+ Simple transformations

source/base/video-integer_geometry-unitary_transformations.ads

@@ -0,0 +1,56 @@
+
+--
+-- Simple affine transformations, that keep scale and ortogonality
+package Video.Integer_Geometry.Unitary_Transformations is
+
+	subtype Unitary_Coordinate is Coordinate range -1 .. 1;
+
+	type Unitary_Vector is record
+		X, Y : Unitary_Coordinate;
+	end record;
+
+	function "+" (P, Q : Unitary_Vector) return Unitary_Vector is
+	(X => P.X + Q.X, Y => P.Y + Q.Y);
+
+	function "*" (P : Unitary_Vector; K : Unitary_Coordinate) return Unitary_Vector is
+	(X => P.X * K, Y => P.Y * K);
+
+	function To_Point (P : Unitary_Vector) return Point is (X => P.X, Y => P.Y);
+
+	type Transformation is record
+		X : Unitary_Vector := (1, 0); -- New direction of original X coordinate axis
+		Y : Unitary_Vector := (0, 1); -- New direction of original Y coordinate axis
+		B : Point          := (0, 0); -- Origin offset
+	end record;
+
+	-- Note: transformation matrix is stored by-column.
+	--       || m_xx m_xy m_xt ||     ((m_xx, m_yx),
+	--       || m_yx m_yy m_yt || ->   (m_xy, m_yy),
+	--       ||  0    0    1   ||      (m_xt, m_yt))
+
+	No_Transformation : constant Transformation :=  ((1,  0),  (0,  1), (0, 0));
+	Flip_X            : constant Transformation := ((-1,  0),  (0,  1), (0, 0));
+	Flip_Y            : constant Transformation :=  ((1,  0),  (0, -1), (0, 0));
+	Exchange_X_Y      : constant Transformation :=  ((0,  1),  (1,  0), (0, 0));
+	Rotate_90         : constant Transformation :=  ((0,  1), (-1,  0), (0, 0));
+	Rotate_180        : constant Transformation := ((-1,  0),  (0, -1), (0, 0));
+	Rotate_270        : constant Transformation :=  ((0, -1),  (1,  0), (0, 0));
+	function Translate (Offset : Point) return Transformation is ((1, 0), (0, 1), Offset);
+
+	-- Apply transformation to point
+	function "*" (M : Transformation; P : Point) return Point is
+	(To_Point (M.X) * P.X + To_Point (M.Y) * P.Y + M.B);
+
+	-- Combining transformations:
+	-- Result is a transformation M applied after transformation N
+	function "*" (M, N : Transformation) return Transformation is (
+		X => M.X * N.X.X + M.Y * N.X.Y,
+		Y => M.X * N.Y.X + M.Y * N.Y.Y,
+		B => M * N.B);
+
+	-- Moves center of transformation from origin to an arbitrary point
+	-- Works in flips and rotations
+	function Transform_About (M : Transformation; P : Point) return Transformation is
+	(Translate (P) * M * Translate (-P));
+
+end Video.Integer_Geometry.Unitary_Transformations;

source/base/video-integer_geometry.ads

@@ -134,7 +134,7 @@ package Video.Integer_Geometry with Pure is
 
 	function "-" (A : Interval; B : Nonempty_Interval) return Interval
 	is (if Is_Empty (A) then Empty_Interval else (
-		(if A.First <= Coordinate'First then A.First else A.First - B.First), 
+		(if A.First <= Coordinate'First then A.First else A.First - B.First),
 		(if A.Last >= Coordinate'Last then A.Last else A.Last - B.Last)));
 	-- Minkowski difference
 	-- That is the result (if not empty) is the argument to minkowski sum with B to get A.