diff --git a/autogen/gen_math.py b/autogen/gen_math.py
index 98da45c1a..e5ef37b6f 100644
--- a/autogen/gen_math.py
+++ b/autogen/gen_math.py
@@ -1,39 +1,70 @@
 import sys
 
-
-VEC3X_TO_VEC3Y = """
+VECX_TO_VECY = """
 /* |description|
-Converts a 3D {{desc}} vector `a` into a 3D {{desc_2}} vector and stores the result in `dest`
+Converts a {{size}}D {{desc}} vector `a` into a {{size}}D {{desc_2}} vector and stores the result in `dest`
 |descriptionEnd| */
-INLINE OPTIMIZE_O3 Vec3{{suffix_2}}p vec3{{suffix}}_to_vec3{{suffix_2}}(OUT Vec3{{suffix_2}} dest, Vec3{{suffix}} a) {
-    dest[0] = a[0]{{rounding_0}};
-    dest[1] = a[1]{{rounding_1}};
-    dest[2] = a[2]{{rounding_2}};
+INLINE OPTIMIZE_O3 Vec{{size}}{{suffix_2}}p vec{{size}}{{suffix}}_to_vec{{size}}{{suffix_2}}(OUT Vec{{size}}{{suffix_2}} dest, Vec{{size}}{{suffix}} a) {
+    {{body}}
     return dest;
 }
 """
 
-ROUNDING_FORMULA = " + ((a[%d] > 0) ? 0.5f : -0.5f)"
+ROUNDING_FORMULA = " + ((a[{i}] > 0) ? 0.5f : -0.5f)"
 
-def vec3_write_conversion_functions(generated: str, curr_template: dict, templates: list, size: int) -> str:
+def vec_write_conversion_functions(generated: str, curr_template: dict, templates: list, size: int) -> str:
     for template in templates:
         if template["suffix"] == curr_template["suffix"]:
             continue
 
-        generated += VEC3X_TO_VEC3Y \
+        body = "\n    ".join([
+            "dest[{i}] = a[{i}]{rounding};".format(
+                i=i,
+                rounding=ROUNDING_FORMULA.format(i=i) if curr_template["rounding"] else ""
+            ) for i in range(size)
+        ])
+
+        generated += VECX_TO_VECY \
+            .replace("{{size}}", str(size)) \
             .replace("{{desc}}", curr_template["desc"]) \
             .replace("{{suffix}}", curr_template["suffix"]) \
             .replace("{{desc_2}}", template["desc"]) \
-            .replace("{{suffix_2}}", template["suffix"])
-
-        for i in range(size):
-            rounding_i = "{{rounding_%d}}" % (i)
-            generated = generated.replace(rounding_i, ROUNDING_FORMULA % (i) if curr_template["rounding"] else "")
+            .replace("{{suffix_2}}", template["suffix"]) \
+            .replace("{{body}}", body)
 
     return generated
 
 
 TEMPLATES = {
+    "src/engine/math_util_vec2.tmpl": {
+        "size": 2,
+        "templates": [
+            {
+                "desc": "floating-point",
+                "type": "f32",
+                "suffix": "f",
+                "rounding": True
+            },
+            {
+                "desc": "integer",
+                "type": "s32",
+                "suffix": "i",
+                "rounding": False
+            },
+            {
+                "desc": "short integer",
+                "type": "s16",
+                "suffix": "s",
+                "rounding": False
+            }
+        ],
+        "post-template": {
+            "function": vec_write_conversion_functions,
+            "args": {
+                "size": 2
+            }
+        }
+    },
     "src/engine/math_util_vec3.tmpl": {
         "size": 3,
         "templates": [
@@ -57,7 +88,7 @@ TEMPLATES = {
             }
         ],
         "post-template": {
-            "function": vec3_write_conversion_functions,
+            "function": vec_write_conversion_functions,
             "args": {
                 "size": 3
             }
diff --git a/data/dynos_bin_gfx.cpp b/data/dynos_bin_gfx.cpp
index 1c686cb50..ae61971cc 100644
--- a/data/dynos_bin_gfx.cpp
+++ b/data/dynos_bin_gfx.cpp
@@ -405,6 +405,7 @@ s64 DynOS_Gfx_ParseGfxConstants(const String& _Arg, bool* found) {
     gfx_constant(G_LIGHT_MAP_EXT);
     gfx_constant(G_LIGHTING_ENGINE_EXT);
     gfx_constant(G_PACKED_NORMALS_EXT);
+    gfx_constant(G_CULL_INVERT_EXT);
     gfx_constant(G_FRESNEL_COLOR_EXT);
     gfx_constant(G_FRESNEL_ALPHA_EXT);
 
