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note 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: 2009-06-10 20:59:07 -0800 (Wed, 10 Jun 2009) $" revision: "$Revision: 79202 $" 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 arc_cosine (v: REAL_64): REAL_64 -- Trigonometric arccosine of radian v -- in the range [0, pi]. -- (from DOUBLE_MATH) ensure -- from DOUBLE_MATH instance_free: class arc_sine (v: REAL_64): REAL_64 -- Trigonometric arcsine of radian v -- in the range [-pi/2, +pi/2]. -- (from DOUBLE_MATH) ensure -- from DOUBLE_MATH instance_free: class arc_tangent (v: REAL_64): REAL_64 -- Trigonometric arctangent of radian v -- in the range [-pi/2, +pi/2]. -- (from DOUBLE_MATH) ensure -- from DOUBLE_MATH instance_free: class ceiling (v: REAL_64): REAL_64 -- Least integral greater than or equal to v. -- (from DOUBLE_MATH) ensure -- from DOUBLE_MATH instance_free: class cosine (v: REAL_64): REAL_64 -- Trigonometric cosine of radian v approximated -- in the range [-pi/4, +pi/4]. -- (from DOUBLE_MATH) ensure -- from DOUBLE_MATH instance_free: class dabs (v: REAL_64): REAL_64 -- Absolute of v. -- (from DOUBLE_MATH) ensure -- from DOUBLE_MATH instance_free: class Euler: REAL_64 = 2.7182818284590452353602874713526625 -- Logarithm base -- (from MATH_CONST) exp (x: REAL_64): REAL_64 -- Exponential of v. -- (from DOUBLE_MATH) ensure -- from DOUBLE_MATH instance_free: class floor (v: REAL_64): REAL_64 -- Greatest integral less than or equal to v. -- (from DOUBLE_MATH) ensure -- from DOUBLE_MATH instance_free: class generating_type: TYPE [detachable EV_MODEL_TRANSFORMATION] -- Type of current object -- (type of which it is a direct instance) -- (from ANY) ensure -- from ANY generating_type_not_void: Result /= Void generator: STRING_8 -- Name of current object's generating class -- (base class of the type of which it is a direct instance) -- (from ANY) ensure -- from ANY generator_not_void: Result /= Void generator_not_empty: not Result.is_empty Height: INTEGER_32 = 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) log (v: REAL_64): REAL_64 -- Natural logarithm of v. -- (from DOUBLE_MATH) ensure -- from DOUBLE_MATH instance_free: class log10 (v: REAL_64): REAL_64 -- Base 10 logarithm of v. -- (from DOUBLE_MATH) ensure -- from DOUBLE_MATH instance_free: class log_2 (v: REAL_64): REAL_64 -- Base 2 logarithm of v. -- (from DOUBLE_MATH) ensure -- from DOUBLE_MATH instance_free: class Pi: REAL_64 = 3.1415926535897932384626433832795029 -- (from MATH_CONST) Pi_2: REAL_64 = 1.5707963267948966192313216916397514 -- (from MATH_CONST) Pi_4: REAL_64 = 0.7853981633974483096156608458198757 -- (from MATH_CONST) sine (v: REAL_64): REAL_64 -- Trigonometric sine of radian v approximated -- in range [-pi/4, +pi/4]. -- (from DOUBLE_MATH) ensure -- from DOUBLE_MATH instance_free: class sqrt (v: REAL_64): REAL_64 -- Square root of v. -- (from DOUBLE_MATH) ensure -- from DOUBLE_MATH instance_free: class Sqrt2: REAL_64 = 1.4142135623730950488016887242096981 -- Square root of 2 -- (from MATH_CONST) tangent (v: REAL_64): REAL_64 -- Trigonometric tangent of radian v approximated -- in range [-pi/4, +pi/4]. -- (from DOUBLE_MATH) ensure -- from DOUBLE_MATH instance_free: class Width: INTEGER_32 = 3 -- Number of columns in the matrix. feature -- Comparison frozen deep_equal (a: detachable ANY; b: like arg #1): BOOLEAN -- Are a and b either both void -- or attached to isomorphic object structures? -- (from ANY) ensure -- from ANY instance_free: class shallow_implies_deep: standard_equal (a, b) implies Result both_or_none_void: (a = Void) implies (Result = (b = Void)) same_type: (Result and (a /= Void)) implies (b /= Void and then a.same_type (b)) symmetric: Result implies deep_equal (b, a) frozen equal (a: