Cat Paving

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2020-03-19 18:01

This example demonstrates the geometric construction of cat paving. It involves concepts such as rectangles, trapeziums, and step functions. Using GeoGebra commands like If, Line, Point, etc., complex geometric shapes can be constructed. Suitable for students at junior high school level and above to learn geometric construction and transformations.

GeoGebra Commands & Parameters

If(a < 2.3, 0, If[a < 3.3, a - 2.3, 1]) → d3
If(a < 1.2, 0, If[a < 2.2, a - 1.2, 1]) → d2
Line(C, D) → b
Point(b) → E
OrthogonalLine(E, b) → d
Point(d) → G
OrthogonalLine(G, d) → f
Point(d) → L
Mirror(L, b) → L'_1
Mirror(E, b) → E'_1
Point(b) → F
OrthogonalLine(F, b) → e
Intersect(e, f) → H
Midpoint(E'_1, H) → T
Mirror(F, b) → F'_1
Midpoint(E'_1, F'_1) → M
Dilate(E'_1, d2, M) → S
Rotate(S, (((-d3) * 180))°, T) → S'
Dilate(L'_1, d2, M) → R
Rotate(R, (((-d3) * 180))°, T) → R'
Dilate(F'_1, d2, M) → N
Rotate(N, (((-d3) * 180))°, T) → N'
Mirror(I, b) → I'_1
Dilate(I'_1, d2, M) → O
Rotate(O, (((-d3) * 180))°, T) → O'
Mirror(J, b) → J'_1
Dilate(J'_1, d2, M) → P
Rotate(P, (((-d3) * 180))°, T) → P'
Mirror(K, b) → K'_1
Dilate(K'_1, d2, M) → Q
Rotate(Q, (((-d3) * 180))°, T) → Q'
Mirror(V, b) → VP1
Dilate(VP1, d2, M) → OO
Rotate(OO, (((-d3) * 180))°, T) → OOO
If(a < 1, a, 1) → d1
Dilate(V, 1 - d1, M) → VP
Dilate(E, 1 - d1, M) → E'
Dilate(L, 1 - d1, M) → L'
Dilate(K, 1 - d1, M) → K'
Dilate(J, 1 - d1, M) → J'
Dilate(I, 1 - d1, M) → I'
Dilate(F, 1 - d1, M) → F'
If(a < 3.4, 0, If[a < 4.4, a - 3.4, 1]) → d4
If(a < 4.5, 0, If[a < 5.5, a - 4.5, 1]) → d5
If(a < 5.6, 0, If[a < 6.6, a - 5.6, 1]) → d6
If(a < 6.7, 0, If[a < 7.7, a - 6.7, 1]) → d7
If(a < 7.8, 0, If[a < 8.8, a - 7.8, 1]) → d8
Polygon(N', OOO, O', P', Q', R', S') → poly1'_1, g_2, h_2, i_3, j_3, k_1, l_1, m_1
Polygon(F', VP, I', J', K', L', E') → poly1', g_3, h_3, i_2, j_2, k_2, l_2, m
Point(e) → E_1
Point(f) → I_1
Point(f) → J_1
Midpoint(F, H) → U
Mirror(F, e) → F'_2
Mirror(E_1, e) → K_1
Mirror(F_1, e) → L_1
Mirror(G_1, e) → M_1
Mirror(H_1, e) → N_1
Mirror(I_1, e) → O_1
Mirror(J_1, e) → P_1
Mirror(D_1, e) → Q_1
Mirror(C_1, e) → R_1
Mirror(B_1, e) → S_1
Mirror(A_1, e) → T_1
Mirror(Z, e) → Z'
Mirror(W, e) → W'
Mirror(V, e) → V'
Dilate(F, 1 - d1, U) → F'_3
Dilate(E_1, 1 - d1, U) → U_1
Dilate(F_1, 1 - d1, U) → V_1
Dilate(G_1, 1 - d1, U) → W_1
Dilate(H_1, 1 - d1, U) → Z_1
Dilate(I_1, 1 - d1, U) → A_2
Dilate(J_1, 1 - d1, U) → B_2
Dilate(D_1, 1 - d1, U) → C_2
Dilate(C_1, 1 - d1, U) → D_2
Dilate(B_1, 1 - d1, U) → E_2
Dilate(A_1, 1 - d1, U) → F_2
Dilate(Z, 1 - d1, U) → Z'_1
Dilate(W, 1 - d1, U) → W'_1
Dilate(V, 1 - d1, U) → V'_1
Polygon(F'_3, U_1, F_2, Z'_1, W'_1, V'_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2) → poly1'_3, f'_3, e_2, f_2, z'_1, w'_1, v'_1, u_1, v_1, w_1, z_1, a_2, b_2, c_2, d_2
Dilate(F'_2, d2, U) → G_2
Dilate(K_1, d2, U) → H_2
Dilate(L_1, d2, U) → I_2
Dilate(M_1, d2, U) → J_2
Dilate(N_1, d2, U) → K_2
Dilate(O_1, d2, U) → L_2
Dilate(P_1, d2, U) → M_2
Dilate(Q_1, d2, U) → N_2
Dilate(R_1, d2, U) → O_2
Dilate(S_1, d2, U) → P_2
Dilate(T_1, d2, U) → Q_2
Dilate(Z', d2, U) → Z''
Dilate(W', d2, U) → W''
Dilate(V', d2, U) → V''
Rotate(G_2, (((-d3) * 180))°, T) → R_2
Rotate(H_2, (((-d3) * 180))°, T) → S_2
Rotate(I_2, (((-d3) * 180))°, T) → T_2
Rotate(J_2, (((-d3) * 180))°, T) → U_2
Rotate(K_2, (((-d3) * 180))°, T) → V_2
