From 79525b9aeecec4c0841269eabb7ce2d6393f0964 Mon Sep 17 00:00:00 2001
From: Eric Wasylishen <ewasylishen@gmail.com>
Date: Tue, 9 Aug 2016 17:20:51 -0600
Subject: [PATCH] common: mathlib: add UniformPointOnSphere

---
 common/mathlib.c         | 16 +++++++++++++---
 include/common/mathlib.h |  2 ++
 2 files changed, 15 insertions(+), 3 deletions(-)

diff --git a/common/mathlib.c b/common/mathlib.c
index 9c4fd451..28701647 100644
--- a/common/mathlib.c
+++ b/common/mathlib.c
@@ -77,10 +77,13 @@ VecStrf(const vec3_t vec)
 // from http://mathworld.wolfram.com/SpherePointPicking.html
 // eqns 6,7,8
 void
-RandomDir(vec3_t dir)
+UniformPointOnSphere(vec3_t dir, float u1, float u2)
 {
-    const vec_t theta = Random() * 2.0 * Q_PI;
-    const vec_t u = (2.0 * Random()) - 1.0;
+    assert(u1 >= 0 && u1 <= 1);
+    assert(u2 >= 0 && u2 <= 1);
+    
+    const vec_t theta = u1 * 2.0 * Q_PI;
+    const vec_t u = (2.0 * u2) - 1.0;
     
     const vec_t s = sqrt(1.0 - (u * u));
     dir[0] = s * cos(theta);
@@ -93,6 +96,13 @@ RandomDir(vec3_t dir)
     }
 }
 
+void
+RandomDir(vec3_t dir)
+{
+    UniformPointOnSphere(dir, Random(), Random());
+}
+
+
 bool AABBsDisjoint(const vec3_t minsA, const vec3_t maxsA,
                    const vec3_t minsB, const vec3_t maxsB)
 {
diff --git a/include/common/mathlib.h b/include/common/mathlib.h
index 01e0130f..a3823dc0 100644
--- a/include/common/mathlib.h
+++ b/include/common/mathlib.h
@@ -176,6 +176,8 @@ VectorNormalize(vec3_t v)
 const char *VecStr(const vec3_t vec);
 const char *VecStrf(const vec3_t vec);
 
+// Maps uniform random variables U and V in [0, 1] to uniformly distributed points on a sphere
+void UniformPointOnSphere(vec3_t dir, float u, float v);
 void RandomDir(vec3_t dir);
 bool AABBsDisjoint(const vec3_t minsA, const vec3_t maxsA, const vec3_t minsB, const vec3_t maxsB);
 void AABB_Init(vec3_t mins, vec3_t maxs, const vec3_t pt);