CSCE 155N Fall Homework Assignment 3: Coordinates Transformation Tool 1. Assigned: September 29, 2016 Due: October 20, 2016

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1 CSCE N Fall 0 Homework Assignment : Coordinates Transformation Tool Assigned: September 9 0 De: Otober 0 0 Note: This assignment is to be ompleted in grops of or Points: 00 points Objeties Memo To: The Programmer Memo From: Yor boss The objeties of this homework assignment:. Master the se of standard I/O in Matlab.. Master the se of seletion statements in Matlab.. Master the se of loops in Matlab.. Familiarize with the se of File Inpt/Otpt (I/O) in Matlab espeially with reading/writing Eel files.. Familiarize with the se of fntions in Matlab. 7. Familiarize with the se of ell arrays in Matlab. 8. Familiarize with the se of matries in Matlab. 9. Familiarize with the onept of ontrol statements (seletion and loop) in soltion design. 0. Be eposed to error handling of data from file I/O.. Be eposed to the onept of problem deomposition and the design-implementation-test yle.. Appreiate and nderstand the appliation of omptational thinking in soling engineering problems Problem Desription A oordinator transformation tool for iil engineers is sally epensie. We hae boght a new eletroni measrement instrment for sreying. Or preios transformation tool does not work for the new mahine. We need a tool to transform the measred data whih are saed in eel files. In this projet yo are reqired to deelop a oordinator transformation tool gien a series of sefl transformation formla. Gien a sample reslt from or instrment please help s to transform them to the longitdelatitde ( y) oordinates. Coordinate transformations are sed in sreying and mapping to transform oordinates in one "system" to oordinates in another system and they may take many forms. For eample: Map projetions are transformation of geographial oordinates latitde and longitde on a sphere or ellipsoid to retanglar (or Cartesian) oordinates on a plane; Polar-retanglar onersions are transformation of oordinates of points in polar oordinates say bearings and distanes to retanglar oordinates; R.E. Deakin Jly 00 Coordinate Transformations in Sreying and Mapping Geospatial Siene.

2 Two-dimensional (D) transformations where the oordinates of points in one retanglar system (y) are transformed into oordinates in another retanglar system (XY); and Three-dimensional (D) transformations where the oordinates of points in one righthanded retanglar system (yz) are transformed into oordinates in another retanglar system (XYZ). Note that in D transformations all points lie in a plane. For this assignment it is assmed that D transformations are transformations from one retanglar oordinate system () to another retanglar system (y). In addition nless stated otherwise a rotation is an angle onsidered to be positie in an antilokwise diretion as determined by the right-hand-grip rle. oordinates are transformed to y oordinates by onsidering a rotation of the oordinate aes throgh a positie antilokwise angle θ. The transformation eqations an be epressed in the following way. Or in matri notation This is the rotation transformation (RT). osθ + y + osθ osθ y osθ oordinates are transformed to y oordinates by onsidering a rotation of the oordinate aes throgh a positie antilokwise angle θ and a saling of the oordinates by a fator s. The transformation eqations an be epressed in the following way Or in matri notation s osθ + s y s + s osθ osθ s y osθ This is the rotation and sale transformation (RST). Often the oeffiients of and are written as a s osθ and b s giing a y b b a Usally a translation (t t y ) is added to the transformation in the following way a y b b + t a t This transformation is referred to -parameter transformations (P). y

3 oordinates are transformed to y oordinates by the following eqations ontaining si parameters; for oeffiients a b d and e and two translations and f. Affine transformations are often alled -parameter transformations (P). The transformation eqations are a y d b + e f On the other hand a polynomial fntion of a single ariable is defined as P ( ) As an eample of a D Polynomial transformation (D) the oordinates are transformed to y oordinates sing a seond-order D Polynomial transformation with the weights (the s and the d s) proided y d d + d + d + d d The seond-order D Polynomial Conformal transformation (D) is the following with the weights (the A s and the B s) proided. A0 + A B + A ( ) B () y B0 + B + A + B ( ) + A () Write a program (that may also inlde seeral programmer-defined fntions) that performs the following: () Read data from an Eel file (as shown as an eample in Figre below) whih ontains all the points from sreying. These are the () points in the aboe formla. Besides the points there is also some information on how the data is measred inlding the aboe si methods. This file also inldes the parameters for eah method. The parameters are saed in the following manner in the eel file. For eample the theta ale (θ) sed for the RT method is saed nder the P olmn and for the RST method the theta ale is saed nder the P olmn and the s ale is saed nder the P olmn. RT: θ P RST: θ P; s P P: a P; b P; t P; t y P P: a P; b P; P; d P; e P; f P D: 0 ~ P~P; d 0 ~d P7~P D: A 0 ~A P~P; B 0 ~B P~P

