Fall 2023 Data 605 Homework 1
Jean Jimenez
2023-08-31
Assignment
For this weeks homework assignment, we had to draw our initials onto a plot in R and then perform shear, scaling, rotation, and projection and then animate the plots.
I am lucky that my initials are JJ.
My strategy was to first draw the letter J.
#My initials are JJ
# Vertical line of J
x1 = rep(0, 1000)
y1 = seq(-1, 1, length.out=1000)
# horizontal bottom of J
x2 = seq(-0.25,0, length.out=125)
y2 = rep(-1,125)
# horizontal top of J
x3 = seq(-0.25,0.25, length.out=250)
y3 = rep(1,250)
#small vertical part of J
x4 = rep(-0.25, 250)
y4 = seq(-1,-0.5, length.out=250)
# Combine the coordinates for the first J
first_x = c(x1,x2,x3,x4)
first_y = c(y1,y2,y3,y4)
plot(first_y~first_x, xlim=c(-3,3), ylim=c(-3,3))
Then I repeated it but shifted to the right. I then combined the two J’s on the same graph.
#Shifting the second J by 2 to the right so i add 2 to x
second_x=first_x+2
second_y=first_y
#Both Js combined
x=c(first_x,second_x)
y=c(first_y,second_y)
# plot
plot(y~x, xlim=c(-3,3), ylim=c(-3,3))
Afterwards, I turned the coordinates of JJ into a matrix.
# matrix from the x and y coordinates
coord_matrix = matrix(c(x, y), ncol=2)
coord_matrix## [,1] [,2]
## [1,] 0.000000000 -1.000000000
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## [3123,] 1.750000000 -0.755020080
## [3124,] 1.750000000 -0.753012048
## [3125,] 1.750000000 -0.751004016
## [3126,] 1.750000000 -0.748995984
## [3127,] 1.750000000 -0.746987952
## [3128,] 1.750000000 -0.744979920
## [3129,] 1.750000000 -0.742971888
## [3130,] 1.750000000 -0.740963855
## [3131,] 1.750000000 -0.738955823
## [3132,] 1.750000000 -0.736947791
## [3133,] 1.750000000 -0.734939759
## [3134,] 1.750000000 -0.732931727
## [3135,] 1.750000000 -0.730923695
## [3136,] 1.750000000 -0.728915663
## [3137,] 1.750000000 -0.726907631
## [3138,] 1.750000000 -0.724899598
## [3139,] 1.750000000 -0.722891566
## [3140,] 1.750000000 -0.720883534
## [3141,] 1.750000000 -0.718875502
## [3142,] 1.750000000 -0.716867470
## [3143,] 1.750000000 -0.714859438
## [3144,] 1.750000000 -0.712851406
## [3145,] 1.750000000 -0.710843373
## [3146,] 1.750000000 -0.708835341
## [3147,] 1.750000000 -0.706827309
## [3148,] 1.750000000 -0.704819277
## [3149,] 1.750000000 -0.702811245
## [3150,] 1.750000000 -0.700803213
## [3151,] 1.750000000 -0.698795181
## [3152,] 1.750000000 -0.696787149
## [3153,] 1.750000000 -0.694779116
## [3154,] 1.750000000 -0.692771084
## [3155,] 1.750000000 -0.690763052
## [3156,] 1.750000000 -0.688755020
## [3157,] 1.750000000 -0.686746988
## [3158,] 1.750000000 -0.684738956
## [3159,] 1.750000000 -0.682730924
## [3160,] 1.750000000 -0.680722892
## [3161,] 1.750000000 -0.678714859
## [3162,] 1.750000000 -0.676706827
## [3163,] 1.750000000 -0.674698795
## [3164,] 1.750000000 -0.672690763
## [3165,] 1.750000000 -0.670682731
## [3166,] 1.750000000 -0.668674699
## [3167,] 1.750000000 -0.666666667
## [3168,] 1.750000000 -0.664658635
## [3169,] 1.750000000 -0.662650602
## [3170,] 1.750000000 -0.660642570
## [3171,] 1.750000000 -0.658634538
## [3172,] 1.750000000 -0.656626506
## [3173,] 1.750000000 -0.654618474
## [3174,] 1.750000000 -0.652610442
## [3175,] 1.750000000 -0.650602410
## [3176,] 1.750000000 -0.648594378
## [3177,] 1.750000000 -0.646586345
## [3178,] 1.750000000 -0.644578313
## [3179,] 1.750000000 -0.642570281
## [3180,] 1.750000000 -0.640562249
## [3181,] 1.750000000 -0.638554217
## [3182,] 1.750000000 -0.636546185
## [3183,] 1.750000000 -0.634538153
## [3184,] 1.750000000 -0.632530120
## [3185,] 1.750000000 -0.630522088
## [3186,] 1.750000000 -0.628514056
## [3187,] 1.750000000 -0.626506024
## [3188,] 1.750000000 -0.624497992
## [3189,] 1.750000000 -0.622489960
## [3190,] 1.750000000 -0.620481928
## [3191,] 1.750000000 -0.618473896
## [3192,] 1.750000000 -0.616465863
