Trabalho 1 – Clausius Reis (66812)
IA841 – Introdução à modelagem de sólidos
Foram criadas cinco figuras geométricas, os sólidos platônicos.
Para a construção destes sólidos, utilizei um tutorial encontrado na internet onde os seguintes números eram calculados:
|
phi = (1 + sqrt(5)) / 2 A = 1/sqrt(3) B = 1 / phi C = 1 / (phi * phi) X = 0.525731112119133606f Z = 0.850650808352039932f |
Com estes valores em mãos, foram criadas matrizes para armazenar os pontos de cada poliedro:
|
// Tetraedro int num_face_tetra = 3; vertice faces_tetra[4][3]
= { {{ A, A, A},{-A,-A, A},{ A,-A,-A}}, {{-A, A,-A},{ A, A, A},{ A,-A,-A}}, {{-A,-A, A},{ A, A, A},{-A, A,-A}}, {{ A,-A,-A},{-A,-A, A},{-A, A,-A}} }; |
|
// Hexaedro int num_face_hexa = 5; vertice faces_hexa[6][4] = { {{A,A,A},{A,A,-A},{-A,A,-A},{-A,A,A}},
{{-A,A,A},{-A,A,-A},{-A,-A,-A},{-A,-A,A}}, {{-A,-A,A},{-A,-A,-A},{A,-A,-A},{A,-A,A}}, {{A,-A,A},{A,-A,-A},{A,A,-A},{A,A,A}}, {{A,A,-A},{A,-A,-A},{-A,-A,-A},{-A,A,-A}}, {{A,A,A},{-A,A,A},{-A,-A,A},{A,-A,A}} }; |
|
// Octaedro int num_face_octa = 7; vertice faces_octa[8][3] =
{ {{1,0,0},{0,1,0},{0,0,1}},
{{0,1,0},{-1,0,0},{0,0,1}},
{{-1,0,0},{0,-1,0},{0,0,1}}, {{0,-1,0},{1,0,0},{0,0,1}},
{{0,1,0},{1,0,0},{0,0,-1}},
{{-1,0,0},{0,1,0},{0,0,-1}}, {{0,-1,0},{-1,0,0},{0,0,-1}}, {{1,0,0},{0,-1,0},{0,0,-1}} }; |
|
// Dodecaedro int num_face_dode = 11; vertice faces_dode[12][5]
= { {{ C, 0, 1},{-C, 0, 1},{-B, B, B},{ 0, 1, C},{ B, B, B}}, {{-C, 0, 1},{ C, 0, 1},{ B,-B, B},{ 0,-1, C},{-B,-B, B}}, {{ C, 0,-1},{-C, 0,-1},{-B,-B,-B},{ 0,-1,-C},{ B,-B,-B}}, {{-C, 0,-1},{ C, 0,-1},{ B, B,-B},{ 0, 1,-C},{-B, B,-B}}, {{ 0, 1,-C},{ 0, 1, C},{ B, B, B},{ {{ 0, 1, C},{ 0, 1,-C},{-B, B,-B},{- {{ 0,-1,-C},{ 0,-1, C},{-B,-B, B},{-1,-C, 0},{-B,-B,-B}}, {{ 0,-1, C},{ 0,-1,-C},{ B,-B,-B},{ 1,-C, 0},{ B,-B, B}}, {{ {{ 1,-C, 0},{ {{- {{-1,-C, 0},{- }; |
|
// Icosaedro int num_face_ico = 19; vertice faces_ico[20][3] =
{ {{ 0, Z, X},{-X, 0, Z},{ X, 0, Z}}, {{-Z, X, 0},{-X, 0, Z},{ 0, Z, X}}, {{ 0, Z,-X},{-Z, X, 0},{ 0, Z, X}}, {{ 0, Z,-X},{ 0, Z, X},{ Z, X, 0}}, {{ Z, X, 0},{ 0, Z, X},{ X, 0, Z}}, {{ Z,-X, 0},{ Z, X,
0},{ X, 0, Z}}, {{ X, 0,-Z},{ Z, X, 0},{ Z,-X, 0}}, {{ X, 0,-Z},{ 0, Z,-X},{ Z, X, 0}}, {{-X, 0,-Z},{ 0, Z,-X},{ X, 0,-Z}}, {{ 0,-Z,-X},{-X, 0,-Z},{ X, 0,-Z}}, {{ Z,-X, 0},{ 0,-Z,-X},{ X, 0,-Z}}, {{ 0,-Z, X},{ 0,-Z,-X},{ Z,-X, 0}}, {{-Z,-X, 0},{ 0,-Z,-X},{ 0,-Z, X}}, {{-X, 0, Z},{-Z,-X, 0},{ 0,-Z, X}}, {{ X, 0, Z},{-X, 0, Z},{ 0,-Z, X}}, {{ X, 0, Z},{ 0,-Z, X},{ Z,-X, 0}}, {{-X, 0, Z},{-Z, X, 0},{-Z,-X, 0}}, {{-Z,-X, 0},{-Z, X, 0},{-X, 0,-Z}}, {{-X, 0,-Z},{-Z, X, 0},{ 0, Z,-X}}, {{-X, 0,-Z},{ 0,-Z,-X},{-Z,-X, 0}} }; |
Com isso em mãos, foram obtidos os seguintes sólidos:
