Added fast, rpg and plt inverses

3 files changed, 60 insertions, 8 deletions

diff --git a/Spear.lkshs b/Spear.lkshs
index 698ee98..6df61b6 100644
--- a/Spear.lkshs
+++ b/Spear.lkshs
@@ -1,8 +1,8 @@
 Version of session file format:
                1
 Time of storage:
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+               "Wed Aug 29 00:16:28 CEST 2012"
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diff --git a/Spear/Math/Matrix3.hs b/Spear/Math/Matrix3.hs
index fe3162e..e24a3e5 100644
--- a/Spear/Math/Matrix3.hs
+++ b/Spear/Math/Matrix3.hs
@@ -7,7 +7,7 @@ module Spear.Math.Matrix3
 ,   m20, m21, m22

 ,   col0, col1, col2

 ,   row0, row1, row2
-,   right, forward, position

+,   right, up, forward, position

     -- * Construction

 ,   mat3

 ,   mat3fromVec
@@ -28,10 +28,10 @@ module Spear.Math.Matrix3
 ,   reflectZ

     -- * Operations

 ,   transpose
-,   mul

+,   mul
+,   inverseTransform

 ,   Spear.Math.Matrix3.zipWith

 ,   Spear.Math.Matrix3.map

---,   inverse

 )

 where

 

@@ -126,6 +126,7 @@ row2 (Matrix3 _   _   _   _   _   _   a02 a12 a22) = vec3 a02 a12 a22
 
 
 right    (Matrix3 a00 _   _   a01 _   _   _ _ _) = vec2 a00 a01
+up       (Matrix3 _   a10 _   _   a11 _   _ _ _) = vec2 a10 a11
 forward  (Matrix3 _   a10 _   _   a11 _   _ _ _) = vec2 a10 a11
 position (Matrix3 _   _   a20 _   _   a21 _ _ _) = vec2 a20 a21  

 

@@ -278,9 +279,16 @@ map f m = Matrix3
     (f . m02 $ m) (f . m12 $ m) (f . m22 $ m)
 

 

--- | Invert the given 'Matrix3'.

-{-inverse :: Matrix3 -> Matrix3

-inverse mat = -}

+-- | Compute the inverse transform of the given transformation matrix.

+inverseTransform :: Matrix3 -> Matrix3

+inverseTransform mat =
+    let r = right mat
+        f = forward mat
+        t = -(position mat)
+    in mat3
+        (V2.x r) (V2.y r) (t `V2.dot` r)
+        (V2.x f) (V2.y f) (t `V2.dot` f)
+        0        0        1
 

 

 fromDeg :: (Floating a) => a -> a

diff --git a/Spear/Math/MatrixUtils.hs b/Spear/Math/MatrixUtils.hs
index 88ad3b1..e6e498f 100644
--- a/Spear/Math/MatrixUtils.hs
+++ b/Spear/Math/MatrixUtils.hs
@@ -7,8 +7,11 @@ where
 
 import Spear.Math.Matrix3 as M3
 import Spear.Math.Matrix4 as M4
+import Spear.Math.Vector2 as V2
+import Spear.Math.Vector3 as V3
 
 
+-- | Compute the normal matrix of the given matrix.
 fastNormalMatrix :: Matrix4 -> Matrix3
 fastNormalMatrix m =
     let m' = M4.transpose . M4.inverseTransform $ m
@@ -16,3 +19,44 @@ fastNormalMatrix m =
         (M4.m00 m') (M4.m10 m') (M4.m20 m')
         (M4.m01 m') (M4.m11 m') (M4.m21 m')
         (M4.m02 m') (M4.m12 m') (M4.m22 m')
+
+
+-- | Compute the inverse transform of the given transformation matrix.
+--
+-- This function maps an object's transform in 2D to the object's inverse in 3D.
+-- 
+-- The XY plane in 2D translates to the X(-Z) plane in 3D.
+--
+-- Use this in games such as RPGs and RTSs.
+rpgInverse :: Float -- ^ Height above the ground.
+           -> Matrix3 -> Matrix4
+rpgInverse h mat =
+    let r = let r' = M3.right mat in vec3 (V2.x r') (V2.y r') 0
+        u = V3.unity
+        f = let f' = M3.forward mat in vec3 (V2.x f') 0 (-V2.y f')
+        t = let t' = M3.position mat in -(vec3 (V2.x t') 0 (-V2.y t'))
+    in mat4
+        (V3.x r) (V3.y r) (V3.z r) (t `V3.dot` r)
+        (V3.x u) (V3.y u) (V3.z u) (t `V3.dot` u)
+        (V3.x f) (V3.y f) (V3.z f) (t `V3.dot` f)
+        0     0     0     1
+
+
+-- | Compute the inverse transform of the given transformation matrix.
+--
+-- This function maps an object's transform in 2D to the object's inverse in 3D.
+-- 
+-- The XY plane in 2D translates to the XY plane in 3D.
+-- 
+-- Use this in games like platformers and space invaders style games.
+pltInverse :: Matrix3 -> Matrix4
+pltInverse mat =
+    let r = let r' = M3.right mat in vec3 (V2.x r') (V2.y r') 0
+        u = let u' = M3.up mat in vec3 (V2.x u') (V2.y u') 0
+        f = V3.unitz
+        t = let t' = M3.position mat in vec3 (V2.x t') (V2.y t') 0
+    in mat4
+        (V3.x r) (V3.y r) (V3.z r) (t `V3.dot` r)
+        (V3.x u) (V3.y u) (V3.z u) (t `V3.dot` u)
+        (V3.x f) (V3.y f) (V3.z f) (t `V3.dot` f)
+        0     0     0     1