Merge branch '3b1b:master' into master

manimlib/__main__.py

@@ -10,7 +10,7 @@ def main():
     print(f"ManimGL \033[32mv{__version__}\033[0m")
 
     args = manimlib.config.parse_cli()
-    if args.version and args.file == None:
+    if args.version and args.file is None:
         return
     if args.log_level:
         manimlib.logger.log.setLevel(args.log_level)
@@ -24,5 +24,6 @@ def main():
         for scene in scenes:
             scene.run()
 
+
 if __name__ == "__main__":
     main()

manimlib/animation/creation.py

@@ -174,16 +174,12 @@ class ShowSubmobjectsOneByOne(ShowIncreasingSubsets):
         "int_func": np.ceil,
     }
 
-    def __init__(self, group, **kwargs):
-        new_group = Group(*group)
-        super().__init__(new_group, **kwargs)
-
     def update_submobject_list(self, index):
         # N = len(self.all_submobs)
         if index == 0:
             self.mobject.set_submobjects([])
         else:
-            self.mobject.set_submobjects(self.all_submobs[index - 1])
+            self.mobject.set_submobjects([self.all_submobs[index - 1]])
 
 
 # TODO, this is broken...

manimlib/animation/indication.py

@@ -224,6 +224,8 @@ class FlashAround(VShowPassingFlash):
     def __init__(self, mobject, **kwargs):
         digest_config(self, kwargs)
         path = self.get_path(mobject)
+        if mobject.is_fixed_in_frame:
+            path.fix_in_frame()
         path.insert_n_curves(self.n_inserted_curves)
         path.set_points(path.get_points_without_null_curves())
         path.set_stroke(self.color, self.stroke_width)

manimlib/camera/camera.py

@@ -1,4 +1,5 @@
 import moderngl
+import math
 from colour import Color
 import OpenGL.GL as gl
 
@@ -121,6 +122,15 @@ class CameraFrame(Mobject):
         self.refresh_rotation_matrix()
         return self
 
+    def get_theta(self):
+        return self.data["euler_angles"][0]
+
+    def get_phi(self):
+        return self.data["euler_angles"][1]
+
+    def get_gamma(self):
+        return self.data["euler_angles"][2]
+
     def get_shape(self):
         return (self.get_width(), self.get_height())
 
@@ -139,6 +149,16 @@ class CameraFrame(Mobject):
     def get_focal_distance(self):
         return self.focal_distance * self.get_height()
 
+    def get_implied_camera_location(self):
+        theta, phi, gamma = self.get_euler_angles()
+        dist = self.get_focal_distance()
+        x, y, z = self.get_center()
+        return (
+            x + dist * math.sin(theta) * math.sin(phi),
+            y - dist * math.cos(theta) * math.sin(phi),
+            z + dist * math.cos(phi)
+        )
+
     def interpolate(self, *args, **kwargs):
         super().interpolate(*args, **kwargs)
         self.refresh_rotation_matrix()
@@ -194,20 +214,30 @@ class Camera(object):
             fbo = self.get_fbo(ctx, 0)
         else:
             fbo = ctx.detect_framebuffer()
+        self.ctx = ctx
+        self.fbo = fbo
+        self.set_ctx_blending()
 
         # For multisample antialiasing
         fbo_msaa = self.get_fbo(ctx, self.samples)
         fbo_msaa.use()
+        self.fbo_msaa = fbo_msaa
 
-        ctx.enable(moderngl.BLEND)
+    def set_ctx_blending(self, enable=True):
-        ctx.blend_func = (
+        if enable:
+            self.ctx.enable(moderngl.BLEND)
+        else:
+            self.ctx.disable(moderngl.BLEND)
+        self.ctx.blend_func = (
             moderngl.SRC_ALPHA, moderngl.ONE_MINUS_SRC_ALPHA,
-            moderngl.ONE, moderngl.ONE
+            # moderngl.ONE, moderngl.ONE
         )
 
-        self.ctx = ctx
+    def set_ctx_depth_test(self, enable=True):
-        self.fbo = fbo
+        if enable:
-        self.fbo_msaa = fbo_msaa
+            self.ctx.enable(moderngl.DEPTH_TEST)
+        else:
+            self.ctx.disable(moderngl.DEPTH_TEST)
 
     def init_light_source(self):
         self.light_source = Point(self.light_source_position)
@@ -297,6 +327,9 @@ class Camera(object):
     def get_frame_center(self):
         return self.frame.get_center()
 
+    def get_location(self):
+        return self.frame.get_implied_camera_location()
+
     def resize_frame_shape(self, fixed_dimension=0):
         """
         Changes frame_shape to match the aspect ratio
@@ -327,17 +360,11 @@ class Camera(object):
         shader_wrapper = render_group["shader_wrapper"]
         shader_program = render_group["prog"]
         self.set_shader_uniforms(shader_program, shader_wrapper)
-        self.update_depth_test(shader_wrapper)
+        self.set_ctx_depth_test(shader_wrapper.depth_test)
         render_group["vao"].render(int(shader_wrapper.render_primitive))
         if render_group["single_use"]:
             self.release_render_group(render_group)
 
-    def update_depth_test(self, shader_wrapper):
-        if shader_wrapper.depth_test:
-            self.ctx.enable(moderngl.DEPTH_TEST)
-        else:
-            self.ctx.disable(moderngl.DEPTH_TEST)
-
     def get_render_group_list(self, mobject):
         try:
             return self.static_mobject_to_render_group_list[id(mobject)]
@@ -410,7 +437,7 @@ class Camera(object):
         for name, path in shader_wrapper.texture_paths.items():
             tid = self.get_texture_id(path)
             shader[name].value = tid
-        for name, value in it.chain(shader_wrapper.uniforms.items(), self.perspective_uniforms.items()):
+        for name, value in it.chain(self.perspective_uniforms.items(), shader_wrapper.uniforms.items()):
             try:
                 if isinstance(value, np.ndarray):
                     value = tuple(value)
@@ -427,14 +454,18 @@ class Camera(object):
         anti_alias_width = self.anti_alias_width / (ph / fh)
         # Orient light
         rotation = frame.get_inverse_camera_rotation_matrix()
-        light_pos = self.light_source.get_location()
+        offset = frame.get_center()
-        light_pos = np.dot(rotation, light_pos)
+        light_pos = np.dot(
+            rotation, self.light_source.get_location() + offset
+        )
+        cam_pos = self.frame.get_implied_camera_location()  # TODO
 
