PORTOFOLIO 7
Kali ini kita akan membahas tentang rekonstruksi objek 2 dimensi menjadi 3 dimensi.
Pada portofolio ini kita memerlukan digipts.m dan portofolio7.m untuk membangkitkan image 3 dimensi.
dibawah ini adalh listing stereo.m
function [XYZ, uv1, uv2] = stereo(im1, im2, C1, C2)
fprintf(1, ‘Digitise some points in figure 1\n’);
figure(1)
imshow(im1);
[u1,v1] = digipts;
uv1 = [u1,v1]’;
fprintf(1, ‘Digitise some points in figure 2\n’);
figure(2)
imshow(im2);
[u2,v2] = digipts;
uv2 = [u2,v2]’;
% check if same number of points are selected
if length(u1) ~= length(u2)
fprintf(1, ‘Same number of points not selected\n’);
end
for i = 1:length(u1)
a = [C1(1:2,1:3) - [u1(i)*C1(3,1:3); v1(i)*C1(3,1:3)];
C2(1:2,1:3) - [u2(i)*C2(3,1:3); v2(i)*C2(3,1:3)]];
c = [u1(i) - C1(1,4);
v1(i) - C1(2,4);
u2(i) - C2(1,4);
v2(i) - C2(2,4)];
b(:, i) = a \ c;
end
XYZ = b’;
Dari fungsi diatas akan dihasilkan titik-titik koordinat 3 dimensi dari ketiga bangun ruang (kubus, balok, dan limas), seperti di bawah ini:
XYZ =
-286.2951 157.9628 143.0423
-175.3818 163.1173 142.7176
-175.5998 16.6768 141.1072
-289.0643 13.0795 143.6164
-285.5844 161.7196 8.2758
-287.0630 12.1030 5.9668
-174.9637 14.4183 4.0810
-86.9674 -69.5001 0.6049
-66.2381 -144.2762 121.3230
20.2380 -180.4104 -4.5407
-136.9644 -207.1403 -0.7542
136.7599 -90.1582 62.6987
208.8604 -92.0420 60.2097
206.8196 -158.9134 58.7466
137.3153 -155.6600 59.8104
133.7304 -94.9047 -4.4448
137.0247 -158.4058 -10.0663
205.6730 -162.3611 -10.7847
Panjang rusuk untuk balok:
slengths =
144.9110 111.0335 146.4495 113.5492
113.5492 137.0463 112.1391 137.6676
137.6676 149.6418 134.8208 144.9110
112.2506 134.8208 111.0335 137.6676
137.6676 146.4495 137.0463 147.7343
147.7343 112.1391 149.6418 112.2506
dengan sisi-sisinya:
nface =
4 1 2 3 4
4 3 7 6 4
4 6 5 1 4
8 5 1 2 8
8 2 3 7 8
8 7 6 5 8
Panjang rusuk untuk limas:
slengths =
143.5062 156.9251 154.3392
143.5062 154.4569 146.4458
154.3392 159.5037 146.4458
156.9251 159.5037 154.4569
dengan sisi-sisinya:
nface =
1 2 3 1
1 2 4 1
1 3 4 1
2 3 4 2
Panjang rusuk untuk kubus:
slengths =
65.5678 72.1681 66.9186 69.5886
69.5886 69.6261 68.7659 69.9313
69.9313 63.8345 67.3792 65.5678
75.0216 67.3792 72.1681 69.9313
69.9313 66.9186 69.6261 67.6446
67.6446 68.7659 63.8345 75.0216
dengan sisi-sisinya:
nface =
4 1 2 3 4
4 3 7 6 4
4 6 5 1 4
8 5 1 2 8
8 2 3 7 8
8 7 6 5 8
Untuk mendapatkan Dua view yang berbeda dari rekonstruksi 3D kubus, balok dan limas dan perkiraan titik koordinat 3D yang tersembunyi, dijalankan fungsi di bawah ini:
function portofolio7()
im1 = imread(’stereo1.jpg’ );
im2 = imread(’stereo2.jpg’ );
C1 = [0.6596 -0.7391 -0.0615 363.4235;
-0.1851 -0.1387 -0.9437 342.7417;
0.0005 0.0003 -0.0003 1.0000];
C2 = [0.9234 -0.2221 -0.0257 347.7796;
-0.0741 -0.2278 -0.9168 339.8960;
0.0002 0.0004 -0.0002 1.0000];
pt3D = stereo(im1, im2, C1, C2)
figure(3)
cube(pt3D(1:7,:));
tetrahedron(pt3D(8:11,:));
cube(pt3D(12:18,:));
% label coordinate axes
text(100,0,0,’x’);
text(0,100,0,’y’);
text(0,0,100,’z’);
% draw in a set of coordinate axes
axislength = 100*eye(3);
for i=1:3
line([0, axislength(i,1)], [0, axislength(i,2)], [0, axislength(i,3)]);
end
axis equal; box on; rotate3D on; grid on;
end
function cube(cubepts3D)
% determine hidden vertex
cubepts3D(8, = - cubepts3D(4, + cubepts3D(6, + cubepts3D(2,:);
% define faces from standard numbering
cubefaces = [4 1 2 3
4 3 7 6
4 6 5 1
8 5 1 2
8 2 3 7
8 7 6 5];
% draw ‘patcheds’ from vertice and face matrix
patch(’Faces’,cubefaces,’Vertices’,cubepts3D, ‘FaceColor’, ‘none’)
fprintf(1, ‘Length matrix of face sides\n’);
[slengths, nface] = sidelengths(cubepts3D, cubefaces)
end
function tetrahedron(tetrahedronpts3D)
% define faces from standard numbering
tetrahedronfaces = [1 2 3
1 2 4
1 3 4
2 3 4];
% draw ‘patcheds’ from vertice and face matrix
patch(’Faces’,tetrahedronfaces,’Vertices’,tetrahedronpts3D, ‘FaceColor’, ‘none’)
fprintf(1, ‘Length matrix of face sides\n’);
[slengths, nface] = sidelengths(tetrahedronpts3D, tetrahedronfaces)
end
function [slengths, nface] = sidelengths(pt3D, face)
[rows, cols] = size(face);
nface = [face face(:,1)];
for i=1:cols
for j=1:rows
slengths(j,i) = norm(pt3D(nface(j,i),:)-pt3D(nface(j,i+1),:));
end
end
end
dari fungsi diatas kita akan menentukan kokordinat titik-titik dengan urutan seperti berikut :
kita akan mendapatkan rekonstruksi 3 D :
