"""Module dedicated for basic primitive."""importmathfromos.pathimportjoinaspjoinimportnumpyasnpfrompackaging.versionimportparsefromscipy.spatialimportConvexHullfromscipy.versionimportshort_versionfromfury.dataimportDATA_DIRfromfury.decoratorsimportwarn_on_args_to_kwargsfromfury.transformimportcart2sphere,sphere2cartfromfury.utilsimportfix_winding_orderSCIPY_1_4_PLUS=parse(short_version)>=parse("1.4.0")SPHERE_FILES={"symmetric362":pjoin(DATA_DIR,"evenly_distributed_sphere_362.npz"),"symmetric642":pjoin(DATA_DIR,"evenly_distributed_sphere_642.npz"),"symmetric724":pjoin(DATA_DIR,"evenly_distributed_sphere_724.npz"),"repulsion724":pjoin(DATA_DIR,"repulsion724.npz"),"repulsion100":pjoin(DATA_DIR,"repulsion100.npz"),"repulsion200":pjoin(DATA_DIR,"repulsion200.npz"),}
[docs]deffaces_from_sphere_vertices(vertices):"""Triangulate a set of vertices on the sphere. Parameters ---------- vertices : (M, 3) ndarray XYZ coordinates of vertices on the sphere. Returns ------- faces : (N, 3) ndarray Indices into vertices; forms triangular faces. """hull=ConvexHull(vertices,qhull_options="Qbb Qc")faces=np.ascontiguousarray(hull.simplices)iflen(vertices)<2**16:returnnp.asarray(faces,np.uint16)else:returnfaces
[docs]@warn_on_args_to_kwargs()defrepeat_primitive_function(func,centers,*,func_args=None,directions=(1,0,0),colors=(1,0,0),scales=1):"""Repeat Vertices and triangles of a specific primitive function. It could be seen as a glyph. The primitive function should generate and return vertices and faces Parameters ---------- func : callable primitive functions centers : ndarray, shape (N, 3) Superquadrics positions func_args : args primitive functions arguments/parameters directions : ndarray, shape (N, 3) or tuple (3,), optional The orientation vector of the cone. colors : ndarray (N,3) or (N, 4) or tuple (3,) or tuple (4,) RGB or RGBA (for opacity) R, G, B and A should be at the range [0, 1] scales : ndarray, shape (N) or (N,3) or float or int, optional The height of the cone. Returns ------- big_vertices: ndarray Expanded vertices at the centers positions big_triangles: ndarray Expanded triangles that composed our shape to duplicate big_colors : ndarray Expanded colors applied to all vertices/faces """iffunc_argsisNone:func_args=[]# Get faces_,faces=func()iflen(func_args)==1:func_args=np.squeeze(np.array([func_args]*centers.shape[0]))eliflen(func_args)!=centers.shape[0]:raiseIOError("sq_params should 1 or equal to the numbers \ of centers")vertices=np.concatenate([func(i)[0]foriinfunc_args])returnrepeat_primitive(vertices,faces,centers,directions=directions,colors=colors,scales=scales,have_tiled_verts=True,)
[docs]@warn_on_args_to_kwargs()defrepeat_primitive(vertices,faces,centers,*,directions=None,colors=(1,0,0),scales=1,have_tiled_verts=False,):"""Repeat Vertices and triangles of a specific primitive shape. It could be seen as a glyph. Parameters ---------- vertices: ndarray vertices coords to duplicate at the centers positions triangles: ndarray triangles that composed our shape to duplicate centers : ndarray, shape (N, 3) Superquadrics positions directions : ndarray, shape (N, 3) or tuple (3,), optional The orientation vector of the cone. colors : ndarray (N,3) or (N, 4) or