         self.perspective_uniforms = {
             "frame_shape": frame.get_shape(),
             "anti_alias_width": anti_alias_width,
-            "camera_center": tuple(frame.get_center()),
+            "camera_offset": tuple(offset),
             "camera_rotation": tuple(np.array(rotation).T.flatten()),
+            "camera_position": tuple(cam_pos),
             "light_source_position": tuple(light_pos),
             "focal_distance": frame.get_focal_distance(),
         }
@@ -445,6 +476,8 @@ class Camera(object):
 
     def get_texture_id(self, path):
         if path not in self.path_to_texture:
+            if self.n_textures == 15:  # I have no clue why this is needed
+                self.n_textures += 1
             tid = self.n_textures
             self.n_textures += 1
             im = Image.open(path).convert("RGBA")
@@ -468,4 +501,5 @@ class Camera(object):
 class ThreeDCamera(Camera):
     CONFIG = {
         "samples": 4,
+        "anti_alias_width": 0,
     }

manimlib/config.py

@@ -5,6 +5,7 @@ import importlib
 import os
 import sys
 import yaml
+from contextlib import contextmanager
 from screeninfo import get_monitors
 
 from manimlib.utils.config_ops import merge_dicts_recursively
@@ -12,6 +13,9 @@ from manimlib.utils.init_config import init_customization
 from manimlib.logger import log
 
 
+__config_file__ = "custom_config.yml"
+
+
 def parse_cli():
     try:
         parser = argparse.ArgumentParser()
@@ -112,6 +116,12 @@ def parse_cli():
                  "in two comma separated values, e.g. \"3,6\", it will end"
                  "the rendering at the second value",
         )
+        parser.add_argument(
+            "-e", "--embed",
+            help="Takes a line number as an argument, and results"
+                 "in the scene being called as if the line `self.embed()`"
+                 "was inserted into the scene code at that line number."
+        )
         parser.add_argument(
             "-r", "--resolution",
             help="Resolution, passed as \"WxH\", e.g. \"1920x1080\"",
@@ -162,14 +172,30 @@ def get_manim_dir():
 def get_module(file_name):
     if file_name is None:
         return None
-    else:
+    module_name = file_name.replace(os.sep, ".").replace(".py", "")
-        module_name = file_name.replace(os.sep, ".").replace(".py", "")
+    spec = importlib.util.spec_from_file_location(module_name, file_name)
-        spec = importlib.util.spec_from_file_location(module_name, file_name)
+    module = importlib.util.module_from_spec(spec)
-        module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
-        spec.loader.exec_module(module)
+    return module
-        return module
+
+
+@contextmanager
+def insert_embed_line(file_name, lineno):
+    with open(file_name, 'r') as fp:
+        lines = fp.readlines()
+    line = lines[lineno - 1]
+    n_spaces = len(line) - len(line.lstrip())
+    lines.insert(lineno - 1, " " * n_spaces + "self.embed()\n")
+
+    alt_file = file_name.replace(".py", "_inserted_embed.py")
+    with open(alt_file, 'w') as fp:
+        fp.writelines(lines)
+
+    try:
+        yield alt_file
+    finally:
+        os.remove(alt_file)
 
-__config_file__ = "custom_config.yml"
 
 def get_custom_config():
     global __config_file__
@@ -197,9 +223,11 @@ def get_custom_config():
 
 def check_temporary_storage(config):
     if config["directories"]["temporary_storage"] == "" and sys.platform == "win32":
-        log.warning("You may be using Windows platform and have not specified the path of"
+        log.warning(
+            "You may be using Windows platform and have not specified the path of"
             " `temporary_storage`, which may cause OSError. So it is recommended"
-            " to specify the `temporary_storage` in the config file (.yml)")
+            " to specify the `temporary_storage` in the config file (.yml)"
+        )
 
 
 def get_configuration(args):
@@ -229,8 +257,10 @@ def get_configuration(args):
 
     elif not os.path.exists(__config_file__):
         log.info(f"Using the default configuration file, which you can modify in `{global_defaults_file}`")
-        log.info("If you want to create a local configuration file, you can create a file named"
+        log.info(
-            f" `{__config_file__}`, or run `manimgl --config`")
+            "If you want to create a local configuration file, you can create a file named"
+            f" `{__config_file__}`, or run `manimgl --config`"
+        )
 
     custom_config = get_custom_config()
     check_temporary_storage(custom_config)
@@ -260,7 +290,12 @@ def get_configuration(args):
         "quiet": args.quiet,
     }
 
-    module = get_module(args.file)
+    if args.embed is None:
+        module = get_module(args.file)
+    else:
+        with insert_embed_line(args.file, int(args.embed)) as alt_file:
+            module = get_module(alt_file)
+
     config = {
         "module": module,
         "scene_names": args.scene_names,
@@ -282,7 +317,7 @@ def get_configuration(args):
     mon_index = custom_config["window_monitor"]
     monitor = monitors[min(mon_index, len(monitors) - 1)]
     window_width = monitor.width
-    if not args.full_screen:
+    if not (args.full_screen or custom_config["full_screen"]):
         window_width //= 2
     window_height = window_width * 9 // 16
     config["window_config"] = {

manimlib/default_config.yml

@@ -34,6 +34,7 @@ style:
 # the window on the monitor, e.g. "960,540"
 window_position: UR
 window_monitor: 0
+full_screen: False
 # If break_into_partial_movies is set to True, then many small
 # files will be written corresponding to each Scene.play and
 # Scene.wait call, and these files will then be combined

manimlib/extract_scene.py

@@ -1,5 +1,6 @@
 import inspect
 import sys
+import copy
 
 from manimlib.scene.scene import Scene
 from manimlib.config import get_custom_config
@@ -38,7 +39,7 @@ def prompt_user_for_choice(scene_classes):
             "\nScene Name or Number: "
         )
         return [
-            name_to_class[split_str] if not split_str.isnumeric() else scene_classes[int(split_str)-1]
+            name_to_class[split_str] if not split_str.isnumeric() else scene_classes[int(split_str) - 1]
             for split_str in user_input.replace(" ", "").split(",")
         ]
     except IndexError:
@@ -67,6 +68,24 @@ def get_scene_config(config):
     ])
 
