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