* Integer_Geometry: Unlimited intervals

source/base/video-integer_geometry.ads

@@ -53,10 +53,16 @@ package Video.Integer_Geometry with Pure is
 	-- Scale down a vector by D
 	--
 
+	--
+	-- An Interval
+	--
+
 	type Interval is record
 		First, Last : Coordinate;
 	end record;
 	-- A type like an Ada range (but a type)
+	-- Values Coordinate'First at First and Coordinate'Last at Last
+	-- are treated specially as 'no limit'
 
 	function Empty_Interval return Interval is (Coordinate'Last, Coordinate'First);
 	-- Interval with nothing in
@@ -66,10 +72,16 @@ package Video.Integer_Geometry with Pure is
 	-- Note: many operations on Full_Interval could cause overflow
 
 	-- Note that transformations can cause overflow when applied to
-	-- Empty and Full intervals. User code should detect that corner cases.
+	-- Empty and Full intervals. Library should treat these corner cases correctly.
 
 	function Is_Empty (A : Interval) return Boolean is (A.First >= A.Last);
-	-- Test is interval have nothing in
+	-- Test if interval have nothing in
+
+	function Is_Negative_Unlimited (A : Interval) return Boolean is (A.First <= Coordinate'First);
+	-- Test if there's no lower limit
+
+	function Is_Positive_Unlimited (A : Interval) return Boolean is (A.Last >= Coordinate'Last);
+	-- Test if there's no upper limit
 
 	subtype Nonempty_Interval is Interval with Dynamic_Predicate => not Is_Empty (Nonempty_Interval);
 	-- A type for an interval that is not empty
@@ -90,29 +102,42 @@ package Video.Integer_Geometry with Pure is
 	-- Identity function
 
 	function "-" (A : Interval) return Interval
-	is (if Is_Empty (A) then Empty_Interval else (-A.Last, -A.First));
+	is (if Is_Empty (A) then Empty_Interval else (
+		(if A.Last >= Coordinate'Last then Coordinate'First else -A.Last),
+		(if A.First <= Coordinate'First then Coordinate'First else -A.First)));
 	-- Negate inverval by flipping it over zero
 
 	function "+" (A : Interval; B : Coordinate) return Interval
-	is (if Is_Empty (A) then Empty_Interval else (A.First + B, A.Last + B));
+	is (if Is_Empty (A) then Empty_Interval else (
+		(if A.First <= Coordinate'First then A.First else A.First + B),
+		(if A.Last >= Coordinate'Last then A.Last else A.Last + B)));
 	-- Translate interval
 
 	function "+" (A : Coordinate; B : Interval) return Interval
-	is (if Is_Empty (B) then Empty_Interval else (A + B.First, A + B.Last));
+	is (if Is_Empty (B) then Empty_Interval else (
+		(if B.First <= Coordinate'First then B.First else A + B.First),
+		(if B.Last >= Coordinate'Last then B.Last else A + B.Last)));
 	-- Translate interval (other form)
 
 	function "+" (A, B : Interval) return Interval
-	is (if Is_Empty (A) or else Is_Empty (B) then Empty_Interval else (A.First + B.First, A.Last + B.Last));
+	is (if Is_Empty (A) or else Is_Empty (B) then Empty_Interval else (
+		(if A.First <= Coordinate'First or B.First <= Coordinate'First then
+			Coordinate'First else A.First + B.First),
+		(if A.Last >= Coordinate'Last or B.Last >= Coordinate'Last then
+			Coordinate'Last else A.Last + B.Last)));
 	-- Minkowski sum
+	-- The area sweeped by one interval when offset by values in other interval.
 
 	function "-" (A : Interval; B : Coordinate) return Interval
 	is (if Is_Empty (A) then Empty_Interval else (A.First - B, A.Last - B));
 	-- Translate interval
 
 	function "-" (A : Interval; B : Nonempty_Interval) return Interval
-	is (if Is_Empty (A) then Empty_Interval else (A.First - B.First, A.Last - B.Last));
+	is (if Is_Empty (A) then Empty_Interval else (
+		(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
+	-- That is the result (if not empty) is the argument to minkowski sum with B to get A.
 	-- Note: Minkowski difference is not the same as sum with negated interval
 
 	function "and" (A, B : Interval) return Interval
@@ -127,11 +152,14 @@ package Video.Integer_Geometry with Pure is
 
 	function Center (A : Nonempty_Interval) return Coordinate
 	is (A.First / 2 + A.Last / 2 + (A.First rem 2 + A.Last rem 2) / 2);
+	-- Central point (equidistant to both limits)
 
 	function Center (A, B : Nonempty_Interval) return Coordinate
 	is ((B.First + B.Last - A.First - A.Last) / 2);
 	-- Offset to translate interval A to match center of interval B
 
+	--
+	-- Box
 	--
 
 	type Box is record
@@ -196,11 +224,11 @@ package Video.Integer_Geometry with Pure is
 	-- Note: Minkowski difference is not the same as sum with negated box
 
 	function "and" (A, B : Box) return Box
-	is (A.X and B.X, A.Y and B.Y);
+	is (X => A.X and B.X, Y => A.Y and B.Y);
 	-- Intersection (like in sets)
 
 	function "or" (A, B : Box) return Box
-	is (A.X or B.X, A.Y or B.Y);
+	is (X => A.X or B.X, Y => A.Y or B.Y);
 	-- Minimal box enclosing both arguments
 	-- Note: contrary to "and" it is not an set union
 
@@ -208,6 +236,6 @@ package Video.Integer_Geometry with Pure is
 	is (X => Center (P.X), Y => Center (P.Y));
 
 	function Center (A, B : Nonempty_Box) return Point
-	is (Center (A.X, B.X), Center (A.Y, B.Y));
+	is (X => Center (A.X, B.X), Y => Center (A.Y, B.Y));
 
 end Video.Integer_Geometry;