 
+def compute_total_frames(scene_class, scene_config):
+    """
+    When a scene is being written to file, a copy of the scene is run with
+    skip_animations set to true so as to count how many frames it will require.
+    This allows for a total progress bar on rendering, and also allows runtime
+    errors to be exposed preemptively for long running scenes. The final frame
+    is saved by default, so that one can more quickly check that the last frame
+    looks as expected.
+    """
+    pre_config = copy.deepcopy(scene_config)
+    pre_config["file_writer_config"]["write_to_movie"] = False
+    pre_config["file_writer_config"]["save_last_frame"] = True
+    pre_config["skip_animations"] = True
+    pre_scene = scene_class(**pre_config)
+    pre_scene.run()
+    return int(pre_scene.time * scene_config["camera_config"]["frame_rate"])
+
+
 def get_scenes_to_render(scene_classes, scene_config, config):
     if config["write_all"]:
         return [sc(**scene_config) for sc in scene_classes]
@@ -76,6 +95,9 @@ def get_scenes_to_render(scene_classes, scene_config, config):
         found = False
         for scene_class in scene_classes:
             if scene_class.__name__ == scene_name:
+                fw_config = scene_config["file_writer_config"]
+                if fw_config["write_to_movie"]:
+                    fw_config["total_frames"] = compute_total_frames(scene_class, scene_config)
                 scene = scene_class(**scene_config)
                 result.append(scene)
                 found = True

manimlib/mobject/coordinate_systems.py

@@ -151,14 +151,14 @@ class CoordinateSystem():
         else:
             alpha = binary_search(
                 function=lambda a: self.point_to_coords(
-                    graph.point_from_proportion(a)
+                    graph.quick_point_from_proportion(a)
                 )[0],
                 target=x,
                 lower_bound=self.x_range[0],
                 upper_bound=self.x_range[1],
             )
             if alpha is not None:
-                return graph.point_from_proportion(alpha)
+                return graph.quick_point_from_proportion(alpha)
             else:
                 return None
 

manimlib/mobject/geometry.py

@@ -507,6 +507,7 @@ class Line(TipableVMobject):
 
     def set_length(self, length, **kwargs):
         self.scale(length / self.get_length(), **kwargs)
+        return self
 
 
 class DashedLine(Line):

manimlib/mobject/mobject.py

@@ -43,10 +43,13 @@ class Mobject(object):
         "opacity": 1,
         "dim": 3,  # TODO, get rid of this
         # Lighting parameters
-        # Positive gloss up to 1 makes it reflect the light.
+        # ...
-        "gloss": 0.0,
+        # Larger reflectiveness makes things brighter when facing the light
-        # Positive shadow up to 1 makes a side opposite the light darker
+        "reflectiveness": 0.0,
+        # Larger shadow makes faces opposite the light darker
         "shadow": 0.0,
+        # Makes parts bright where light gets reflected toward the camera
+        "gloss": 0.0,
         # For shaders
         "shader_folder": "",
         "render_primitive": moderngl.TRIANGLE_STRIP,
@@ -82,11 +85,11 @@ class Mobject(object):
     def __str__(self):
         return self.__class__.__name__
 
-    def __add__(self, other : 'Mobject') -> 'Mobject':
+    def __add__(self, other: 'Mobject') -> 'Mobject':
         assert(isinstance(other, Mobject))
         return self.get_group_class()(self, other)
 
-    def __mul__(self, other : 'int') -> 'Mobject':
+    def __mul__(self, other: 'int') -> 'Mobject':
         assert(isinstance(other, int))
         return self.replicate(other)
 
@@ -102,6 +105,7 @@ class Mobject(object):
             "is_fixed_in_frame": float(self.is_fixed_in_frame),
             "gloss": self.gloss,
             "shadow": self.shadow,
+            "reflectiveness": self.reflectiveness,
         }
 
     def init_colors(self):
@@ -153,6 +157,7 @@ class Mobject(object):
         for mob in self.get_family():
             for key in mob.data:
                 mob.data[key] = mob.data[key][::-1]
+        self.refresh_unit_normal()
         return self
 
     def apply_points_function(self, func, about_point=None, about_edge=ORIGIN, works_on_bounding_box=False):
@@ -308,6 +313,11 @@ class Mobject(object):
         self.assemble_family()
         return self
 
+    def insert_submobject(self, index, new_submob):
+        self.submobjects.insert(index, new_submob)
+        self.assemble_family()
+        return self
+
     def set_submobjects(self, submobject_list):
         self.remove(*self.submobjects)
         self.add(*submobject_list)
@@ -394,6 +404,7 @@ class Mobject(object):
             self.submobjects.sort(key=submob_func)
         else:
             self.submobjects.sort(key=lambda m: point_to_num_func(m.get_center()))
+        self.assemble_family()
         return self
 
     def shuffle(self, recurse=False):
@@ -401,6 +412,7 @@ class Mobject(object):
             for submob in self.submobjects:
                 submob.shuffle(recurse=True)
         random.shuffle(self.submobjects)
+        self.assemble_family()
         return self
 
     # Copying
@@ -974,12 +986,12 @@ class Mobject(object):
     def fade(self, darkness=0.5, recurse=True):
         self.set_opacity(1.0 - darkness, recurse=recurse)
 
-    def get_gloss(self):
+    def get_reflectiveness(self):
-        return self.uniforms["gloss"]
+        return self.uniforms["reflectiveness"]
 
-    def set_gloss(self, gloss, recurse=True):
+    def set_reflectiveness(self, reflectiveness, recurse=True):
         for mob in self.get_family(recurse):
-            mob.uniforms["gloss"] = gloss
+            mob.uniforms["reflectiveness"] = reflectiveness
         return self
 
     def get_shadow(self):
@@ -990,6 +1002,14 @@ class Mobject(object):
             mob.uniforms["shadow"] = shadow
         return self
 
+    def get_gloss(self):
+        return self.uniforms["gloss"]
+
+    def set_gloss(self, gloss, recurse=True):
+        for mob in self.get_family(recurse):
+            mob.uniforms["gloss"] = gloss
+        return self
+
     # Background rectangle
 
     def add_background_rectangle(self, color=None, opacity=0.75, **kwargs):
@@ -1371,11 +1391,13 @@ class Mobject(object):
     @affects_shader_info_id
     def fix_in_frame(self):
         self.uniforms["is_fixed_in_frame"] = 1.0
+        self.is_fixed_in_frame = True
         return self
 
     @affects_shader_info_id
     def unfix_from_frame(self):
         self.uniforms["is_fixed_in_frame"] = 0.0
+        self.is_fixed_in_frame = False
         return self
 