tuple (3,) or tuple (4,) RGB or RGBA (for opacity) R, G, B and A should be at the range [0, 1] scales : ndarray, shape (N) or (N,3) or float or int, optional The height of the cone. have_tiled_verts : bool option to control if we need to duplicate vertices of a shape or not Returns ------- big_vertices: ndarray Expanded vertices at the centers positions big_triangles: ndarray Expanded triangles that composed our shape to duplicate big_colors : ndarray Expanded colors applied to all vertices/faces big_centers : ndarray Expanded centers for all vertices/faces """# duplicated vertices if neededifnothave_tiled_verts:vertices=np.tile(vertices,(centers.shape[0],1))big_vertices=vertices# Get unit shapeunit_verts_size=vertices.shape[0]//centers.shape[0]unit_triangles_size=faces.shape[0]# scale themifnotisinstance(scales,np.ndarray):scales=np.array(scales)ifscales.ndim==1:ifscales.size==centers.shape[0]:scales=np.repeat(scales,unit_verts_size,axis=0)scales=scales.reshape((big_vertices.shape[0],1))elifscales.ndim==2:scales=np.repeat(scales,unit_verts_size,axis=0)big_vertices*=scales# update trianglesbig_triangles=np.array(np.tile(faces,(centers.shape[0],1)),dtype=np.int32)big_triangles+=np.repeat(np.arange(0,centers.shape[0]*unit_verts_size,step=unit_verts_size),unit_triangles_size,axis=0,).reshape((big_triangles.shape[0],1))@warn_on_args_to_kwargs()defnormalize_input(arr,*,arr_name=""):if(isinstance(arr,(tuple,list,np.ndarray))andlen(arr)in[3,4]andnotall(isinstance(i,(list,tuple,np.ndarray))foriinarr)):returnnp.array([arr]*centers.shape[0])elifisinstance(arr,np.ndarray)andlen(arr)==1:returnnp.repeat(arr,centers.shape[0],axis=0)elifarrisNone:returnnp.array([])eliflen(arr)!=len(centers):msg="{} size should be 1 or ".format(arr_name)msg+="equal to the numbers of centers"raiseIOError(msg)else:returnnp.array(arr)# update colorscolors=normalize_input(colors,arr_name="colors")big_colors=np.repeat(colors,unit_verts_size,axis=0)big_colors*=255# update orientationsdirections=normalize_input(directions,arr_name="directions")forpts,dirsinenumerate(directions):# Normal vector of the object.dir_abs=np.linalg.norm(dirs)ifdir_abs:normal=np.array([1.0,0.0,0.0])dirs=dirs/dir_absv=np.cross(normal,dirs)c=np.dot(normal,dirs)v1,v2,v3=vVmat=np.array([[0,-v3,v2],[v3,0,-v1],[-v2,v1,0]])ifc==-1.0:rotation_matrix=-np.eye(3,dtype=np.float64)else:h=1/(1+c)rotation_matrix=(np.eye(3,dtype=np.float64)+Vmat+(Vmat.dot(Vmat)*h))else:rotation_matrix=np.identity(3)big_vertices[pts*unit_verts_size:(pts+1)*unit_verts_size]=np.dot(rotation_matrix[:3,:3],big_vertices[pts*unit_verts_size:(pts+1)*unit_verts_size].T,).T# apply centers positionbig_centers=np.repeat(centers,unit_verts_size,axis=0)big_vertices+=big_centersreturnbig_vertices,big_triangles,big_colors,big_centers
[docs]defprim_square():"""Return vertices and triangles for a square geometry. Returns ------- vertices: ndarray 4 vertices coords that composed our square triangles: ndarray 2 triangles that composed our square """vertices=np.array([[-0.5,-0.5,0.0],[-0.5,0.5,0.0],[0.5,0.5,0.0],[0.5,-0.5,0.0]])triangles=np.array([[0,1,2],[2,3,0]],dtype="i8")returnvertices,triangles