Rotate(L_2, (((-d3) * 180))°, T) → W_2
Rotate(M_2, (((-d3) * 180))°, T) → Z_2
Rotate(N_2, (((-d3) * 180))°, T) → A_3
Rotate(O_2, (((-d3) * 180))°, T) → B_3
Rotate(P_2, (((-d3) * 180))°, T) → C_3
Rotate(Q_2, (((-d3) * 180))°, T) → D_3
Rotate(Z'', (((-d3) * 180))°, T) → Z'''
Rotate(W'', (((-d3) * 180))°, T) → W'''
Rotate(V'', (((-d3) * 180))°, T) → V'''
Polygon(R_2, S_2, D_3, Z''', W''', V''', T_2, U_2, V_2, W_2, Z_2, A_3, B_3, C_3) → poly1'_2, r_2, c_3, d_3, z''', w''', v''', s_2, t_2, u_2, v_2, w_2, z_2, a_3, b_3
Polygon(L, K, D_1, J_1, I_1, H_1, G_1, F_1, E_1, H, G, J, I, V, W, Z, A_1, B_1, C_1) → poly1, l, c_1, d_1, j_1, i_1, h_1, g_1, f_1, e_1, h, g, k, j, i, v_3, w, z, a_1, b_1
Line(U, b) → n_1
Point(n_1) → E_3
Vector(F, E) → v
Translate(L, p) → L'_2
Translate(K, p) → K'_2
Translate(J, p) → J'_2
Translate(I, p) → I'_2
Translate(V, p) → V'_2
Translate(W, p) → W'_2
Translate(Z, p) → Z'_2
Translate(A_1, p) → F_3
Translate(B_1, p) → G_3
Translate(C_1, p) → H_3
Translate(D_1, p) → I_3
Translate(J_1, p) → J_3
Translate(I_1, p) → K_3
Translate(H_1, p) → L_3
Translate(G_1, p) → M_3
Translate(F_1, p) → N_3
Translate(E_1, p) → O_3
Translate(H, p) → H'
Translate(G, p) → G'
Translate(N', p) → N''
Translate(OOO, p) → OOO'
Translate(O', p) → O''
Translate(P', p) → P''
Translate(Q', p) → Q''
Translate(R', p) → R''
Translate(S', p) → S''
Translate(R_2, p) → P_3
Translate(S_2, p) → Q_3
Translate(T_2, p) → R_3
Translate(U_2, p) → S_3
Translate(V_2, p) → T_3
Translate(W_2, p) → U_3
Translate(Z_2, p) → V_3
Translate(A_3, p) → W_3
Translate(B_3, p) → Z_3
Translate(C_3, p) → A_4
Translate(D_3, p) → B_4
Translate(Z''', p) → C_4
Translate(W''', p) → D_4
Translate(V''', p) → E_4
Mirror(P_3, n_1) → F_4
Mirror(Q_3, n_1) → G_4
Mirror(R_3, n_1) → H_4
Mirror(S_3, n_1) → I_4
Mirror(T_3, n_1) → J_4
Mirror(U_3, n_1) → K_4
Mirror(V_3, n_1) → L_4
Mirror(W_3, n_1) → M_4
Mirror(Z_3, n_1) → N_4
Mirror(A_4, n_1) → O_4
Mirror(B_4, n_1) → P_4
Mirror(C_4, n_1) → Q_4
Mirror(D_4, n_1) → R_4
Mirror(E_4, n_1) → S_4
Mirror(L'_2, n_1) → T_4
Mirror(K'_2, n_1) → U_4
Mirror(J'_2, n_1) → V_4
Mirror(I'_2, n_1) → W_4
Mirror(V'_2, n_1) → Z_4
Mirror(W'_2, n_1) → A_5
Mirror(Z'_2, n_1) → B_5
Mirror(F_3, n_1) → C_5
Mirror(G_3, n_1) → D_5
Mirror(H_3, n_1) → E_5
Mirror(I_3, n_1) → F_5
Mirror(J_3, n_1) → G_5
Mirror(K_3, n_1) → H_5
Mirror(L_3, n_1) → I_5
Mirror(M_3, n_1) → J_5
Mirror(N_3, n_1) → K_5
Mirror(O_3, n_1) → L_5
Mirror(H', n_1) → H''
Mirror(G', n_1) → G''
Mirror(N'', n_1) → N'''
Mirror(OOO', n_1) → OOO''
Mirror(O'', n_1) → O'''
Mirror(P'', n_1) → P'''
Mirror(Q'', n_1) → Q'''
Mirror(R'', n_1) → R'''
Mirror(S'', n_1) → S'''
Dilate(L'_2, 1 - d5, E_3) → M_5
Dilate(K'_2, 1 - d5, E_3) → N_5
Dilate(J'_2, 1 - d5, E_3) → O_5
Dilate(I'_2, 1 - d5, E_3) → P_5
Dilate(V'_2, 1 - d5, E_3) → Q_5
Dilate(W'_2, 1 - d5, E_3) → R_5
Dilate(Z'_2, 1 - d5, E_3) → S_5
Dilate(F_3, 1 - d5, E_3) → T_5
Dilate(G_3, 1 - d5, E_3) → U_5
Dilate(H_3, 1 - d5, E_3) → V_5
Dilate(I_3, 1 - d5, E_3) → W_5
Dilate(J_3, 1 - d5, E_3) → Z_5
Dilate(K_3, 1 - d5, E_3) → A_6
Dilate(L_3, 1 - d5, E_3) → B_6
Dilate(M_3, 1 - d5, E_3) → C_6
Dilate(N_3, 1 - d5, E_3) → D_6
Dilate(O_3, 1 - d5, E_3) → E_6
Dilate(H', 1 - d5, E_3) → H''_1
Dilate(G', 1 - d5, E_3) → G''_1
Polygon(M_5, N_5, W_5, Z_5, A_6, B_6, C_6, D_6, E_6, H''_1, G''_1, O_5, P_5, Q_5, R_5, S_5, T_5, U_5, V_5) → poly5, m_5, v_6, w_5, z_5, a_6, b_6, c_6, d_6, e_6, h''_1, g''_1, n_5, o_5, p_5, q_5, r_5, s_5, t_5, u_5