     @affects_shader_info_id
@@ -1618,7 +1640,7 @@ class Group(Mobject):
         Mobject.__init__(self, **kwargs)
         self.add(*mobjects)
 
-    def __add__(self, other : 'Mobject' or 'Group'):
+    def __add__(self, other: 'Mobject' or 'Group'):
         assert(isinstance(other, Mobject))
         return self.add(other)
 

manimlib/mobject/svg/drawings.py

@@ -200,12 +200,11 @@ class Laptop(VGroup):
 
 class VideoIcon(SVGMobject):
     CONFIG = {
-        "file_name": "video_icon",
         "width": FRAME_WIDTH / 12.,
     }
 
     def __init__(self, **kwargs):
-        SVGMobject.__init__(self, **kwargs)
+        super().__init__(file_name="video_icon", **kwargs)
         self.center()
         self.set_width(self.width)
         self.set_stroke(color=WHITE, width=0)

manimlib/mobject/svg/text_mobject.py

@@ -1,4 +1,3 @@
-import copy
 import hashlib
 import os
 import re

manimlib/mobject/three_dimensions.py

@@ -6,6 +6,7 @@ from manimlib.mobject.types.surface import SGroup
 from manimlib.mobject.types.vectorized_mobject import VGroup
 from manimlib.mobject.types.vectorized_mobject import VMobject
 from manimlib.mobject.geometry import Square
+from manimlib.utils.bezier import interpolate
 from manimlib.utils.config_ops import digest_config
 from manimlib.utils.space_ops import get_norm
 from manimlib.utils.space_ops import z_to_vector
@@ -14,9 +15,9 @@ from manimlib.utils.space_ops import compass_directions
 
 class SurfaceMesh(VGroup):
     CONFIG = {
-        "resolution": (21, 21),
+        "resolution": (21, 11),
         "stroke_width": 1,
-        "normal_nudge": 1e-3,
+        "normal_nudge": 1e-2,
         "depth_test": True,
         "flat_stroke": False,
     }
@@ -32,8 +33,11 @@ class SurfaceMesh(VGroup):
 
         full_nu, full_nv = uv_surface.resolution
         part_nu, part_nv = self.resolution
-        u_indices = np.linspace(0, full_nu, part_nu).astype(int)
+        # 'indices' are treated as floats. Later, there will be
-        v_indices = np.linspace(0, full_nv, part_nv).astype(int)
+        # an interpolation between the floor and ceiling of these
+        # indices
+        u_indices = np.linspace(0, full_nu - 1, part_nu)
+        v_indices = np.linspace(0, full_nv - 1, part_nv)
 
         points, du_points, dv_points = uv_surface.get_surface_points_and_nudged_points()
         normals = uv_surface.get_unit_normals()
@@ -42,12 +46,28 @@ class SurfaceMesh(VGroup):
 
         for ui in u_indices:
             path = VMobject()
-            full_ui = full_nv * ui
+            # full_ui = full_nv * ui
-            path.set_points_smoothly(nudged_points[full_ui:full_ui + full_nv])
+            # path.set_points_smoothly(
+            #     nudged_points[full_ui:full_ui + full_nv]
+            # )
+            low_ui = full_nv * int(math.floor(ui))
+            high_ui = full_nv * int(math.ceil(ui))
+            path.set_points_smoothly(interpolate(
+                nudged_points[low_ui:low_ui + full_nv],
+                nudged_points[high_ui:high_ui + full_nv],
+                ui % 1
+            ))
             self.add(path)
         for vi in v_indices:
             path = VMobject()
-            path.set_points_smoothly(nudged_points[vi::full_nv])
+            # path.set_points_smoothly(
+            #     nudged_points[vi::full_nv]
+            # )
+            path.set_points_smoothly(interpolate(
+                nudged_points[int(math.floor(vi))::full_nv],
+                nudged_points[int(math.ceil(vi))::full_nv],
+                vi % 1
+            ))
             self.add(path)
 
 

manimlib/mobject/types/dot_cloud.py

@@ -17,6 +17,7 @@ class DotCloud(PMobject):
         "color": GREY_C,
         "opacity": 1,
         "radius": DEFAULT_DOT_RADIUS,
+        "glow_factor": 0,
         "shader_folder": "true_dot",
         "render_primitive": moderngl.POINTS,
         "shader_dtype": [
@@ -36,6 +37,10 @@ class DotCloud(PMobject):
         self.data["radii"] = np.zeros((1, 1))
         self.set_radius(self.radius)
 
+    def init_uniforms(self):
+        super().init_uniforms()
+        self.uniforms["glow_factor"] = self.glow_factor
+
     def to_grid(self, n_rows, n_cols, n_layers=1,
                 buff_ratio=None,
                 h_buff_ratio=1.0,
@@ -85,6 +90,12 @@ class DotCloud(PMobject):
     def get_radius(self):
         return self.get_radii().max()
 
+    def set_glow_factor(self, glow_factor):
+        self.uniforms["glow_factor"] = glow_factor
+
+    def get_glow_factor(self):
+        return self.uniforms["glow_factor"]
+
     def compute_bounding_box(self):
         bb = super().compute_bounding_box()
         radius = self.get_radius()
@@ -98,8 +109,8 @@ class DotCloud(PMobject):
             self.set_radii(scale_factor * self.get_radii())
         return self
 
-    def make_3d(self, gloss=0.5, shadow=0.2):
+    def make_3d(self, reflectiveness=0.5, shadow=0.2):
-        self.set_gloss(gloss)
+        self.set_reflectiveness(reflectiveness)
         self.set_shadow(shadow)
         self.apply_depth_test()
         return self

manimlib/mobject/types/surface.py

@@ -20,7 +20,8 @@ class Surface(Mobject):
         "resolution": (101, 101),
         "color": GREY,
         "opacity": 1.0,
-        "gloss": 0.3,
+        "reflectiveness": 0.3,
+        "gloss": 0.1,
         "shadow": 0.4,
         "prefered_creation_axis": 1,
         # For du and dv steps.  Much smaller and numerical error
@@ -161,6 +162,11 @@ class Surface(Mobject):
             tri_is[k::3] = tri_is[k::3][indices]
         return self
 
