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Follows Num laws

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Yann Esposito (Yogsototh) 2012-06-25 11:32:47 +02:00
parent 25451cd06c
commit ac176d22ad
12 changed files with 724 additions and 708 deletions
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2
content/html/en/blog/Haskell-OpenGL-Mandelbrot.md
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@ -581,7 +581,7 @@ instance Num ExtComplex where
fromInteger n = C (fromIntegral n, 0, 0)
C (x,y,z) + C (x',y',z') = C (x+x', y+y', z+z')
abs (C (x,y,z)) = C (sqrt (x*x + y*y + z*z), 0, 0)
signum (C (x,y,z)) = C (signum x, 0, 0)
signum (C (x,y,z)) = C (signum x, signum y, signum z)
</code>
</div>

2
content/html/fr/blog/Haskell-OpenGL-Mandelbrot.md
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@ -581,7 +581,7 @@ instance Num ExtComplex where
fromInteger n = C (fromIntegral n, 0, 0)
C (x,y,z) + C (x',y',z') = C (x+x', y+y', z+z')
abs (C (x,y,z)) = C (sqrt (x*x + y*y + z*z), 0, 0)
signum (C (x,y,z)) = C (signum x, 0, 0)
signum (C (x,y,z)) = C (signum x, signum y, signum z)
</code>
</div>

2
multi/blog/Haskell-OpenGL-Mandelbrot.md
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@ -589,7 +589,7 @@ instance Num ExtComplex where
fromInteger n = C (fromIntegral n, 0, 0)
C (x,y,z) + C (x',y',z') = C (x+x', y+y', z+z')
abs (C (x,y,z)) = C (sqrt (x*x + y*y + z*z), 0, 0)
signum (C (x,y,z)) = C (signum x, 0, 0)
signum (C (x,y,z)) = C (signum x, signum y, signum z)
</code>
</div>

2
output/Scratch/en/blog/Haskell-OpenGL-Mandelbrot/code/03_Mandelbulb/Mandelbulb.lhs
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@ -65,7 +65,7 @@ An extension of complex numbers with a third component:
> fromInteger n = C (fromIntegral n, 0, 0)
> C (x,y,z) + C (x',y',z') = C (x+x', y+y', z+z')
> abs (C (x,y,z)) = C (sqrt (x*x + y*y + z*z), 0, 0)
> signum (C (x,y,z)) = C (signum x, 0, 0)
> signum (C (x,y,z)) = C (signum x, signum y, signum z)
The most important part is the new multiplication instance.
Modifying this formula will change radically the shape of the result.

28
output/Scratch/en/blog/Haskell-OpenGL-Mandelbrot/code/04_Mandelbulb/ExtComplex.hs
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@ -2,32 +2,36 @@ module ExtComplex where
import Graphics.Rendering.OpenGL
data ExtComplex = C (GLfloat,GLfloat,GLfloat)
-- This time I use unpacked strict data type
-- Far faster when compiled.
data ExtComplex = C {-# UNPACK #-} !GLfloat
{-# UNPACK #-} !GLfloat
{-# UNPACK #-} !GLfloat
deriving (Show,Eq)
instance Num ExtComplex where
-- The shape of the 3D mandelbrot
-- will depend on this formula
C (x,y,z) * C (x',y',z') = C (x*x' - y*y' - z*z',
x*y' + y*x' + z*z',
x*z' + z*x' )
(C x y z) * (C x' y' z') = C (x*x' - y*y' - z*z')
(x*y' + y*x' + z*z')
(x*z' + z*x' )
-- The rest is straightforward
fromInteger n = C (fromIntegral n, 0, 0)
C (x,y,z) + C (x',y',z') = C (x+x', y+y', z+z')
abs (C (x,y,z)) = C (sqrt (x*x + y*y + z*z), 0, 0)
signum (C (x,y,z)) = C (signum x, 0, 0)
fromInteger n = C (fromIntegral n) 0 0
(C x y z) + (C x' y' z') = C (x+x') (y+y') (z+z')
abs (C x y z) = C (sqrt (x*x + y*y + z*z)) 0 0
signum (C x y z) = C (signum x) (signum y) (signum z)
extcomplex :: GLfloat -> GLfloat -> GLfloat -> ExtComplex
extcomplex x y z = C (x,y,z)
extcomplex x y z = C x y z
real :: ExtComplex -> GLfloat
real (C (x,y,z)) = x
real (C x _ _) = x
im :: ExtComplex -> GLfloat
im (C (x,y,z)) = y
im (C _ y _) = y
strange :: ExtComplex -> GLfloat
strange (C (x,y,z)) = z
strange (C _ _ z) = z
magnitude :: ExtComplex -> GLfloat
magnitude = real.abs