diff --git a/docs/lua/examples/gfx-vtx-demo/actors/shape/model.inc.c b/docs/lua/examples/gfx-vtx-demo/actors/shape/model.inc.c
index e29ce377a..46f01d338 100644
--- a/docs/lua/examples/gfx-vtx-demo/actors/shape/model.inc.c
+++ b/docs/lua/examples/gfx-vtx-demo/actors/shape/model.inc.c
@@ -15,5 +15,6 @@ Gfx shape_template_dl[] = {
 /* [11] */ gsSPDisplayList(NULL),
 /* [12] */ gsSPTexture(0xFFFF, 0xFFFF, 0, G_TX_RENDERTILE, G_OFF),
 /* [13] */ gsDPSetCombineMode(G_CC_SHADE, G_CC_SHADE),
-/* [14] */ gsSPEndDisplayList(),
+/* [14] */ gsSPLoadGeometryMode(G_LIGHTING | G_CULL_BACK),
+/* [15] */ gsSPEndDisplayList(),
 };
diff --git a/docs/lua/lua.md b/docs/lua/lua.md
index 05d165769..4d579c0a9 100644
--- a/docs/lua/lua.md
+++ b/docs/lua/lua.md
@@ -69,7 +69,11 @@ All of this is a holdover from when there were only two players. It was a reason
 - [Custom HUD Texture](examples/custom-hud-texture)
 - [Custom Audio Test](examples/audio-test)
 - [Custom Texture Overriding](examples/texture-override)
+- [Custom Animations (DynOS)](examples/custom-animations-dynos)
+- [Custom Animations (Lua)](examples/custom-animations-lua)
 - [Bytestring Packet Example](examples/bytestring-packet-example.lua)
+- [Gfx/Vtx Demo](examples/gfx-vtx-demo)
+- [Lighting Engine Demo](examples/lighting-engine-demo)
 
 ## Example Lua mods (large)
 - [Hide and Seek Gamemode](../../mods/hide-and-seek.lua)
diff --git a/include/PR/gbi_extension.h b/include/PR/gbi_extension.h
index f87933cc0..1aba0aa61 100644
--- a/include/PR/gbi_extension.h
+++ b/include/PR/gbi_extension.h
@@ -7,6 +7,7 @@
 #define G_LIGHT_MAP_EXT       0x00000800
 #define G_LIGHTING_ENGINE_EXT 0x00004000
 #define G_PACKED_NORMALS_EXT  0x00000080
+#define G_CULL_INVERT_EXT     0x00000100
 #define G_FRESNEL_COLOR_EXT   0x00000040
 #define G_FRESNEL_ALPHA_EXT   0x00400000
 
diff --git a/src/engine/math_util.c b/src/engine/math_util.c
index fc3562799..a5a82e602 100644
--- a/src/engine/math_util.c
+++ b/src/engine/math_util.c
@@ -233,6 +233,30 @@ OPTIMIZE_O3 s32 anim_spline_poll(struct MarioState* m, OUT Vec3f result) {
     return hasEnded;
 }
 
+  ///////////
+ // Vec2f //
+///////////
+
+Vec2f gVec2fZero = { 0.0f, 0.0f };
+
+Vec2f gVec2fOne = { 1.0f, 1.0f };
+
+  ///////////
+ // Vec2i //
+///////////
+
+Vec2i gVec2iZero = { 0, 0 };
+
+Vec2i gVec2iOne = { 1, 1 };
+
+  ///////////
+ // Vec2s //
+///////////
+
+Vec2s gVec2sZero = { 0, 0 };
+
+Vec2s gVec2sOne = { 1, 1 };
+
   ///////////
  // Vec3f //
 ///////////
diff --git a/src/engine/math_util.h b/src/engine/math_util.h
index 72ead474d..16e30eba2 100644
--- a/src/engine/math_util.h
+++ b/src/engine/math_util.h
@@ -87,6 +87,12 @@ extern f32 gCosineTable[];
 