+    def always_sort_to_camera(self, camera):
+        self.add_updater(lambda m: m.sort_faces_back_to_front(
+            camera.get_location() - self.get_center()
+        ))
+
     # For shaders
     def get_shader_data(self):
         s_points, du_points, dv_points = self.get_surface_points_and_nudged_points()

manimlib/mobject/types/vectorized_mobject.py

@@ -12,6 +12,7 @@ from manimlib.utils.bezier import get_smooth_quadratic_bezier_handle_points
 from manimlib.utils.bezier import get_smooth_cubic_bezier_handle_points
 from manimlib.utils.bezier import get_quadratic_approximation_of_cubic
 from manimlib.utils.bezier import interpolate
+from manimlib.utils.bezier import inverse_interpolate
 from manimlib.utils.bezier import integer_interpolate
 from manimlib.utils.bezier import partial_quadratic_bezier_points
 from manimlib.utils.color import rgb_to_hex
@@ -74,7 +75,6 @@ class VMobject(Mobject):
         self.needs_new_triangulation = True
         self.triangulation = np.zeros(0, dtype='i4')
         super().__init__(**kwargs)
-        self.refresh_unit_normal()
 
     def get_group_class(self):
         return VGroup
@@ -135,6 +135,10 @@ class VMobject(Mobject):
                 mob.draw_stroke_behind_fill = background
         return self
 
+    def set_backstroke(self, color=BLACK, width=3, background=True):
+        self.set_stroke(color, width, background=background)
+        return self
+
     def align_stroke_width_data_to_points(self, recurse=True):
         for mob in self.get_family(recurse):
             mob.data["stroke_width"] = resize_with_interpolation(
@@ -150,6 +154,7 @@ class VMobject(Mobject):
                   stroke_rgba=None,
                   stroke_width=None,
                   stroke_background=True,
+                  reflectiveness=None,
                   gloss=None,
                   shadow=None,
                   recurse=True):
@@ -177,6 +182,8 @@ class VMobject(Mobject):
                 background=stroke_background,
             )
 
+        if reflectiveness is not None:
+            self.set_reflectiveness(reflectiveness, recurse=recurse)
         if gloss is not None:
             self.set_gloss(gloss, recurse=recurse)
         if shadow is not None:
@@ -185,10 +192,11 @@ class VMobject(Mobject):
 
     def get_style(self):
         return {
-            "fill_rgba": self.data['fill_rgba'],
+            "fill_rgba": self.data['fill_rgba'].copy(),
-            "stroke_rgba": self.data['stroke_rgba'],
+            "stroke_rgba": self.data['stroke_rgba'].copy(),
-            "stroke_width": self.data['stroke_width'],
+            "stroke_width": self.data['stroke_width'].copy(),
             "stroke_background": self.draw_stroke_behind_fill,
+            "reflectiveness": self.get_reflectiveness(),
             "gloss": self.get_gloss(),
             "shadow": self.get_shadow(),
         }
@@ -218,16 +226,17 @@ class VMobject(Mobject):
         return self
 
     def fade(self, darkness=0.5, recurse=True):
-        factor = 1.0 - darkness
+        mobs = self.get_family() if recurse else [self]
-        self.set_fill(
+        for mob in mobs:
-            opacity=factor * self.get_fill_opacity(),
+            factor = 1.0 - darkness
-            recurse=False,
+            mob.set_fill(
-        )
+                opacity=factor * mob.get_fill_opacity(),
-        self.set_stroke(
+                recurse=False,
-            opacity=factor * self.get_stroke_opacity(),
+            )
-            recurse=False,
+            mob.set_stroke(
-        )
+                opacity=factor * mob.get_stroke_opacity(),
-        super().fade(darkness, recurse)
+                recurse=False,
+            )
         return self
 
     def get_fill_colors(self):
@@ -277,9 +286,9 @@ class VMobject(Mobject):
         return self.get_stroke_opacities()[0]
 
     def get_color(self):
-        if self.has_stroke():
+        if self.has_fill():
-            return self.get_stroke_color()
+            return self.get_fill_color()
-        return self.get_fill_color()
+        return self.get_stroke_color()
 
     def has_stroke(self):
         return self.get_stroke_widths().any() and self.get_stroke_opacities().any()
@@ -504,10 +513,10 @@ class VMobject(Mobject):
         nppc = self.n_points_per_curve
         remainder = len(points) % nppc
         points = points[:len(points) - remainder]
-        return [
+        return (
             points[i:i + nppc]
             for i in range(0, len(points), nppc)
-        ]
+        )
 
     def get_bezier_tuples(self):
         return self.get_bezier_tuples_from_points(self.get_points())
@@ -543,12 +552,35 @@ class VMobject(Mobject):
     def get_num_curves(self):
         return self.get_num_points() // self.n_points_per_curve
 
-    def point_from_proportion(self, alpha):
+    def quick_point_from_proportion(self, alpha):
+        # Assumes all curves have the same length, so is inaccurate
         num_curves = self.get_num_curves()
         n, residue = integer_interpolate(0, num_curves, alpha)
         curve_func = self.get_nth_curve_function(n)
         return curve_func(residue)
 
+    def point_from_proportion(self, alpha):
+        if alpha <= 0:
+            return self.get_start()
+        elif alpha >= 1:
+            return self.get_end()
+
+        partials = [0]
+        for tup in self.get_bezier_tuples():
+            # Approximate length with straight line from start to end
+            arclen = get_norm(tup[0] - tup[-1])
+            partials.append(partials[-1] + arclen)
+        full = partials[-1]
+        if full == 0:
+            return self.get_start()
+        # First index where the partial lenth is more alpha times the full length
+        i = next(
+            (i for i, x in enumerate(partials) if x >= full * alpha),
+            len(partials)  # Default
+        )
+        residue = inverse_interpolate(partials[i - 1] / full, partials[i] / full, alpha)
+        return self.get_nth_curve_function(i - 1)(residue)
+
     def get_anchors_and_handles(self):
         """
         returns anchors1, handles, anchors2,
@@ -629,17 +661,19 @@ class VMobject(Mobject):
         area_vect = self.get_area_vector()
         area = get_norm(area_vect)
         if area > 0:
-            return area_vect / area
+            normal = area_vect / area
         else:
             points = self.get_points()
-            return get_unit_normal(
+            normal = get_unit_normal(
                 points[1] - points[0],
                 points[2] - points[1],
             )
+        self.data["unit_normal"][:] = normal
+        return normal
 
     def refresh_unit_normal(self):
         for mob in self.get_family():
-            mob.data["unit_normal"][:] = mob.get_unit_normal(recompute=True)
+            mob.get_unit_normal(recompute=True)
         return self
 
