Remove the coincident vertices guards from the Tetrahedron volume function.

[spline3.git] / src / Tetrahedron.hs

diff --git a/src/Tetrahedron.hs b/src/Tetrahedron.hs
index a9e6c2c6c299a9ec8df42af3a3b137b5c97728b1..2a4227a7f1bbee2d10a99baa66a07904e1e16c15 100644 (file)
--- a/src/Tetrahedron.hs
+++ b/src/Tetrahedron.hs
@@ -5,7 +5,9 @@ module Tetrahedron (
   b1, -- Cube test
   b2, -- Cube test
   b3, -- Cube test
+  barycenter,
   c,
+  contains_point,
   polynomial,
   tetrahedron_properties,
   tetrahedron_tests,
@@ -30,7 +32,6 @@ import FunctionValues (FunctionValues(..), empty_values)
 import Misc (factorial)
 import Point (Point(..), scale)
 import RealFunction (RealFunction, cmult, fexp)
-import ThreeDimensional (ThreeDimensional(..))
 
 data Tetrahedron =
   Tetrahedron { function_values :: FunctionValues,
@@ -67,36 +68,42 @@ instance Show Tetrahedron where
              "  v3: " ++ (show (v3 t)) ++ "\n"
 
 
-instance ThreeDimensional Tetrahedron where
-    center (Tetrahedron _ v0' v1' v2' v3' _) =
-        (v0' + v1' + v2' + v3') `scale` (1/4)
-
-    -- contains_point is only used in tests.
-    contains_point t p0 =
-      b0_unscaled `nearly_ge` 0 &&
-      b1_unscaled `nearly_ge` 0 &&
-      b2_unscaled `nearly_ge` 0 &&
-      b3_unscaled `nearly_ge` 0
+-- | Find the barycenter of the given tetrahedron.
+--   We just average the four vertices.
+barycenter :: Tetrahedron -> Point
+barycenter (Tetrahedron _ v0' v1' v2' v3' _) =
+  (v0' + v1' + v2' + v3') `scale` (1/4)
+
+-- | A point is internal to a tetrahedron if all of its barycentric
+--   coordinates with respect to that tetrahedron are non-negative.
+contains_point :: Tetrahedron -> Point -> Bool
+contains_point t p0 =
+  b0_unscaled `nearly_ge` 0 &&
+  b1_unscaled `nearly_ge` 0 &&
+  b2_unscaled `nearly_ge` 0 &&
+  b3_unscaled `nearly_ge` 0
+  where
+    -- Drop the useless division and volume calculation that we
+    -- would do if we used the regular b0,..b3 functions.
+    b0_unscaled :: Double
+    b0_unscaled = volume inner_tetrahedron
       where
-        -- Drop the useless division and volume calculation that we
-        -- would do if we used the regular b0,..b3 functions.
-        b0_unscaled :: Double
-        b0_unscaled = volume inner_tetrahedron
-          where inner_tetrahedron = t { v0 = p0 }
+        inner_tetrahedron = t { v0 = p0 }
 
-        b1_unscaled :: Double
-        b1_unscaled = volume inner_tetrahedron
-          where inner_tetrahedron = t { v1 = p0 }
+    b1_unscaled :: Double
+    b1_unscaled = volume inner_tetrahedron
+      where inner_tetrahedron = t { v1 = p0 }
 
-        b2_unscaled :: Double
-        b2_unscaled = volume inner_tetrahedron
-          where inner_tetrahedron = t { v2 = p0 }
+    b2_unscaled :: Double
+    b2_unscaled = volume inner_tetrahedron
+      where inner_tetrahedron = t { v2 = p0 }
 
-        b3_unscaled :: Double
-        b3_unscaled = volume inner_tetrahedron
-          where inner_tetrahedron = t { v3 = p0 }
+    b3_unscaled :: Double
+    b3_unscaled = volume inner_tetrahedron
+      where inner_tetrahedron = t { v3 = p0 }
 
 
+{-# INLINE polynomial #-}
 polynomial :: Tetrahedron -> (RealFunction Point)
 polynomial t =
     V.sum $ V.singleton ((c t 0 0 0 3) `cmult` (beta t 0 0 0 3)) `V.snoc`
@@ -125,10 +132,8 @@ polynomial t =
 -- | The Bernstein polynomial on t with indices i,j,k,l. Denoted by a
 --   capital 'B' in the Sorokina/Zeilfelder paper.
 beta :: Tetrahedron -> Int -> Int -> Int -> Int -> (RealFunction Point)
-beta t i j k l
-  | (i + j + k + l == 3) =
-      coefficient `cmult` (b0_term * b1_term * b2_term * b3_term)
-  | otherwise = error "basis function index out of bounds"
+beta t i j k l =
+  coefficient `cmult` (b0_term * b1_term * b2_term * b3_term)
   where
     denominator = (factorial i)*(factorial j)*(factorial k)*(factorial l)
     coefficient = 6 / (fromIntegral denominator)
@@ -141,8 +146,8 @@ beta t i j k l
 -- | The coefficient function. c t i j k l returns the coefficient
 --   c_ijkl with respect to the tetrahedron t. The definition uses
 --   pattern matching to mimic the definitions given in Sorokina and
---   Zeilfelder, pp. 84-86. If incorrect indices are supplied, the
---   function will simply error.
+--   Zeilfelder, pp. 84-86. If incorrect indices are supplied, the world
+--   will end. This is for performance reasons.
 c :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
 c !t !i !j !k !l =
   coefficient i j k l
@@ -271,8 +276,6 @@ c !t !i !j !k !l =
                + (1/96)*(lt + fl + ft + rt + bt + fr)
                + (1/96)*(fd + ld + bd + br + rd + bl)
 
-    coefficient _ _ _ _ = error "coefficient index out of bounds"
-
 
 
 -- | Compute the determinant of the 4x4 matrix,
@@ -310,20 +313,8 @@ det p0 p1 p2 p3 =
 --   page 436.
 {-# INLINE volume #-}
 volume :: Tetrahedron -> Double
-volume t
-       | v0' == v1' = 0
-       | v0' == v2' = 0
-       | v0' == v3' = 0
-       | v1' == v2' = 0
-       | v1' == v3' = 0
-       | v2' == v3' = 0
-       | otherwise = (1/6)*(det v0' v1' v2' v3')
-  where
-    v0' = v0 t
-    v1' = v1 t
-    v2' = v2 t
-    v3' = v3 t
-
+volume (Tetrahedron _ v0' v1' v2' v3' _) =
+  (1/6)*(det v0' v1' v2' v3')
 
 -- | The barycentric coordinates of a point with respect to v0.
 {-# INLINE b0 #-}
@@ -646,9 +637,8 @@ p78_24_properties =
   where
     -- | Returns the domain point of t with indices i,j,k,l.
     domain_point :: Tetrahedron -> Int -> Int -> Int -> Int -> Point
-    domain_point t i j k l
-      | i + j + k + l == 3 = weighted_sum `scale` (1/3)
-      | otherwise = error "domain point index out of bounds"
+    domain_point t i j k l =
+      weighted_sum `scale` (1/3)
       where
         v0' = (v0 t) `scale` (fromIntegral i)
         v1' = (v1 t) `scale` (fromIntegral j)