaux aux triangles de la surface */
+void snormals(surface_t * s) {
+  int i;
+  for(i = 0; i < s->n; ++i)
+    tnormal(&(s->t[i]));
+}
+
+/*!\brief affecte les normales aux triangles de la surface à ses vertices */
+void tnormals2vertices(surface_t * s) {
+  int i;
+  for(i = 0; i < s->n; ++i)
+    s->t[i].v[0].normal = s->t[i].v[1].normal = s->t[i].v[2].normal = s->t[i].normal;
+}
+
+/*!\brief affecte l'identifiant de texture de la surface */
+void set_texture_id(surface_t * s, GLuint tex_id) {
+  s->tex_id = tex_id;
+}
+
+/*!\brief affecte la couleur diffuse de la surface */
+void set_diffuse_color(surface_t * s, vec4 dcolor) {
+  s->dcolor = dcolor;
+}
+
+/*!\brief active une option de la surface */
+void enable_surface_option(surface_t * s, soptions_t option) {
+  if(!(s->options & option))
+    s->options |= option;
+  updatesfuncs(s);
+}
+
+/*!\brief désactive une option de la surface */
+void disable_surface_option(surface_t * s, soptions_t option) {
+  if(s->options & option)
+    s->options ^= option;
+  updatesfuncs(s);
+}
+
+/*!\brief créé et renvoie une surface (allouée) à partir de \a n
+ * triangles pointés par \a t. Quand \a duplicateTriangles est vrai
+ * (1), elle alloue de la mémoire pour copier les triangles dedans,
+ * sinon ( si faux (0) ) elle se contente de copier le pointeur
+ * (attention ce dernier doit donc correspondre à une mémoire allouée
+ * avec malloc et dont le développeur ne s'en servira pas pour autre
+ * chose ; elle sera libérée par freeSurface). Quand \a hasNormals est
+ * faux (0) elle force le calcul des normales par triangle et les
+ * affecte aux sommets. */
+surface_t * new_surface(triangle_t * t, int n, int duplicate_triangles, int has_normals) {
+  const vec4 dcolor = { 0.42f, 0.1f, 0.1f, 1.0f };
+  surface_t * s = malloc(1 * sizeof *s);
+  assert(s);
+  s->n = n;
+  if(duplicate_triangles) {
+    s->t = malloc(s->n * sizeof *(s->t));
+    assert(s->t);
+    memcpy(s->t, t, s->n * sizeof *(s->t));
+  } else
+    s->t = t;
+  set_diffuse_color(s, dcolor);
+  s->options = SO_DEFAULT;
+  s->tex_id = 0;
+  updatesfuncs(s);
+  if(!has_normals) {
+    snormals(s);
+    tnormals2vertices(s);
+  }
+  return s;
+}
+
+/*!\brief libère la mémoire utilisée par la surface */
+void free_surface(surface_t * s) {
+  free(s->t);
+  free(s);
+}
+/*!\brief charge et fabrique un identifiant pour une texture issue
+ * d'un fichier BMP */
+GLuint get_texture_from_BMP(const char * filename) {
+  GLuint id, old_id;
+  /* chargement d'une image dans une surface SDL */
+  SDL_Surface * s = SDL_LoadBMP(filename);
+  assert(s);
+  old_id = gl4dpGetTextureId(); /* au cas où */
+  /* création d'un screen GL4Dummies aux dimensions de la texture */
+  id = gl4dpInitScreenWithDimensions(s->w, s->h);
+  /* copie de la surface SDL vers le screen en cours */
+  {
+    GLuint * p = gl4dpGetPixels();
+    SDL_Surface * d = SDL_CreateRGBSurface(0, s->w, s->h, 32, R_MASK, G_MASK, B_MASK, A_MASK);
+    SDL_BlitSurface(s, NULL, d, NULL);
+    memcpy(p, d->pixels, d->w * d->h * sizeof *p);
+    SDL_FreeSurface(d);
+  }
+  /* libération de la surface SDL */
+  SDL_FreeSurface(s);
+  if(old_id)
+    gl4dpSetScreen(old_id);
+  return id;
+}

vtransform.c

@@ -0,0 +1,243 @@
+/*!\file vtransforms.c
+ * \brief transformations spatiales pour un moteur de rendu basé raster DIY.