28
output/Scratch/en/blog/Haskell-OpenGL-Mandelbrot/code/05_Mandelbulb/ExtComplex.hs
View file

@ -2,32 +2,36 @@ module ExtComplex where
import Graphics.Rendering.OpenGL
data ExtComplex = C (GLfloat,GLfloat,GLfloat)
-- This time I use unpacked strict data type
-- Far faster when compiled.
data ExtComplex = C {-# UNPACK #-} !GLfloat
{-# UNPACK #-} !GLfloat
{-# UNPACK #-} !GLfloat
deriving (Show,Eq)
instance Num ExtComplex where
-- The shape of the 3D mandelbrot
-- will depend on this formula
C (x,y,z) * C (x',y',z') = C (x*x' - y*y' - z*z',
x*y' + y*x' + z*z',
x*z' + z*x' )
(C x y z) * (C x' y' z') = C (x*x' - y*y' - z*z')
(x*y' + y*x' + z*z')
(x*z' + z*x' )
-- The rest is straightforward
fromInteger n = C (fromIntegral n, 0, 0)
C (x,y,z) + C (x',y',z') = C (x+x', y+y', z+z')
abs (C (x,y,z)) = C (sqrt (x*x + y*y + z*z), 0, 0)
signum (C (x,y,z)) = C (signum x, 0, 0)
fromInteger n = C (fromIntegral n) 0 0
(C x y z) + (C x' y' z') = C (x+x') (y+y') (z+z')
abs (C x y z) = C (sqrt (x*x + y*y + z*z)) 0 0
signum (C x y z) = C (signum x) (signum y) (signum z)
extcomplex :: GLfloat -> GLfloat -> GLfloat -> ExtComplex
extcomplex x y z = C (x,y,z)
extcomplex x y z = C x y z
real :: ExtComplex -> GLfloat
real (C (x,y,z)) = x
real (C x _ _) = x
im :: ExtComplex -> GLfloat
im (C (x,y,z)) = y
im (C _ y _) = y
strange :: ExtComplex -> GLfloat
strange (C (x,y,z)) = z
strange (C _ _ z) = z
magnitude :: ExtComplex -> GLfloat
magnitude = real.abs

2
output/Scratch/en/blog/Haskell-OpenGL-Mandelbrot/index.html
View file

@ -714,7 +714,7 @@ instance Num ExtComplex where
fromInteger n = C (fromIntegral n, 0, 0)
C (x,y,z) + C (x',y',z') = C (x+x', y+y', z+z')
abs (C (x,y,z)) = C (sqrt (x*x + y*y + z*z), 0, 0)
signum (C (x,y,z)) = C (signum x, 0, 0)
signum (C (x,y,z)) = C (signum x, signum y, signum z)
</code></pre>

2
output/Scratch/fr/blog/Haskell-OpenGL-Mandelbrot/code/03_Mandelbulb/Mandelbulb.lhs
View file

@ -65,7 +65,7 @@ An extension of complex numbers with a third component:
> fromInteger n = C (fromIntegral n, 0, 0)
> C (x,y,z) + C (x',y',z') = C (x+x', y+y', z+z')
> abs (C (x,y,z)) = C (sqrt (x*x + y*y + z*z), 0, 0)
> signum (C (x,y,z)) = C (signum x, 0, 0)
> signum (C (x,y,z)) = C (signum x, signum y, signum z)
The most important part is the new multiplication instance.
Modifying this formula will change radically the shape of the result.

