Description
Instructions: Please show your solutions to each problem in full, writing them neatly. For computer programs, please remember to turn in your code through the course’s blackboard session, as well as any plots / figures that are requested. If you have collaborated with another student on solving this homework assignment please state so (e.g. “1 helped John with question
LEARNING GOALS:
Working with Vectors & Matrices in Matlab
Visualizing data in Matlab.
Input & Output of essential file-types for this 3ioE 1330 / 2330.
Visualization of data using Visualization Tool Kit (WK).
BASIC MATH & APPLIED PROGRAMING
1. Part I (25 points): Find the unit normal vector the following three points and HINT: The vector normal to two vectors in-plane is in the direction of their cross product. Finally, write a Matlab
for this which accepts three vectors as input, function computeNorma1s (PI, P2, P3), where PI, P2 and P3 are Ix3 vectors.
Remember to upload your code through Blackboard.
Part 2 (40 points) : Extrapolate this logic used above (i.e. Part I) to compute the normal directions of each of the triangles in the following
STL surface geometry and subsequently write out a file containing the points (i.e. vertices), triangles and normal vectors of the geometry (one normal vector per vertex) as a Legacy VTK (visualization toolkit)
file:
• Source STL File: CoronaryArteryBranch.stl
2.
• Visualize your results using “Glyphs” shaped like “arrows” in Paraview (Kitware Inc., NY: www.pa__væw.org) — the open source visualization engine based on VTK.
personal computing devices for this assignment.
+ Icode is provided on Blackboard to help VOU qet started:
• Matlab function to write VTK PolyData (surface) files: write_vtk_Surface
• Matlab function to read STL (binary) surface geometries: st/read
v is the list of vertices of the geometry and L is the list of faces of the geometry.
(20 points) Curve Fitting: For the production of X-ray in a CT scanner, we use Tungsten as a popular choice of material. However, not all the radiation produced by Tungsten results in Strong X-rays; some are weak, with lower energy (measured in keV) and need to be filtered to prevent the patient from extra exposure to radiation. This process is called Beam Hardening. For this purpose, we install metal filters that can absorb this unwanted lower energy radiation. In this question, we want to design a beam hardening filter to absorb 25 kev Of energy and Our material Of choice for a beam-hardening metal filter is copper. Let’s say that copper has different energy-absorption capabilities at different temperatures given by the table below:
Energy
Temperature, T
Absorption
(keV)
15.4
16.7
18.6
19.8 -40
-20
20
I This means that “code” provided on gjackboard requires to be used in this And remember, this assignment require submission / up’oading of your code addition to an inserted snapshot of the fina,’ rendermq outputted and Visualized in Paravjew for your reports.
22.7
26.6
29.5
25
40
60
(2) Solve this curve fitting problem by hand by now, assuming that the relationship between Energy and Temperature is linear. Obtain a system of linear equation of the form, Ax h and solve to obtain a linear fit after first conditioning the A matrix by pre-multiplying your matrix equation with AT , first . What is your interpolated answer now?
(3) Find the linear fit from part (2) again using backslash operator of MATLAB also. Does your answer match the one obtained in part (2)..? If not, why..?