[docs]defprim_box():"""Return vertices and triangle for a box geometry. Returns ------- vertices: ndarray 8 vertices coords that composed our box triangles: ndarray 12 triangles that composed our box """vertices=np.array([[-0.5,-0.5,-0.5],[-0.5,-0.5,0.5],[-0.5,0.5,-0.5],[-0.5,0.5,0.5],[0.5,-0.5,-0.5],[0.5,-0.5,0.5],[0.5,0.5,-0.5],[0.5,0.5,0.5],])triangles=np.array([[0,6,4],[0,2,6],[0,3,2],[0,1,3],[2,7,6],[2,3,7],[4,6,7],[4,7,5],[0,4,5],[0,5,1],[1,5,7],[1,7,3],],dtype="i8",)returnvertices,triangles
[docs]@warn_on_args_to_kwargs()defprim_sphere(*,name="symmetric362",gen_faces=False,phi=None,theta=None):"""Provide vertices and triangles of the spheres. Parameters ---------- name : str, optional which sphere - one of: * 'symmetric362' * 'symmetric642' * 'symmetric724' * 'repulsion724' * 'repulsion100' * 'repulsion200' gen_faces : bool, optional If True, triangulate a set of vertices on the sphere to get the faces. Otherwise, we load the saved faces from a file. Default: False phi : int, optional Set the number of points in the latitude direction theta : int, optional Set the number of points in the longitude direction Returns ------- vertices: ndarray vertices coords that composed our sphere triangles: ndarray triangles that composed our sphere Examples -------- >>> import numpy as np >>> from fury.primitive import prim_sphere >>> verts, faces = prim_sphere('symmetric362') >>> verts.shape == (362, 3) True >>> faces.shape == (720, 3) True """ifphiisNoneorthetaisNone:fname=SPHERE_FILES.get(name)iffnameisNone:raiseValueError('No sphere called "%s"'%name)res=np.load(fname)verts=res["vertices"].copy()faces=faces_from_sphere_vertices(verts)ifgen_faceselseres["faces"]faces=fix_winding_order(res["vertices"],faces,clockwise=True)returnverts,faceselse:phi=phiifphi>=3else3theta=thetaiftheta>=3else3phi_indices,theta_indices=np.arange(0,phi),np.arange(1,theta-1)# phi and theta angles are same as standard physics conventionphi_angles=2*np.pi*phi_indices/phitheta_angles=np.pi*theta_indices/(theta-1)# combinations of all phi and theta anglesmesh=np.array(np.meshgrid(phi_angles,theta_angles))combs=mesh.T.reshape(-1,2)_angles=np.array([[1,1],[0,np.pi],[np.pi/2,-np.pi/2]])_points=np.array(sphere2cart(_angles[0],_angles[1],_angles[2])).Tx,y,z=sphere2cart(1,combs[:,1:],combs[:,:1])x=np.reshape(np.append(x,_points[:,:1]),(-1,))y=np.reshape(np.append(y,_points[:,1:2]),(-1,))z=np.reshape(np.append(z,_points[:,-1:]),(-1,))verts=np.vstack([x,y,z]).Tfaces=faces_from_sphere_vertices(verts)faces=fix_winding_order(verts,faces,clockwise=True)returnverts,faces
[docs]defprim_superquadric(roundness=(1,1),sphere_name="symmetric362"):"""Provide vertices and triangles of a superquadrics. Parameters ---------- roundness : tuple, optional parameters (Phi and Theta) that control the shape of the superquadric sphere_name : str, optional which sphere - one of: * 'symmetric362' * 'symmetric642' * 'symmetric724' * 'repulsion724' * 'repulsion100' * 'repulsion200' Returns ------- vertices: ndarray vertices coords that composed our sphere triangles: ndarray triangles that composed our sphere Examples -------- >>> import numpy as np >>> from fury.primitive import prim_superquadric >>> verts, faces = prim_superquadric(roundness=(1, 1)) >>> verts.shape == (362, 3) True >>> faces.shape == (720, 3) True """def_fexp(x,p):"""Return a different kind of exponentiation."""returnnp.sign(x)*(np.abs(x)**p)sphere_verts,sphere_triangles=prim_sphere(name=sphere_name)_,sphere_phi,sphere_theta=cart2sphere(*sphere_verts.T)phi,theta=roundnessx=_fexp(np.sin(sphere_phi),phi)*_fexp(np.cos(sphere_theta),theta)y=_fexp(np.sin(sphere_phi),phi)*_fexp(np.sin(sphere_theta),theta)z=_fexp(np.cos(sphere_phi),phi)xyz=np.vstack([x,y,z]).Tvertices=np.ascontiguousarray(xyz)returnvertices,sphere_triangles
[docs]defprim_tetrahedron():"""Return vertices and triangles for a tetrahedron. This shape has a side length of two units. Returns ------- pyramid_vert: numpy.ndarray 4 vertices coordinates triangles: numpy.ndarray 4 triangles representing the tetrahedron """pyramid_vert=np.array([[0.5,0.5,0.5],[0.5,-0.5,-0.5],[-0.5,0.5,-0.5],[-0.5,-0.5,0.5]])pyramid_triag=np.array([[2,0,1],[0,2,3],[0,3,1],[1,3,2]],dtype="i8")returnpyramid_vert,pyramid_triag
[docs]defprim_icosahedron():"""Return vertices and triangles for icosahedron. Returns ------- icosahedron_vertices: numpy.ndarray 12 vertices coordinates to the icosahedron icosahedron_mesh: numpy.ndarray 20 triangles representing the tetrahedron """phi=(1+math.sqrt(5))/2.0icosahedron_vertices=np.array([[-1.0,0.0,phi],[0.0,phi,1.0],[1.0,0.0,phi],[-phi,1.0,0.0],[0.0,phi,-1.0],[phi,1.0,0.0],[-phi,-1.0,0.0],[0.0,-phi,1.0],[phi,-1.0,0.0],[-1.0,0.0,-phi],[0.0,-phi,-1.0],[1.0,0.0,-phi],])icosahedron_mesh=np.array([[1,0,2],[2,5,1],[5,4,1],[3,1,4],[0,1,3],[0,6,3],[9,3,6],[8,2,7],[2,0,7],[0,7,6],[5,2,8],[11,5,8],[11,4,5],[9,11,4],[4,3,9],[11,10,8],[8,10,7],[6,7,10],[10,9,6],[9,10,11],],dtype="i8",)returnicosahedron_vertices,icosahedron_mesh
[docs]defprim_rhombicuboctahedron():"""Return vertices and triangles for rhombicuboctahedron. Returns ------- vertices: numpy.ndarray 24 vertices coordinates to the rhombicuboctahedron triangles: numpy.ndarray 44 triangles representing the rhombicuboctahedron """phi=(math.sqrt(2)-1)/2.0vertices=np.array([[0.5,phi,phi],[0.5,phi,-phi],[0.5,-phi,phi],[0.5,-phi,-phi],[phi,0.5,phi],[phi,0.5,-phi],[-phi,0.5,phi],[-phi,0.5,-phi],[phi,phi,0.5],[phi,-phi,0.5],[-phi,phi,0.5],[-phi,-phi,0.5],[-0.5,phi,phi],[-0.5,phi,-phi],[-0.5,-phi,phi],[-0.5,-phi,-phi],[phi,-0.5,phi],[phi,-0.5,-phi],[-phi,-0.5,phi],[-phi,-0.5,-phi],[phi,phi,-0.5],[phi,-phi,-0.5],[-phi,phi,-0.5],[-phi,-phi,-0.5],])triangles=np.array([[0,1,2],[1,3,2],[0,4,5],[0,5,1],[6,4,7],[4,5,7],[0,8,4],[0,2,8],[2,9,8],[8,9,10],[9,11,10],[6,8,10],[6,8,4],[6,10,12],[6,12,7],[7,12,13],[10,11,14],[10,14,12],[12,14,15],[12,15,13],[2,3,16],[3,17,16],[2,16,9],[9,16,11],[11,16,18],[18,16,19],[16,17,19],[11,18,14],[14,18,19],[14,19,15],[1,21,3],[1,20,21],[3,21,17],[17,21,23],[17,23,19],[21,20,23],[23,20,22],[19,23,15],[15,23,13],[13,23,22],[13,22,7],[22,7,5],[22,20,5],[20,1,5],],dtype="i8",)triangles=fix_winding_order(vertices,triangles,clockwise=True)returnvertices,triangles