Dilate(N'', 1 - d5, E_3) → N'''_1
Dilate(OOO', 1 - d5, E_3) → OOO''_1
Dilate(O'', 1 - d5, E_3) → O'''_1
Dilate(P'', 1 - d5, E_3) → P'''_1
Dilate(Q'', 1 - d5, E_3) → Q'''_1
Dilate(R'', 1 - d5, E_3) → R'''_1
Dilate(S'', 1 - d5, E_3) → S'''_1
Polygon(N'''_1, OOO''_1, O'''_1, P'''_1, Q'''_1, R'''_1, S'''_1) → poly2'_1, n'''_1, ooo''_1, o'''_1, p'''_1, q'''_1, r'''_1, s'''_1
Dilate(P_3, 1 - d5, E_3) → F_6
Dilate(Q_3, 1 - d5, E_3) → G_6
Dilate(R_3, 1 - d5, E_3) → H_6
Dilate(S_3, 1 - d5, E_3) → I_6
Dilate(T_3, 1 - d5, E_3) → J_6
Dilate(U_3, 1 - d5, E_3) → K_6
Dilate(V_3, 1 - d5, E_3) → L_6
Dilate(W_3, 1 - d5, E_3) → M_6
Dilate(Z_3, 1 - d5, E_3) → N_6
Dilate(A_4, 1 - d5, E_3) → O_6
Dilate(B_4, 1 - d5, E_3) → P_6
Dilate(C_4, 1 - d5, E_3) → Q_6
Dilate(D_4, 1 - d5, E_3) → R_6
Dilate(E_4, 1 - d5, E_3) → S_6
Polygon(F_6, G_6, P_6, Q_6, R_6, S_6, H_6, I_6, J_6, K_6, L_6, M_6, N_6, O_6) → poly3'_1, f_6, o_6, p_6, q_6, r_6, s_6, g_6, h_6, i_6, j_6, k_6, l_6, m_6, n_6
Dilate(T_4, d6, E_3) → T_6
Dilate(U_4, d6, E_3) → U_6
Dilate(V_4, d6, E_3) → V_6
Dilate(W_4, d6, E_3) → W_6
Dilate(Z_4, d6, E_3) → Z_6
Dilate(A_5, d6, E_3) → A_7
Dilate(B_5, d6, E_3) → B_7
Dilate(C_5, d6, E_3) → C_7
Dilate(D_5, d6, E_3) → D_7
Dilate(E_5, d6, E_3) → E_7
Dilate(F_5, d6, E_3) → F_7
Dilate(G_5, d6, E_3) → G_7
Dilate(H_5, d6, E_3) → H_7
Dilate(I_5, d6, E_3) → I_7
Dilate(J_5, d6, E_3) → J_7
Dilate(K_5, d6, E_3) → K_7
Dilate(L_5, d6, E_3) → L_7
Dilate(H'', d6, E_3) → H'''
Dilate(G'', d6, E_3) → G'''
Polygon(T_6, U_6, F_7, G_7, H_7, I_7, J_7, K_7, L_7, H''', G''', V_6, W_6, Z_6, A_7, B_7, C_7, D_7, E_7) → poly4', t_6, e_7, f_7, g_7, h_7, i_7, j_7, k_7, l_7, h''', g''', u_6, v_4, w_6, z_6, a_7, b_7, c_7, d_7
Dilate(F_4, d6, E_3) → M_7
Dilate(G_4, d6, E_3) → N_7
Dilate(H_4, d6, E_3) → O_7
Dilate(I_4, d6, E_3) → P_7
Dilate(J_4, d6, E_3) → Q_7
Dilate(K_4, d6, E_3) → R_7
Dilate(L_4, d6, E_3) → S_7
Dilate(M_4, d6, E_3) → T_7
Dilate(N_4, d6, E_3) → U_7
Dilate(O_4, d6, E_3) → V_7
Dilate(P_4, d6, E_3) → W_7
Dilate(Q_4, d6, E_3) → Z_7
Dilate(R_4, d6, E_3) → A_8
Dilate(S_4, d6, E_3) → B_8
Polygon(M_7, N_7, W_7, Z_7, A_8, B_8, O_7, P_7, Q_7, R_7, S_7, T_7, U_7, V_7) → poly3'', m_7, v_7, w_7, z_7, a_8, b_8, n_7, o_7, p_7, q_7, r_7, s_7, t_7, u_7
Dilate(N''', d6, E_3) → C_8
Dilate(OOO'', d6, E_3) → OOO'''
Dilate(O''', d6, E_3) → D_8
Dilate(P''', d6, E_3) → E_8
Dilate(Q''', d6, E_3) → F_8
Dilate(R''', d6, E_3) → G_8
Dilate(S''', d6, E_3) → H_8
Polygon(C_8, OOO''', D_8, E_8, F_8, G_8, H_8) → poly2'', c_8, ooo''', d_8, e_8, f_8, g_8, h_8
Rotate(N', ((d7 * 180))°, G) → N''_1
Rotate(OOO, ((d7 * 180))°, G) → OOO'_1
Rotate(O', ((d7 * 180))°, G) → O''_1
Rotate(P', ((d7 * 180))°, G) → P''_1
Rotate(Q', ((d7 * 180))°, G) → Q''_1
Rotate(R', ((d7 * 180))°, G) → R''_1
Rotate(S', ((d7 * 180))°, G) → S''_1
Polygon(N''_1, OOO'_1, O''_1, P''_1, Q''_1, R''_1, S''_1) → poly2, n''_1, ooo'_1, o''_1, p''_1, q''_1, r''_1, s''_1
Rotate(L, ((d7 * 180))°, G) → L'_3
Rotate(K, ((d7 * 180))°, G) → K'_3
Rotate(J, ((d7 * 180))°, G) → J'_3
Rotate(I, ((d7 * 180))°, G) → I'_3
Rotate(V, ((d7 * 180))°, G) → V'_3
Rotate(W, ((d7 * 180))°, G) → W'_3
Rotate(Z, ((d7 * 180))°, G) → Z'_3
Rotate(A_1, ((d7 * 180))°, G) → I_8
Rotate(B_1, ((d7 * 180))°, G) → J_8
Rotate(C_1, ((d7 * 180))°, G) → K_8
Rotate(D_1, ((d7 * 180))°, G) → L_8
Rotate(J_1, ((d7 * 180))°, G) → M_8
