Tutorial on Meshing¶

In [1]:
%%javascript
IPython.OutputArea.prototype._should_scroll = function(lines) {
return false;
}
In [2]:
import numpy as np
import os
import pandas as pd
import gstlearn as gl
import gstlearn.plot as gp

Standard Meshing based on an Irregular Data Set¶

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

In [3]:
nech = 40
extendmin = [0,0]
extendmax = [150,100]
data = gl.Db.createFromBox(nech,extendmin, extendmax)
data
Out[3]:
Data Base Characteristics
=========================

Data Base Summary
-----------------
File is organized as a set of isolated points
Space dimension              = 2
Number of Columns            = 3
Maximum Number of UIDs       = 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 [4]:
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 [5]:
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 [6]:
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 [7]:
grid = gl.DbGrid()
err = grid.resetCoveringDb(data, [50,50])

Define a Polygon as the Convex hull of the data

In [8]:
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 [9]:
err = gl.db_polygon(grid, polygon)

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

In [10]:
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 [11]:
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 [12]:
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 [13]:
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 [14]:
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
Maximum Number of UIDs       = 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 [15]:
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 [16]:
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 [17]:
ax = mesh6.plot()
ax = gp.point(grid,color="black")
ax.decoration(title="Turbo Meshing for Rotated Grid")