    indexing
    	description: "[
    							An EV_TRANSFORMATION is basicaly a matrix
    							discribing a projection from one coordinate system
    							into another with homogeneouse coordinates.
    							You can use an EV_TRANSFORMATION to change
    							shape of any transformable EV_FIGURE.

    							examples:
    								translating (x, y) to (x + dx, y + dy):

    								| 1  0  dx |    |x|    |x + dx|
    								| 0  1  dy |  * |y|  = |y + dy|
    								| 0  0  1  |    |1|    |  1   |

    								rotation matrix around (0, 0) for angle:

    								| cosine angle   -sine angle   0 |
    								|  sine angle   cosine angle   0 |
    								|      0             0         1 |

    								scaling for sx in x direction and sy in y direction:

    								| sx  0   0 |
    								|  0 sy   0 |
    								|  0  0   1 |

    							This transformations can be combined by just multipling the
    							matrixes togetter. For example a rotation around (px, py) is
    							achieved by first translating a point such that px, py is at
    							(0, 0), then rotating and then translating back:

    							|1 0 px|   |cosine angle   -sine angle  0|   |1 0 -px|
    							|0 1 py| * | sine angle   cosine angle  0| * |0 1 -py|
    							|0 0 1 |   |    0              0        1|   |0 0  1 |

    							(read from right to left)
    							The result matrix is build when calling rotate.

    							The beauty of the approach is no matter how
    							complex your transformation is the complexity is allways:
    								4 multiplications and 4 additions per point (see project)

    							See the book: Computer Graphics by Foley et all, side 201 for more informations.
    	]"
    	legal: "See notice at end of class."
    	status: "See notice at end of class."
    	date: "$Date: 2006-01-22 18:25:44 -0800 (Sun, 22 Jan 2006) $"
    	revision: "$Revision: 56675 $"

    class interface
    	EV_MODEL_TRANSFORMATION

    create
    	make_zero
    			-- Create a transformation matrix with all elements 0.0

    	make_id
    			-- Create an identity transformation matrix

    feature -- Access

    	generating_type: STRING_8
    			-- Name of current object's generating type
    			-- (type of which it is a direct instance)
    			-- (from ANY)

    	generator: STRING_8
    			-- Name of current object's generating class
    			-- (base class of the type of which it is a direct instance)
    			-- (from ANY)

    	height: INTEGER_32 is 3
    			-- Number of rows in the matrix.

    	item (row, column: INTEGER_32): REAL_64
    			-- Entry at position (`row', `column')
    		require
    			valid_row: (1 <= row) and (row <= height)
    			valid_column: (1 <= column) and (column <= width)

    	width: INTEGER_32 is 3
    			-- Number of columns in the matrix.

    feature -- Comparison

    	frozen deep_equal (some: ANY; other: like arg #1): BOOLEAN
    			-- Are `some' and `other' either both void
    			-- or attached to isomorphic object structures?
    			-- (from ANY)
    		ensure -- from ANY
    			shallow_implies_deep: standard_equal (some, other) implies Result
    			both_or_none_void: (some = Void) implies (Result = (other = Void))
    			same_type: (Result and (some /= Void)) implies some.same_type (other)
    			symmetric: Result implies deep_equal (other, some)

    	frozen equal (some: ANY; other: like arg #1): BOOLEAN
    			-- Are `some' and `other' either both void or attached
    			-- to objects considered equal?
    			-- (from ANY)
    		ensure -- from ANY
    			definition: Result = (some = Void and other = Void) or else ((some /= Void and other /= Void) and then some.is_equal (other))

    	is_equal (other: like Current): BOOLEAN
    			-- Is `other' attached to an object considered
    			-- equal to current object?
    			-- (from ANY)
    		require -- from ANY
    			other_not_void: other /= Void
    		ensure -- from ANY
    			symmetric: Result implies other.is_equal (Current)
    			consistent: standard_is_equal (other) implies Result

    	frozen standard_equal (some: ANY; other: like arg #1): BOOLEAN
    			-- Are `some' and `other' either both void or attached to
    			-- field-by-field identical objects of the same type?
    			-- Always uses default object comparison criterion.
    			-- (from ANY)
    		ensure -- from ANY
    			definition: Result = (some = Void and other = Void) or else ((some /= Void and other /= Void) and then some.standard_is_equal (other))

    	frozen standard_is_equal (other: like Current): BOOLEAN
    			-- Is `other' attached to an object of the same type
    			-- as current object, and field-by-field identical to it?
    			-- (from ANY)
    		require -- from ANY
    			other_not_void: other /= Void
    		ensure -- from ANY
    			same_type: Result implies same_type (other)
    			symmetric: Result implies other.standard_is_equal (Current)

    feature -- Status report

    	conforms_to (other: ANY): BOOLEAN
    			-- Does type of current object conform to type
    			-- of `other' (as per Eiffel: The Language, chapter 13)?
    			-- (from ANY)
    		require -- from ANY
    			other_not_void: other /= Void

    	same_type (other: ANY): BOOLEAN
    			-- Is type of current object identical to type of `other'?
    			-- (from ANY)
    		require -- from ANY
    			other_not_void: other /= Void
    		ensure -- from ANY
    			definition: Result = (conforms_to (other) and other.conforms_to (Current))

