Transcript Adventures of The Cube Roland Miezianko CIS 581 Computer Graphics and Image Processing

Adventures of The Cube
Roland Miezianko
CIS 581
Computer Graphics and Image Processing
Prof. Longin Jan Latecki
Roland Miezianko, CIS581
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Objective
 Construct a 3D object in Matlab (Cube)
 Create and use Homogenous Coordinates
 Compute all transformations:
•
•
•
•
Translation
Scaling
Rotation x,y,z-axis
Flyby
Roland Miezianko, CIS581
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Construct the Cube, matrix data
 Define matrix of vertices
• 8x3 matrix
 Define matrix of faces
• 6x4 matrix
 Define matrix of vertex and face colors
• 6x3 matrix
Roland Miezianko, CIS581
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Construct the Cube, display
 Construct cube using the patch
command
• patch('Vertices', v, 'Faces', f, 'FaceVertexCData',
fvc, 'FaceColor', 'flat', 'EdgeColor', 'none')
 Set colors to be transparent
• alpha(.5);
Roland Miezianko, CIS581
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Homogeneous Equations
 Matlab vertices are defined as triplet
• N x 3 matrix
 Must add additional column to the vertex
matrix (N x 4 matrix)
• Vw = [v vw]';
Roland Miezianko, CIS581
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Matrix Operations
 Matrix operation to translate, scale, and
rotate
• Rotate about x-axis example
rx = [
1
0
0
0
0
cos(xang)
sin(xang)
0
0
-sin(xang)
cos(xang)
0
0;
0;
0;
1];
Vw = [v vw]';
Vcomp = ( rx * Vw )';
Vnew = Vcomp(:,1:3);
Roland Miezianko, CIS581
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The Movie
"Adventures of The Cube"
Roland Miezianko, CIS581
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