4 Figre. Eample Eel file of the inpt data IMPORTANT: Note that bease eah row in the Eel file onsists of string and nmeri entries yo are reqired to se ell arrays to store the information of the Eel file ontent. To read an eel file yo an se the lsread fntion. Yo an se the following ommand to read the file and the ell arrays are in the ariable alldata. Note yo annot se lsread nless yo hae Mirosoft Offie installed on yor ompter. If in that ase yo may se the ompters in the lab Aery A. [ndata tet alldata] lsread('data.ls') The angle in the file is in degrees. To se sin and os fntions yo shold hange the angle in radians. (Note in Matlab pi is a onstant ariable to denote π) rad deg* π 80 () Design a fntion for eah transformation method. Eah fntion mst hae a set of inpt argments and a set of otpt argments. () Using the parameter to transform the () oordinate to (y) oordinate based on the CODE. Yor program shold be smart to find the errors from the inpt file. If the inpt file has less data than the reqired parameters for eample only P-P eists for P method. The program shold otpt an error message for inorret inpt. () Sae the new reslt and the original data into a new Eel file. A sample of the otpt eel file is as following in Figre. The reslt (y) shold be saed in the olmn X and Y. To sae ell arrays yo an se the ommand lswrite lswrite('data.ls'alldata) Figre. Eample otpt Eel file.

5 All eample inpt files (inlding those for the Challenge problem) are aailable online for download. Please hek with yor instrtor for the files. Challenge Etra Credit (0 points) The hallenge is now we hae two deies! The differene between the new deie and the old one is that they se different oordinates. Consider two different files whih sae the measrement of the same objet (i.e. a bilding) measred by the old deie and the new deie how an we transform from an old file to a new file? In another word we need to sae the data generated by the old deie to the oordinates the new deie ses and keep all the data in the same oordinates. To work ot this problem iil engineers se the different deies to measre the same objet in the same plae. And they get two different data sets. Yor job is to design a program to read these two data sets and then tell s whih CODE is sed to transform from the old file to the new file. Figre is an eample of the inpt file. The olmns A and B sae the data from the old deie while the C and D olmns sae the data from the new deie. Regarding this file yor program shold determine that it ses RT transformation and the parameter for RT is angle θ 0. Figre. Eample inpt Eel file. A arefl reader may find RT RST P and P are all linear eqations. A RT transformation is also a RST transformation with s. Similarly a RST is also a P with (t t y ) (00). And a P transformation of orse belongs to a P transformation with a e and b -d. We need a program to allate the si parameters for P then hek if a e and b -d. If yes then it is a P. If it is a P we shold frther hek if (t t y ) (00) then it is a RST. If it is a RST then we an frther hek whether it is a RT or not. Yo an hek if a D transformation is a D transformation in a similar manner. The problem then is how to design sh a program to allate the si parameters for P. What we hae is a series of () from the old deie measrement and a series of (y) from the new deie measrement. a y d b + e f

6 Consider a +b + and a +b + ths ( - ) a( - )+b( - ). With three pairs of data sets ths (ab) an be allated by MATLAB α A\β. (Note that α A and β are defined in the formlae below). After this yo an allate. To allate d e and f yo an se the same way. b a A b a β α For the D transformation a larger matri is sed. Yo do not need to onsider whether it is a linear transformation or a seond order transformation. We will proide yo data sets to test the linear transformation and also data sets to test the seond order transformation. (When yo get the matri A and β to ompte α yo old also se the Matlab fntion regress instead of α A\β.) Sbmission Proedre This assignment is de at :9:00pm (Central Time) Otober 0 0. Assignments sbmitted later will NOT be aepted. Remember yor program shold follow a good programming style inlde plenty of omments both inline domentation and Matlabdo domentation and perform all of the fntionality otlined aboe. Also in the welome message of yor program state whether yo are implementing the etra redit fntionality so that yor program will reeie the proper redit. Yo mst handin the following files on-line ( /handin/):. Sore files: iesol.m *.m. Projet Report: iesol.pdf (Inlding a oer page that has all team members name and address smmary of yor projet disssion of yor design proess a flowhart of yor algorithm a sample rn eplanation of how yo tested yor projet an instrtion manal for a non-programmer on how to rn yor projet and itations of sores yo onslted). members0projet.tt. ontribtions0projet.tt (indiidally for eah grop member)

7 Hints. Hint: Yo may want to se the bilt-in Matlab fntion isnan to hek if a ell is empty in the ell arrays. Also the inerse fntion for os is aos in Matlab.). Hint: Here we proide additional hints and gidelines for the Challenge Etra Credit part of the HW assignment. In this program yo may find does not eqal 0 bease we saled fied point format with digits when we sae the reslt in eel file. So when we reerse the omptation the parameters we get may not be eqal. Yo annot simply se to determine whether two nmbers are eqal hene. As a reslt yo may need to design a fntion to do this. For eample to ompare two ariable a and b if the absolte differene between a and b is less than then onsider a and b eqal. Name this fntion as issame or some other appropriate names bt do not name it iseqal sine this is already sed by Matlab for is bilt-in fntion. From the handot A RT transformation is also a RST transformation with s. Similarly a RST is also a P with (t t y ) (00). And a P transformation of orse belongs to a P transformation with a e and b -d yo shold all the aforementioned stomized fntion issame to do all the omparison instead of.. Hint: Here we proide a sample inpt/otpt for the Challenge Etra Credit part of the HW assignment.. 7