[docs]@warn_on_args_to_kwargs()defprim_star(*,dim=2):"""Return vertices and triangle for star geometry. Parameters ---------- dim: int Represents the dimension of the wanted star Returns ------- vertices: ndarray vertices coords that composed our star triangles: ndarray Triangles that composed our star """ifdim==2:vert=np.array([[-2.0,-3.0,0.0],[0.0,-2.0,0.0],[3.0,-3.0,0.0],[2.0,-1.0,0.0],[3.0,1.0,0.0],[1.0,1.0,0.0],[0.0,3.0,0.0],[-1.0,1.0,0.0],[-3.0,1.0,0.0],[-2.0,-1.0,0.0],])triangles=np.array([[1,9,0],[1,2,3],[3,4,5],[5,6,7],[7,8,9],[1,9,3],[3,7,9],[3,5,7],],dtype="i8",)ifdim==3:vert=np.array([[-2.0,-3.0,0.0],[0.0,-2,0.0],[3.0,-3.0,0.0],[2.0,-1.0,0.0],[3.0,0.5,0.0],[1.0,0.5,0.0],[0,3.0,0.0],[-1.0,0.5,0.0],[-3.0,0.5,0.0],[-2.0,-1.0,0.0],[0.0,0.0,0.5],[0.0,0.0,-0.5],])triangles=np.array([[1,9,0],[1,2,3],[3,4,5],[5,6,7],[7,8,9],[1,9,3],[3,7,9],[3,5,7],[1,0,10],[0,9,10],[10,9,8],[7,8,10],[6,7,10],[5,6,10],[5,10,4],[10,3,4],[3,10,2],[10,1,2],[1,0,11],[0,9,11],[11,9,8],[7,8,10],[6,7,11],[5,6,11],[5,10,4],[11,3,4],[3,11,2],[11,1,2],],dtype="i8",)returnvert,triangles
[docs]defprim_triangularprism():"""Return vertices and triangle for a regular triangular prism. Returns ------- vertices: ndarray vertices coords that compose our prism triangles: ndarray triangles that compose our prism """# Local variable to represent the square root of three rounded# to 7 decimal placesthree=float("{:.7f}".format(math.sqrt(3)))vertices=np.array([[0,-1/three,1/2],[-1/2,1/2/three,1/2],[1/2,1/2/three,1/2],[-1/2,1/2/three,-1/2],[1/2,1/2/three,-1/2],[0,-1/three,-1/2],])triangles=np.array([[0,1,2],[2,1,3],[2,3,4],[1,0,5],[1,5,3],[0,2,4],[0,4,5],[5,4,3],])triangles=fix_winding_order(vertices,triangles,clockwise=True)returnvertices,triangles
[docs]defprim_pentagonalprism():"""Return vertices and triangles for a pentagonal prism. Returns ------- vertices: ndarray vertices coords that compose our prism triangles: ndarray triangles that compose our prism """# Local variable to represent the square root of fivefive=math.sqrt(5)onec=(five-1)/4.0twoc=(five+1)/4.0sone=(math.sqrt(10+(2*five)))/4.0stwo=(math.sqrt(10-(2*five)))/4.0vertices=np.array([[stwo/2,twoc/2,-0.5],[sone/2,-onec/2,-0.5],[0,-1/2,-0.5],[-sone/2,-onec/2,-0.5],[-stwo/2,twoc/2,-0.5],[stwo/2,twoc/2,0.5],[sone/2,-onec/2,0.5],[0,-1/2,0.5],[-sone/2,-onec/2,0.5],[-stwo/2,twoc/2,0.5],])triangles=np.array([[9,5,4],[4,5,0],[5,6,0],[0,6,1],[6,7,1],[1,7,2],[7,8,2],[2,8,3],[8,9,3],[3,9,4],[0,1,4],[1,4,3],[1,3,2],[5,6,9],[6,8,9],[6,7,8],])triangles=fix_winding_order(vertices,triangles,clockwise=True)returnvertices,triangles
[docs]defprim_octagonalprism():"""Return vertices and triangle for an octagonal prism. Returns ------- vertices: ndarray vertices coords that compose our prism triangles: ndarray triangles that compose our prism """# Local variable to represent the square root of two rounded# to 7 decimal placestwo=float("{:.7f}".format(math.sqrt(2)))vertices=np.array([[-1,-(1+two),-1],[1,-(1+two),-1],[1,(1+two),-1],[-1,(1+two),-1],[-(1+two),-1,-1],[(1+two),-1,-1],[(1+two),1,-1],[-(1+two),1,-1],[-1,-(1+two),1],[1,-(1+two),1],[1,(1+two),1],[-1,(1+two),1],[-(1+two),-1,1],[(1+two),-1,1],[(1+two),1,1],[-(1+two),1,1],])triangles=np.array([[0,8,9],[9,1,0],[5,13,9],[9,1,5],[3,11,10],[10,2,3],[2,10,14],[14,6,2],[5,13,14],[14,6,5],[7,15,11],[11,3,7],[7,15,12],[12,4,7],[0,8,12],[12,4,0],[0,3,4],[3,4,7],[0,3,1],[1,2,3],[2,5,6],[5,2,1],[8,11,12],[11,12,15],[8,11,9],[9,10,11],[10,13,14],[13,10,9],],dtype="u8",)vertices/=4triangles=fix_winding_order(vertices,triangles,clockwise=True)returnvertices,triangles