 #endif
 
+extern Vec2f gVec2fZero;
+extern Vec2i gVec2iZero;
+extern Vec2s gVec2sZero;
+extern Vec2f gVec2fOne;
+extern Vec2i gVec2iOne;
+extern Vec2s gVec2sOne;
 extern Vec3f gVec3fZero;
 extern Vec3i gVec3iZero;
 extern Vec3s gVec3sZero;
@@ -143,6 +149,24 @@ Advances the spline-based animation associated with `m` and stores the current i
 |descriptionEnd| */
 OPTIMIZE_O3 s32 anim_spline_poll(struct MarioState* m, OUT Vec3f result);
 
+  ///////////
+ // Vec2f //
+///////////
+
+#include "math_util_vec2f.inl"
+
+  ///////////
+ // Vec2i //
+///////////
+
+#include "math_util_vec2i.inl"
+
+  ///////////
+ // Vec2s //
+///////////
+
+#include "math_util_vec2s.inl"
+
   ///////////
  // Vec3f //
 ///////////
diff --git a/src/engine/math_util_vec2.tmpl b/src/engine/math_util_vec2.tmpl
new file mode 100644
index 000000000..bfb24f14a
--- /dev/null
+++ b/src/engine/math_util_vec2.tmpl
@@ -0,0 +1,157 @@
+#pragma once
+
+/* |description|
+Sets the components of the 2D {{desc}} vector `v` to 0
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2{{suffix}}p vec2{{suffix}}_zero(OUT Vec2{{suffix}} v) {
+    memset(v, 0, sizeof(Vec2{{suffix}}));
+    return v;
+}
+
+/* |description|
+Copies the contents of a 2D {{desc}} vector (`src`) into another 2D {{desc}} vector (`dest`)
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2{{suffix}}p vec2{{suffix}}_copy(OUT Vec2{{suffix}} dest, Vec2{{suffix}} src) {
+    dest[0] = src[0];
+    dest[1] = src[1];
+    return dest;
+}
+
+/* |description|
+Sets the values of the 2D {{desc}} vector `dest` to the given x and y values
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2{{suffix}}p vec2{{suffix}}_set(OUT Vec2{{suffix}} dest, {{type}} x, {{type}} y) {
+    dest[0] = x;
+    dest[1] = y;
+    return dest;
+}
+
+/* |description|
+Adds the components of the 2D {{desc}} vector `a` to `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2{{suffix}}p vec2{{suffix}}_add(OUT Vec2{{suffix}} dest, Vec2{{suffix}} a) {
+    dest[0] += a[0];
+    dest[1] += a[1];
+    return dest;
+}
+
+/* |description|
+Adds the components of two 2D {{desc}} vectors `a` and `b` and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2{{suffix}}p vec2{{suffix}}_sum(OUT Vec2{{suffix}} dest, Vec2{{suffix}} a, Vec2{{suffix}} b) {
+    dest[0] = a[0] + b[0];
+    dest[1] = a[1] + b[1];
+    return dest;
+}
+
+/* |description|
+Subtracts the components of the 2D {{desc}} vector `a` from `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2{{suffix}}p vec2{{suffix}}_sub(OUT Vec2{{suffix}} dest, Vec2{{suffix}} a) {
+    dest[0] -= a[0];
+    dest[1] -= a[1];
+    return dest;
+}
+
+/* |description|
+Subtracts the components of the 2D {{desc}} vector `b` from the components of `a` and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2{{suffix}}p vec2{{suffix}}_dif(OUT Vec2{{suffix}} dest, Vec2{{suffix}} a, Vec2{{suffix}} b) {
+    dest[0] = a[0] - b[0];
+    dest[1] = a[1] - b[1];
+    return dest;
+}
+
+/* |description|
+Multiplies each component of the 2D {{desc}} vector `dest` by the scalar value `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2{{suffix}}p vec2{{suffix}}_mul(OUT Vec2{{suffix}} dest, f32 a) {
+    dest[0] *= a;
+    dest[1] *= a;
+    return dest;
+}
+
+/* |description|
+Multiplies the components of the 2D {{desc}} vector `dest` with the components of `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2{{suffix}}p vec2{{suffix}}_mult(OUT Vec2{{suffix}} dest, Vec2{{suffix}} a) {
+    dest[0] *= a[0];
+    dest[1] *= a[1];
+    return dest;
+}
+
+/* |description|
+Multiplies the components of two 2D {{desc}} vectors `a` and `b` and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2{{suffix}}p vec2{{suffix}}_prod(OUT Vec2{{suffix}} dest, Vec2{{suffix}} a, Vec2{{suffix}} b) {