## [3193,] 1.750000000 -0.614457831
## [3194,] 1.750000000 -0.612449799
## [3195,] 1.750000000 -0.610441767
## [3196,] 1.750000000 -0.608433735
## [3197,] 1.750000000 -0.606425703
## [3198,] 1.750000000 -0.604417671
## [3199,] 1.750000000 -0.602409639
## [3200,] 1.750000000 -0.600401606
## [3201,] 1.750000000 -0.598393574
## [3202,] 1.750000000 -0.596385542
## [3203,] 1.750000000 -0.594377510
## [3204,] 1.750000000 -0.592369478
## [3205,] 1.750000000 -0.590361446
## [3206,] 1.750000000 -0.588353414
## [3207,] 1.750000000 -0.586345382
## [3208,] 1.750000000 -0.584337349
## [3209,] 1.750000000 -0.582329317
## [3210,] 1.750000000 -0.580321285
## [3211,] 1.750000000 -0.578313253
## [3212,] 1.750000000 -0.576305221
## [3213,] 1.750000000 -0.574297189
## [3214,] 1.750000000 -0.572289157
## [3215,] 1.750000000 -0.570281124
## [3216,] 1.750000000 -0.568273092
## [3217,] 1.750000000 -0.566265060
## [3218,] 1.750000000 -0.564257028
## [3219,] 1.750000000 -0.562248996
## [3220,] 1.750000000 -0.560240964
## [3221,] 1.750000000 -0.558232932
## [3222,] 1.750000000 -0.556224900
## [3223,] 1.750000000 -0.554216867
## [3224,] 1.750000000 -0.552208835
## [3225,] 1.750000000 -0.550200803
## [3226,] 1.750000000 -0.548192771
## [3227,] 1.750000000 -0.546184739
## [3228,] 1.750000000 -0.544176707
## [3229,] 1.750000000 -0.542168675
## [3230,] 1.750000000 -0.540160643
## [3231,] 1.750000000 -0.538152610
## [3232,] 1.750000000 -0.536144578
## [3233,] 1.750000000 -0.534136546
## [3234,] 1.750000000 -0.532128514
## [3235,] 1.750000000 -0.530120482
## [3236,] 1.750000000 -0.528112450
## [3237,] 1.750000000 -0.526104418
## [3238,] 1.750000000 -0.524096386
## [3239,] 1.750000000 -0.522088353
## [3240,] 1.750000000 -0.520080321
## [3241,] 1.750000000 -0.518072289
## [3242,] 1.750000000 -0.516064257
## [3243,] 1.750000000 -0.514056225
## [3244,] 1.750000000 -0.512048193
## [3245,] 1.750000000 -0.510040161
## [3246,] 1.750000000 -0.508032129
## [3247,] 1.750000000 -0.506024096
## [3248,] 1.750000000 -0.504016064
## [3249,] 1.750000000 -0.502008032
## [3250,] 1.750000000 -0.500000000plot(coord_matrix, xlim=c(-3,3), ylim=c(-3,3))
Then, I made plots for each of the linear transformations I performed. I also defined the identity matrix and used that for some of the plots.
# Identity matrix
identity_matrix = matrix(c(1, 0, 0, 1), ncol=2)
identity_matrix## [,1] [,2]
## [1,] 1 0
## [2,] 0 1#shear randomly
shear_matrix=identity_matrix
shear_matrix[1,2]=3
shear_matrix[2,1]=2
transformed_matrix_shear= coord_matrix %*% shear_matrix
#scaling making JJ smaller by half
scale_matrix=identity_matrix
scale_matrix[1,1]=0.5
scale_matrix[2,2]=0.5
transformed_matrix_scale=coord_matrix %*% scale_matrix
#rotation clockwise .8 rad
rot_matrix=matrix(c(cos(0.8),-sin(0.8),sin(0.8),cos(0.8)),ncol=2)
transformed_matrix_rot=coord_matrix %*% rot_matrix
#projecting onto x axis
proj_matrix=matrix(c(1,0,0,0),ncol=2)
transformed_matrix_proj=coord_matrix %*% proj_matrixFinally, I combined all plots in a loop at the end.
I had to put all of the plots in a list so that I can loop through them all.
I also added a title for each transformation.
I added the sleep function so that it can slow down the loop an we can see it.
x11() to open new window
matrices = list(coord_matrix, transformed_matrix_shear, coord_matrix, transformed_matrix_scale, coord_matrix, transformed_matrix_rot, coord_matrix, transformed_matrix_proj)
titles = c("Original JJ", "Shear Transformation", "Original JJ", "Scaling Transformation", "Original JJ", "Rotation Transformation", "Original JJ", "Projection Transformation")
# Open a new plotting window
x11()
for (i in 1:length(matrices)) {
# Clear the plot window
plot.new()
plot(matrices[[i]][,2] ~ matrices[[i]][,1], xlim=c(-3,5), ylim=c(-3,3))
#cycle thru titles
title(main=titles[i])
#wait b4 continuing
Sys.sleep(3)
}
