From 8927adb056aed0080cf38124b6dbf602676fa8e3 Mon Sep 17 00:00:00 2001
From: Michael Will <m_will15@cs.uni-kl.de>
Date: Wed, 8 Jul 2020 16:54:43 +0200
Subject: [PATCH] assignment 10

---
 README.md                     |    5 +-
 ex10/.gitkeep                 |    0
 ex10/README.md                |   68 +
 ex10/ReadVectorfield.py       |   36 +
 ex10/Tensors.py               |   49 +
 ex10/doublePushPullStrain.vtk | 6157 +++++++++++++++++++++++++++++++++
 ex10/img/.gitkeep             |    0
 ex10/img/critical.png         |  Bin 0 -> 166780 bytes
 ex10/img/tensor.png           |  Bin 0 -> 165712 bytes
 ex10/img/timeline.gif         |  Bin 0 -> 5325458 bytes
 ex10/vector.vti               |  Bin 0 -> 394380 bytes
 11 files changed, 6313 insertions(+), 2 deletions(-)
 create mode 100644 ex10/.gitkeep
 create mode 100644 ex10/README.md
 create mode 100644 ex10/ReadVectorfield.py
 create mode 100644 ex10/Tensors.py
 create mode 100644 ex10/doublePushPullStrain.vtk
 create mode 100644 ex10/img/.gitkeep
 create mode 100644 ex10/img/critical.png
 create mode 100644 ex10/img/tensor.png
 create mode 100644 ex10/img/timeline.gif
 create mode 100644 ex10/vector.vti

diff --git a/README.md b/README.md
index bbf5f2f..d87f188 100644
--- a/README.md
+++ b/README.md
@@ -7,8 +7,9 @@
 - [Assignment 5](ex5/README.md) (due June 17, 2020)
 - [Assignment 6](ex6/README.md) (due June 24, 2020)
 - [Assignment 7](ex7/README.md) (due July 1, 2020)
-- [Assignment 8](ex7/README.md) (due July 8, 2020)
-- [Assignment 9](ex7/README.md) (due July 15, 2020)
+- [Assignment 8](ex8/README.md) (due July 8, 2020)
+- [Assignment 9](ex9/README.md) (due July 15, 2020)
+- [Assignment 10](ex10/README.md) (due July 22, 2020), Bonus
 
