lathe/lib/vertex2d.js

A discrete solid modeller using BSPs

// Vertex3D objects
// 
// Vertices are defined as the intersection of 2, similar to 3d vertices
// are the intersection of 3 planes.
// 

define(['./matrix', './plane2d'], function(matrix, Plane2D) {

  'use strict';

  var Vertex2D = function(p,q) {
    if (!((p instanceof Plane2D) && (q instanceof Plane2D))) {
      throw new Error('invalid vertex construction: ' + [p,q].join(','));
    }
    this.p = p;
    this.q = q;
    if (!this.isValid()) {
      throw new Error('invalid vertex construction: ' + [p,q].join(','));
    }
  };

  // Is valid if the derminant is zero. See Vertex3D.
  //
  // | pa, pb | 
  // | qa, qb | 
  //
  Vertex2D.prototype.isValid = function() {
    var m = [
      [this.p.a, this.p.b],
      [this.q.a, this.q.b],
    ];
    return matrix.determinant2x2(m) !== 0;

  };

  // See Vertex3D.orientationToPlane3D 
  // 
  Vertex2D.prototype.orientationToPlane = function(s) {
    var m1 = [
      [this.p.a, this.p.b],
      [this.q.a, this.q.b],
    ];
    var m2 = [
      [this.p.a, this.p.b, this.p.c],
      [this.q.a, this.q.b, this.q.c],
      [s.a,    s.b,    s.c],
    ];
    var d1d2 = matrix.determinant2x2(m1)*matrix.determinant3x3(m2);
    if (d1d2 > 0) {
      return '-';
    } else if (d1d2 < 0) {
      return '+';
    } else {
      return '0';
    }
  };   

  // Find the intersection of the planes by solving the 
  // simultaneous equations of the 2 planes
  // 
  // [ pa pb ][ x ]   [ pc ]
  // [ qa qb ][ y ] = [ qc ]
  Vertex2D.prototype.toCoordinate = function() {
    var a = [
          [this.p.a, this.p.b],
          [this.q.a, this.q.b],
        ];
    var detA = matrix.determinant2x2(a);

    var aInverse = [
      [a[1][1]/detA, -a[0][1]/detA],
      [-a[1][0]/detA, a[0][0]/detA],
    ];
    return {
      x: (aInverse[0][0]*this.p.c + aInverse[0][1]*this.q.c),
      y: (aInverse[1][0]*this.p.c + aInverse[1][1]*this.q.c),
    };
  };  

  return Vertex2D;

});