lathe/lib/vertex3d.js

A discrete solid modeller using BSPs

// Vertex3D objects
// 
// Vertices are defined as the intersection of 3 planes as per [1]\
// 
// References:
// [1] http://homes.cs.washington.edu/~gilbo/repofiles/booleans2009.pdf

define([
    'gl-matrix',
    './vector3',
    './matrix',
    './plane3d'
  ], function(
    glMatrix,
    Vector3, 
    matrix, 
    Plane3D) {

    'use strict';

    var vec3 = glMatrix.vec3;
    var mat3 = glMatrix.mat3;
    var mat4 = glMatrix.mat4;

    var Vertex3D = function(p,q,r) {
      if (!((p instanceof Plane3D) && (q instanceof Plane3D) && (r instanceof Plane3D))) {
        throw { 
          name: 'InvalidVertex',
          message: 'invalid vertex construction: ' + [p,q,r].join(',')
        };
      }
      this.p = p;
      this.q = q;
      this.r = r;
    };

    // Creating Float32Arrays are quite slow, so re-use
    // them for calculations
    var m4 = mat4.create();
    var m3 = mat3.create();
    var m3inv = mat3.create();
    var m3invT = mat3.create();
    var coordinate = vec3.create();

    // Is valid if the derminant is non-zero. [1] § 3.1
    //
    // | pa, pb, pc |
    // | qa, qb, qc |
    // | ra, rb, rc |
    //
    Vertex3D.prototype.isValid = function() {
      m3[0] = this.p.a;
      m3[1] = this.p.b;
      m3[2] = this.p.c;

      m3[3] = this.q.a;
      m3[4] = this.q.b;
      m3[5] = this.q.c;

      m3[6] = this.r.a;
      m3[7] = this.r.b;
      m3[8] = this.r.c;

      return mat3.determinant(m3) !== 0;
    };

    // [1] § 3.1
    // Given that the point (p,q,r) is valid, it lies
    // behind, on, or in-front of the plane s if and only if the 
    // following expression is negative, zero, or positive, respectively:
    //
    // |pa pb pc|  |pa pb pc pd|
    // |qa qb qc|* |qa qb qc qd|
    // |ra rb rc|  |ra rb rc rd|
    //       |sa sb sc sd|
    //



    Vertex3D.prototype.orientationToPlane = function(s) {
      m4[0] = this.p.a;
      m4[1] = this.p.b;
      m4[2] = this.p.c;
      m4[3] = this.p.d;

      m4[4] = this.q.a;
      m4[5] = this.q.b;
      m4[6] = this.q.c;
      m4[7] = this.q.d;

      m4[8]  = this.r.a;
      m4[9]  = this.r.b;
      m4[10] = this.r.c;
      m4[11] = this.r.d;

      m4[12] = s.a;
      m4[13] = s.b;
      m4[14] = s.c;
      m4[15] = s.d;

      mat3.fromMat4(m3, m4);

      // Caching the determinant on creation actually makes in slower
      var d1d2 = mat3.determinant(m3)*mat4.determinant(m4);
      var eps = 1e-10;
      if (d1d2 > eps) {
        return '-';
      } else if (d1d2 < -eps) {
        return '+';
      } else {
        return '0';
      }
    };

    // Find the intersection of the planes by solving the 
    // simultaneous equations of the 3 planes
    // 
    // Based on http://maths.ucd.ie/courses/math1200/algebra/algebranotes4-3.pdf
    // but merging step1 and step2
    //
    // [ pa pb pc ][ x ]   [ pd ]
    // [ qa qb qc ][ y ] = [ qd ]
    // [ qa qb qc ][ z ]   [ rd ]
    
    Vertex3D.prototype.toCoordinate = function() {
      m3[0] = this.p.a;
      m3[1] = this.p.b;
      m3[2] = this.p.c;

      m3[3] = this.q.a;
      m3[4] = this.q.b;
      m3[5] = this.q.c;

      m3[6] = this.r.a;
      m3[7] = this.r.b;
      m3[8] = this.r.c;

      mat3.invert(m3inv, m3);
      mat3.transpose(m3invT, m3inv);

      var xyz = vec3.fromValues(this.p.d, this.q.d, this.r.d);
      glMatrix.vec3.transformMat3(coordinate, xyz, m3invT);
      return new Vector3(coordinate[0], coordinate[1], coordinate[2]);

    };

    return Vertex3D;

  });