math: add orthogonal() and orthonormal() for 3-component vectors.

src/lol/math/vector.h

@@ -1298,12 +1298,29 @@ extern Quat<T> slerp(Quat<T> const &qa, Quat<T> const &qb, T f);
     }
 
 #define LOL_VEC_3_FUNS(tname, tprefix, type) \
+    /* Return the cross product (vector product) of "a" and "b" */ \
     tprefix \
     inline tname<type> cross(tname<type> const &a, tname<type> const &b) \
     { \
         return tname<type>((type)(a.y * b.z - a.z * b.y), \
                            (type)(a.z * b.x - a.x * b.z), \
                            (type)(a.x * b.y - a.y * b.x)); \
+    } \
+    \
+    /* Return a vector that is orthogonal to "a" */ \
+    tprefix \
+    inline tname<type> orthogonal(tname<type> const &a) \
+    { \
+        return lol::abs(a.x) > lol::abs(a.z) \
+             ? tname<type>(-a.y, a.x, (type)0) \
+             : tname<type>((type)0, -a.z, a.y); \
+    } \
+    \
+    /* Return a vector that is orthonormal to "a" */ \
+    tprefix \
+    inline tname<type> orthonormal(tname<type> const &a) \
+    { \
+        return normalize(orthogonal(a)); \
     }
 
 #define LOL_BINARY_NONVECTOR_OPS(tname, tprefix, type) \

test/unit/vector.cpp

@@ -124,6 +124,32 @@ LOLUNIT_FIXTURE(VectorTest)
         LOLUNIT_ASSERT_EQUAL(c.w, 0.0f);
         LOLUNIT_ASSERT_EQUAL(a3, a1);
     }
+
+    LOLUNIT_TEST(Orthogonal)
+    {
+        vec3 a(1.f, 0.f, 0.f);
+        vec3 b(0.f, 1.f, 0.f);
+        vec3 c(0.f, 0.f, 1.f);
+
+        LOLUNIT_ASSERT_DOUBLES_EQUAL(dot(orthogonal(a), a), 0.f, 1e-6f);
+        LOLUNIT_ASSERT_DOUBLES_EQUAL(dot(orthogonal(b), b), 0.f, 1e-6f);
+        LOLUNIT_ASSERT_DOUBLES_EQUAL(dot(orthogonal(c), c), 0.f, 1e-6f);
+
+        /* The length of the orthogonal vector should be at least
+         * sqrt(2)/2 times the length of the original vector. */
+        LOLUNIT_ASSERT_GREATER(length(orthogonal(a)), 0.7f);
+        LOLUNIT_ASSERT_GREATER(length(orthogonal(b)), 0.7f);
+        LOLUNIT_ASSERT_GREATER(length(orthogonal(c)), 0.7f);
+
+        LOLUNIT_ASSERT_DOUBLES_EQUAL(dot(orthonormal(a), a), 0.f, 1e-6f);
+        LOLUNIT_ASSERT_DOUBLES_EQUAL(dot(orthonormal(b), b), 0.f, 1e-6f);
+        LOLUNIT_ASSERT_DOUBLES_EQUAL(dot(orthonormal(c), c), 0.f, 1e-6f);
+
+        /* The length of the orthonormal vector should be 1. */
+        LOLUNIT_ASSERT_DOUBLES_EQUAL(length(orthonormal(a)), 1.f, 1e-6f);
+        LOLUNIT_ASSERT_DOUBLES_EQUAL(length(orthonormal(b)), 1.f, 1e-6f);
+        LOLUNIT_ASSERT_DOUBLES_EQUAL(length(orthonormal(c)), 1.f, 1e-6f);
+    }
 };
 
 } /* namespace lol */