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Example 1 : Tentukan matriks refleksi terhadap garis y = x Jawab: K = R(-45 0 ) * Refleksi thd sb-y * R(45 0 ). 2/2 2/2 0 -2/2 2/2 0 0 0 1. -1 0 0 0 1 0 0 0 1. 2/2 - 2/2 0 2/2 2/2 0 0 0 1. 0 1 0

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  1. Example 1 : Tentukan matriks refleksi terhadap garis y = xJawab:K = R(-450) * Refleksi thd sb-y * R(450) 2/22/2 0 -2/22/2 0 0 0 1 -1 0 0 0 1 0 0 0 1 2/2 -2/2 0 2/22/2 0 0 0 1 0 1 0 10 0 0 0 1 = =

  2. Example 2 Bila refleksi dilakukan terhadap garis y = 1/2 (x + 4). Menurut Sdr bagaimanakah matriks komposisinya ? Jawab: K = T(0,2) R( = tan-1 ½) Refleksi thd sb-X R( = -tan-1 ½) T(0,-2) 1 0 0 01 2 0 0 1 1 0 0 0 -1 0 0 0 1 1 0 0 01 -2 0 0 1 2/5 -1/5 0 1/5 2/5 0 0 0 1 2/5 1/5 0 -1/5 2/5 0 0 0 1 K = 3/5 4/5 -8/5 4/5-3/5 16/5 0 0 1 K = 3/5 4/5 -8/5 4/5-3/5 16/5 0 0 1 2 4 2 4 6 6 = 1 1 1 14/5 28/5 22/5 12/514/5 6/5 1 1 1 O* = K * O =

  3. Problem 1 : Buktikan bahwa matriks komposisi untuk rotasi terhadap titik sembarang (x,y) adalah cos  -sin  x(1 - cos ) + ysin  sin  cos  y(1 - cos ) - xsin  0 0 1 K = Problem 2 : Buktikan bahwa matriks komposisi untuk penyekalaan terhadap titik sembarang (x,y) adalah Sx 0 x(1 - Sx) 0 Sy y(1 - Sy) 0 0 1 K =

  4. Problem 3 : (lihat Foley & Van Dam, hal 210) Tentukan matriks komposisi KWV untuk pemetaan obyek segi 3 ABC dari window ke viewport dan hitung posisi A*, B* dan C* setelah pemetaan

  5. Object_array = 2 5 5 6 4 8 1 1 1 Translation_matrix_2_origin = 1 0 -4 0 1 -6 0 0 1 Rotation_matrix = 0 -1 0 1 0 0 0 0 1 Translation_matrix_2_previous_position = 1 0 4 0 1 6 0 0 1 New_obj_array = 4 6 2 4 7 7 1 1 1 • Translasikan obyek ke origin sebesar T(-4,-6), kemudian • rotasikan sebesar R(900). Kembalikan ke posisi semula • dengan T(4,6). Matriks komposisi yang pertama adalah • K1 = T(4,6) * R(900) * T(-4,-6)

  6. Object_array = 4 62 4 7 7 111 Translation_matrix_2_origin = 1 0 -1 0 1 -3 00 1 Scaling_matrix = 0.75 0 0 0 1.33 0 0 0 1.00 Translation_matrix_2_previous_position = 1 0 3 0 1 1 00 1 New_obj_array = 5.25 5.753.75 2.33 6.32 6.32 1 1 1 • Proses pemetaan ke viewport dilakukan dengan cara • mengalikan obyek hasil transformasi dari proses pertama • dengan matriks komposisi K2 = T(3,1) * S(0.75, 1.33) * T(-1,-3) • yaitu • New_obj_array = K2 * New_obj_array sehingga diperoleh :

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