+ *
+ * IL RESTE DES CHOSES À IMPLÉMENTER OU À OPTIMISER.
+ *
+ * \author Farès BELHADJ, amsi@up8.edu
+ * \date November 17, 2021.
+ *
+ * \todo COMPLÉTER LE CLIPPING POUR GÉRER ICI LES TRIANGLES
+ * PARTIELLEMENT HORS-CHAMP ET ÉVITER DES TESTS GOURMANDS DANS \ref
+ * rasterize.c
+ */
+#include "rasterize.h"
+#include <assert.h>
+
+/* fonctions locale (static) */
+static inline void clip2_unit_cube(triangle_t * t);
+
+/*!\brief projette le sommet \a v à l'écran (le \a viewport) selon la
+   matrice de model-view \a model_view_matrix et de projection \a projection_matrix. \a
+   ti_model_view_matrix est la transposée de l'inverse de la matrice \a model_view_matrix.*/
+vertex_t vtransform(surface_t * s, vertex_t v, float * model_view_matrix, float * ti_model_view_matrix, float * projection_matrix, float * viewport) {
+  float dist = 1.0f;
+  vec4 r1, r2;
+  v.state = PS_NONE;
+  MMAT4XVEC4((float *)&r1, model_view_matrix, (float *)&(v.position));
+  MMAT4XVEC4((float *)&r2, projection_matrix, (float *)&r1);
+  r2.x /= r2.w;
+  r2.y /= r2.w;
+  r2.z /= r2.w;
+  r2.w = 1.0f;
+  /* dist doit être à 1 ci-après */
+  if(r2.x < -dist) v.state |= PS_OUT_LEFT;
+  if(r2.x >  dist) v.state |= PS_OUT_RIGHT;
+  if(r2.y < -dist) v.state |= PS_OUT_BOTTOM;
+  if(r2.y >  dist) v.state |= PS_OUT_TOP;
+  if(r2.z < -dist) v.state |= PS_OUT_NEAR;
+  if(r2.z >  dist) v.state |= PS_OUT_FAR;
+  /* "hack" pas terrible permettant d'éviter les gros triangles
+     partiellement hors-champ. Modifier dist pour jouer sur la taille
+     (une fois projetés) des triangles qu'on laisse passer (plus c'est
+     gros plus c'est lent avec les gros triangles). La "vraie"
+     solution est obtenue en calculant l'intersection exacte entre le
+     triangle et le cube unitaire ; attention, ceci produit
+     potentiellement une nouvelle liste de triangles à chaque frame,
+     et les attributs des sommets doivent être recalculés. */
+  dist = 10.0f;
+  if(r2.x < -dist || r2.x > dist || r2.y < -dist || r2.y > dist || r2.z < -dist || r2.z > dist) {
+    v.state |= PS_TOO_FAR;
+    return v;
+  }
+  /* Gouraud */
+  if(s->options & SO_USE_LIGHTING) {
+    /* la lumière est positionnelle et fixe dans la scène. \todo dans
+       scene.c la rendre modifiable, voire aussi pouvoir la placer par
+       rapport aux objets (elle subirait la matrice modèle). */
+    const vec4 lp[1] = { {0.0f, 0.0f, 1.0f} };
+    vec4 ld = {lp[0].x - r1.x, lp[0].y - r1.y, lp[0].z - r1.z, lp[0].w - r1.w};
+    float n[4] = {v.normal.x, v.normal.y, v.normal.z, 0.0f}, res[4];
+    MMAT4XVEC4(res, ti_model_view_matrix, n);
+    MVEC3NORMALIZE(res);
+    MVEC3NORMALIZE((float *)&ld);
+    v.li = MVEC3DOT(res, (float *)&ld);
+    v.li = MIN(MAX(0.0f, v.li), 1.0f);
+  } else
+    v.li = 1.0f;
+  v.icolor = v.color0;
+  /* Mapping du cube unitaire vers l'écran */
+  v.x = viewport[0] + ((r2.x + 1.0f) * 0.5f) * (viewport[2] - EPSILON);
+  v.y = viewport[1] + ((r2.y + 1.0f) * 0.5f) * (viewport[3] - EPSILON);
+  v.z = pow((-r2.z + 1.0f) * 0.5f, 0.5);
+  /* sinon pour near = 0.1f et far = 10.0f on peut rendre non linéaire la depth avec */
+  /* v.z = 1.0f - (1.0f / r2.z - 1.0f / 0.1f) / (1.0f / 10.0f - 1.0f / 0.1f); */
+  v.zmod = r1.z;
+  return v;
+}
+
+/*!\brief projette le triangle \a t à l'écran (\a W x \a H) selon la
+ * matrice de model-view \a model_view_matrix et de projection \a projection_matrix.