    feature -- Element change

    	put (v: like item; row, column: INTEGER_32)
    			-- Put `v' to position (`row', `column')
    		require
    			valid_row: (1 <= row) and (row <= height)
    			valid_column: (1 <= column) and (column <= width)

    feature -- Duplication

    	copy (other: like Current)
    			-- Update current object using fields of object attached
    			-- to `other', so as to yield equal objects.
    			-- (from ANY)
    		require -- from ANY
    			other_not_void: other /= Void
    			type_identity: same_type (other)
    		ensure -- from ANY
    			is_equal: is_equal (other)

    	frozen deep_copy (other: like Current)
    			-- Effect equivalent to that of:
    			--		copy (`other' . deep_twin)
    			-- (from ANY)
    		require -- from ANY
    			other_not_void: other /= Void
    		ensure -- from ANY
    			deep_equal: deep_equal (Current, other)

    	frozen deep_twin: like Current
    			-- New object structure recursively duplicated from Current.
    			-- (from ANY)
    		ensure -- from ANY
    			deep_equal: deep_equal (Current, Result)

    	frozen standard_copy (other: like Current)
    			-- Copy every field of `other' onto corresponding field
    			-- of current object.
    			-- (from ANY)
    		require -- from ANY
    			other_not_void: other /= Void
    			type_identity: same_type (other)
    		ensure -- from ANY
    			is_standard_equal: standard_is_equal (other)

    	frozen standard_twin: like Current
    			-- New object field-by-field identical to `other'.
    			-- Always uses default copying semantics.
    			-- (from ANY)
    		ensure -- from ANY
    			standard_twin_not_void: Result /= Void
    			equal: standard_equal (Result, Current)

    	frozen twin: like Current
    			-- New object equal to `Current'
    			-- twin calls copy; to change copying/twining semantics, redefine copy.
    			-- (from ANY)
    		ensure -- from ANY
    			twin_not_void: Result /= Void
    			is_equal: Result.is_equal (Current)

    feature -- Basic operations

    	frozen default: like Current
    			-- Default value of object's type
    			-- (from ANY)

    	frozen default_pointer: POINTER
    			-- Default value of type `POINTER'
    			-- (Avoid the need to write `p'.default for
    			-- some `p' of type `POINTER'.)
    			-- (from ANY)

    	default_rescue
    			-- Process exception for routines with no Rescue clause.
    			-- (Default: do nothing.)
    			-- (from ANY)

    	frozen do_nothing
    			-- Execute a null action.
    			-- (from ANY)

    feature -- Basic operation

    	project (point: EV_COORDINATE)
    			-- Project `point' using `Current' transformation.

    	rotate (an_angle: like item; a_x: like item; a_y: like item)
    			-- Set values of matrix describing a
    			-- rotation around the point (`a_x', `a_y') for
    			-- angle (clockwise).

    	scale (a_scale_x: like item; a_scale_y: like item; a_x: like item; a_y: like item; an_angle: like item)
    			-- Build a matrix describing a rotation around (`a_x', `a_y') for -`an_angle', a scale
    			-- of `a_scale_x' in x direction and a scale of `a_scale_y' in
    			-- y direction and a rotation of `angle' around (`a_x', `a_y')

    	scale_abs (a_scale_x: like item; a_scale_y: like item; a_x: like item; a_y: like item)
    			-- Build a matrix describing a translation to -`ax' -`ay', a scale
    			-- of `a_scale_x' in x direction and a scale of `a_scale_y' in
    			-- y direction and a translation to `ax' `ay'.

    	translate (a_x: like item; a_y: like item)
    			-- Build a matrix describing a translation for
    			-- `a_x' `a_y' pixel.

    	infix "*" (other: like Current): like Current
    			-- Calculate result := Current * other.
    		require
    			other_not_void: other /= Void
    		ensure
    			result_not_void: Result /= Void

    feature -- Output

    	io: STD_FILES
    			-- Handle to standard file setup
    			-- (from ANY)

    	out: STRING_8
    			-- New string containing terse printable representation
    			-- of current object
    			-- Was declared in ANY as synonym of tagged_out.
    			-- (from ANY)

    	print (some: ANY)
    			-- Write terse external representation of `some'
    			-- on standard output.
    			-- (from ANY)

    	frozen tagged_out: STRING_8
    			-- New string containing terse printable representation
    			-- of current object
    			-- Was declared in ANY as synonym of out.
    			-- (from ANY)

    feature -- Platform

    	operating_environment: OPERATING_ENVIRONMENT
    			-- Objects available from the operating system
    			-- (from ANY)

    invariant
    	area_not_void: area /= Void

    		-- from ANY
    	reflexive_equality: standard_is_equal (Current)
    	reflexive_conformance: conforms_to (Current)

    indexing
    	copyright: "Copyright (c) 1984-2006, Eiffel Software and others"
    	license: "Eiffel Forum License v2 (see http://www.eiffel.com/licensing/forum.txt)"
    	source: "[
    		Eiffel Software
    		356 Storke Road, Goleta, CA 93117 USA
    		Telephone 805-685-1006, Fax 805-685-6869
    		Website http://www.eiffel.com
    		Customer support http://support.eiffel.com
    	]"

    end -- class EV_MODEL_TRANSFORMATION