add polytopes back

src/aztec/run_domino_shuffling_animation.py

@@ -69,9 +69,7 @@ def make_animation(order, size, filename):
     parser.add_argument(
         "-order", metavar="o", type=int, default=30, help="order of aztec diamond"
     )
-    parser.add_argument(
-        "-size", metavar="s", type=int, default=400, help="image size"
-    )
+    parser.add_argument("-size", metavar="s", type=int, default=400, help="image size")
     parser.add_argument(
         "-filename", metavar="f", default="domino_shuffling.gif", help="output filename"
     )

src/polytopes/README.md

@@ -0,0 +1,5 @@
++ `example_curved_polychora.py`: Render 3d/4d polytopes in POV-Ray (projected to the 3/4-sphere).
++ `example_polyhedra_mirrors_shader.py`: A shader program draws polytopes with mirrors.
++ `example_polytope_animation.py`: Render 3d/4d polytopes in POV-Ray (projected to the 3d space).
++ `example_run_coset_enumeration.py`: Compute coset table of a finitely represented group.
++ `example_wythoff_shader_animation.py`: A shader program exported from Matt Zucker's shadertoy work.

src/polytopes/example_curved_polychora.py

@@ -0,0 +1,299 @@
+"""
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+Render curved 4d polychoron examples in POV-Ray
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+:copyright (c) 2018 by Zhao Liang.
+"""
+import os
+import subprocess
+from fractions import Fraction
+
+from polytopes.models import Polychora
+from polytopes.povray import pov_index_array1d, pov_vector
+
+
+IMAGE_DIR = "polychora_frames"  # directory to save the frames
+POV_EXE = "povray"  # POV-Ray exe binary
+SCENE_FILE = "polychora_curved.pov"  # the main scene file
+IMAGE_SIZE = 600  # image size in pixels
+FRAMES = 1  # number of frames
+IMAGE_QUALITY_LEVEL = 11  # between 0-11
+SUPER_SAMPLING_LEVEL = 5  # between 1-9
+ANTIALIASING_LEVEL = 0.001  # lower for better quality
+DATAFILE_NAME = "polychora-data.inc"  # export data to this file
+
+data_file = os.path.join(os.getcwd(), "povray", DATAFILE_NAME)
+
+if not os.path.exists(IMAGE_DIR):
+    os.makedirs(IMAGE_DIR)
+
+POV_COMMAND = (
+    " cd povray && "
+    + " {} +I{}".format(POV_EXE, SCENE_FILE)
+    + " +W{} +H{}".format(IMAGE_SIZE, IMAGE_SIZE)
+    + " +Q{}".format(IMAGE_QUALITY_LEVEL)
+    + " +A{}".format(ANTIALIASING_LEVEL)
+    + " +R{}".format(SUPER_SAMPLING_LEVEL)
+    + " +KFI0"
+    + " +KFF{}".format(FRAMES - 1)
+    + " -V"
+    + " +O../{}/".format(IMAGE_DIR)
+    + "{}"
+)
+
+POV_TEMPLATE = """
+#declare bg_color = {};
+#declare vertex_size = {};
+#declare edge_size = {};
+#declare camera_loc = {};
+#declare obj_rotation = {};
+#declare size_func = {};
+#declare face_max= {};
+#declare face_min = {};
+#declare face_index = {};
+#declare use_area_light = {};
+
+// this macro is used for adjusting the size of edges
+// according to their positions in the space.
+#macro get_size(q)
+  #local len = vlength(q);
+  #if (size_func = 0)
+    #local len = (1.0 + len * len) / 4;
+  #else #if (size_func = 1)
+    #local len = 2.0 * log(2.0 + len * len);
+  #else
+    #local len = 2.0 * log(1.13 + len * len);
+  #end
+  #end
+  len
+#end
+
+#macro choose_face(i, face_size)
+  #local chosen = false;
+  #for (ind, 0, dimension_size(face_index, 1) - 1)
+    #if (i = face_index[ind])
+      #if (face_size > face_min & face_size < face_max)
+        #local chosen = true;
+      #end
+    #end
+  #end
+  chosen
+#end
+
+#declare vertices = {};
+
+#declare edges = {};
+
+#declare faces = {};
+"""
+
+
+def draw(
+    coxeter_diagram,
+    trunc_type,
+    extra_relations=(),
+    description="polychora",
+    bg_color="SkyBlue",
+    camera_loc=(0, 0, 30),
+    rotation=(0, 0, 0),
+    vertex_size=0.04,
+    edge_size=0.02,
+    size_func=0,
+    face_index=(0,),
+    face_max=3.0,
+    face_min=0.5,
+    use_area_light=False,
+):
+    """
+    Export data to povray .inc file and call the rendering process.
+
+    :param camera_loc:
+        location of the camera.
+
+    :param size_func:
+        choose which sizing funcion to use, currently only 0, 1, 2.
+
+    :param face_index:
+        a list controls which types of faces are shown.
+
+    :param face_max:
+        only faces smaller than this threshold are shown.
+
+    :param face_min:
+        only faces larger than this threshold are shown.
+    """
+    P = Polychora(coxeter_diagram, trunc_type, extra_relations)