     # Alignment
@@ -701,7 +735,7 @@ class VMobject(Mobject):
         if len(points) == 1:
             return np.repeat(points, nppc * n, 0)
 
-        bezier_groups = self.get_bezier_tuples_from_points(points)
+        bezier_groups = list(self.get_bezier_tuples_from_points(points))
         norms = np.array([
             get_norm(bg[nppc - 1] - bg[0])
             for bg in bezier_groups
@@ -797,7 +831,7 @@ class VMobject(Mobject):
         # how to send the points as to the vertex shader.
         # First triangles come directly from the points
         if normal_vector is None:
-            normal_vector = self.get_unit_normal()
+            normal_vector = self.get_unit_normal(recompute=True)
 
         if not self.needs_new_triangulation:
             return self.triangulation

manimlib/scene/scene.py

@@ -135,7 +135,7 @@ class Scene(object):
         for term in ("play", "wait", "add", "remove", "clear", "save_state", "restore"):
             local_ns[term] = getattr(self, term)
         log.info("Tips: Now the embed iPython terminal is open. But you can't interact with"
-            " the window directly. To do so, you need to type `touch()` or `self.interact()`")
+                 " the window directly. To do so, you need to type `touch()` or `self.interact()`")
         shell(local_ns=local_ns, stack_depth=2)
         # End scene when exiting an embed.
         raise EndSceneEarlyException()
@@ -282,48 +282,42 @@ class Scene(object):
             self.skip_time += self.time
 
     # Methods associated with running animations
-    def get_time_progression(self, run_time, n_iterations=None, override_skip_animations=False):
+    def get_time_progression(self, run_time, n_iterations=None, desc="", override_skip_animations=False):
         if self.skip_animations and not override_skip_animations:
-            times = [run_time]
+            return [run_time]
         else:
             step = 1 / self.camera.frame_rate
             times = np.arange(0, run_time, step)
-        time_progression = ProgressDisplay(
+
+        if self.file_writer.has_progress_display:
+            self.file_writer.set_progress_display_subdescription(desc)
+            return times
+
+        return ProgressDisplay(
             times,
             total=n_iterations,
             leave=self.leave_progress_bars,
-            ascii=True if platform.system() == 'Windows' else None
+            ascii=True if platform.system() == 'Windows' else None,
+            desc=desc,
         )
-        return time_progression
 
     def get_run_time(self, animations):
         return np.max([animation.run_time for animation in animations])
 
     def get_animation_time_progression(self, animations):
         run_time = self.get_run_time(animations)
-        time_progression = self.get_time_progression(run_time)
+        description = f"{self.num_plays} {animations[0]}"
-        time_progression.set_description("".join([
+        if len(animations) > 1:
-            f"Animation {self.num_plays}: {animations[0]}",
+            description += ", etc."
-            ", etc." if len(animations) > 1 else "",
+        time_progression = self.get_time_progression(run_time, desc=description)
-        ]))
         return time_progression
 
-    def get_wait_time_progression(self, duration, stop_condition):
+    def get_wait_time_progression(self, duration, stop_condition=None):
+        kw = {"desc": f"{self.num_plays} Waiting"}
         if stop_condition is not None:
-            time_progression = self.get_time_progression(
+            kw["n_iterations"] = -1  # So it doesn't show % progress
-                duration,
+            kw["override_skip_animations"] = True
-                n_iterations=-1,  # So it doesn't show % progress
+        return self.get_time_progression(duration, **kw)
-                override_skip_animations=True
-            )
-            time_progression.set_description(
-                "Waiting for {}".format(stop_condition.__name__)
-            )
-        else:
-            time_progression = self.get_time_progression(duration)
-            time_progression.set_description(
-                "Waiting {}".format(self.num_plays)
-            )
-        return time_progression
 
     def anims_from_play_args(self, *args, **kwargs):
         """
@@ -488,13 +482,9 @@ class Scene(object):
                     time_progression.close()
                     break
             self.unlock_mobject_data()
-        elif self.skip_animations:
-            # Do nothing
-            return self
         else:
             self.update_frame(duration)
-            n_frames = int(duration * self.camera.frame_rate)
+            for n in self.get_wait_time_progression(duration):
-            for n in range(n_frames):
                 self.emit_frame()
         return self
 

manimlib/scene/scene_file_writer.py

@@ -5,6 +5,7 @@ import subprocess as sp
 import os
 import sys
 import platform
+from tqdm import tqdm as ProgressDisplay
 
 from manimlib.constants import FFMPEG_BIN
 from manimlib.utils.config_ops import digest_config
@@ -35,12 +36,15 @@ class SceneFileWriter(object):
         "open_file_upon_completion": False,
         "show_file_location_upon_completion": False,
         "quiet": False,
+        "total_frames": 0,
+        "progress_description_len": 35,
     }
 
     def __init__(self, scene, **kwargs):
         digest_config(self, kwargs)
         self.scene = scene
         self.writing_process = None
+        self.has_progress_display = False
         self.init_output_directories()
         self.init_audio()
 
@@ -205,15 +209,37 @@ class SceneFileWriter(object):
         command += [self.temp_file_path]
         self.writing_process = sp.Popen(command, stdin=sp.PIPE)
 
+        if self.total_frames > 0:
+            self.progress_display = ProgressDisplay(
+                range(self.total_frames),
+                leave=False,
+                ascii=True if platform.system() == 'Windows' else None,
+                desc="Full render: "
+            )
+            self.has_progress_display = True
+
+    def set_progress_display_subdescription(self, desc):
+        desc_len = self.progress_description_len
+        full_desc = f"Full render ({desc})"
+        if len(full_desc) > desc_len:
+            full_desc = full_desc[:desc_len - 4] + "...)"
+        else:
+            full_desc += " " * (desc_len - len(full_desc))
+        self.progress_display.set_description(full_desc)
+
     def write_frame(self, camera):
         if self.write_to_movie:
             raw_bytes = camera.get_raw_fbo_data()
             self.writing_process.stdin.write(raw_bytes)
+            if self.has_progress_display:
+                self.progress_display.update()
 
     def close_movie_pipe(self):
         self.writing_process.stdin.close()
         self.writing_process.wait()
         self.writing_process.terminate()
+        if self.has_progress_display:
+            self.progress_display.close()
         shutil.move(self.temp_file_path, self.final_file_path)
 
     def combine_movie_files(self):