+ *
+ * Cette fonction utilise \a vtransform sur chaque sommet de la
+ * surface. Elle utilise aussi \a clip2_unit_cube pour connaître l'état
+ * du triangle par rapport au cube unitaire.
+ *
+ * \see vtransform 
+ * \see clip2_unit_cube
+ */
+void stransform(surface_t * s, float * model_view_matrix, float * projection_matrix, float * viewport) {
+  int i, j;
+  float ti_model_view_matrix[16];
+  triangle_t vcull;
+  /* calcul de la transposée de l'inverse de la matrice model-view
+     pour la transformation des normales et le calcul du lambertien
+     utilisé par le shading Gouraud dans vtransform. */
+  memcpy(ti_model_view_matrix, model_view_matrix, sizeof ti_model_view_matrix);
+  MMAT4INVERSE(ti_model_view_matrix);
+  MMAT4TRANSPOSE(ti_model_view_matrix);
+  for(i = 0; i < s->n; ++i) {
+    s->t[i].state = PS_NONE;
+    for(j = 0; j < 3; ++j) {
+      s->t[i].v[j] = vtransform(s, s->t[i].v[j], model_view_matrix, ti_model_view_matrix, projection_matrix, viewport);
+      if(s->options & SO_CULL_BACKFACES) {
+	vcull.v[j].position.x = s->t[i].v[j].x;
+	vcull.v[j].position.y = s->t[i].v[j].y;
+	vcull.v[j].position.z = 0.0f;
+      }
+    }
+    if(s->options & SO_CULL_BACKFACES) {
+      tnormal(&vcull);
+      if(vcull.normal.z <= 0.0f) {
+	s->t[i].state |= PS_CULL;
+	continue;
+      }
+    }
+    clip2_unit_cube(&(s->t[i]));
+  }
+}
+
+/*!\brief multiplie deux matrices : \a res = \a res x \a m */
+void mult_matrix(float * res, float * m) {
+  /* res = res x m */
+  float cpy[16];
+  memcpy(cpy, res, sizeof cpy);
+  MMAT4XMAT4(res, cpy, m);
+}
+
+/*!\brief ajoute (multiplication droite) une translation à la matrice
+ * \a m */
+void translate(float * m, float tx, float ty, float tz) {
+  float mat[] = { 1.0f, 0.0f, 0.0f, tx,
+		  0.0f, 1.0f, 0.0f, ty,
+		  0.0f, 0.0f, 1.0f, tz,
+		  0.0f, 0.0f, 0.0f, 1.0f };
+  mult_matrix(m, mat);
+}
+
+/*!\brief ajoute (multiplication droite) une rotation à la matrice \a
+ * m */
+void rotate(float * m, float angle, float x, float y, float z) {
+  float n = sqrtf(x * x + y * y + z * z);
+  if ( n > 0.0f ) {
+    float a, s, c, cc, x2, y2, z2, xy, yz, zx, xs, ys, zs;
+    float mat[] = { 0.0f, 0.0f, 0.0f, 0.0f,
+		    0.0f, 0.0f, 0.0f, 0.0f,
+		    0.0f, 0.0f, 0.0f, 0.0f,
+		    0.0f, 0.0f, 0.0f, 1.0f };
+    s  = sinf ( a = (angle * (float)M_PI / 180.0f) );
+    cc = 1.0f - (c = cosf ( a ));
+    x /= n;     y /= n;     z /= n;
+    x2 = x * x; y2 = y * y; z2 = z * z;
+    xy = x * y; yz = y * z; zx = z * x;
+    xs = x * s; ys = y * s; zs = z * s;
+    mat[0]  = (cc * x2) + c;
+    mat[1]  = (cc * xy) - zs;
+    mat[2]  = (cc * zx) + ys;
+    /* mat[3]  = 0.0f; */
+    mat[4]  = (cc * xy) + zs;
+    mat[5]  = (cc * y2) + c;
+    mat[6]  = (cc * yz) - xs;
+    /* mat[7]  = 0.0f; */
+    mat[8]  = (cc * zx) - ys;
