6. Creating 3D shape - Block (2) | Making Animation with MATLAB | Resources

Making Animation with MATLAB

6. Creating 3D shape - Block (2)

A block shape in a general configuration as shown in Figure 1 can be defined by the position and the orientation of the reference frame attached to one of the vertices and the length of each side (Lx, Ly, Lz). If the position coordinate and the orientation matrix of the reference frame are r and R, respectively, then the coordinates of the vertices are obtained by the following equation:

where p⁰_i is the coordinate of the i-th vertex in the basic configuration. If the coordinates of the vertices are obtained, we can make the block shape by combining six polygons using patch command in the same way as in the last section.

Figure 1: Block shape (in a general configuration)

A MATLAB script to draw a block shape in a general configuration is shown in Code 1. The result of the drawing by this script is shown in Figure 2. Function eulerXYZ() used in the script is a function that converts XYZ Euler angles to the corresponding rotation matrix and is defined as in Code 2.

make_block_general.m

% make_block_general.m

clear; close all;

% Reference position
r = [1; 1; 1];

% Reference orientation
R = eulerXYZ(-pi/3, 0, pi/6);

% Side lengths
Lx = 0.15;
Ly = 0.05;
Lz = 0.30;

% Vertices
vertices_0 = [
    0,   0,  0;  % #1
    Lx,  0,  0;  % #2
    0,  Ly,  0;  % #3
    0,   0, Lz;  % #4
    Lx, Ly,  0;  % #5
    0,  Ly, Lz;  % #6
    Lx,  0, Lz;  % #7
    Lx, Ly, Lz]; % #8

vertices = r' + vertices_0*R';

% Faces
faces = [
    1, 2, 5, 3;  % #1
    1, 3, 6, 4;  % #2
    1, 4, 7, 2;  % #3
    4, 7, 8, 6;  % #4
    2, 5, 8, 7;  % #5
    3, 6, 8, 5]; % #6

% Draw patch
figure(1);
h = patch('Faces', faces, 'Vertices', vertices, 'FaceColor', 'y');

% Axes settings
xlabel('x'); ylabel('y'); zlabel('z');
axis vis3d equal;
view([-37.5, 30]);
camlight;
grid on;
xlim([0.8, 1.3]);
ylim([0.9, 1.4]);
zlim([0.8, 1.3]);

Code 1: MATLAB script to draw a block shape (in a general configuration)

eulerXYZ.m

function R = eulerXYZ(a1, a2, a3)
% Convert XYZ Euler angles to rotation matrix

R1 = [
1, 0, 0;
0, cos(a1), -sin(a1);
0, sin(a1), cos(a1)];

R2 = [
cos(a2), 0, sin(a2);
0, 1, 0;
-sin(a2), 0, cos(a2)];

R3 = [
cos(a3), -sin(a3), 0;
sin(a3), cos(a3), 0;
0, 0, 1];

R = R1*R2*R3;

end

Code 2: MATLAB function that converts XYZ Euler angles to the corresponding rotation matrix

Figure 2: A block shape made of six polygons (in a general configuration)

<< 5. Creating 3D shape - Block (1)

>> 7. Creating 3D shape - Cylinder (1)

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