manimlib/scene/three_d_scene.py

@@ -5,7 +5,6 @@ class ThreeDScene(Scene):
     CONFIG = {
         "camera_config": {
             "samples": 4,
-            "anti_alias_width": 0,
         }
     }
 

manimlib/shaders/inserts/camera_uniform_declarations.glsl

@@ -1,6 +1,6 @@
 uniform vec2 frame_shape;
 uniform float anti_alias_width;
-uniform vec3 camera_center;
+uniform vec3 camera_offset;
 uniform mat3 camera_rotation;
 uniform float is_fixed_in_frame;
 uniform float focal_distance;

manimlib/shaders/inserts/finalize_color.glsl

@@ -13,39 +13,56 @@ vec4 add_light(vec4 color,
                vec3 point,
                vec3 unit_normal,
                vec3 light_coords,
+               vec3 cam_coords,
+               float reflectiveness,
                float gloss,
                float shadow){
-    if(gloss == 0.0 && shadow == 0.0) return color;
+    if(reflectiveness == 0.0 && gloss == 0.0 && shadow == 0.0) return color;
 
-    float camera_distance = focal_distance;
+    vec4 result = color;
     // Assume everything has already been rotated such that camera is in the z-direction
-    vec3 to_camera = vec3(0, 0, camera_distance) - point;
+    // cam_coords = vec3(0, 0, focal_distance);
-    vec3 to_light = light_coords - point;
+    vec3 to_camera = normalize(cam_coords - point);
+    vec3 to_light = normalize(light_coords - point);
 
-    // TODO, do we actually want this?  It effectively treats surfaces as two-sided
+    // Note, this effectively treats surfaces as two-sided
-    if(dot(to_camera,unit_normal) < 0){
+    // if(dot(to_camera, unit_normal) < 0) unit_normal *= -1;
-            unit_normal *= -1;
-    }
 
+    float light_to_normal = dot(to_light, unit_normal);
+    // When unit normal points towards light, brighten
+    float bright_factor = max(light_to_normal, 0) * reflectiveness;
+    // For glossy surface, add extra shine if light beam go towards camera
     vec3 light_reflection = -to_light + 2 * unit_normal * dot(to_light, unit_normal);
-    float dot_prod = dot(normalize(light_reflection), normalize(to_camera));
+    float light_to_cam = dot(light_reflection, to_camera);
-    float shine = gloss * exp(-3 * pow(1 - dot_prod, 2));
+    float shine = gloss * exp(-3 * pow(1 - light_to_cam, 2));
-    float dp2 = dot(normalize(to_light), unit_normal);
+    bright_factor += shine;
-    float darkening = mix(1, max(dp2, 0), shadow);
+
-    return vec4(
+    result.rgb = mix(result.rgb, vec3(1.0), bright_factor);
-            darkening * mix(color.rgb, vec3(1.0), shine),
+    if (light_to_normal < 0){
-            color.a
+        // Darken
-    );
+        result.rgb = mix(result.rgb, vec3(0.0), -light_to_normal * shadow);
+    }
+    // float darkening = mix(1, max(light_to_normal, 0), shadow);
+    // return vec4(
+    //     darkening * mix(color.rgb, vec3(1.0), shine),
+    //     color.a
+    // );
+    return result;
 }
 
 vec4 finalize_color(vec4 color,
                     vec3 point,
                     vec3 unit_normal,
                     vec3 light_coords,
+                    vec3 cam_coords,
+                    float reflectiveness,
                     float gloss,
                     float shadow){
     ///// INSERT COLOR FUNCTION HERE /////
     // The line above may be replaced by arbitrary code snippets, as per
     // the method Mobject.set_color_by_code
-    return add_light(color, point, unit_normal, light_coords, gloss, shadow);
+    return add_light(
+        color, point, unit_normal, light_coords, cam_coords,
+        reflectiveness, gloss, shadow
+    );
 }

manimlib/shaders/inserts/get_rotated_surface_unit_normal_vector.glsl

@@ -1,5 +1,5 @@
 // Assumes the following uniforms exist in the surrounding context:
-// uniform vec3 camera_center;
+// uniform vec3 camera_offset;
 // uniform mat3 camera_rotation;
 
 vec3 get_rotated_surface_unit_normal_vector(vec3 point, vec3 du_point, vec3 dv_point){

manimlib/shaders/inserts/position_point_into_frame.glsl

@@ -1,6 +1,6 @@
 // Assumes the following uniforms exist in the surrounding context:
 // uniform float is_fixed_in_frame;
-// uniform vec3 camera_center;
+// uniform vec3 camera_offset;
 // uniform mat3 camera_rotation;
 
 vec3 rotate_point_into_frame(vec3 point){
@@ -15,5 +15,5 @@ vec3 position_point_into_frame(vec3 point){
     if(bool(is_fixed_in_frame)){
         return point;
     }
-    return rotate_point_into_frame(point - camera_center);
+    return rotate_point_into_frame(point - camera_offset);
 }

manimlib/shaders/mandelbrot_fractal/frag.glsl

@@ -1,6 +1,8 @@
 #version 330
 
 uniform vec3 light_source_position;
+uniform vec3 camera_position;
+uniform float reflectiveness;
 uniform float gloss;
 uniform float shadow;
 uniform float focal_distance;
@@ -71,6 +73,8 @@ void main() {
         xyz_coords,
         vec3(0.0, 0.0, 1.0),
         light_source_position,
+        camera_position,
+        reflectiveness,
         gloss,
         shadow
     );

manimlib/shaders/newton_fractal/frag.glsl

@@ -1,6 +1,8 @@
 #version 330
 
 uniform vec3 light_source_position;
+uniform vec3 camera_position;
+uniform float reflectiveness;
 uniform float gloss;
 uniform float shadow;
 uniform float focal_distance;
@@ -75,7 +77,7 @@ vec2 seek_root(vec2 z, vec2[MAX_DEGREE + 1] coefs, int max_steps, out float n_it
         }
         z = z - step;
     }
-    n_iters -= clamp((threshold - curr_len) / (last_len - curr_len), 0.0, 1.0);
+    n_iters -= log(curr_len) / log(threshold);
 
     return z;
 }
@@ -118,7 +120,7 @@ void main() {
             color = colors[i];
         }
     }
-    color *= 1.0 + (0.01 * saturation_factor) * (n_iters - 5 * saturation_factor);
+    color *= 1.0 + (0.01 * saturation_factor) * (n_iters - 2 * saturation_factor);
 
