Adventures of The Cube

1
Adventures of The Cube

• Roland Miezianko
• CIS 581
• Computer Graphics and Image Processing
• Prof. Longin Jan Latecki

2
Objective

• Construct a 3D object in Matlab (Cube)
• Create and use Homogenous Coordinates
• Compute all transformations
• Translation
• Scaling
• Rotation x,y,z-axis
• Flyby

3
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

4
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)

5
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'

6
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 s
in(xang) cos(xang) 0 0 0 0 1 Vw v
vw' Vcomp ( rx Vw )' Vnew Vcomp(,13)
7
The Movie

• "Adventures of The Cube"