 ## FAQ and HOWTOs
 
diff --git a/ex10/.gitkeep b/ex10/.gitkeep
new file mode 100644
index 0000000..e69de29
diff --git a/ex10/README.md b/ex10/README.md
new file mode 100644
index 0000000..500b640
--- /dev/null
+++ b/ex10/README.md
@@ -0,0 +1,68 @@
+# Assignment 10 - Bonus
+In this final assignment, we will leave further look at vector fields and briefly touch on tensor fields. For this assignment, you should have watched all the videos. This assignment is a **bonus** assignment, which means that you can use it to get some additional points if it is close, but it is not necessary to submit this assignment to get the qualification.
+
+
+## Task 1: Timelines (2P)
+In the previous assignment we worked on a glyph-based visualization of vector fields and streamlines. There are some other types of field lines which are closely connected to streamlines called streaklines, pathlines and timelines. When the vector field is static, most of these look similar. The only line type with big differences is the timeline. This is why we want to implement them in this assignment.
+
+Timelines are formed by a set of particles seeded on a line. By observing how this line moves throughout the vector field and eventually breaks up, we can deduce many things about the flow of the field.
+
+Start by copying your solution from last week into the `main`-method of `ReadVectorfield.py` and running it. If you have done the last assignment correctly, you should see the colored vector field with streamlines in it. If you had problem with the last assignment or are in any way unable to get a basic script running, contact us.
+
+Given in the script is the method `get_val_at_coord(output, point)`. This method takes the output of the dataset reader and an arbitrary point in the field (not necessarily a data point itself e.g. (0.5, 0.7, 0) would be valid) and returns the interpolated value of the vector field at this point.
+
+Start by seeding points on a line. This can be done in `init_timeline`. Then, either by using threading or by [researching](https://medium.com/@daniel.stjnv/animation-and-callbacks-with-vtk-dd4bd5e55c13) how [animation](https://lorensen.github.io/VTKExamples/site/Python/Utilities/Animation/) in vtk works, you should check the field value for each point in each timestep and move the points according to the vector field (you should probably scale the movement up, otherwise it could be pretty slow).
+
+The result should look somewhat like this:
+
+<img width="500px" src="img/timeline.gif">
+
+**Summary of Tasks:** Create a timeline visualization for this vector field.
+
+
+## Task 2: Going critical... (3P)
+A central ingredient in vector field topology are so-called critical points where the vector field vanishes, i. e. a
+point x where v(x) = 0.
+
+Considering a dataset described over a regular grid, per cell the vector field is given by the bilinear interpolant
+
+v(r,s) := (1 − s)((1 − r)v i,j + rv i+1,j ) + s((1 − r)v i,j+1 + rv i+1,j+i )),
+
+with local coordinates (r,s). Implement a function that iterates over each cell and determines whether the cell contains a critical point, and
+if it does, its location. Display the resulting critical points (e.g. with spheres).
+
+Remark: Solving the above equation for v(r,s) = 0 leads to a system of nonlinear equations. As there is no
+general formula for solving such systems, one has to use a numerical approximation such as e.g. [Newton’s
+method](https://en.wikipedia.org/wiki/Newton's_method#Nonlinear_systems_of_equations). In our case, you have to compute the vector field [Jacobian matrix](https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant) ∇ (r,s) in local coordinates. For
+each iteration of Newton’s method, solve a linear [2 × 2-system](http://www.mathwords.com/i/inverse_of_a_matrix.htm) (you may use additional libraries e.g. scipy with fsolve is _very_ helpful).
+Remember, the critical point is only contained in the cell if 0 ≤ r,s ≤ 1. You may also have to ignore cells
+where one of the vertices is zero as well as if the Jacobian matrix has no inverse.
+Note: if you are unsure whether you have located all critical points, color mapping on the vector field magnitude may serve as a debugging tool.
+
+*Hint:* The following code may be used to iterate over the cells. After the inner loop, you have the values at the 4 vertices and are free to work with them as you like
+``` 
+    for i in range(output.GetNumberOfCells()):
+        cell = output.GetCell(i)
+        ids = cell.GetPointIds()
+
+        values = []
+        for i in range(ids.GetNumberOfIds()):
+            values.append(output.GetPointData().GetAbstractArray(0).GetTuple(ids.GetId(i)))
+```
+
+The result should look like this:
+
+<img width="500px" src="img/critical.png">
+
+**Summary of Tasks:** Calculate and display critical points.
+
+## Task 3: Tensor Fields (1P)
+After scalar fields and vector fields, the next dimension is tensor fields. As you should have learned in the lecture, visualizing tensor fields directly is almost impossible and you need special methods to visualize them in a meaningful way. One of the methods is computing the eigenvalues and using a glyph-based approach.
+
+Luckily for you vtk implements this by itself using the `vtkTensorGlyph` class. Be cautious however, as your glyphs may be much too large! You may need to scale it by a factor of 10e-6 or even less.
+
+The result should look somewhat like this:
+
+<img width="500px" src="img/tensor.png">
+
+**Summary of Tasks:** Create a glyph based visualization for the tensor field.
\ No newline at end of file
diff --git a/ex10/ReadVectorfield.py b/ex10/ReadVectorfield.py
new file mode 100644
index 0000000..d5f02e9
--- /dev/null
+++ b/ex10/ReadVectorfield.py
@@ -0,0 +1,36 @@
+import vtk
+
+
+def get_val_at_coord(output, point):
+    weights = [0.0, 0.0, 0.0, 0.0]
+    outputcell = vtk.vtkPixel()
+    idtype = 8
+    subid = vtk.reference(0)
+    pcoords = [0.0, 0.0, 0.0]
+    cell = output.FindAndGetCell(point, outputcell, idtype, 0.001, subid, pcoords, weights)
+    if cell is None:
+        return 0, 0, 0
+    ids = cell.GetPointIds()
+    values = []
+    for i in range(ids.GetNumberOfIds()):
+        values.append(output.GetPointData().GetAbstractArray(0).GetTuple(ids.GetId(i)))
+
+    x_val = weights[0] * values[0][0] + weights[1] * values[1][0] + weights[2] * values[2][0] + weights[3] * values[3][
+        0]
+    y_val = weights[0] * values[0][1] + weights[1] * values[1][1] + weights[2] * values[2][1] + weights[3] * values[3][
+        1]
+    z_val = 0
+    val_at_coord = (x_val, y_val, z_val)
+    return val_at_coord
+
+
+def init_timeline(n, renderer):
+    return 0
+
+
+def main():
+    return 0
+
+
+if __name__ == '__main__':
+    main()
diff --git a/ex10/Tensors.py b/ex10/Tensors.py
new file mode 100644
index 0000000..1b4bf31
--- /dev/null
+++ b/ex10/Tensors.py
@@ -0,0 +1,49 @@
+import vtk
+
+
+def main():
+    colors = vtk.vtkNamedColors()
+    color_bg = map(lambda x: x / 255.0, [255,255, 255, 255])
+    colors.SetColor("BackGroundColor", *color_bg)
+
+    file_name = 'doublePushPullStrain.vtk'
+
+    # Read the source file.
+    reader = vtk.vtkRectilinearGridReader()
+    reader.SetFileName(file_name)
+    reader.Update()  # Needed because of GetScalarRange
+    output = reader.GetOutput()
+
+    # Create the mapper that creates graphics elements
+    mapper = vtk.vtkPolyDataMapper()
+    mapper.SetInputConnection(reader.GetOutputPort())
+
+    # Create the Actor
+    actor = vtk.vtkActor()
+    actor.SetMapper(mapper)
+
+    # Create the Renderer
+    renderer = vtk.vtkRenderer()
+    renderer.AddActor(actor)
+    renderer.ResetCamera()
+    renderer.SetBackground(colors.GetColor3d("Silver"))
+
+    # Create the RendererWindow
+    render_window = vtk.vtkRenderWindow()
+    render_window.AddRenderer(renderer)
+    render_window.SetMultiSamples(642)
+
+    # Render and interact
+    render_window.Render()
+
+    # Create the RendererWindowInteractor and display the vti file
+    interactor = vtk.vtkRenderWindowInteractor()
+    interactor.SetRenderWindow(render_window)
+    interactor.Initialize()
+
+    interactor.Start()
+
+
+
+if __name__ == '__main__':
+    main()
diff --git a/ex10/doublePushPullStrain.vtk b/ex10/doublePushPullStrain.vtk
new file mode 100644
index 0000000..4691164
--- /dev/null
+++ b/ex10/doublePushPullStrain.vtk
@@ -0,0 +1,6157 @@
+# vtk DataFile Version 3.0
+a funny dataset
+ASCII
+DATASET RECTILINEAR_GRID
+DIMENSIONS 16 8 16
+X_COORDINATES 16 float 
+-7.5 -6.5 -5.5 -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5
+Y_COORDINATES 8 float 
+0 -1 -2 -3 -4 -5 -6 -7
+Z_COORDINATES 16 float 
+-7.5 -6.5 -5.5 -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5
+POINT_DATA 2048
+TENSORS justForFun float
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-- 
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