Trafo

Extension

Create new Basis from basis Vectors.// set basis and d ( t = Trafo.new([ [0, 2, 0], [0, 0, 6], [5, 0, 0] ], [3, 4, 5]) ) // set d, only t = Trafo.new(d: [0,0,0])

Arguments:

Create new Basis from transformation.

Create new Basis from 3d Points.( t = Trafo.from3dPoints( [0, 2, 0], [3, 3, 0], [15, 2, 0] ) ) /* returns Trafo.basicNew( Matrix[ [ 0.94868329805051, 0.31622776601684, 0, 0 ], [ 0.31622776601684, -0.94868329805051, 0, 2 ], [ 0, 0, -1, 0 ], [ 0, 0, 0, 1 ] ] ) */ // doesn't work, since basis is collinear... t = Trafo.from3dPoints( [0, 2, 0], [0, 2, 0], [15, 2, 0] )

Create new Basis from 3d Points.( t = Trafo.inverseFrom3dPoints( [0, 2, 0], [3, 3, 0], [15, 2, 0] ); u = Trafo.inverseFrom3dPoints( [0, 2, 0], [3, 3, 0], [15, 2, 0] ); ) ( {200.do{ Trafo.inverseFrom3dPoints( [0, 2, 0], [3, 3, 0], [15, 2, 0] ); }}.bench; {200.do{ Trafo.from3dPoints( [0, 2, 0], [3, 3, 0], [15, 2, 0] ).inverse; }}.bench; )

Return the used rotation matrix( t = Trafo.from3dPoints( [0, 0, 0], [pi, 3, 0], [15, 2, 0] ); t.rotMatrix ) ( t = Trafo.new; t.rotMatrix )

Return the basis vectors as: [[x1, x2, x3],[y1, y2, y3],[z1, z2, z3]]( t = Trafo([ [0, 2, 0], [3, 0, 0], [0, 0, 15] ]); t.basis )

Return the translative part.( t = Trafo.new; t.position )

Return a new instance where (t * t.inverse vmul: v) == v;( t = Trafo.new; t.inverse )

Transform aVec with scaling scale to the trafo-inherited basis.t = Trafo.new; // the identity t.vmul( [1, 0, 0]); ( {2000.do{ t = Trafo.new({{1.0.rand}!3}!3, {1.0.rand}!3); t vmul: ({1.0.rand}!3) }}.bench ) t = Trafo.from3dPoints( [0, 0, 0], [pi, 3, 0], [15, 2, 0] ) t.vmul( [1, 0, 0])