Add mirror primitives

This leaves the integration with the parser for a later patch.

Graphics/Implicit/Definitions.hs

@@ -102,6 +102,7 @@ data SymbolicObj2 =
 	| IntersectR2 ℝ [SymbolicObj2]
 	-- Simple transforms
 	| Translate2 ℝ2 SymbolicObj2
+	| Mirror2 ℝ2 SymbolicObj2
 	| Scale2 ℝ2 SymbolicObj2
 	| Rotate2 ℝ SymbolicObj2
 	-- Boundary mods
@@ -125,6 +126,7 @@ data SymbolicObj3 =
 	| DifferenceR3 ℝ [SymbolicObj3]
 	-- Simple transforms
 	| Translate3 ℝ3 SymbolicObj3
+	| Mirror3 ℝ3 SymbolicObj3
 	| Scale3 ℝ3 SymbolicObj3
 	| Rotate3 (ℝ,ℝ,ℝ) SymbolicObj3
 	-- Boundary mods

Graphics/Implicit/ObjectUtil/GetBox2.hs

@@ -68,6 +68,15 @@ getBox2 (Translate2 v symbObj) =
 		then ((0,0),(0,0))
 		else (a^+^v, b^+^v)
 
+getBox2 (Mirror2 a symbObj) =
+	let
+		(a,b) = getBox2 symbObj
+		mirror p =
+		  let c = 2 * (p ⋅ a) / (a ⋅ a)
+		  in c *^ a ^-^ p
+	in
+		(mirror a, mirror b)
+
 getBox2 (Scale2 s symbObj) =
 	let
 		(a,b) = getBox2 symbObj

Graphics/Implicit/ObjectUtil/GetBox3.hs

@@ -79,6 +79,15 @@ getBox3 (Translate3 v symbObj) =
 	in
 		(a^+^v, b^+^v)
 
+getBox3 (Mirror3 a symbObj) =
+	let
+		(a,b) = getBox3 symbObj
+		mirror p =
+		  let c = 2 * (p ⋅ a) / (a ⋅ a)
+		  in p ^-^ c *^ a
+	in
+		(mirror a, mirror b)
+
 getBox3 (Scale3 s symbObj) =
 	let
 		(a,b) = getBox3 symbObj

Graphics/Implicit/ObjectUtil/GetImplicit2.hs

@@ -75,6 +75,15 @@ getImplicit2 (Translate2 v symbObj) =
 	in
 		\p -> obj (p ^-^ v)
 
+getImplicit2 (Mirror2 a symbObj) =
+	let
+		obj = getImplicit2 symbObj
+	in
+		\p ->
+			let
+				c = 2 * (p ⋅ a) / (a ⋅ a)
+			in obj $ c *^ a ^-^ p
+
 getImplicit2 (Scale2 s@(sx,sy) symbObj) =
 	let
 		obj = getImplicit2 symbObj

Graphics/Implicit/ObjectUtil/GetImplicit3.hs

@@ -77,6 +77,15 @@ getImplicit3 (Scale3 s@(sx,sy,sz) symbObj) =
 	in
 		\p -> k * obj (p ⋯/ s)
 
+getImplicit3 (Mirror3 a symbObj) =
+	let
+		obj = getImplicit3 symbObj
+	in
+		\p ->
+			let
+				c = 2 * (p ⋅ a) / (a ⋅ a)
+			in obj $ p ^-^ c *^ a
+
 getImplicit3 (Rotate3 (yz, xz, xy) symbObj) = 
 	let
 		obj = getImplicit3 symbObj

Graphics/Implicit/Primitives.hs

@@ -71,6 +71,12 @@ class Object obj vec | obj -> vec where
 		-> obj   -- ^ Object to translate
 		-> obj   -- ^ Resulting object
 
+	-- | Mirror an object
+	mirror :: 
+		vec     -- ^ Vector defining plane to mirror across
+		-> obj  -- ^ Object to mirror
+		-> obj  -- ^ Resulting mirrored object	
+
 	-- | Scale an object
 	scale :: 
 		vec     -- ^ Amount to scale by
@@ -130,6 +136,7 @@ class Object obj vec | obj -> vec where
 
 instance Object SymbolicObj2 ℝ2 where
 	translate   = Translate2
+	mirror      = Mirror2
 	scale       = Scale2
 	complement  = Complement2
 	unionR      = UnionR2
@@ -143,6 +150,7 @@ instance Object SymbolicObj2 ℝ2 where
 
 instance Object SymbolicObj3 ℝ3 where
 	translate   = Translate3
+	mirror      = Mirror3
 	scale       = Scale3
 	complement  = Complement3
 	unionR      = UnionR3