Basic Examples (7)
Basic Examples
(7)
Get the measure of a :
In[1]:=
Out[1]=
2
(x1-x2)
2
(y1-y2)
Compare to Euclidean distance:
In[2]:=
ResourceFunction["RealEuclideanDistance"][{x1,y1},{x2,y2}]
Out[2]=
2
(x1-x2)
2
(y1-y2)
———
Get the measure of a :
In[1]:=
Out[1]=
1
2
2
(x2y1-x3y1-x1y2+x3y2+x1y3-x2y3)
Compare to :
In[2]:=
Area[Triangle[{{x1,y1},{x2,y2},{x3,y3}}]]
Out[2]=
1
2
———
Get the measure of a random 100-dimensional :
In[1]:=
Out[1]=
0.1318155083592108
———
Get the measure of a simplicial complex, represented as a list of simplices:
In[1]:=
Out[1]=
2-4x1x2+2+2-4y1y2+2
2
x1
2
x2
2
y1
2
y2
2
2-4x3x4+2+2-4y3y4+2
2
x3
2
x4
2
y3
2
y4
2
———
Get the measure of a simplicial complex, represented by lists of vertices:
In[1]:=
Out[1]=
2+
2
———
Specify a dimension to measure:
In[1]:=
complex={Point[{x1,y1}],Line[{{x2,y2},{x3,y3}}],Triangle[{{x4,y4},{x5,y5},{x6,y6}}]}
Out[1]=
{Point[{x1,y1}],Line[{{x2,y2},{x3,y3}}],Triangle[{{x4,y4},{x5,y5},{x6,y6}}]}
In[2]:=
Out[2]=
2
(x2-x3)
2
(y2-y3)
In[3]:=
Out[3]=
1
2
2
(x5y4-x6y4-x4y5+x6y5+x4y6-x5y6)
———
Get the measure of a :
In[1]:=
mesh=MeshRegion[{{0,0},{1,0},{0,1},{1,1},{2,1},{2,0}},Simplex[{{1,2,3},{4,5,6}}]]
Out[1]=
In[2]:=
Out[2]=
1.
Properties and Relations (7)
Properties and Relations
(7)
Possible Issues (1)
Possible Issues
(1)