Rotate(I_1, ((d7 * 180))°, G) → N_8
Rotate(H_1, ((d7 * 180))°, G) → O_8
Rotate(G_1, ((d7 * 180))°, G) → P_8
Rotate(F_1, ((d7 * 180))°, G) → Q_8
Rotate(E_1, ((d7 * 180))°, G) → R_8
Rotate(H, ((d7 * 180))°, G) → H'_1
Rotate(G, ((d7 * 180))°, G) → G'_1
Polygon(L'_3, K'_3, L_8, M_8, N_8, O_8, P_8, Q_8, R_8, H'_1, G'_1, J'_3, I'_3, V'_3, W'_3, Z'_3, I_8, J_8, K_8) → poly1'_4, l'_3, k_8, l_8, m_8, n_8, o_8, p_8, q_8, r_8, h'_1, g'_1, k'_3, j'_3, i'_3, v'_3, w'_3, z'_3, i_8, j_8
Rotate(R_2, ((d7 * 180))°, G) → S_8
Rotate(S_2, ((d7 * 180))°, G) → T_8
Rotate(T_2, ((d7 * 180))°, G) → U_8
Rotate(U_2, ((d7 * 180))°, G) → V_8
Rotate(V_2, ((d7 * 180))°, G) → W_8
Rotate(W_2, ((d7 * 180))°, G) → Z_8
Rotate(Z_2, ((d7 * 180))°, G) → A_9
Rotate(A_3, ((d7 * 180))°, G) → B_9
Rotate(B_3, ((d7 * 180))°, G) → C_9
Rotate(C_3, ((d7 * 180))°, G) → D_9
Rotate(D_3, ((d7 * 180))°, G) → E_9
Rotate(Z''', ((d7 * 180))°, G) → F_9
Rotate(W''', ((d7 * 180))°, G) → G_9
Rotate(V''', ((d7 * 180))°, G) → H_9
Polygon(S_8, T_8, E_9, F_9, G_9, H_9, U_8, V_8, W_8, Z_8, A_9, B_9, C_9, D_9) → poly3, s_8, d_9, e_9, f_9, g_9, h_9, t_8, u_8, v_8, w_8, z_8, a_9, b_9, c_9
Rotate(M_7, ((d7 * 180))°, G) → I_9
Rotate(N_7, ((d7 * 180))°, G) → J_9
Rotate(O_7, ((d7 * 180))°, G) → K_9
Rotate(P_7, ((d7 * 180))°, G) → L_9
Rotate(Q_7, ((d7 * 180))°, G) → M_9
Rotate(R_7, ((d7 * 180))°, G) → N_9
Rotate(S_7, ((d7 * 180))°, G) → O_9
Rotate(T_7, ((d7 * 180))°, G) → P_9
Rotate(U_7, ((d7 * 180))°, G) → Q_9
Rotate(V_7, ((d7 * 180))°, G) → R_9
Rotate(W_7, ((d7 * 180))°, G) → S_9
Rotate(Z_7, ((d7 * 180))°, G) → T_9
Rotate(A_8, ((d7 * 180))°, G) → U_9
Rotate(B_8, ((d7 * 180))°, G) → V_9
Polygon(I_9, J_9, S_9, T_9, U_9, V_9, K_9, L_9, M_9, N_9, O_9, P_9, Q_9, R_9) → poly3''', i_9, r_9, s_9, t_9, u_9, v_9, j_9, k_9, l_9, m_9, n_9, o_9, p_9, q_9
Rotate(T_6, ((d7 * 180))°, G) → W_9
Rotate(U_6, ((d7 * 180))°, G) → Z_9
Rotate(V_6, ((d7 * 180))°, G) → A_{10}
Rotate(W_6, ((d7 * 180))°, G) → B_{10}
Rotate(Z_6, ((d7 * 180))°, G) → C_{10}
Rotate(A_7, ((d7 * 180))°, G) → D_{10}
Rotate(B_7, ((d7 * 180))°, G) → E_{10}
Rotate(C_7, ((d7 * 180))°, G) → F_{10}
Rotate(D_7, ((d7 * 180))°, G) → G_{10}
Rotate(E_7, ((d7 * 180))°, G) → H_{10}
Rotate(F_7, ((d7 * 180))°, G) → I_{10}
Rotate(G_7, ((d7 * 180))°, G) → J_{10}
Rotate(H_7, ((d7 * 180))°, G) → K_{10}
Rotate(I_7, ((d7 * 180))°, G) → L_{10}
Rotate(J_7, ((d7 * 180))°, G) → M_{10}
Rotate(K_7, ((d7 * 180))°, G) → N_{10}
Rotate(L_7, ((d7 * 180))°, G) → O_{10}
Rotate(H''', ((d7 * 180))°, G) → P_{10}
Rotate(G''', ((d7 * 180))°, G) → Q_{10}
Polygon(W_9, Z_9, I_{10}, J_{10}, K_{10}, L_{10}, M_{10}, N_{10}, O_{10}, P_{10}, Q_{10}, A_{10}, B_{10}, C_{10}, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}) → poly4'', w_9, h_{10}, i_{10}, j_{10}, k_{10}, l_{10}, m_{10}, n_{10}, o_{10}, p_{10}, q_{10}, z_9, a_{10}, b_{10}, c_{10}, d_{10}, e_{10}, f_{10}, g_{10}
Rotate(C_8, ((d7 * 180))°, G) → R_{10}
Rotate(OOO''', ((d7 * 180))°, G) → S_{10}
Rotate(D_8, ((d7 * 180))°, G) → T_{10}
Rotate(E_8, ((d7 * 180))°, G) → U_{10}
Rotate(F_8, ((d7 * 180))°, G) → V_{10}
Rotate(G_8, ((d7 * 180))°, G) → W_{10}
Rotate(H_8, ((d7 * 180))°, G) → Z_{10}
Polygon(R_{10}, S_{10}, T_{10}, U_{10}, V_{10}, W_{10}, Z_{10}) → poly2''', r_{10}, s_{10}, t_{10}, u_{10}, v_{10}, w_{10}, z_{10}
Mirror(E, G) → E'_2
Rotate(R_{10}, (((-d8) * 180))°, E'_2) → A_{11}
Rotate(S_{10}, (((-d8) * 180))°, E'_2) → B_{11}