28
output/Scratch/fr/blog/Haskell-OpenGL-Mandelbrot/code/04_Mandelbulb/ExtComplex.hs
View file

@ -2,32 +2,36 @@ module ExtComplex where
import Graphics.Rendering.OpenGL
data ExtComplex = C (GLfloat,GLfloat,GLfloat)
-- This time I use unpacked strict data type
-- Far faster when compiled.
data ExtComplex = C {-# UNPACK #-} !GLfloat
{-# UNPACK #-} !GLfloat
{-# UNPACK #-} !GLfloat
deriving (Show,Eq)
instance Num ExtComplex where
-- The shape of the 3D mandelbrot
-- will depend on this formula
C (x,y,z) * C (x',y',z') = C (x*x' - y*y' - z*z',
x*y' + y*x' + z*z',
x*z' + z*x' )
(C x y z) * (C x' y' z') = C (x*x' - y*y' - z*z')
(x*y' + y*x' + z*z')
(x*z' + z*x' )
-- The rest is straightforward
fromInteger n = C (fromIntegral n, 0, 0)
C (x,y,z) + C (x',y',z') = C (x+x', y+y', z+z')
abs (C (x,y,z)) = C (sqrt (x*x + y*y + z*z), 0, 0)
signum (C (x,y,z)) = C (signum x, 0, 0)
fromInteger n = C (fromIntegral n) 0 0
(C x y z) + (C x' y' z') = C (x+x') (y+y') (z+z')
abs (C x y z) = C (sqrt (x*x + y*y + z*z)) 0 0
signum (C x y z) = C (signum x) (signum y) (signum z)
extcomplex :: GLfloat -> GLfloat -> GLfloat -> ExtComplex
extcomplex x y z = C (x,y,z)
extcomplex x y z = C x y z
real :: ExtComplex -> GLfloat
real (C (x,y,z)) = x
real (C x _ _) = x
im :: ExtComplex -> GLfloat
im (C (x,y,z)) = y
im (C _ y _) = y
strange :: ExtComplex -> GLfloat
strange (C (x,y,z)) = z
strange (C _ _ z) = z
magnitude :: ExtComplex -> GLfloat
magnitude = real.abs

28
output/Scratch/fr/blog/Haskell-OpenGL-Mandelbrot/code/05_Mandelbulb/ExtComplex.hs
View file

@ -2,32 +2,36 @@ module ExtComplex where
import Graphics.Rendering.OpenGL
data ExtComplex = C (GLfloat,GLfloat,GLfloat)
-- This time I use unpacked strict data type
-- Far faster when compiled.
data ExtComplex = C {-# UNPACK #-} !GLfloat
{-# UNPACK #-} !GLfloat
{-# UNPACK #-} !GLfloat
deriving (Show,Eq)
instance Num ExtComplex where
-- The shape of the 3D mandelbrot
-- will depend on this formula
C (x,y,z) * C (x',y',z') = C (x*x' - y*y' - z*z',
x*y' + y*x' + z*z',
x*z' + z*x' )
(C x y z) * (C x' y' z') = C (x*x' - y*y' - z*z')
(x*y' + y*x' + z*z')
(x*z' + z*x' )
-- The rest is straightforward
fromInteger n = C (fromIntegral n, 0, 0)
C (x,y,z) + C (x',y',z') = C (x+x', y+y', z+z')
abs (C (x,y,z)) = C (sqrt (x*x + y*y + z*z), 0, 0)
signum (C (x,y,z)) = C (signum x, 0, 0)
fromInteger n = C (fromIntegral n) 0 0
(C x y z) + (C x' y' z') = C (x+x') (y+y') (z+z')
abs (C x y z) = C (sqrt (x*x + y*y + z*z)) 0 0
signum (C x y z) = C (signum x) (signum y) (signum z)
extcomplex :: GLfloat -> GLfloat -> GLfloat -> ExtComplex
extcomplex x y z = C (x,y,z)
extcomplex x y z = C x y z
real :: ExtComplex -> GLfloat
real (C (x,y,z)) = x
real (C x _ _) = x
im :: ExtComplex -> GLfloat
im (C (x,y,z)) = y
im (C _ y _) = y
strange :: ExtComplex -> GLfloat
strange (C (x,y,z)) = z
strange (C _ _ z) = z
magnitude :: ExtComplex -> GLfloat
magnitude = real.abs

2
output/Scratch/fr/blog/Haskell-OpenGL-Mandelbrot/index.html
View file

@ -714,7 +714,7 @@ instance Num ExtComplex where
fromInteger n = C (fromIntegral n, 0, 0)
C (x,y,z) + C (x',y',z') = C (x+x', y+y', z+z')
abs (C (x,y,z)) = C (sqrt (x*x + y*y + z*z), 0, 0)
signum (C (x,y,z)) = C (signum x, 0, 0)
signum (C (x,y,z)) = C (signum x, signum y, signum z)
</code></pre>

1306
output/Scratch/sitemap.xml
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