     if(black_for_cycles > 0 && min_dist > CLOSE_ENOUGH){
         color = vec4(0.0, 0.0, 0.0, 1.0);
@@ -151,6 +153,8 @@ void main() {
         xyz_coords,
         vec3(0.0, 0.0, 1.0),
         light_source_position,
+        camera_position,
+        reflectiveness,
         gloss,
         shadow
     );

manimlib/shaders/quadratic_bezier_fill/frag.glsl

@@ -3,7 +3,7 @@
 #INSERT camera_uniform_declarations.glsl
 
 in vec4 color;
-in float fill_all;  // Either 0 or 1e
+in float fill_all;  // Either 0 or 1
 in float uv_anti_alias_width;
 
 in vec3 xyz_coords;

manimlib/shaders/quadratic_bezier_fill/geom.glsl

@@ -11,6 +11,8 @@ uniform float focal_distance;
 uniform float is_fixed_in_frame;
 // Needed for finalize_color
 uniform vec3 light_source_position;
+uniform vec3 camera_position;
+uniform float reflectiveness;
 uniform float gloss;
 uniform float shadow;
 
@@ -44,6 +46,8 @@ void emit_vertex_wrapper(vec3 point, int index){
         point,
         v_global_unit_normal[index],
         light_source_position,
+        camera_position,
+        reflectiveness,
         gloss,
         shadow
     );

manimlib/shaders/quadratic_bezier_stroke/geom.glsl

@@ -13,7 +13,9 @@ uniform float flat_stroke;
 
 //Needed for lighting
 uniform vec3 light_source_position;
+uniform vec3 camera_position;
 uniform float joint_type;
+uniform float reflectiveness;
 uniform float gloss;
 uniform float shadow;
 
@@ -259,6 +261,8 @@ void main() {
             xyz_coords,
             v_global_unit_normal[index_map[i]],
             light_source_position,
+            camera_position,
+            reflectiveness,
             gloss,
             shadow
         );

manimlib/shaders/surface/frag.glsl

@@ -1,6 +1,8 @@
 #version 330
 
 uniform vec3 light_source_position;
+uniform vec3 camera_position;
+uniform float reflectiveness;
 uniform float gloss;
 uniform float shadow;
 uniform float focal_distance;
@@ -19,6 +21,8 @@ void main() {
         xyz_coords,
         normalize(v_normal),
         light_source_position,
+        camera_position,
+        reflectiveness,
         gloss,
         shadow
     );

manimlib/shaders/textured_surface/frag.glsl

@@ -4,6 +4,8 @@ uniform sampler2D LightTexture;
 uniform sampler2D DarkTexture;
 uniform float num_textures;
 uniform vec3 light_source_position;
+uniform vec3 camera_position;
+uniform float reflectiveness;
 uniform float gloss;
 uniform float shadow;
 uniform float focal_distance;
@@ -36,6 +38,8 @@ void main() {
         xyz_coords,
         normalize(v_normal),
         light_source_position,
+        camera_position,
+        reflectiveness,
         gloss,
         shadow
     );

manimlib/shaders/true_dot/frag.glsl

@@ -1,10 +1,13 @@
 #version 330
 
 uniform vec3 light_source_position;
+uniform vec3 camera_position;
+uniform float reflectiveness;
 uniform float gloss;
 uniform float shadow;
 uniform float anti_alias_width;
 uniform float focal_distance;
+uniform float glow_factor;
 
 in vec4 color;
 in float radius;
@@ -22,14 +25,23 @@ void main() {
     if (signed_dist > 0.5 * anti_alias_width){
         discard;
     }
-    vec3 normal = vec3(diff / radius, sqrt(1 - (dist * dist) / (radius * radius)));
+    frag_color = color;
-    frag_color = finalize_color(
+    if(gloss > 0 || shadow > 0){
-        color,
+        vec3 normal = vec3(diff / radius, sqrt(1 - (dist * dist) / (radius * radius)));
-        vec3(point.xy, 0.0),
+        frag_color = finalize_color(
-        normal,
+            frag_color,
-        light_source_position,
+            vec3(point.xy, 0.0),
-        gloss,
+            normal,
-        shadow
+            light_source_position,
-    );
+            camera_position,
+            reflectiveness,
+            gloss,
+            shadow
+        );
+    }
+    if(glow_factor > 0){
+        frag_color.a *= pow(1 - dist / radius, glow_factor);
+    }
+
     frag_color.a *= smoothstep(0.5, -0.5, signed_dist / anti_alias_width);
 }

manimlib/utils/space_ops.py

@@ -10,6 +10,15 @@ from manimlib.constants import OUT
 from manimlib.constants import PI
 from manimlib.constants import TAU
 from manimlib.utils.iterables import adjacent_pairs
+from manimlib.utils.simple_functions import clip
+
+
+def cross(v1, v2):
+    return [
+        v1[1] * v2[2] - v1[2] * v2[1],
+        v1[2] * v2[0] - v1[0] * v2[2],
+        v1[0] * v2[1] - v1[1] * v2[0]
+    ]
 
 
 def get_norm(vect):
@@ -147,6 +156,15 @@ def z_to_vector(vector):
     return rotation_matrix(angle, axis=axis)
 
 
+def rotation_between_vectors(v1, v2):
+    if np.all(np.isclose(v1, v2)):
+        return np.identity(3)
+    return rotation_matrix(
+        angle=angle_between_vectors(v1, v2),
+        axis=normalize(np.cross(v1, v2))
+    )
+
+
 def angle_of_vector(vector):
     """
     Returns polar coordinate theta when vector is project on xy plane
@@ -159,8 +177,7 @@ def angle_between_vectors(v1, v2):
     Returns the angle between two 3D vectors.
     This angle will always be btw 0 and pi
     """
-    diff = (angle_of_vector(v2) - angle_of_vector(v1)) % TAU
+    return math.acos(clip(np.dot(normalize(v1), normalize(v2)), -1, 1))
-    return min(diff, TAU - diff)
 
 
 def project_along_vector(point, vector):
@@ -186,14 +203,6 @@ def normalize_along_axis(array, axis, fall_back=None):
     return array
 
 
-def cross(v1, v2):
-    return np.array([
-        v1[1] * v2[2] - v1[2] * v2[1],
-        v1[2] * v2[0] - v1[0] * v2[2],
-        v1[0] * v2[1] - v1[1] * v2[0]
-    ])
-
-
 def get_unit_normal(v1, v2, tol=1e-6):
     v1 = normalize(v1)
     v2 = normalize(v2)