Rotate(T_{10}, (((-d8) * 180))°, E'_2) → C_{11}
Rotate(U_{10}, (((-d8) * 180))°, E'_2) → D_{11}
Rotate(V_{10}, (((-d8) * 180))°, E'_2) → E_{11}
Rotate(W_{10}, (((-d8) * 180))°, E'_2) → F_{11}
Rotate(Z_{10}, (((-d8) * 180))°, E'_2) → G_{11}
Polygon(A_{11}, B_{11}, C_{11}, D_{11}, E_{11}, F_{11}, G_{11}) → poly4, a_{11}, b_{11}, c_{11}, d_{11}, e_{11}, f_{11}, g_{11}
Rotate(W_9, (((-d8) * 180))°, E'_2) → H_{11}
Rotate(Z_9, (((-d8) * 180))°, E'_2) → I_{11}
Rotate(A_{10}, (((-d8) * 180))°, E'_2) → J_{11}
Rotate(B_{10}, (((-d8) * 180))°, E'_2) → K_{11}
Rotate(C_{10}, (((-d8) * 180))°, E'_2) → L_{11}
Rotate(D_{10}, (((-d8) * 180))°, E'_2) → M_{11}
Rotate(E_{10}, (((-d8) * 180))°, E'_2) → N_{11}
Rotate(F_{10}, (((-d8) * 180))°, E'_2) → O_{11}
Rotate(G_{10}, (((-d8) * 180))°, E'_2) → P_{11}
Rotate(H_{10}, (((-d8) * 180))°, E'_2) → Q_{11}
Rotate(I_{10}, (((-d8) * 180))°, E'_2) → R_{11}
Rotate(J_{10}, (((-d8) * 180))°, E'_2) → S_{11}
Rotate(K_{10}, (((-d8) * 180))°, E'_2) → T_{11}
Rotate(L_{10}, (((-d8) * 180))°, E'_2) → U_{11}
Rotate(M_{10}, (((-d8) * 180))°, E'_2) → V_{11}
Rotate(N_{10}, (((-d8) * 180))°, E'_2) → W_{11}
Rotate(O_{10}, (((-d8) * 180))°, E'_2) → Z_{11}
Rotate(P_{10}, (((-d8) * 180))°, E'_2) → A_{12}
Rotate(Q_{10}, (((-d8) * 180))°, E'_2) → B_{12}
Polygon(H_{11}, I_{11}, R_{11}, S_{11}, T_{11}, U_{11}, V_{11}, W_{11}, Z_{11}, A_{12}, B_{12}, J_{11}, K_{11}, L_{11}, M_{11}, N_{11}, O_{11}, P_{11}, Q_{11}) → poly4''', h_{11}, q_{11}, r_{11}, s_{11}, t_{11}, u_{11}, v_{11}, w_{11}, z_{11}, a_{12}, b_{12}, i_{11}, j_{11}, k_{11}, l_{11}, m_{11}, n_{11}, o_{11}, p_{11}
Rotate(I_9, (((-d8) * 180))°, E'_2) → C_{12}
Rotate(J_9, (((-d8) * 180))°, E'_2) → D_{12}
Rotate(K_9, (((-d8) * 180))°, E'_2) → E_{12}
Rotate(L_9, (((-d8) * 180))°, E'_2) → F_{12}
Rotate(M_9, (((-d8) * 180))°, E'_2) → G_{12}
Rotate(N_9, (((-d8) * 180))°, E'_2) → H_{12}
Rotate(O_9, (((-d8) * 180))°, E'_2) → I_{12}
Rotate(P_9, (((-d8) * 180))°, E'_2) → J_{12}
Rotate(Q_9, (((-d8) * 180))°, E'_2) → K_{12}
Rotate(R_9, (((-d8) * 180))°, E'_2) → L_{12}
Rotate(S_9, (((-d8) * 180))°, E'_2) → M_{12}
Rotate(T_9, (((-d8) * 180))°, E'_2) → N_{12}
Rotate(U_9, (((-d8) * 180))°, E'_2) → O_{12}
Rotate(V_9, (((-d8) * 180))°, E'_2) → P_{12}
Polygon(C_{12}, D_{12}, M_{12}, N_{12}, O_{12}, P_{12}, E_{12}, F_{12}, G_{12}, H_{12}, I_{12}, J_{12}, K_{12}, L_{12}) → poly6, c_{12}, l_{12}, m_{12}, n_{12}, o_{12}, p_{12}, d_{12}, e_{12}, f_{12}, g_{12}, h_{12}, i_{12}, j_{12}, k_{12}
Rotate(L'_3, (((-d8) * 180))°, E'_2) → Q_{12}
Rotate(K'_3, (((-d8) * 180))°, E'_2) → R_{12}
Rotate(J'_3, (((-d8) * 180))°, E'_2) → S_{12}
Rotate(I'_3, (((-d8) * 180))°, E'_2) → T_{12}
Rotate(V'_3, (((-d8) * 180))°, E'_2) → U_{12}
Rotate(W'_3, (((-d8) * 180))°, E'_2) → V_{12}
Rotate(Z'_3, (((-d8) * 180))°, E'_2) → W_{12}
Rotate(I_8, (((-d8) * 180))°, E'_2) → Z_{12}
Rotate(J_8, (((-d8) * 180))°, E'_2) → A_{13}
Rotate(K_8, (((-d8) * 180))°, E'_2) → B_{13}
Rotate(L_8, (((-d8) * 180))°, E'_2) → C_{13}
Rotate(M_8, (((-d8) * 180))°, E'_2) → D_{13}
Rotate(N_8, (((-d8) * 180))°, E'_2) → E_{13}
Rotate(O_8, (((-d8) * 180))°, E'_2) → F_{13}
Rotate(P_8, (((-d8) * 180))°, E'_2) → G_{13}
Rotate(Q_8, (((-d8) * 180))°, E'_2) → H_{13}
Rotate(R_8, (((-d8) * 180))°, E'_2) → I_{13}
Rotate(H'_1, (((-d8) * 180))°, E'_2) → J_{13}
Rotate(G'_1, (((-d8) * 180))°, E'_2) → K_{13}
