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Adventure of The Cube: Constructing and Transforming a 3D Object in Matlab

Learn how to create a 3D cube in Matlab with homogeneous coordinates, apply translations, scaling, rotation, and display it using patch commands. Understand matrix operations for transformations and the concept of homogeneous equations for vertices.

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Adventure of The Cube: Constructing and Transforming a 3D Object in Matlab

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  1. Adventures of The Cube Roland Miezianko CIS 581 Computer Graphics and Image Processing Prof. Longin Jan Latecki Roland Miezianko, CIS581

  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 Roland Miezianko, CIS581

  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 Roland Miezianko, CIS581

  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); Roland Miezianko, CIS581

  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]'; Roland Miezianko, CIS581

  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 sin(xang) cos(xang) 0; 0 0 0 1]; Vw = [v vw]'; Vcomp = ( rx * Vw )'; Vnew = Vcomp(:,1:3); Roland Miezianko, CIS581

  7. The Movie "Adventures of The Cube" Roland Miezianko, CIS581

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