[docs]defprim_frustum():"""Return vertices and triangle for a square frustum prism. Returns ------- vertices: ndarray vertices coords that compose our prism triangles: ndarray triangles that compose our prism """vertices=np.array([[-0.5,-0.5,0.5],[0.5,-0.5,0.5],[0.5,0.5,0.5],[-0.5,0.5,0.5],[-1,-1,-0.5],[1,-1,-0.5],[1,1,-0.5],[-1,1,-0.5],])triangles=np.array([[4,6,5],[6,4,7],[0,2,1],[2,0,3],[4,3,0],[3,4,7],[7,2,3],[2,7,6],[6,1,2],[1,6,5],[5,0,1],[0,5,4],],dtype="u8",)vertices/=2triangles=fix_winding_order(vertices,triangles,clockwise=True)returnvertices,triangles
[docs]@warn_on_args_to_kwargs()defprim_cylinder(*,radius=0.5,height=1,sectors=36,capped=True):"""Return vertices and triangles for a cylinder. Parameters ---------- radius: float Radius of the cylinder height: float Height of the cylinder sectors: int Sectors in the cylinder capped: bool Whether the cylinder is capped at both ends or open Returns ------- vertices: ndarray vertices coords that compose our cylinder triangles: ndarray triangles that compose our cylinder """ifnotisinstance(sectors,int):raiseTypeError("Only integers are allowed for sectors parameter")ifnotsectors>7:raiseValueError("Sectors parameter should be greater than 7")sector_step=2*math.pi/sectorsunit_circle_vertices=[]# generate a unit circle on YZ planeforiinrange(sectors+1):sector_angle=i*sector_stepunit_circle_vertices.append(0)unit_circle_vertices.append(math.cos(sector_angle))unit_circle_vertices.append(math.sin(sector_angle))vertices=[]# generate vertices for a cylinderforiinrange(2):h=-height/2+i*heightk=0for_inrange(sectors+1):uy=unit_circle_vertices[k+1]uz=unit_circle_vertices[k+2]# position vectorvertices.append(h)vertices.append(uy*radius)vertices.append(uz*radius)k+=3# base and top circle verticesbase_center_index=Nonetop_center_index=Noneifcapped:base_center_index=int(len(vertices)/3)top_center_index=base_center_index+sectors+1foriinrange(2):h=-height/2+i*heightvertices.append(h)vertices.append(0)vertices.append(0)k=0for_inrange(sectors):uy=unit_circle_vertices[k+1]uz=unit_circle_vertices[k+2]# position vectorvertices.append(h)vertices.append(uy*radius)vertices.append(uz*radius)k+=3ifcapped:vertices=np.array(vertices).reshape(2*(sectors+1)+2*sectors+2,3)else:vertices=np.array(vertices).reshape(2*(sectors+1),3)triangles=[]k1=0k2=sectors+1# triangles for the side surfacefor_inrange(sectors):triangles.append(k1)triangles.append(k2)triangles.append(k1+1)triangles.append(k2)triangles.append(k2+1)triangles.append(k1+1)k1+=1k2+=1ifcapped:k=base_center_index+1foriinrange(sectors):ifi<sectors-1:triangles.append(base_center_index)triangles.append(k)triangles.append(k+1)else:triangles.append(base_center_index)triangles.append(k)triangles.append(base_center_index+1)k+=1k=top_center_index+1foriinrange(sectors):ifi<sectors-1:triangles.append(top_center_index)triangles.append(k+1)triangles.append(k)else:triangles.append(top_center_index)triangles.append(top_center_index+1)triangles.append(k)k+=1ifcapped:triangles=np.array(triangles).reshape(4*sectors,3)else:triangles=np.array(triangles).reshape(2*sectors,3)returnvertices,triangles
