GeometryUtils.js 6.5 KB

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249
  1. import {
  2. Vector3
  3. } from '../../../build/three.module.js';
  4. var GeometryUtils = {
  5. /**
  6. * Generates 2D-Coordinates in a very fast way.
  7. *
  8. * Based on work by:
  9. * @link http://www.openprocessing.org/sketch/15493
  10. *
  11. * @param center Center of Hilbert curve.
  12. * @param size Total width of Hilbert curve.
  13. * @param iterations Number of subdivisions.
  14. * @param v0 Corner index -X, -Z.
  15. * @param v1 Corner index -X, +Z.
  16. * @param v2 Corner index +X, +Z.
  17. * @param v3 Corner index +X, -Z.
  18. */
  19. hilbert2D: function ( center, size, iterations, v0, v1, v2, v3 ) {
  20. // Default Vars
  21. var center = center !== undefined ? center : new Vector3( 0, 0, 0 ),
  22. size = size !== undefined ? size : 10,
  23. half = size / 2,
  24. iterations = iterations !== undefined ? iterations : 1,
  25. v0 = v0 !== undefined ? v0 : 0,
  26. v1 = v1 !== undefined ? v1 : 1,
  27. v2 = v2 !== undefined ? v2 : 2,
  28. v3 = v3 !== undefined ? v3 : 3
  29. ;
  30. var vec_s = [
  31. new Vector3( center.x - half, center.y, center.z - half ),
  32. new Vector3( center.x - half, center.y, center.z + half ),
  33. new Vector3( center.x + half, center.y, center.z + half ),
  34. new Vector3( center.x + half, center.y, center.z - half )
  35. ];
  36. var vec = [
  37. vec_s[ v0 ],
  38. vec_s[ v1 ],
  39. vec_s[ v2 ],
  40. vec_s[ v3 ]
  41. ];
  42. // Recurse iterations
  43. if ( 0 <= -- iterations ) {
  44. var tmp = [];
  45. Array.prototype.push.apply( tmp, GeometryUtils.hilbert2D( vec[ 0 ], half, iterations, v0, v3, v2, v1 ) );
  46. Array.prototype.push.apply( tmp, GeometryUtils.hilbert2D( vec[ 1 ], half, iterations, v0, v1, v2, v3 ) );
  47. Array.prototype.push.apply( tmp, GeometryUtils.hilbert2D( vec[ 2 ], half, iterations, v0, v1, v2, v3 ) );
  48. Array.prototype.push.apply( tmp, GeometryUtils.hilbert2D( vec[ 3 ], half, iterations, v2, v1, v0, v3 ) );
  49. // Return recursive call
  50. return tmp;
  51. }
  52. // Return complete Hilbert Curve.
  53. return vec;
  54. },
  55. /**
  56. * Generates 3D-Coordinates in a very fast way.
  57. *
  58. * Based on work by:
  59. * @link http://www.openprocessing.org/visuals/?visualID=15599
  60. *
  61. * @param center Center of Hilbert curve.
  62. * @param size Total width of Hilbert curve.
  63. * @param iterations Number of subdivisions.
  64. * @param v0 Corner index -X, +Y, -Z.
  65. * @param v1 Corner index -X, +Y, +Z.
  66. * @param v2 Corner index -X, -Y, +Z.
  67. * @param v3 Corner index -X, -Y, -Z.
  68. * @param v4 Corner index +X, -Y, -Z.
  69. * @param v5 Corner index +X, -Y, +Z.
  70. * @param v6 Corner index +X, +Y, +Z.
  71. * @param v7 Corner index +X, +Y, -Z.