+    mat[9]  = (cc * yz) + xs;
+    mat[10] = (cc * z2) + c;
+    /* mat[11] = 0.0f; */
+    /* mat[12] = 0.0f; mat[= 0.0f; mat[14] = 0.0f; mat[15] = 1.0f; */
+    mult_matrix(m, mat);
+  }
+}
+
+/*!\brief ajoute (multiplication droite) un scale à la matrice \a m */
+void scale(float * m, float sx, float sy, float sz) {
+  float mat[] = { sx  , 0.0f, 0.0f, 0.0f,
+		  0.0f,   sy, 0.0f, 0.0f,
+		  0.0f, 0.0f,   sz, 0.0f,
+		  0.0f, 0.0f, 0.0f, 1.0f };
+  mult_matrix(m, mat);
+}
+
+/*!\brief simule une free camera, voir la doc de gluLookAt */
+void lookAt(float * m, float eyeX, float eyeY, float eyeZ, float centerX, float centerY, float centerZ, float upX, float upY, float upZ) {
+  float forward[3], side[3], up[3];
+  float mat[] = {
+		 1.0f,       0.0f,       0.0f,       0.0f,
+		 0.0f,       1.0f,       0.0f,       0.0f,
+		 0.0f,       0.0f,       1.0f,       0.0f,
+		 0.0f,       0.0f,       0.0f,       1.0f
+  };
+  forward[0] = centerX - eyeX;
+  forward[1] = centerY - eyeY;
+  forward[2] = centerZ - eyeZ;
+  up[0] = upX;
+  up[1] = upY;
+  up[2] = upZ;
+  MVEC3NORMALIZE(forward);
+  /* side = forward x up */
+  MVEC3CROSS(side, forward, up);
+  MVEC3NORMALIZE(side);
+  /* up = side x forward */
+  MVEC3CROSS(up, side, forward);
+  mat[0] = side[0];
+  mat[1] = side[1];
+  mat[2] = side[2];
+  mat[4] = up[0];
+  mat[5] = up[1];
+  mat[6] = up[2];
+  mat[8] = -forward[0];
+  mat[9] = -forward[1];
+  mat[10] = -forward[2];
+  mult_matrix(m, mat);
+  translate(m, -eyeX, -eyeY, -eyeZ);
+}
+
+/*!\brief intersection triangle-cube unitaire, à compléter (voir le
+ * todo du fichier et le commentaire dans le code) */
+void clip2_unit_cube(triangle_t * t) {
+    int i, oleft = 0, oright = 0, obottom = 0, otop = 0, onear = 0, ofar = 0;
+    for (i = 0; i < 3; ++i) {
+      if(t->v[i].state & PS_OUT_LEFT) ++oleft;
+      if(t->v[i].state & PS_OUT_RIGHT) ++oright;
+      if(t->v[i].state & PS_OUT_BOTTOM) ++obottom;
+      if(t->v[i].state & PS_OUT_TOP) ++otop;
+      if(t->v[i].state & PS_OUT_NEAR) ++onear;
+      if(t->v[i].state & PS_OUT_FAR) ++ofar;
+    }
+    if(!(oleft | oright | obottom | otop | onear | ofar))
+      return;
+    if(oleft == 3 || oright == 3 || obottom == 3 || otop == 3 || onear == 3 || ofar == 3) {
+      t->state |= PS_TOTALLY_OUT;
+      return;
+    }
+    t->state |= PS_PARTIALLY_OUT;
+    /* le cas PARTIALLY_OUT n'est pas réellement géré. Il serait
+       nécessaire à partir d'ici de construire la liste des triangles
+       qui repésentent l'intersection entre le triangle d'origine et
+       le cube unitaire. Ceci permettrait de ne plus avoir besoin de
+       tester si le pixel produit par le raster est bien dans le
+       "screen" avant d'écrire ; et aussi de se passer du "hack"
+       PS_TOO_FAR qui est problématique.  Vous pouvez vous inspirer de