Polygon(Q_{12}, R_{12}, C_{13}, D_{13}, E_{13}, F_{13}, G_{13}, H_{13}, I_{13}, J_{13}, K_{13}, S_{12}, T_{12}, U_{12}, V_{12}, W_{12}, Z_{12}, A_{13}, B_{13}) → poly7, q_{12}, b_{13}, c_{13}, d_{13}, e_{13}, f_{13}, g_{13}, h_{13}, i_{13}, j_{13}, k_{13}, r_{12}, s_{12}, t_{12}, u_{12}, v_{12}, w_{12}, z_{12}, a_{13}
Rotate(S_8, (((-d8) * 180))°, E'_2) → L_{13}
Rotate(T_8, (((-d8) * 180))°, E'_2) → M_{13}
Rotate(U_8, (((-d8) * 180))°, E'_2) → N_{13}
Rotate(V_8, (((-d8) * 180))°, E'_2) → O_{13}
Rotate(W_8, (((-d8) * 180))°, E'_2) → P_{13}
Rotate(Z_8, (((-d8) * 180))°, E'_2) → Q_{13}
Rotate(A_9, (((-d8) * 180))°, E'_2) → R_{13}
Rotate(B_9, (((-d8) * 180))°, E'_2) → S_{13}
Rotate(C_9, (((-d8) * 180))°, E'_2) → T_{13}
Rotate(D_9, (((-d8) * 180))°, E'_2) → U_{13}
Rotate(E_9, (((-d8) * 180))°, E'_2) → V_{13}
Rotate(F_9, (((-d8) * 180))°, E'_2) → W_{13}
Rotate(G_9, (((-d8) * 180))°, E'_2) → Z_{13}
Rotate(H_9, (((-d8) * 180))°, E'_2) → A_{14}
Polygon(L_{13}, M_{13}, V_{13}, W_{13}, Z_{13}, A_{14}, N_{13}, O_{13}, P_{13}, Q_{13}, R_{13}, S_{13}, T_{13}, U_{13}) → poly3', l_{13}, u_{13}, v_{13}, w_{13}, z_{13}, a_{14}, m_{13}, n_{13}, o_{13}, p_{13}, q_{13}, r_{13}, s_{13}, t_{13}
Rotate(N''_1, (((-d8) * 180))°, E'_2) → B_{14}
Rotate(OOO'_1, (((-d8) * 180))°, E'_2) → C_{14}
Rotate(O''_1, (((-d8) * 180))°, E'_2) → D_{14}
Rotate(P''_1, (((-d8) * 180))°, E'_2) → E_{14}
Rotate(Q''_1, (((-d8) * 180))°, E'_2) → F_{14}
Rotate(R''_1, (((-d8) * 180))°, E'_2) → G_{14}
Rotate(S''_1, (((-d8) * 180))°, E'_2) → H_{14}
Polygon(B_{14}, C_{14}, D_{14}, E_{14}, F_{14}, G_{14}, H_{14}) → poly2', b_{14}, c_{14}, d_{14}, e_{14}, f_{14}, g_{14}, h_{14}
Intersect(b, d) → I_{14}
Intersect(f, d) → J_{14}
Intersect(e, f) → K_{14}
Intersect(b, e) → L_{14}
Vector(F'_1, H) → u
Vector(L'_1, N') → q
Vector(U, M_5) → r
Sequence(Sequence[Polygon[Translate[R_2, Vector[(s * u) + (t * v)]], Translate[S_2, Vector[(s * u) + (t * v)]], Translate[T_2, Vector[(s * u) + (t * v)]], Translate[U_2, Vector[(s * u) + (t * v)]], Translate[V_2, Vector[(s * u) + (t * v)]], Translate[W_2, Vector[(s * u) + (t * v)]], Translate[Z_2, Vector[(s * u) + (t * v)]], Translate[A_3, Vector[(s * u) + (t * v)]], Translate[B_3, Vector[(s * u) + (t * v)]], Translate[C_3, Vector[(s * u) + (t * v)]], Translate[D_3, Vector[(s * u) + (t * v)]], Translate[Z''', Vector[(s * u) + (t * v)]], Translate[W''', Vector[(s * u) + (t * v)]], Translate[V''', Vector[(s * u) + (t * v)]]], s, (-n), n, 2], t, (-n), n, 2) → liste1
Sequence(Sequence[Polygon[Translate[L, Vector[(s * u) + (t * v)]], Translate[K, Vector[(s * u) + (t * v)]], Translate[J, Vector[(s * u) + (t * v)]], Translate[I, Vector[(s * u) + (t * v)]], Translate[V, Vector[(s * u) + (t * v)]], Translate[W, Vector[(s * u) + (t * v)]], Translate[Z, Vector[(s * u) + (t * v)]], Translate[A_1, Vector[(s * u) + (t * v)]], Translate[B_1, Vector[(s * u) + (t * v)]], Translate[C_1, Vector[(s * u) + (t * v)]], Translate[D_1, Vector[(s * u) + (t * v)]], Translate[J_1, Vector[(s * u) + (t * v)]], Translate[I_1, Vector[(s * u) + (t * v)]], Translate[H_1, Vector[(s * u) + (t * v)]], Translate[G_1, Vector[(s * u) + (t * v)]], Translate[F_1, Vector[(s * u) + (t * v)]], Translate[E_1, Vector[(s * u) + (t * v)]], Translate[H, Vector[(s * u) + (t * v)]], Translate[G, Vector[(s * u) + (t * v)]]], s, (-n), n, 2], t, (-n), n, 2) → liste2