detachable ANY; b: like arg #1): BOOLEAN -- Are a and b either both void or attached -- to objects considered equal? -- (from ANY) ensure -- from ANY instance_free: class definition: Result = (a = Void and b = Void) or else ((a /= Void and b /= Void) and then a.is_equal (b)) frozen is_deep_equal alias "≡≡≡" (other: EV_MODEL_TRANSFORMATION): BOOLEAN -- Are Current and other attached to isomorphic object structures? -- (from ANY) require -- from ANY other_not_void: other /= Void ensure -- from ANY shallow_implies_deep: standard_is_equal (other) implies Result same_type: Result implies same_type (other) symmetric: Result implies other.is_deep_equal (Current) is_equal (other: EV_MODEL_TRANSFORMATION): 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 ~ Current consistent: standard_is_equal (other) implies Result frozen standard_equal (a: detachable ANY; b: like arg #1): BOOLEAN -- Are a and b 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 instance_free: class definition: Result = (a = Void and b = Void) or else ((a /= Void and b /= Void) and then a.standard_is_equal (b)) frozen standard_is_equal alias "" (other: EV_MODEL_TRANSFORMATION): 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: EV_MODEL_TRANSFORMATION) -- 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: Current ~ other frozen deep_copy (other: EV_MODEL_TRANSFORMATION) -- 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: EV_MODEL_TRANSFORMATION -- New object structure recursively duplicated from Current. -- (from ANY) ensure -- from ANY deep_twin_not_void: Result /= Void deep_equal: deep_equal (Current, Result) frozen standard_copy (other: EV_MODEL_TRANSFORMATION) -- 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: EV_MODEL_TRANSFORMATION -- 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: EV_MODEL_TRANSFORMATION -- New object equal to Current -- twin calls copy; to change copying/twinning semantics, redefine copy. -- (from ANY) ensure -- from ANY twin_not_void: Result /= Void is_equal: Result ~ Current feature -- Basic operations frozen default: detachable EV_MODEL_TRANSFORMATION -- 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) ensure -- from ANY instance_free: class default_rescue -- Process exception for routines with no Rescue clause. -- (Default: do nothing.) -- (from ANY) frozen do_nothing -- Execute a null action. -- (from ANY) ensure -- from ANY instance_free: class feature -- Basic operation product alias "*" (other: like Current): like Current -- Calculate result := Current * other. require other_not_void: other /= Void ensure result_not_void: Result /= Void 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. feature -- Output Io: STD_FILES -- Handle to standard file setup -- (from ANY) ensure -- from ANY instance_free: class io_not_void: Result /= Void out: STRING_8 -- New string containing terse printable representation -- of current object -- (from ANY) ensure -- from ANY out_not_void: Result /= Void print (o: detachable ANY) -- Write terse external representation of o -- on standard output. -- (from ANY) ensure -- from ANY instance_free: class frozen tagged_out: STRING_8 -- New string containing terse printable representation -- of current object -- (from ANY) ensure -- from ANY tagged_out_not_void: Result /= Void feature -- Platform Operating_environment: OPERATING_ENVIRONMENT -- Objects available from the operating system -- (from ANY) ensure -- from ANY instance_free: class operating_environment_not_void: Result /= Void invariant area_not_void: area /= Void -- from ANY reflexive_equality: standard_is_equal (Current) reflexive_conformance: conforms_to (Current) note 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
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