+       ce qui est fait là :
+       https://github.com/erich666/GraphicsGems/blob/master/gems/PolyScan/poly_clip.c
+       en le ramenant au cas d'un triangle.
+    */
+}

window.c

@@ -0,0 +1,213 @@
+/*!\file window.c 
+ * \brief Utilisation du raster DIY comme pipeline de rendu 3D. Cet
+ * exemple montre les géométries disponibles et quelques
+ * transformations dessus.
+ * \author Farès BELHADJ, amsi@up8.edu
+ * \date November 16, 2021.
+ * \todo exercice intéressant à faire : changer la variation de
+ * l'angle de rotation pour qu'il soit dépendant du temps et non du
+ * framerate
+ */
+#include <assert.h>
+/* inclusion des entêtes de fonctions de gestion de primitives simples
+ * de dessin. La lettre p signifie aussi bien primitive que
+ * pédagogique. */
+#include <GL4D/gl4dp.h>
+/* inclure la bibliothèque de rendu DIY */
+#include "rasterize.h"
+
+/* inclusion des entêtes de fonctions de création et de gestion de
+ * fenêtres système ouvrant un contexte favorable à GL4dummies. Cette
+ * partie est dépendante de la bibliothèque SDL2 */
+#include <GL4D/gl4duw_SDL2.h>
+
+/* protos de fonctions locales (static) */
+static void init(void);
+static void draw(void);
+static void key(int keycode);
+static void sortie(void);
+
+/*!\brief une surface représentant un quadrilatère */
+static surface_t * _quad = NULL;
+/*!\brief une surface représentant un cube */
+static surface_t * _cube = NULL;
+/*!\brief une surface représentant une sphere */
+static surface_t * _sphere = NULL;
+
+/* des variable d'états pour activer/désactiver des options de rendu */
+static int _use_tex = 1, _use_color = 1, _use_lighting = 1;
+
+/*!\brief on peut bouger la caméra vers le haut et vers le bas avec cette variable */
+static float _ycam = 3.0f;
+
+/*!\brief paramètre l'application et lance la boucle infinie. */
+int main(int argc, char ** argv) {
+  /* tentative de création d'une fenêtre pour GL4Dummies */
+  if(!gl4duwCreateWindow(argc, argv, /* args du programme */
+			 "The DIY Rasterizer", /* titre */
+			 10, 10, 800, 600, /* x, y, largeur, heuteur */
+			 GL4DW_SHOWN) /* état visible */) {
+    /* ici si échec de la création souvent lié à un problème d'absence
+     * de contexte graphique ou d'impossibilité d'ouverture d'un
+     * contexte OpenGL (au moins 3.2) */
+    return 1;
+  }
+  init();
+  /* mettre en place la fonction d'interception clavier */
+  gl4duwKeyDownFunc(key);
+  /* mettre en place la fonction de display */
+  gl4duwDisplayFunc(draw);
+  /* boucle infinie pour éviter que le programme ne s'arrête et ferme
+   * la fenêtre immédiatement */
+  gl4duwMainLoop();
+  return 0;
+}
+
+/*!\brief init de nos données, spécialement les trois surfaces
+ * utilisées dans ce code */
+void init(void) {
+  GLuint id;