+    dest[0] = a[0] * b[0];
+    dest[1] = a[1] * b[1];
+    return dest;
+}
+
+/* |description|
+Divides each component of the 2D {{desc}} vector `dest` by the scalar value `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2{{suffix}}p vec2{{suffix}}_div(OUT Vec2{{suffix}} dest, f32 a) {
+    if (a == 0) { return dest; }
+    dest[0] /= a;
+    dest[1] /= a;
+    return dest;
+}
+
+/* |description|
+Calculates the length (magnitude) of the 2D {{desc}} vector `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 f32 vec2{{suffix}}_length(Vec2{{suffix}} a) {
+    return sqrtf(a[0] * a[0] + a[1] * a[1]);
+}
+
+/* |description|
+Normalizes the 2D {{desc}} vector `v` so that its length (magnitude) becomes 1, while retaining its direction
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2{{suffix}}p vec2{{suffix}}_normalize(OUT Vec2{{suffix}} v) {
+    f32 mag = vec2{{suffix}}_length(v);
+    vec2{{suffix}}_div(v, mag);
+    return v;
+}
+
+/* |description|
+Sets the length (magnitude) of 2D {{desc}} vector `v`, while retaining its direction
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2{{suffix}}p vec2{{suffix}}_set_magnitude(OUT Vec2{{suffix}} v, f32 mag) {
+    vec2{{suffix}}_normalize(v);
+    vec2{{suffix}}_mul(v, mag);
+    return v;
+}
+
+/* |description|
+Computes the dot product of the two 2D {{desc}} vectors `a` and `b`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 f32 vec2{{suffix}}_dot(Vec2{{suffix}} a, Vec2{{suffix}} b) {
+    return (f32) (a[0] * b[0] + a[1] * b[1]);
+}
+
+/* |description|
+Takes two 2D {{desc}} vectors `vecA` and `vecB`, multiplies them by `sclA` and `sclB` respectively, adds the scaled vectors together and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2{{suffix}}p vec2{{suffix}}_combine(OUT Vec2{{suffix}} dest, Vec2{{suffix}} vecA, Vec2{{suffix}} vecB, f32 sclA, f32 sclB) {
+    dest[0] = vecA[0] * sclA + vecB[0] * sclB;
+    dest[1] = vecA[1] * sclA + vecB[1] * sclB;
+    return dest;
+}
+
+/* |description|
+Calculates the distance between two 2D {{desc}} vectors `v1` and `v2`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 f32 vec2{{suffix}}_dist(Vec2{{suffix}} v1, Vec2{{suffix}} v2) {
+    Vec2{{suffix}} diff;
+    vec2{{suffix}}_dif(diff, v1, v2);
+    return vec2{{suffix}}_length(diff);
+}
+
+/* |description|
+Returns `true` if all components of the 2D {{desc}} vector `v` are zero
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 bool vec2{{suffix}}_is_zero(Vec2{{suffix}} v) {
+    return memcmp(v, gVec2{{suffix}}Zero, sizeof(Vec2{{suffix}})) == 0;
+}
diff --git a/src/engine/math_util_vec2f.inl b/src/engine/math_util_vec2f.inl
new file mode 100644
index 000000000..edea0385b
--- /dev/null
+++ b/src/engine/math_util_vec2f.inl
@@ -0,0 +1,178 @@
+/* THIS FILE IS AUTO-GENERATED */
+/*   DO NOT EDIT IT MANUALLY   */
+
+#pragma once
+
+/* |description|
+Sets the components of the 2D floating-point vector `v` to 0
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2f_zero(OUT Vec2f v) {
+    memset(v, 0, sizeof(Vec2f));
+    return v;
+}
+
+/* |description|
+Copies the contents of a 2D floating-point vector (`src`) into another 2D floating-point vector (`dest`)
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2f_copy(OUT Vec2f dest, Vec2f src) {
+    dest[0] = src[0];
+    dest[1] = src[1];
+    return dest;
+}
+
+/* |description|
+Sets the values of the 2D floating-point vector `dest` to the given x and y values
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2f_set(OUT Vec2f dest, f32 x, f32 y) {
+    dest[0] = x;
+    dest[1] = y;
+    return dest;
+}
+
+/* |description|
+Adds the components of the 2D floating-point vector `a` to `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2f_add(OUT Vec2f dest, Vec2f a) {