[docs]@warn_on_args_to_kwargs()defprim_arrow(*,height=1.0,resolution=10,tip_length=0.35,tip_radius=0.1,shaft_radius=0.03,):"""Return vertices and triangle for arrow geometry. Parameters ---------- height : float The height of the arrow (default: 1.0). resolution : int The resolution of the arrow. tip_length : float The tip size of the arrow (default: 0.35) tip_radius : float the tip radius of the arrow (default: 0.1) shaft_radius : float The shaft radius of the arrow (default: 0.03) Returns ------- vertices: ndarray vertices of the Arrow triangles: ndarray Triangles of the Arrow """shaft_height=height-tip_lengthall_faces=[]shaft_outer_circle_down=[]shaft_outer_circle_up=[]tip_outer_circle=[]# calculating verticesforiinrange(resolution+1):x=math.cos((i*2)*math.pi/resolution)y=math.sin((i*2)*math.pi/resolution)shaft_x=x*shaft_radiusshaft_y=y*shaft_radiustip_x=x*tip_radiustip_y=y*tip_radius# lower shaft circle (d)shaft_outer_circle_down.append((0.0,shaft_x,shaft_y))# upper shaft circle (u)shaft_outer_circle_up.append((shaft_height,shaft_x,shaft_y))# tip outer circletip_outer_circle.append((shaft_height,tip_x,tip_y))# center, center at shaft height, center at overall heightv1,v2,v3=(0.0,0.0,0.0),(shaft_height,0.0,0.0),(height,0.0,0.0)all_verts=([v1,v2,v3]+shaft_outer_circle_down+shaft_outer_circle_up+tip_outer_circle)offset=len(shaft_outer_circle_down)off_1=3off_2=off_1+offsetoff_3=off_2+offset# calculating trianglesforiinrange(resolution):# down circle d[i] , 0, d[i + 1]all_faces.append((i+off_1+1,i+off_1,0))# cylinder triangles 1 d[i], d[i + 1], u[i + 1]all_faces.append((i+off_2+1,i+off_1,i+off_1+1))# cylinder triangles 2 u[i + 1], u[i], d[i]all_faces.append((i+off_1,i+off_2+1,i+off_2))# tip circle u[i] , 1, d[i + 1]all_faces.append((i+off_3+1,i+off_3,1))# tip cone t[i], t[i + 1], 2all_faces.append((2,i+off_3,i+off_3+1))vertices=np.asarray(all_verts)triangles=np.asarray(all_faces,dtype=int)returnvertices,triangles
[docs]@warn_on_args_to_kwargs()defprim_cone(*,radius=0.5,height=1,sectors=10):"""Return vertices and triangle of a Cone. Parameters ---------- radius: float, optional Radius of the cone height: float, optional Height of the cone sectors: int, optional Sectors in the cone Returns ------- vertices: ndarray vertices coords that compose our cone triangles: ndarray triangles that compose our cone """ifsectors<3:raiseValueError("Sectors parameter should be greater than 2")sector_angles=2*np.pi/sectors*np.arange(sectors)# Circle in YZ planeh=height/2.0x=np.full((sectors,),-h)y,z=radius*np.cos(sector_angles),radius*np.sin(sector_angles)x=np.concatenate((x,np.array([h,-h])))y=np.concatenate((y,np.array([0,0])))z=np.concatenate((z,np.array([0,0])))vertices=np.vstack(np.array([x,y,z])).T# index of base and top centersbase_center_index=int(len(vertices)-1)top_center_index=base_center_index-1triangles=[]foriinrange(sectors):ifnoti+1==top_center_index:triangles.append(top_center_index)triangles.append(i)triangles.append(i+1)triangles.append(base_center_index)triangles.append(i+1)triangles.append(i)else:triangles.append(top_center_index)triangles.append(i)triangles.append(0)triangles.append(base_center_index)triangles.append(0)triangles.append(i)triangles=np.array(triangles).reshape(-1,3)returnvertices,triangles
