GeometryUtils.js 5.8 KB

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