+    dest[0] += a[0];
+    dest[1] += a[1];
+    return dest;
+}
+
+/* |description|
+Adds the components of two 2D floating-point vectors `a` and `b` and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2f_sum(OUT Vec2f dest, Vec2f a, Vec2f b) {
+    dest[0] = a[0] + b[0];
+    dest[1] = a[1] + b[1];
+    return dest;
+}
+
+/* |description|
+Subtracts the components of the 2D floating-point vector `a` from `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2f_sub(OUT Vec2f dest, Vec2f a) {
+    dest[0] -= a[0];
+    dest[1] -= a[1];
+    return dest;
+}
+
+/* |description|
+Subtracts the components of the 2D floating-point vector `b` from the components of `a` and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2f_dif(OUT Vec2f dest, Vec2f a, Vec2f b) {
+    dest[0] = a[0] - b[0];
+    dest[1] = a[1] - b[1];
+    return dest;
+}
+
+/* |description|
+Multiplies each component of the 2D floating-point vector `dest` by the scalar value `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2f_mul(OUT Vec2f dest, f32 a) {
+    dest[0] *= a;
+    dest[1] *= a;
+    return dest;
+}
+
+/* |description|
+Multiplies the components of the 2D floating-point vector `dest` with the components of `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2f_mult(OUT Vec2f dest, Vec2f a) {
+    dest[0] *= a[0];
+    dest[1] *= a[1];
+    return dest;
+}
+
+/* |description|
+Multiplies the components of two 2D floating-point vectors `a` and `b` and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2f_prod(OUT Vec2f dest, Vec2f a, Vec2f b) {
+    dest[0] = a[0] * b[0];
+    dest[1] = a[1] * b[1];
+    return dest;
+}
+
+/* |description|
+Divides each component of the 2D floating-point vector `dest` by the scalar value `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2f_div(OUT Vec2f dest, f32 a) {
+    if (a == 0) { return dest; }
+    dest[0] /= a;
+    dest[1] /= a;
+    return dest;
+}
+
+/* |description|
+Calculates the length (magnitude) of the 2D floating-point vector `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 f32 vec2f_length(Vec2f a) {
+    return sqrtf(a[0] * a[0] + a[1] * a[1]);
+}
+
+/* |description|
+Normalizes the 2D floating-point vector `v` so that its length (magnitude) becomes 1, while retaining its direction
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2f_normalize(OUT Vec2f v) {
+    f32 mag = vec2f_length(v);
+    vec2f_div(v, mag);
+    return v;
+}
+
+/* |description|
+Sets the length (magnitude) of 2D floating-point vector `v`, while retaining its direction
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2f_set_magnitude(OUT Vec2f v, f32 mag) {
+    vec2f_normalize(v);
+    vec2f_mul(v, mag);
+    return v;
+}
+
+/* |description|
+Computes the dot product of the two 2D floating-point vectors `a` and `b`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 f32 vec2f_dot(Vec2f a, Vec2f b) {
+    return (f32) (a[0] * b[0] + a[1] * b[1]);
+}
+
+/* |description|
+Takes two 2D floating-point vectors `vecA` and `vecB`, multiplies them by `sclA` and `sclB` respectively, adds the scaled vectors together and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2f_combine(OUT Vec2f dest, Vec2f vecA, Vec2f vecB, f32 sclA, f32 sclB) {
+    dest[0] = vecA[0] * sclA + vecB[0] * sclB;
+    dest[1] = vecA[1] * sclA + vecB[1] * sclB;
+    return dest;
+}
+
+/* |description|
+Calculates the distance between two 2D floating-point vectors `v1` and `v2`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 f32 vec2f_dist(Vec2f v1, Vec2f v2) {
+    Vec2f diff;
+    vec2f_dif(diff, v1, v2);
+    return vec2f_length(diff);
+}
+
+/* |description|
+Returns `true` if all components of the 2D floating-point vector `v` are zero
