Meshing¶

In [1]:
import numpy as np
import os
import pandas as pd
import gstlearn as gl
import gstlearn.plot as gp
import gstlearn.document as gdoc

gdoc.setNoScroll()

Standard Meshing based on an Irregular Data Set¶

We construct a Meshing Standard based on a set of Data Points

In [2]:
nech = 40
extendmin = [0,0]
extendmax = [150,100]
data = gl.Db.createFromBox(nech,extendmin, extendmax)
data
Out[2]:
Data Base Characteristics
=========================

Data Base Summary
-----------------
File is organized as a set of isolated points
Space dimension              = 2
Number of Columns            = 3
Total number of samples      = 40

Variables
---------
Column = 0 - Name = rank - Locator = NA
Column = 1 - Name = x-1 - Locator = x1
Column = 2 - Name = x-2 - Locator = x2
In [3]:
gp.setDefaultGeographic(dims=[7,7])

ax = data.plot()
ax.decoration(title="Display of Data Set")

Creating the Meshing

Turbo Meshing¶

Instead we can use Turbo Meshing to cover an area, without specifically honoring each datum

In [4]:
mesh3 = gl.MeshETurbo()
err = mesh3.initFromExtend(extendmin, extendmax, [5,5])
mesh3.display()

Grid characteristics:
---------------------
Origin :      0.000     0.000
Mesh   :      5.000     5.000
Number :         31        21
 
Turbo Meshing
=============
Euclidean Geometry
Space Dimension           = 2
Number of Apices per Mesh = 3
Number of Meshes          = 1200
Number of Apices          = 651

Bounding Box Extension
----------------------
Dim #1 - Min:0 - Max:150
Dim #2 - Min:0 - Max:100
In [5]:
ax = mesh3.plot()
ax.decoration(title="Turbo Meshing on the whole area")
ax = data.plot(color="black")

We can create a regular grid covering the same area (based on the data set)

In [6]:
grid = gl.DbGrid()
err = grid.resetCoveringDb(data, [50,50])

Define a Polygon as the Convex hull of the data

In [7]:
polygon = gl.Polygons()
err = polygon.resetFromDb(data)

Use the Polygon to mask off some nodes of the regular grid, located too far from the data

In [8]:
err = gl.db_polygon(grid, polygon)

We create a Turbo Meshing from the grid (which contains a selection)

In [9]:
mesh4 = gl.MeshETurbo(grid)
mesh4.display()

Grid characteristics:
---------------------
Origin :      0.648     3.385
Mesh   :      2.892     1.928
Number :         50        50
 
Turbo Meshing
=============
Euclidean Geometry
Space Dimension           = 2
Number of Apices per Mesh = 3
Number of Meshes          = 3481
Number of Apices          = 1830

Bounding Box Extension
----------------------
Dim #1 - Min:0.648392 - Max:142.336
Dim #2 - Min:3.38503 - Max:97.8622

Mask Information
................
Mesh Masking Indexing
- Information (AToR) is stored as a Map
- Number of absolute positions = 4802
- Number of active positions   = 3481

Grid Masking Indexing
- Information (AToR) is stored as a Map
- Number of absolute positions = 2500
- Number of active positions   = 1830
In [10]:
ax = mesh4.plot()
ax = data.plot(color="black")
ax = polygon.plot()
ax.decoration(title="Turbo Meshing restricted to the Convex Hull of Data")

Read and Write in Neutral File¶

Testing the read and write into a Neutral File (with masked meshes)

In [11]:
gl.ASerializable.setContainerName(True)
gl.ASerializable.setPrefixName("Tuto-Meshing")

err = mesh4.dumpToNF("Mesh_masked")
mesh5 = gl.MeshETurbo.createFromNF("Mesh_masked")
mesh5.display()

Grid characteristics:
---------------------
Origin :      0.648     3.385
Mesh   :      2.892     1.928
Number :         50        50
 
Turbo Meshing
=============
Euclidean Geometry
Space Dimension           = 2
Number of Apices per Mesh = 3
Number of Meshes          = 3481
Number of Apices          = 1830

