Meshing¶
In [1]:
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.plot(data)
gp.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()
Turbo Meshing ============= Grid characteristics: --------------------- Origin : 0.000 0.000 Mesh : 5.000 5.000 Number : 31 21 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]:
gp.plot(mesh3)
gp.plot(data, c="black")
gp.decoration(title="Turbo Meshing on the whole area")
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()
Turbo Meshing ============= Grid characteristics: --------------------- Origin : 0.648 3.385 Mesh : 2.892 1.928 Number : 50 50 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]:
gp.plot(mesh4)
gp.plot(data, c="black")
gp.plot(polygon)
gp.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.setPrefixName("Tuto-Meshing")
err = mesh4.dumpToNF("Mesh_masked")
mesh5 = gl.MeshETurbo.createFromNF("Mesh_masked")
mesh5.display()
Turbo Meshing ============= Grid characteristics: --------------------- Origin : 0.648 3.385 Mesh : 2.892 1.928 Number : 50 50 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 [12]:
mesh5.display()
Turbo Meshing ============= Grid characteristics: --------------------- Origin : 0.648 3.385 Mesh : 2.892 1.928 Number : 50 50 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
Turbo Meshing on Rotated Grid¶
In [13]:
grid = gl.DbGrid.create(nx=[6, 4], dx=[1.0, 5.0], x0=[10.0, 20.0], angles=[-80.0, 0.0])
grid.display()
res = gp.symbol(grid, c="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=[10.0, 5.0], angles=[30.0, 0.0])
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
Known Mean(s) 0.000
In [15]:
mesh6 = gl.MeshETurbo()
mesh6.initFromCova(model.getCovAniso(0), grid, ratio=10, nbExt=2, useSel=True)
mesh6.display()
Turbo Meshing
=============
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
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]:
gp.plot(mesh6)
gp.symbol(grid, c="black")
gp.decoration(title="Turbo Meshing for Rotated Grid")