+  vec4 r = {1, 0, 0, 1}, g = {0, 1, 0, 1}, b = {0, 0, 1, 1};
+  /* création d'un screen GL4Dummies (texture dans laquelle nous
+   * pouvons dessiner) aux dimensions de la fenêtre.  IMPORTANT de
+   * créer le screen avant d'utiliser les fonctions liées au
+   * textures */
+  gl4dpInitScreen();
+  /* Pour forcer la désactivation de la synchronisation verticale */
+  SDL_GL_SetSwapInterval(0);
+  /* on créé nos trois type de surfaces */
+  _quad   =   mk_quad();         /* ça fait 2 triangles        */
+  _cube   =   mk_cube();         /* ça fait 2x6 triangles      */
+  _sphere =   mk_sphere(12, 12); /* ça fait 12x12x2 trianles ! */
+  /* on change les couleurs de surfaces */
+  _quad->dcolor = r; _cube->dcolor = b; _sphere->dcolor = g; 
+  /* on leur rajoute à toutes la même texture */
+  id = get_texture_from_BMP("images/tex.bmp");
+  set_texture_id(  _quad, id);
+  set_texture_id(  _cube, id);
+  set_texture_id(_sphere, id);
+  /* si _use_tex != 0, on active l'utilisation de la texture pour les
+   * trois */
+  if(_use_tex) {
+    enable_surface_option(  _quad, SO_USE_TEXTURE);
+    enable_surface_option(  _cube, SO_USE_TEXTURE);
+    enable_surface_option(_sphere, SO_USE_TEXTURE);
+  }
+  /* si _use_lighting != 0, on active l'ombrage */
+  if(_use_lighting) {
+    enable_surface_option(  _quad, SO_USE_LIGHTING);
+    enable_surface_option(  _cube, SO_USE_LIGHTING);
+    enable_surface_option(_sphere, SO_USE_LIGHTING);
+  }
+  /* on désactive le back cull face pour le quadrilatère, ainsi on
+   * peut voir son arrière quand le lighting est inactif */
+  disable_surface_option(_quad, SO_CULL_BACKFACES);
+  /* mettre en place la fonction à appeler en cas de sortie */
+  atexit(sortie);
+}
+
+/*!\brief la fonction appelée à chaque display. */
+void draw(void) {
+  static float a = 0.0f;
+  float model_view_matrix[16], projection_matrix[16], nmv[16];
+  /* effacer l'écran et le buffer de profondeur */
+  gl4dpClearScreen();
+  clear_depth_map();
+  /* des macros facilitant le travail avec des matrices et des
+   * vecteurs se trouvent dans la bibliothèque GL4Dummies, dans le
+   * fichier gl4dm.h */
+  /* charger un frustum dans projection_matrix */
+  MFRUSTUM(projection_matrix, -0.05f, 0.05f, -0.05f, 0.05f, 0.1f, 1000.0f);
+  /* charger la matrice identité dans model-view */
+  MIDENTITY(model_view_matrix);
+  /* on place la caméra en arrière-haut, elle regarde le centre de la scène */
+  lookAt(model_view_matrix, 0, _ycam, 10, 0, 0, 0, 0, 1, 0);
+  /* le quadrilatère est mis à gauche et tourne autour de son axe x */
+  memcpy(nmv, model_view_matrix, sizeof nmv); /* copie model_view_matrix dans nmv */
+  translate(nmv, -3.0f, 0.0f, 0.0f);
+  rotate(nmv, a, 1.0f, 0.0f, 0.0f);
+  transform_n_rasterize(_quad, nmv, projection_matrix);
+  /* le cube est mis à droite et tourne autour de son axe z */
