// The point B is determined by taking twice the vector A from the origin

var p0 = board.create('point', [0, 3], {name: 'A'}),
    t = board.create('transform', [function(){ return p0.X(); }, "Y(A)"], {type: 'translate'}),
    p1 = board.create('point', [p0, t], {color: 'blue'});

// The point B is the result of scaling the point A with factor 2 in horizontal direction
// and with factor 0.5 in vertical direction.

var p1 = board.create('point', [1, 1]),
    t = board.create('transform', [2, 0.5], {type: 'scale'}),
    p2 = board.create('point', [p1, t], {color: 'blue'});

// The point B is rotated around C which gives point D. The angle is determined
// by the vertical height of point A.

var p0 = board.create('point', [0, 3], {name: 'A'}),
    p1 = board.create('point', [1, 1]),
    p2 = board.create('point', [2, 1], {name:'C', fixed: true}),

    // angle, rotation center:
    t = board.create('transform', ['Y(A)', p2], {type: 'rotate'}),
    p3 = board.create('point', [p1, t], {color: 'blue'});

// A concatenation of several transformations.
var p1 = board.create('point', [1, 1]),
    t1 = board.create('transform', [-2, -1], {type: 'translate'}),
    t2 = board.create('transform', [Math.PI/4], {type: 'rotate'}),
    t3 = board.create('transform', [2, 1], {type: 'translate'}),
    p2 = board.create('point', [p1, [t1, t2, t3]], {color: 'blue'});

// Reflection of point A
var p1 = board.create('point', [1, 1]),
    p2 = board.create('point', [1, 3]),
    p3 = board.create('point', [-2, 0]),
    l = board.create('line', [p2, p3]),
    t = board.create('transform', [l], {type: 'reflect'}),  // Possible are l, l.id, l.name
    p4 = board.create('point', [p1, t], {color: 'blue'});

// One time application of a transform to points A, B
var p1 = board.create('point', [1, 1]),
    p2 = board.create('point', [-1, -2]),
    t = board.create('transform', [3, 2], {type: 'shear'});
t.applyOnce([p1, p2]);

// Construct a square of side length 2 with the
// help of transformations
    var sq = [],
        right = board.create('transform', [2, 0], {type: 'translate'}),
        up = board.create('transform', [0, 2], {type: 'translate'}),
        pol, rot, p0;

    // The first point is free
    sq[0] = board.create('point', [0, 0], {name: 'Drag me'}),

    // Construct the other free points by transformations
    sq[1] = board.create('point', [sq[0], right]),
    sq[2] = board.create('point', [sq[0], [right, up]]),
    sq[3] = board.create('point', [sq[0], up]),

    // Polygon through these four points
    pol = board.create('polygon', sq, {
            fillColor:'blue',
            gradient:'radial',
            gradientsecondcolor:'white',
            gradientSecondOpacity:'0'
    }),

    p0 = board.create('point', [0, 3], {name: 'angle'}),
    // Rotate the square around point sq[0] by dragging A vertically.
    rot = board.create('transform', ['Y(angle)', sq[0]], {type: 'rotate'});

    // Apply the rotation to all but the first point of the square
    rot.bindTo(sq.slice(1));

// Text transformation
var p0 = board.create('point', [0, 0], {name: 'p_0'});
var p1 = board.create('point', [3, 0], {name: 'p_1'});
var txt = board.create('text',[0.5, 0, 'Hello World'], {display:'html'});

// If p_0 is dragged, translate p_1 and text accordingly
var tOff = board.create('transform', [() => p0.X(), () => p0.Y()], {type:'translate'});
tOff.bindTo(txt);
tOff.bindTo(p1);

// Rotate text around p_0 by dragging point p_1
var tRot = board.create('transform', [
    () => Math.atan2(p1.Y() - p0.Y(), p1.X() - p0.X()), p0], {type:'rotate'});
tRot.bindTo(txt);

// Scale text by dragging point "p_1"
// We do this by
// - moving text by -p_0 (inverse of transformation tOff),
// - scale the text (because scaling is relative to (0,0))
// - move the text back by +p_0
var tOffInv = board.create('transform', [
        () => -p0.X(),
        () => -p0.Y()
], {type:'translate'});
var tScale = board.create('transform', [
        // Some scaling factor
        () => p1.Dist(p0) / 3,
        () => p1.Dist(p0) / 3
], {type:'scale'});
tOffInv.bindTo(txt); tScale.bindTo(txt); tOff.bindTo(txt);