"""Möbius pencil of circles example for use in a tutorial in the docs. Portions of this file are included in the docs. Comments of the form "# [...]" Mark sections that should become code blocks in the docs. Keep this in mind when editing this file! These markers are not necessary when including a whole function/class/method etc. """ # [imports] import numpy as np import ddg from ddg.blender.collection import collection from ddg.blender.material import material # [imports] # # BLENDER COLLECTIONS # ------------------- # [clear] ddg.blender.scene.clear(remove_collections=True) ddg.blender.material.clear() # [clear] # [collection setup] # for objects that were created for didactical purposes example_coll = collection("example stuff") # for objects belonging to the 3D moebius picture mob_geo_coll = collection( "Moebius geometry", children=[ ["lines", "points on line", "points on polar line"], "spherical circles", "polar spherical circles", ], ) # for objects belonging to the 2D euclidean picture euc_geo_coll = collection( "Euclidean geometry", children=["Euclidean circles", "orthogonal Euclidean circles"] ) # for objects belonging to the light projection picture projection_coll = collection("projection with light") # for the slider function slider_circles_coll = collection("slider circles") # [collection setup] # ------------------------------------------------------------ # # BLENDER MATERIALS # ----------------- # [materials] material(name="s2", color=(0.413, 0.828, 0.990), specular=0.4, roughness=0.6, alpha=0.5) material(name="euc plane", color=(0, 0, 0), specular=0.5, roughness=1, alpha=1) material( name="polar spherical circle", color=(1, 0.533, 0.044), specular=0.1, roughness=1, alpha=1, ) material( name="spherical circle", color=(0.029, 0.139, 1), specular=0.1, roughness=1, alpha=1 ) material( name="polar planar circle", color=(1, 0.533, 0.044), specular=0.1, roughness=0.9, alpha=1, ) material( name="planar circle", color=(0.029, 0.139, 1), specular=1, roughness=1, alpha=1 ) # [materials] # ------------------------------------------------------------ # # SPHERE S2 # --------- # [create sphere as quadric] s2 = ddg.geometry.Quadric(np.diag([1, 1, 1, -1])) # [create sphere as quadric] # [display sphere] bobj_s2 = ddg.blender.convert(s2, "s2", material="s2", collection=mob_geo_coll) ddg.blender.mesh.shade_smooth(bobj_s2) # [display sphere] # ------------------------------------------------------------ # # LINE L THROUGH S2 # ----------------- # [create line as subspace] # line through S2 p1, p2 = np.array([-4, 0, 0.5, 1]), np.array([4, 0, 0.5, 1]) # # p1, p2 = np.array([-1, 1, 0, 1]), np.array([1, 1, 0, 1]) l = ddg.geometry.Subspace(p1, p2) # [create line as subspace] # [line to smooth net] # orthonormalize and center l l = l.orthonormalize_and_center((p1 + p2) / 2) # create smooth net l_net = ddg.to_smooth_net(l, domain=[[-4, 4]], affine=True, convex=True) # [line to smooth net] # [line to blender object] # to blender bobj_l = ddg.blender.convert( l, "line", collection=mob_geo_coll.children[0], material="line", ) bobj_l.data.bevel_depth = 0.01 # [line to blender object] # ------------------------------------------------------------- # # SPHERICAL AND PLANAR CIRCLES # ---------------------------- # # Spherical Circles # # [get a point] # get a point pt = l_net(2) # [get a point] # [homogenize point] # homogenize pt pt_homogenized = ddg.math.projective.homogenize(pt) # [homogenize point] # [convert point to subspace] # convert point to subspace pt_projective = ddg.geometry.Subspace(pt_homogenized) # [convert point to subspace] # [display point] # display point in blender bobj_pt = ddg.blender.vertices( pt_projective, "point", radius=0.05, material="point", collection=example_coll, ) # [display point] # [calculate polar plane] # calculate its polar plane plane = s2.polarize(pt_projective) # [calculate polar plane] # [calculate intersection circle] # calculate intersection circle circ_on_sphere = ddg.geometry.meet(plane, s2) # [calculate intersection circle] # [check for empty intersection] # check if intersection is not empty if circ_on_sphere.dimension != -1: bobj_circ_on_sphere = ddg.blender.convert( circ_on_sphere, "spherical circle", collection=example_coll, material="spherical circle", ) bobj_circ_on_sphere.data.bevel_depth = 0.005 # [check for empty intersection] # # Planar Circles # # [stereographic project and display circle] # stereographic project euc_plane = ddg.geometry.subspace_from_affine_points_and_directions( [[0, 0, 0]], [[1, 0, 0], [0, 1, 0]] ) circ_on_plane = ddg.geometry.stereographic_project(circ_on_sphere, euc_plane) # convert to blender bobj_circ_on_plane = ddg.blender.convert( circ_on_plane, "planar circle", collection=example_coll, material="planar circle", ) bobj_circ_on_plane.data.bevel_depth = 0.005 bobj_euc_plane = ddg.blender.convert( euc_plane, "euc_plane", material="euc