Bounding Box Extension
----------------------
Dim #1 - Min:0.648392 - Max:142.336
Dim #2 - Min:3.38503 - Max:97.8624

Mask Information
................
Mesh Masking Indexing
- Information (AToR) is stored as a Map
- Number of absolute positions = 4802
- Number of active positions   = 3481

Grid Masking Indexing
- Information (AToR) is stored as a Map
- Number of absolute positions = 2500
- Number of active positions   = 1830
In [12]:
mesh5.display()

Grid characteristics:
---------------------
Origin :      0.648     3.385
Mesh   :      2.892     1.928
Number :         50        50
 
Turbo Meshing
=============
Euclidean Geometry
Space Dimension           = 2
Number of Apices per Mesh = 3
Number of Meshes          = 3481
Number of Apices          = 1830

Bounding Box Extension
----------------------
Dim #1 - Min:0.648392 - Max:142.336
Dim #2 - Min:3.38503 - Max:97.8624

Mask Information
................
Mesh Masking Indexing
- Information (AToR) is stored as a Map
- Number of absolute positions = 4802
- Number of active positions   = 3481

Grid Masking Indexing
- Information (AToR) is stored as a Map
- Number of absolute positions = 2500
- Number of active positions   = 1830

Turbo Meshing on Rotated Grid¶

In [13]:
grid = gl.DbGrid.create(nx=[6,4], dx=[1.,5.], x0=[10.,20.], angles=[-80.,0.])
grid.display()
ax = gp.point(grid,color="black")

Data Base Grid Characteristics
==============================

Data Base Summary
-----------------
File is organized as a regular grid
Space dimension              = 2
Number of Columns            = 3
Total number of samples      = 24

Grid characteristics:
---------------------
Origin :     10.000    20.000
Mesh   :      1.000     5.000
Number :          6         4
Rotation Angles        =    -80.000     0.000
Direct Rotation Matrix
               [,  0]    [,  1]
     [  0,]     0.174     0.985
     [  1,]    -0.985     0.174
Inverse Rotation Matrix
               [,  0]    [,  1]
     [  0,]     0.174    -0.985
     [  1,]     0.985     0.174

Variables
---------
Column = 0 - Name = rank - Locator = NA
Column = 1 - Name = x1 - Locator = x1
Column = 2 - Name = x2 - Locator = x2
In [14]:
model = gl.Model.createFromParam(gl.ECov.CUBIC,ranges=[10.,5.], angles=[30.,0.])
model.display()

Model characteristics
=====================
Space dimension              = 2
Number of variable(s)        = 1
Number of basic structure(s) = 1
Number of drift function(s)  = 0
Number of drift equation(s)  = 0

Covariance Part
---------------
Cubic
- Sill         =      1.000
- Ranges       =     10.000     5.000
- Angles       =     30.000     0.000
- Rotation Matrix
               [,  0]    [,  1]
     [  0,]     0.866    -0.500
     [  1,]     0.500     0.866
Total Sill     =      1.000
In [15]:
mesh6 = gl.MeshETurbo()
mesh6.initFromCova(model.getCova(0),grid,ratio=10,nbExt=2,flagNoStatRot=False,useSel=True)
mesh6.display()

Grid characteristics:
---------------------
Origin :     12.201     8.767
Mesh   :      1.000     0.500
Number :         21        25
Rotation Angles        =     30.000     0.000
Direct Rotation Matrix
               [,  0]    [,  1]
     [  0,]     0.866    -0.500
     [  1,]     0.500     0.866
Inverse Rotation Matrix
               [,  0]    [,  1]
     [  0,]     0.866     0.500
     [  1,]    -0.500     0.866
 
Turbo Meshing
=============
Diamond construction is activated
Euclidean Geometry
Space Dimension           = 2
Number of Apices per Mesh = 3
Number of Meshes          = 960
Number of Apices          = 525

Bounding Box Extension
----------------------
Dim #1 - Min:12.2013 - Max:32.2013
Dim #2 - Min:8.76696 - Max:20.767
In [16]:
ax = mesh6.plot()
ax = gp.point(grid,color="black")
ax.decoration(title="Turbo Meshing for Rotated Grid")