Add Vec2/3/4:angle(other)

Functions to calculate the angle between two vectors. Angle is always
positive. Implementations give the same result as this Lua code:

```lua
local function lua_angle(v1, v2)
  return math.acos(v1:dot(v2) / (v1:length() * v2:length()))
end
```

If either vector is zero-length, the pi/2 value is returned.

src/api/l_math_vectors.c

@@ -253,7 +253,7 @@ static int l_lovrVec2Distance(lua_State* L) {
     uvec[1] = luax_checkfloat(L, 3);
     u = uvec;
   } else {
-    u = luax_checkvector(L, 2, V_VEC2, NULL);
+    u = luax_checkvector(L, 2, V_VEC2, "vec2 or number");
   }
   float dx = v[0] - u[0];
   float dy = v[1] - u[1];
@@ -270,7 +270,7 @@ static int l_lovrVec2Dot(lua_State* L) {
     uvec[1] = luax_checkfloat(L, 3);
     u = uvec;
   } else {
-    u = luax_checkvector(L, 2, V_VEC2, NULL);
+    u = luax_checkvector(L, 2, V_VEC2, "vec2 or number");
   }
   lua_pushnumber(L, v[0] * u[0] + v[1] * u[1]);
   return 1;
@@ -287,7 +287,7 @@ static int l_lovrVec2Lerp(lua_State* L) {
     u = uvec;
     t = luax_checkfloat(L, 4);
   } else {
-    u = luax_checkvector(L, 2, V_VEC2, NULL);
+    u = luax_checkvector(L, 2, V_VEC2, "vec2 or number");
     t = luax_checkfloat(L, 3);
   }
   v[0] = v[0] + (u[0] - v[0]) * t;
@@ -296,6 +296,29 @@ static int l_lovrVec2Lerp(lua_State* L) {
   return 1;
 }
 
+static int l_lovrVec2Angle(lua_State* L) {
+  float* v = luax_checkvector(L, 1, V_VEC2, NULL);
+  float* u;
+  float uvec[2];
+  float dot, length_v, length_u;
+  if (lua_type(L, 2) == LUA_TNUMBER) {
+    uvec[0] = lua_tonumber(L, 2);
+    uvec[1] = luax_checkfloat(L, 3);
+    u = uvec;
+  } else {
+    u = luax_checkvector(L, 2, V_VEC2, "vec2 or number");
+  }
+  length_v = sqrtf(v[0] * v[0] + v[1] * v[1]);
+  length_u = sqrtf(u[0] * u[0] + u[1] * u[1]);
+  if ((length_v == 0.f) || (length_u == 0.f)) {
+    lua_pushnumber(L, (float) M_PI / 2);
+  } else {
+    dot = v[0] * u[0] + v[1] * u[1];
+    lua_pushnumber(L, acosf(dot / (length_v * length_u)));
+  }
+  return 1;
+}
+
 static int l_lovrVec2__add(lua_State* L) {
   float* out = luax_newtempvector(L, V_VEC2);
   if (lua_type(L, 1) == LUA_TNUMBER) {
@@ -497,6 +520,7 @@ const luaL_Reg lovrVec2[] = {
   { "distance", l_lovrVec2Distance },
   { "dot", l_lovrVec2Dot },
   { "lerp", l_lovrVec2Lerp },
+  { "angle", l_lovrVec2Angle },
   { "__add", l_lovrVec2__add },
   { "__sub", l_lovrVec2__sub },
   { "__mul", l_lovrVec2__mul },
@@ -687,6 +711,22 @@ static int l_lovrVec3Lerp(lua_State* L) {
   return 1;
 }
 
