From: Zefram <zefram@fysh.org>
Date: Thu, 24 Jul 2014 12:49:15 +0000 (+0100)
Subject: Vector math improvements
X-Git-Url: http://81.2.79.47:8989/gitweb/?a=commitdiff_plain;h=refs%2Fheads%2Fzefram%2Fuse;p=zefram%2Fminetest%2Fminetest_engine.git

Vector math improvements

Rewrite math.hypot() to compute more directly, with far fewer operations.
Rewrite vector.length() and vector.distance() to each use a single
sqrt operation, rather than two (which they were doing via math.hypot).
Add vector.length_square() and vector.distance_square(), which return
squared distance more cheaply by omitting the sqrt operation.
---

diff --git a/builtin/common/misc_helpers.lua b/builtin/common/misc_helpers.lua
index f57efc13..76fdee8d 100644
--- a/builtin/common/misc_helpers.lua
+++ b/builtin/common/misc_helpers.lua
@@ -127,14 +127,7 @@ assert(string.trim("\n \t\tfoo bar\t ") == "foo bar")
 
 --------------------------------------------------------------------------------
 function math.hypot(x, y)
-	local t
-	x = math.abs(x)
-	y = math.abs(y)
-	t = math.min(x, y)
-	x = math.max(x, y)
-	if x == 0 then return 0 end
-	t = t / x
-	return x * math.sqrt(1 + t * t)
+	return math.sqrt(x*x + y*y)
 end
 
 --------------------------------------------------------------------------------
diff --git a/builtin/common/vector.lua b/builtin/common/vector.lua
index 88ccfe6d..dfb4fb0e 100644
--- a/builtin/common/vector.lua
+++ b/builtin/common/vector.lua
@@ -18,8 +18,12 @@ function vector.equals(a, b)
 	       a.z == b.z
 end
 
+function vector.length_square(v)
+	return v.x*v.x + v.y*v.y + v.z*v.z
+end
+
 function vector.length(v)
-	return math.hypot(v.x, math.hypot(v.y, v.z))
+	return math.sqrt(vector.length_square(v))
 end
 
 function vector.normalize(v)
@@ -39,11 +43,15 @@ function vector.round(v)
 	}
 end
 
-function vector.distance(a, b)
+function vector.distance_square(a, b)
 	local x = a.x - b.x
 	local y = a.y - b.y
 	local z = a.z - b.z
-	return math.hypot(x, math.hypot(y, z))
+	return x*x + y*y + z*z
+end
+
+function vector.distance(a, b)
+	return math.sqrt(vector.distance_square(a, b))
 end
 
 function vector.direction(pos1, pos2)
diff --git a/doc/lua_api.txt b/doc/lua_api.txt
index 19269ebf..7955f9dc 100644
--- a/doc/lua_api.txt
+++ b/doc/lua_api.txt
@@ -1241,7 +1241,11 @@ vector.new([x[, y, z]]) -> vector
  ^ x is a table or the x position.
 vector.direction(p1, p2) -> vector
 vector.distance(p1, p2) -> number
+vector.distance_square(p1, p2) -> number
+^ Cheaper than squaring vector.distance(p1, p2)
 vector.length(v) -> number
+vector.length_square(v) -> number
+^ Cheaper than squaring vector.length(v)
 vector.normalize(v) -> vector
 vector.round(v) -> vector
 vector.equals(v1, v2) -> bool