Sequence(Sequence[Polygon[Translate[N', Vector[(s * u) + (t * v)]], Translate[OOO, Vector[(s * u) + (t * v)]], Translate[O', Vector[(s * u) + (t * v)]], Translate[P', Vector[(s * u) + (t * v)]], Translate[Q', Vector[(s * u) + (t * v)]], Translate[R', Vector[(s * u) + (t * v)]], Translate[S', Vector[(s * u) + (t * v)]]], s, (-n), n, 2], t, (-n), n, 2) → liste3
Sequence(Sequence[Polygon[Translate[W_9, Vector[(s * u) + (t * v)]], Translate[Z_9, Vector[(s * u) + (t * v)]], Translate[A_{10}, Vector[(s * u) + (t * v)]], Translate[B_{10}, Vector[(s * u) + (t * v)]], Translate[C_{10}, Vector[(s * u) + (t * v)]], Translate[D_{10}, Vector[(s * u) + (t * v)]], Translate[E_{10}, Vector[(s * u) + (t * v)]], Translate[F_{10}, Vector[(s * u) + (t * v)]], Translate[G_{10}, Vector[(s * u) + (t * v)]], Translate[H_{10}, Vector[(s * u) + (t * v)]], Translate[I_{10}, Vector[(s * u) + (t * v)]], Translate[J_{10}, Vector[(s * u) + (t * v)]], Translate[K_{10}, Vector[(s * u) + (t * v)]], Translate[L_{10}, Vector[(s * u) + (t * v)]], Translate[M_{10}, Vector[(s * u) + (t * v)]], Translate[N_{10}, Vector[(s * u) + (t * v)]], Translate[O_{10}, Vector[(s * u) + (t * v)]], Translate[P_{10}, Vector[(s * u) + (t * v)]], Translate[Q_{10}, Vector[(s * u) + (t * v)]]], s, (-n), n, 2], t, (-n), n, 2) → liste4
Sequence(Sequence[Polygon[Translate[R_{10}, Vector[(s * u) + (t * v)]], Translate[S_{10}, Vector[(s * u) + (t * v)]], Translate[T_{10}, Vector[(s * u) + (t * v)]], Translate[U_{10}, Vector[(s * u) + (t * v)]], Translate[V_{10}, Vector[(s * u) + (t * v)]], Translate[W_{10}, Vector[(s * u) + (t * v)]], Translate[Z_{10}, Vector[(s * u) + (t * v)]]], s, (-n), n, 2], t, (-n), n, 2) → liste5
Sequence(Sequence[Polygon[Translate[I_9, Vector[(s * u) + (t * v)]], Translate[J_9, Vector[(s * u) + (t * v)]], Translate[K_9, Vector[(s * u) + (t * v)]], Translate[L_9, Vector[(s * u) + (t * v)]], Translate[M_9, Vector[(s * u) + (t * v)]], Translate[N_9, Vector[(s * u) + (t * v)]], Translate[O_9, Vector[(s * u) + (t * v)]], Translate[P_9, Vector[(s * u) + (t * v)]], Translate[Q_9, Vector[(s * u) + (t * v)]], Translate[R_9, Vector[(s * u) + (t * v)]], Translate[S_9, Vector[(s * u) + (t * v)]], Translate[T_9, Vector[(s * u) + (t * v)]], Translate[U_9, Vector[(s * u) + (t * v)]], Translate[V_9, Vector[(s * u) + (t * v)]]], s, (-n), n, 2], t, (-n), n, 2) → liste6
Sequence(Sequence[Polygon[Translate[M_7, Vector[(s * u) + (t * v)]], Translate[N_7, Vector[(s * u) + (t * v)]], Translate[O_7, Vector[(s * u) + (t * v)]], Translate[P_7, Vector[(s * u) + (t * v)]], Translate[Q_7, Vector[(s * u) + (t * v)]], Translate[R_7, Vector[(s * u) + (t * v)]], Translate[S_7, Vector[(s * u) + (t * v)]], Translate[T_7, Vector[(s * u) + (t * v)]], Translate[U_7, Vector[(s * u) + (t * v)]], Translate[V_7, Vector[(s * u) + (t * v)]], Translate[W_7, Vector[(s * u) + (t * v)]], Translate[Z_7, Vector[(s * u) + (t * v)]], Translate[A_8, Vector[(s * u) + (t * v)]], Translate[B_8, Vector[(s * u) + (t * v)]]], s, (-n), n, 2], t, (-n), n, 2) → liste7
