Element Transformation
JXG.Transformation
↳ Transformation
This element is used to provide projective transformations.
Defined in: transformation.js.
Extends
JXG.Transformation.
| Constructor Attributes | Constructor Name and Description |
|---|---|
|
A transformation consists of a 3x3 matrix, i.e.
|
- Methods borrowed from class JXG.Transformation:
- apply, applyOnce, bindTo, melt, setAttribute, setMatrix, setProperty, update
Element Detail
Transformation
A transformation consists of a 3x3 matrix, i.e. it is a projective transformation.
Internally, a transformation is applied to an element by multiplying the 3x3 matrix from the left to the homogeneous coordinates of the element. JSXGraph represents homogeneous coordinates in the order (z, x, y). The matrix has the form
( a b c ) ( z ) ( d e f ) * ( x ) ( g h i ) ( y )where in general a=1. If b = c = 0, the transformation is called affine. In this case, finite points will stay finite. This is not the case for general projective coordinates.
Transformations acting on texts and images are considered to be affine, i.e. b and c are ignored.
-
This element has no direct constructor. To create an instance of this element you have to call JXG.Board#create
with type "transformation".
- Possible parent array combinations are:
-
{numbers|functions} parameters
- The parameters depend on the transformation type, supplied as attribute 'type'.
Possible transformation types are
- 'translate'
- 'scale'
- 'reflect'
- 'rotate'
- 'shear'
- 'generic'
Translation matrix:
( 1 0 0) ( z ) ( a 1 0) * ( x ) ( b 0 1) ( y )
Scale matrix:
( 1 0 0) ( z ) ( 0 a 0) * ( x ) ( 0 0 b) ( y )
A rotation matrix with angle a (in Radians)
( 1 0 0 ) ( z ) ( 0 cos(a) -sin(a)) * ( x ) ( 0 sin(a) cos(a) ) ( y )
Shear matrix:
( 1 0 0) ( z ) ( 0 1 a) * ( x ) ( 0 b 1) ( y )
Generic transformation:
( a b c ) ( z ) ( d e f ) * ( x ) ( g h i ) ( y )
- Throws:
- {Exception}
- If the element cannot be constructed with the given parent objects an exception is thrown.
- Examples:
// 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);
Attributes borrowed from other Elements
Fields borrowed from other Elements
Methods borrowed from other Elements
- Methods borrowed from class JXG.Transformation:
- apply, applyOnce, bindTo, melt, setAttribute, setMatrix, setProperty, update
Events borrowed from other Elements