Plot Mesh

Curves, surfaces, polyhedra are basic topics in geometry. Here shows some interesting geometry models with visual and algebraic representaions. Mathcurve is a very helpful curve and surface library.

Mesh are discretized surfaces. They are represented by straight edges connecting ranges of points as vertices.

from geometrylab.vtkplot.edgesource import Edges
from geometrylab.vtkplot.facesource import Faces
def plot_mesh(self, mesh, name):
    showe = Edges(mesh,color='black',tube_radius=1*self.meshmanager.r,name=name+'e')
    showf = Faces(mesh,color=(160,197,194),glossy=1,name=name+'f')
    self.meshmanager.add([showe, showf])

Quad mesh

Quad Planarity

def plot_planarity(self, mesh, name):
    data = mesh.face_planarity()
    val = np.max(data)
    print('max. planarity =','%.2g' % val)
    showe = Edges(mesh,color='black',name=name+'e')
    showf = Faces(mesh,face_data=data,glossy=1,opacity=1,color='coolwarm',lut_range=[0,val],name=name+'f')
    self.meshmanager.add([showe, showf])

Planarity of a quad mesh

Gaussian Curvature

def plot_gaussian_curvature(self, mesh, name):
    vertex_data = mesh.gaussian_curvature()
    vertex_data = mesh.smooth_vertex_data(vertex_data)
    showe = Edges(mesh,color='black',name=name+'e')
    showf = Faces(mesh,vertex_data=vertex_data,color='coolwarm',lut_range='-:0:+',name=name+'f')
    self.meshmanager.add([showe, showf])

Gaussian curvature of a quad mesh

Mean Curvature

def plot_mean_curvature(self, mesh, name):
    vertex_data = mesh.mean_curvature()
    vertex_data = mesh.smooth_vertex_data(vertex_data)
    showe = Edges(mesh,color='black',name=name+'e')
    showf = Faces(mesh,vertex_data=vertex_data,color='coolwarm',lut_range='-:0:+',name=name+'f')
    self.meshmanager.add([showe, showf])

Mean curvature of a quad mesh

Curve network

def plot_curvenet(self, mesh, name):
    poly1 = mesh.get_both_isopolyline(True)
    poly2 = mesh.get_both_isopolyline(False)
    self.meshmanager.plot_polyline(polyline=poly1,color='black',name=name+'1')
    self.meshmanager.plot_polyline(polyline=poly2,color=(240,114,114),name=name+'2')

Curve network of a quad mesh

Isolines

def plot_isolines(self, mesh, name, w_smooth_vertex=0.1,num_contour=20):
    ## plot the isoline of Gaussian curvature K (red) and Mean curvature H (blue)
    mesh,k1,k2,K,H = mesh.get_curvature_disk_polylines(is_quad=True,is_sub=True)

    showf = Faces(mesh,color='white',opacity=0.99,name=name)
    self.meshmanager.add(showf) 

    if w_smooth_vertex!=0:
        K = mesh.smooth_vertex_data(K,smoothing=w_smooth_vertex)
        H = mesh.smooth_vertex_data(H,smoothing=w_smooth_vertex)

    showK = Faces(mesh,vertex_data=K,iso_surface=True,
                    color=(162,20,47),glossy=0.8,
                    tube_radius=3,number_of_contours=num_contour,
                    name = name+'K')

    showH = Faces(mesh,vertex_data=H,iso_surface=True,
                    color=(2,52,118),glossy=0.8,
                    tube_radius=3,number_of_contours=num_contour,
                    name = name+'H')

    self.meshmanager.add([showK, showH])

Isolines of a quad mesh

Support Structures

def plot_support_structures(self, mesh, name):
    sm = mesh.get_both_support_structures_from_edges(
                    dist=self.scale_dist_offset,
                    is_central=self.is_middle_ss,
                    diagnet=self.switch_diagnet,
                    ss1=False,ss2=False) 
    data = sm.face_planarity()
    showe = Edges(sm,color='black',name=name+'e')
    showf = Faces(sm,face_data=data,color='coolwarm',lut_range='-:0:+',name=name+'f')
    self.meshmanager.add([showe, showf])

Support structures of a quad mesh