+    P.build_geometry()
+    vert_data, edge_data, face_data = P.get_povray_data()
+    with open(data_file, "w") as f:
+        f.write(
+            POV_TEMPLATE.format(
+                bg_color,
+                vertex_size,
+                edge_size,
+                pov_vector(camera_loc),
+                pov_vector(rotation),
+                size_func,
+                face_max,
+                face_min,
+                pov_index_array1d(face_index),
+                int(use_area_light),
+                vert_data,
+                edge_data,
+                face_data,
+            )
+        )
+
+    print(
+        "rendering {}: {} vertices, {} edges, {} faces".format(
+            description, P.num_vertices, P.num_edges, P.num_faces
+        )
+    )
+
+    process = subprocess.Popen(
+        POV_COMMAND.format(description),
+        shell=True,
+        stderr=subprocess.PIPE,
+        stdin=subprocess.PIPE,
+        stdout=subprocess.PIPE,
+    )
+
+    _, err = process.communicate()
+    if process.returncode:
+        print(type(err), err)
+        raise IOError("POVRay error: " + err.decode("ascii"))
+
+
+def main():
+    draw(
+        (3, 2, 2, 3, 2, 3),
+        (1, 0, 0, 0),
+        description="5-cell",
+        camera_loc=(0, 0, 120),
+        vertex_size=0.08,
+        rotation=(-30, 60, 0),
+        edge_size=0.04,
+        size_func=1,
+    )
+
+    draw(
+        (4, 2, 2, 3, 2, 3),
+        (1, 0, 0, 0),
+        description="4d-cube",
+        camera_loc=(0, 0, 130),
+        vertex_size=0.06,
+        rotation=(60, 0, 0),
+        edge_size=0.03,
+        size_func=1,
+        face_min=0.2,
+        face_max=0.8,
+    )
+
+    draw(
+        (3, 2, 2, 3, 2, 4),
+        (1, 0, 0, 0),
+        description="16-cell",
+        camera_loc=(0, 0, 160),
+        vertex_size=0.08,
+        edge_size=0.03,
+        size_func=2,
+        face_min=1.0,
+        face_max=1.2,
+    )
+
+    draw(
+        (3, 2, 2, 4, 2, 3),
+        (1, 0, 0, 0),
+        description="24-cell",
+        camera_loc=(0, 0, 200),
+        vertex_size=0.06,
+        edge_size=0.04,
+        size_func=2,
+        face_min=0.2,
+        face_max=0.8,
+    )
+
+    draw(
+        (5, 2, 2, 3, 2, 3),
+        (1, 0, 0, 0),
+        description="120-cell",
+        camera_loc=(0, 0, 400),
+        vertex_size=0.05,
+        edge_size=0.025,
+        size_func=0,
+        face_min=3.0,
+        face_max=100.0,
+    )
+
+    draw(
+        (3, 2, 2, 3, 2, 5),
+        (1, 0, 0, 0),
+        description="600-cell",
+        bg_color="White",
+        camera_loc=(0, 0, 500),
+        vertex_size=0.12,
+        edge_size=0.04,
+        size_func=2,
+        face_max=4.0,
+        face_min=3.0,
+    )
+
+    draw(
+        (3, 2, 2, 3, 2, 4),
+        (1, 0, 0, 1),
+        description="runcinated-16-cell",
+        bg_color="White",
+        camera_loc=(0, 0, 450),
+        vertex_size=0.1,
+        face_index=(0, 1, 2, 3),
+        edge_size=0.04,
+        size_func=1,
+        face_min=0,
+        face_max=3,
+    )
+
+    draw(
+        (5, 2, 2, 3, 2, 3),
+        (1, 0, 0, 1),
+        description="runcinated-120-cell",
+        camera_loc=(0, 0, 360),
+        vertex_size=0.028,
+        edge_size=0.014,
+        face_min=20,
+    )
+
+    # this is the settings I used to render the movie at
+    # http://pywonderland.com/images/polytopes/rectified-grand-stellated-120-cell.mp4
+    # (the parameters are not exactly the same but very similar)
+    # take quite a while to render.
+    draw(
+        (Fraction(5, 2), 2, 2, 5, 2, Fraction(5, 2)),
+        (0, 1, 0, 0),
+        extra_relations=((0, 1, 2, 1) * 3, (1, 2, 3, 2) * 3),
+        description="rectified-grand-stellated-120-cell",
+        size_func=1,
+        vertex_size=0.06,
+        edge_size=0.03,
+        use_area_light=1,
+        face_max=0.0,
+        camera_loc=(0, 0, 400),
+    )
+
+    draw(
+        (Fraction(5, 2), 2, 2, 5, 2, Fraction(5, 2)),
+        (0, 1, 1, 0),
+        extra_relations=((0, 1, 2, 1) * 3, (1, 2, 3, 2) * 3),
+        description="runcinated-grand-stellated-120-cell",
+        size_func=1,
+        vertex_size=0.06,
+        edge_size=0.03,
+        use_area_light=1,
+        face_min=0.3,
+        face_max=1,
+        camera_loc=(0, 0, 380),
+    )
+
+
+if __name__ == "__main__":
+    main()