plane", collection=euc_geo_coll, ) # [stereographic project and display circle] # [stereographic project with a light] # stereographic project light = ddg.blender.light.light( type_="POINT", location=[0, 0, 1], energy=600, collection=projection_coll ) light.data.shadow_soft_size = 0 bobj_euc_plane.is_shadow_catcher = True # [stereographic project with a light] # ------------------------------------------------------------- # # Möbius Pencil of Circles # ------------------------ # # Spherical and Planar Circles Function # def circles_from_point( pt, pt_name, circ_name, planar_name, pt_coll=None, spherical_coll=None, planar_coll=None, material_spherical=None, material_planar=None, ): """ Create the point, the corresp. spherical circle, and the corresp. planar circle. Parameters ---------- pt : array of length 3 pt_coll, spherical_coll, planar_ coll : Blender Collections (default=None) material_spherical: string or bpy.tupes.Material material_planar: string or bpy.types.Material Returns ------- None or list """ # display point in blender bobj_pt = ddg.blender.vertices( ddg.nets.PointNet(pt), pt_name, radius=0.05, collection=pt_coll, material="point", ) # homogenize pt pt_homogenized = ddg.math.projective.homogenize(pt) # convert point to subspace pt_homogenized = ddg.geometry.Subspace(pt_homogenized) # calculate its polar plane plane = s2.polarize(pt_homogenized) # calculate intersection circle circ_on_sphere = ddg.geometry.meet(plane, s2) # check if intersection is not empty if circ_on_sphere.dimension != -1: # convert spherical circle to blender bobj_circ_on_sphere = ddg.blender.convert( circ_on_sphere, circ_name, collection=spherical_coll, material=material_spherical, ) bobj_circ_on_sphere.data.bevel_depth = 0.006 # stereographic project circ_on_plane = ddg.geometry.stereographic_project(circ_on_sphere, euc_plane) # convert planar circle to blender bobj_circ_on_plane = ddg.blender.convert( circ_on_plane, planar_name, collection=planar_coll, material=material_planar, ) bobj_circ_on_plane.data.bevel_depth = 0.006 return [bobj_pt, bobj_circ_on_sphere, bobj_circ_on_plane] else: return [bobj_pt] # # Wrapper Function for Points on a Line # # [get circles for a point] circles_from_point( l_net(1.3), "p1.3", "circ1.3", "plan1.3", pt_coll=mob_geo_coll.children[0].children[0], spherical_coll=mob_geo_coll.children[1], planar_coll=euc_geo_coll.children[0], material_spherical="spherical circle", material_planar="planar circle", ) # [get circles for a point] # Adding Slider # [add slider] callback_collection = ddg.blender.collection.collection("callback") def callback(t): ddg.blender.collection.clear([callback_collection], deep=True) circles_from_point( l_net(t), "p_slider", "circ_slider", "plan_slider", pt_coll=callback_collection, spherical_coll=callback_collection, planar_coll=callback_collection, ) ddg.blender.props.add_props_with_callback(callback, ("t",), 1.0) # [add slider] # # Visualize some Circles in Pencil # # [sample domain of line] # LINEAR SAMPLING OF DOMAIN # this function takes arg3 samples equidistantly of the intervall [arg1,ag2] sample = np.linspace(-3, 3, 30) # [sample domain of line] # [visualize pencil] # visualize pencil for i, t in enumerate(sample): circles_from_point( l_net(t), f"p_{i}", f"circ_{i}", f"plane_{i}", pt_coll=mob_geo_coll.children[0].children[0], spherical_coll=mob_geo_coll.children[1], planar_coll=euc_geo_coll.children[0], material_spherical="spherical circle", material_planar="planar circle", ) # [visualize pencil] # # POLAR LINE TO L # ---------------- # [orthogonal pencil] # get polar subspace of l polar_l = s2.polarize(l) # orthonormalize polar_l = polar_l.orthonormalize() # convert to net polar_l_net = ddg.to_smooth_net(polar_l, domain=[[-4, 4]], affine=True, convex=True) # convert to blender bobj_polar = ddg.blender.convert( polar_l, "polar line", collection=mob_geo_coll.children[0], ) bobj_polar.data.bevel_depth = 0.01 # visualize orthogonal pencil for i, t in enumerate(sample): circles_from_point( polar_l_net(t), f"polar_p_{i}", f"polar_c_{i}", f"polar_plane_{i}", pt_coll=mob_geo_coll.children[0].children[1], spherical_coll=mob_geo_coll.children[2], planar_coll=euc_geo_coll.children[1], material_spherical="polar spherical circle", material_planar="polar planar circle", ) # [orthogonal pencil] # ------------------------------------------------------------- # # CAMERA AND LIGHT # # [camera and light] # add camera and light cam = ddg.blender.camera.camera(location=(0, 0, 19)) light = ddg.blender.light.light(location=(0, 0, 50)) light.data.use_shadow = False # [camera and light] # ------------------------------------------------------------- # # HIDE COLLECTIONS # # [hide collections] example_coll.hide_render = True example_coll.hide_viewport = True projection_coll.hide_render = True projection_coll.hide_viewport = True slider_circles_coll.hide_render = True slider_circles_coll.hide_viewport = True # [hide collections]