Sequence(Sequence[Polygon[Translate[T_6, Vector[(s * u) + (t * v)]], Translate[U_6, Vector[(s * u) + (t * v)]], Translate[V_6, Vector[(s * u) + (t * v)]], Translate[W_6, Vector[(s * u) + (t * v)]], Translate[Z_6, Vector[(s * u) + (t * v)]], Translate[A_7, Vector[(s * u) + (t * v)]], Translate[B_7, Vector[(s * u) + (t * v)]], Translate[C_7, Vector[(s * u) + (t * v)]], Translate[D_7, Vector[(s * u) + (t * v)]], Translate[E_7, Vector[(s * u) + (t * v)]], Translate[F_7, Vector[(s * u) + (t * v)]], Translate[G_7, Vector[(s * u) + (t * v)]], Translate[H_7, Vector[(s * u) + (t * v)]], Translate[I_7, Vector[(s * u) + (t * v)]], Translate[J_7, Vector[(s * u) + (t * v)]], Translate[K_7, Vector[(s * u) + (t * v)]], Translate[L_7, Vector[(s * u) + (t * v)]], Translate[H''', Vector[(s * u) + (t * v)]], Translate[G''', Vector[(s * u) + (t * v)]]], s, (-n), n, 2], t, (-n), n, 2) → liste8
Sequence(Sequence[Polygon[Translate[C_8, Vector[(s * u) + (t * v)]], Translate[OOO''', Vector[(s * u) + (t * v)]], Translate[D_8, Vector[(s * u) + (t * v)]], Translate[E_8, Vector[(s * u) + (t * v)]], Translate[F_8, Vector[(s * u) + (t * v)]], Translate[G_8, Vector[(s * u) + (t * v)]], Translate[H_8, Vector[(s * u) + (t * v)]]], s, (-n), n, 2], t, (-n), n, 2) → liste9
Sequence(Sequence[Polygon[Translate[S_8, Vector[(s * u) + (t * v)]], Translate[T_8, Vector[(s * u) + (t * v)]], Translate[U_8, Vector[(s * u) + (t * v)]], Translate[V_8, Vector[(s * u) + (t * v)]], Translate[W_8, Vector[(s * u) + (t * v)]], Translate[Z_8, Vector[(s * u) + (t * v)]], Translate[A_9, Vector[(s * u) + (t * v)]], Translate[B_9, Vector[(s * u) + (t * v)]], Translate[C_9, Vector[(s * u) + (t * v)]], Translate[D_9, Vector[(s * u) + (t * v)]], Translate[E_9, Vector[(s * u) + (t * v)]], Translate[F_9, Vector[(s * u) + (t * v)]], Translate[G_9, Vector[(s * u) + (t * v)]], Translate[H_9, Vector[(s * u) + (t * v)]]], s, (-n), n, 2], t, (-n), n, 2) → liste10
Sequence(Sequence[Polygon[Translate[L'_3, Vector[(s * u) + (t * v)]], Translate[K'_3, Vector[(s * u) + (t * v)]], Translate[J'_3, Vector[(s * u) + (t * v)]], Translate[I'_3, Vector[(s * u) + (t * v)]], Translate[V'_3, Vector[(s * u) + (t * v)]], Translate[W'_3, Vector[(s * u) + (t * v)]], Translate[Z'_3, Vector[(s * u) + (t * v)]], Translate[I_8, Vector[(s * u) + (t * v)]], Translate[J_8, Vector[(s * u) + (t * v)]], Translate[K_8, Vector[(s * u) + (t * v)]], Translate[L_8, Vector[(s * u) + (t * v)]], Translate[M_8, Vector[(s * u) + (t * v)]], Translate[N_8, Vector[(s * u) + (t * v)]], Translate[O_8, Vector[(s * u) + (t * v)]], Translate[P_8, Vector[(s * u) + (t * v)]], Translate[Q_8, Vector[(s * u) + (t * v)]], Translate[R_8, Vector[(s * u) + (t * v)]], Translate[H'_1, Vector[(s * u) + (t * v)]], Translate[G'_1, Vector[(s * u) + (t * v)]]], s, (-n), n, 2], t, (-n), n, 2) → liste11
Sequence(Sequence[Polygon[Translate[N''_1, Vector[(s * u) + (t * v)]], Translate[OOO'_1, Vector[(s * u) + (t * v)]], Translate[O''_1, Vector[(s * u) + (t * v)]], Translate[P''_1, Vector[(s * u) + (t * v)]], Translate[Q''_1, Vector[(s * u) + (t * v)]], Translate[R''_1, Vector[(s * u) + (t * v)]], Translate[S''_1, Vector[(s * u) + (t * v)]]], s, (-n), n, 2], t, (-n), n, 2) → liste12

AI Drawing Prompt Reference

Draw a cat-shaped paving pattern composed of multiple trapezoids and rectangles. Start by drawing two parallel lines, then draw multiple trapezoids and rectangles along these lines, with the top and bottom bases of each trapezoid connected to adjacent rectangles. Use mirroring, rotation, and translation transformations to ensure the correct positions and sizes of each trapezoid and rectangle. Finally, combine all trapezoids and rectangles to form a complete cat-shaped pattern.

The prompt above was compiled from the original drawing commands and is for reference only.