+  memcpy(nmv, model_view_matrix, sizeof nmv); /* copie model_view_matrix dans nmv */
+  translate(nmv, 3.0f, 0.0f, 0.0f);
+  rotate(nmv, a, 0.0f, 0.0f, 1.0f);
+  transform_n_rasterize(_cube, nmv, projection_matrix);
+  /* la sphère est laissée au centre et tourne autour de son axe y */
+  memcpy(nmv, model_view_matrix, sizeof nmv); /* copie model_view_matrix dans nmv */
+  rotate(nmv, a, 0.0f, 1.0f, 0.0f);
+  transform_n_rasterize(_sphere, nmv, projection_matrix);
+  /* déclarer qu'on a changé des pixels du screen (en bas niveau) */
+  gl4dpScreenHasChanged();
+  /* fonction permettant de raffraîchir l'ensemble de la fenêtre*/
+  gl4dpUpdateScreen(NULL);
+  a += 0.1f;
+}
+
+/*!\brief intercepte l'événement clavier pour modifier les options. */
+void key(int keycode) {
+  switch(keycode) {
+  case GL4DK_UP:
+    _ycam += 0.05f;
+    break;
+  case GL4DK_DOWN:
+    _ycam -= 0.05f;
+    break;
+  case GL4DK_t: /* 't' la texture */
+    _use_tex = !_use_tex;
+    if(_use_tex) {
+      enable_surface_option(  _quad, SO_USE_TEXTURE);
+      enable_surface_option(  _cube, SO_USE_TEXTURE);
+      enable_surface_option(_sphere, SO_USE_TEXTURE);
+    } else {
+      disable_surface_option(  _quad, SO_USE_TEXTURE);
+      disable_surface_option(  _cube, SO_USE_TEXTURE);
+      disable_surface_option(_sphere, SO_USE_TEXTURE);
+    }
+    break;
+  case GL4DK_c: /* 'c' utiliser la couleur */
+    _use_color = !_use_color;
+    if(_use_color) {
+      enable_surface_option(  _quad, SO_USE_COLOR);
+      enable_surface_option(  _cube, SO_USE_COLOR);
+      enable_surface_option(_sphere, SO_USE_COLOR);
+    } else { 
+      disable_surface_option(  _quad, SO_USE_COLOR);
+      disable_surface_option(  _cube, SO_USE_COLOR);
+      disable_surface_option(_sphere, SO_USE_COLOR);
+    }
+    break;
+  case GL4DK_l: /* 'l' utiliser l'ombrage par la méthode Gouraud */
+    _use_lighting = !_use_lighting;
+    if(_use_lighting) {
+      enable_surface_option(  _quad, SO_USE_LIGHTING);
+      enable_surface_option(  _cube, SO_USE_LIGHTING);
+      enable_surface_option(_sphere, SO_USE_LIGHTING);
+    } else { 
+      disable_surface_option(  _quad, SO_USE_LIGHTING);
+      disable_surface_option(  _cube, SO_USE_LIGHTING);
+      disable_surface_option(_sphere, SO_USE_LIGHTING);
+    }
+    break;
+  default: break;
+  }
+}
+
+/*!\brief à appeler à la sortie du programme. */
+void sortie(void) {
+  /* on libère nos trois surfaces */
+  if(_quad) {
+    free_surface(_quad);
+    _quad = NULL;
+  }
+  if(_cube) {
+    free_surface(_cube);
+    _cube = NULL;
+  }
+  if(_sphere) {
+    free_surface(_sphere);
+    _sphere = NULL;
+  }
+  /* libère tous les objets produits par GL4Dummies, ici
+   * principalement les screen */
+  gl4duClean(GL4DU_ALL);
+}