  72. */
  73. hilbert3D: function ( center, size, iterations, v0, v1, v2, v3, v4, v5, v6, v7 ) {
  74. // Default Vars
  75. var center = center !== undefined ? center : new Vector3( 0, 0, 0 ),
  76. size = size !== undefined ? size : 10,
  77. half = size / 2,
  78. iterations = iterations !== undefined ? iterations : 1,
  79. v0 = v0 !== undefined ? v0 : 0,
  80. v1 = v1 !== undefined ? v1 : 1,
  81. v2 = v2 !== undefined ? v2 : 2,
  82. v3 = v3 !== undefined ? v3 : 3,
  83. v4 = v4 !== undefined ? v4 : 4,
  84. v5 = v5 !== undefined ? v5 : 5,
  85. v6 = v6 !== undefined ? v6 : 6,
  86. v7 = v7 !== undefined ? v7 : 7
  87. ;
  88. var vec_s = [
  89. new Vector3( center.x - half, center.y + half, center.z - half ),
  90. new Vector3( center.x - half, center.y + half, center.z + half ),
  91. new Vector3( center.x - half, center.y - half, center.z + half ),
  92. new Vector3( center.x - half, center.y - half, center.z - half ),
  93. new Vector3( center.x + half, center.y - half, center.z - half ),
  94. new Vector3( center.x + half, center.y - half, center.z + half ),
  95. new Vector3( center.x + half, center.y + half, center.z + half ),
  96. new Vector3( center.x + half, center.y + half, center.z - half )
  97. ];
  98. var vec = [
  99. vec_s[ v0 ],
  100. vec_s[ v1 ],
  101. vec_s[ v2 ],
  102. vec_s[ v3 ],
  103. vec_s[ v4 ],
  104. vec_s[ v5 ],
  105. vec_s[ v6 ],
  106. vec_s[ v7 ]
  107. ];
  108. // Recurse iterations
  109. if ( -- iterations >= 0 ) {
  110. var tmp = [];
  111. Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 0 ], half, iterations, v0, v3, v4, v7, v6, v5, v2, v1 ) );
  112. Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 1 ], half, iterations, v0, v7, v6, v1, v2, v5, v4, v3 ) );
  113. Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 2 ], half, iterations, v0, v7, v6, v1, v2, v5, v4, v3 ) );
  114. Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 3 ], half, iterations, v2, v3, v0, v1, v6, v7, v4, v5 ) );
  115. Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 4 ], half, iterations, v2, v3, v0, v1, v6, v7, v4, v5 ) );
  116. Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 5 ], half, iterations, v4, v3, v2, v5, v6, v1, v0, v7 ) );
  117. Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 6 ], half, iterations, v4, v3, v2, v5, v6, v1, v0, v7 ) );
  118. Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 7 ], half, iterations, v6, v5, v2, v1, v0, v3, v4, v7 ) );
  119. // Return recursive call
  120. return tmp;
  121. }
  122. // Return complete Hilbert Curve.
  123. return vec;
  124. },
  125. /**
  126. * Generates a Gosper curve (lying in the XY plane)
  127. *
  128. * https://gist.github.com/nitaku/6521802
  129. *
  130. * @param size The size of a single gosper island.
  131. */
  132. gosper: function ( size ) {
  133. size = ( size !== undefined ) ? size : 1;
  134. function fractalize( config ) {
  135. var output;
  136. var input = config.axiom;
  137. for ( var i = 0, il = config.steps; 0 <= il ? i < il : i > il; 0 <= il ? i ++ : i -- ) {
  138. output = '';
  139. for ( var j = 0, jl = input.length; j < jl; j ++ ) {
  140. var char = input[ j ];
  141. if ( char in config.rules ) {
  142. output += config.rules[ char ];
  143. } else {
  144. output += char;
  145. }
  146. }
  147. input = output;
  148. }
  149. return output;
  150. }
  151. function toPoints( config ) {
  152. var currX = 0, currY = 0;
  153. var angle = 0;
  154. var path = [ 0, 0, 0 ];
  155. var fractal = config.fractal;
  156. for ( var i = 0, l = fractal.length; i < l; i ++ ) {
  157. var char = fractal[ i ];
  158. if ( char === '+' ) {
  159. angle += config.angle;
  160. } else if ( char === '-' ) {
  161. angle -= config.angle;
  162. } else if ( char === 'F' ) {
  163. currX += config.size * Math.cos( angle );
  164. currY += - config.size * Math.sin( angle );
  165. path.push( currX, currY, 0 );
  166. }
  167. }
  168. return path;
  169. }
  170. //
  171. var gosper = fractalize( {
  172. axiom: 'A',
  173. steps: 4,
  174. rules: {
  175. A: 'A+BF++BF-FA--FAFA-BF+',
  176. B: '-FA+BFBF++BF+FA--FA-B'
  177. }
  178. } );
  179. var points = toPoints( {
  180. fractal: gosper,
  181. size: size,
  182. angle: Math.PI / 3 // 60 degrees
  183. } );
  184. return points;
  185. }
  186. };
  187. export { GeometryUtils };