+static int l_lovrVec3Angle(lua_State* L) {
+  vec3 v = luax_checkvector(L, 1, V_VEC3, NULL);
+  vec3 u;
+  float uvec[4];
+  if (lua_type(L, 2) == LUA_TNUMBER) {
+    uvec[0] = lua_tonumber(L, 2);
+    uvec[1] = luax_checkfloat(L, 3);
+    uvec[2] = luax_checkfloat(L, 4);
+    u = uvec;
+  } else {
+    u = luax_checkvector(L, 2, V_VEC3, "vec3 or number");
+  }
+  lua_pushnumber(L, vec3_angle(v, u));
+  return 1;
+}
+
 static int l_lovrVec3__add(lua_State* L) {
   vec3 out = luax_newtempvector(L, V_VEC3);
   if (lua_type(L, 1) == LUA_TNUMBER) {
@@ -891,6 +931,7 @@ const luaL_Reg lovrVec3[] = {
   { "dot", l_lovrVec3Dot },
   { "cross", l_lovrVec3Cross },
   { "lerp", l_lovrVec3Lerp },
+  { "angle", l_lovrVec3Angle },
   { "__add", l_lovrVec3__add },
   { "__sub", l_lovrVec3__sub },
   { "__mul", l_lovrVec3__mul },
@@ -1039,7 +1080,7 @@ static int l_lovrVec4Distance(lua_State* L) {
     uvec[3] = luax_checkfloat(L, 5);
     u = uvec;
   } else {
-    u = luax_checkvector(L, 2, V_VEC4, NULL);
+    u = luax_checkvector(L, 2, V_VEC4, "vec4 or number");
   }
   float dx = v[0] - u[0];
   float dy = v[1] - u[1];
@@ -1060,7 +1101,7 @@ static int l_lovrVec4Dot(lua_State* L) {
     uvec[3] = luax_checkfloat(L, 5);
     u = uvec;
   } else {
-    u = luax_checkvector(L, 2, V_VEC4, NULL);
+    u = luax_checkvector(L, 2, V_VEC4, "vec4 or number");
   }
   lua_pushnumber(L, v[0] * u[0] + v[1] * u[1] + v[2] * u[2] + v[3] * u[3]);
   return 1;
@@ -1079,7 +1120,7 @@ static int l_lovrVec4Lerp(lua_State* L) {
     u = uvec;
     t = luax_checkfloat(L, 6);
   } else {
-    u = luax_checkvector(L, 2, V_VEC4, NULL);
+    u = luax_checkvector(L, 2, V_VEC4, "vec4 or number");
     t = luax_checkfloat(L, 3);
   }
   v[0] = v[0] + (u[0] - v[0]) * t;
@@ -1090,6 +1131,31 @@ static int l_lovrVec4Lerp(lua_State* L) {
   return 1;
 }
 
+static int l_lovrVec4Angle(lua_State* L) {
+  float* v = luax_checkvector(L, 1, V_VEC4, NULL);
+  float* u;
+  float uvec[4];
+  float dot, length_v, length_u;
+  if (lua_type(L, 2) == LUA_TNUMBER) {
+    uvec[0] = lua_tonumber(L, 2);
+    uvec[1] = luax_checkfloat(L, 3);
+    uvec[2] = luax_checkfloat(L, 4);
+    uvec[3] = luax_checkfloat(L, 5);
+    u = uvec;
+  } else {
+    u = luax_checkvector(L, 2, V_VEC4, "vec4 or number");
+  }
+  length_v = sqrtf(v[0] * v[0] + v[1] * v[1] + v[2] * v[2] + v[3] * v[3]);
+  length_u = sqrtf(u[0] * u[0] + u[1] * u[1] + u[2] * u[2] + u[3] * u[3]);
+  if ((length_v == 0.f) || (length_u == 0.f)) {
+    lua_pushnumber(L, (float) M_PI / 2);
+  } else {
+    dot = v[0] * u[0] + v[1] * u[1] + v[2] * u[2] + v[3] * u[3];
+    lua_pushnumber(L, acosf(dot / (length_v * length_u)));
+  }
+  return 1;
+}
+
 static int l_lovrVec4__add(lua_State* L) {
   float* out = luax_newtempvector(L, V_VEC4);
   if (lua_type(L, 1) == LUA_TNUMBER) {
@@ -1329,6 +1395,7 @@ const luaL_Reg lovrVec4[] = {
   { "distance", l_lovrVec4Distance },
   { "dot", l_lovrVec4Dot },
   { "lerp", l_lovrVec4Lerp },
+  { "angle", l_lovrVec4Angle },
   { "__add", l_lovrVec4__add },
   { "__sub", l_lovrVec4__sub },
   { "__mul", l_lovrVec4__mul },

src/core/maf.h

@@ -122,6 +122,15 @@ MAF vec3 vec3_max(vec3 v, const vec3 u) {
   return v;
 }
 
+MAF float vec3_angle(const vec3 v, const vec3 u) {
+  float denom = vec3_length(v) * vec3_length(u);
+  if (denom == 0.f) {
+    return (float) M_PI / 2;
+  } else {
+    return acosf(vec3_dot(v, u) / denom);
+  }
+}
+
 // quat
 
 MAF quat quat_set(quat q, float x, float y, float z, float w) {