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 bool vec2f_is_zero(Vec2f v) {
+    return memcmp(v, gVec2fZero, sizeof(Vec2f)) == 0;
+}
+
+/* |description|
+Converts a 2D floating-point vector `a` into a 2D integer vector and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2f_to_vec2i(OUT Vec2i dest, Vec2f a) {
+    dest[0] = a[0] + ((a[0] > 0) ? 0.5f : -0.5f);
+    dest[1] = a[1] + ((a[1] > 0) ? 0.5f : -0.5f);
+    return dest;
+}
+
+/* |description|
+Converts a 2D floating-point vector `a` into a 2D short integer vector and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2f_to_vec2s(OUT Vec2s dest, Vec2f a) {
+    dest[0] = a[0] + ((a[0] > 0) ? 0.5f : -0.5f);
+    dest[1] = a[1] + ((a[1] > 0) ? 0.5f : -0.5f);
+    return dest;
+}
diff --git a/src/engine/math_util_vec2i.inl b/src/engine/math_util_vec2i.inl
new file mode 100644
index 000000000..774bedb38
--- /dev/null
+++ b/src/engine/math_util_vec2i.inl
@@ -0,0 +1,178 @@
+/* THIS FILE IS AUTO-GENERATED */
+/*   DO NOT EDIT IT MANUALLY   */
+
+#pragma once
+
+/* |description|
+Sets the components of the 2D integer vector `v` to 0
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2i_zero(OUT Vec2i v) {
+    memset(v, 0, sizeof(Vec2i));
+    return v;
+}
+
+/* |description|
+Copies the contents of a 2D integer vector (`src`) into another 2D integer vector (`dest`)
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2i_copy(OUT Vec2i dest, Vec2i src) {
+    dest[0] = src[0];
+    dest[1] = src[1];
+    return dest;
+}
+
+/* |description|
+Sets the values of the 2D integer vector `dest` to the given x and y values
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2i_set(OUT Vec2i dest, s32 x, s32 y) {
+    dest[0] = x;
+    dest[1] = y;
+    return dest;
+}
+
+/* |description|
+Adds the components of the 2D integer vector `a` to `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2i_add(OUT Vec2i dest, Vec2i a) {
+    dest[0] += a[0];
+    dest[1] += a[1];
+    return dest;
+}
+
+/* |description|
+Adds the components of two 2D integer vectors `a` and `b` and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2i_sum(OUT Vec2i dest, Vec2i a, Vec2i b) {
+    dest[0] = a[0] + b[0];
+    dest[1] = a[1] + b[1];
+    return dest;
+}
+
+/* |description|
+Subtracts the components of the 2D integer vector `a` from `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2i_sub(OUT Vec2i dest, Vec2i a) {
+    dest[0] -= a[0];
+    dest[1] -= a[1];
+    return dest;
+}
+
+/* |description|
+Subtracts the components of the 2D integer vector `b` from the components of `a` and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2i_dif(OUT Vec2i dest, Vec2i a, Vec2i b) {
+    dest[0] = a[0] - b[0];
+    dest[1] = a[1] - b[1];
+    return dest;
+}
+
+/* |description|
+Multiplies each component of the 2D integer vector `dest` by the scalar value `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2i_mul(OUT Vec2i dest, f32 a) {
+    dest[0] *= a;
+    dest[1] *= a;
+    return dest;
+}
+
+/* |description|
+Multiplies the components of the 2D integer vector `dest` with the components of `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2i_mult(OUT Vec2i dest, Vec2i a) {
+    dest[0] *= a[0];
+    dest[1] *= a[1];
+    return dest;
+}
+
+/* |description|
+Multiplies the components of two 2D integer vectors `a` and `b` and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2i_prod(OUT Vec2i dest, Vec2i a, Vec2i b) {
+    dest[0] = a[0] * b[0];
+    dest[1] = a[1] * b[1];
+    return dest;
+}
+
+/* |description|
+Divides each component of the 2D integer vector `dest` by the scalar value `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2i_div(OUT Vec2i dest, f32 a) {
+    if (a == 0) { return dest; }
+    dest[0] /= a;
+    dest[1] /= a;
+    return dest;
+}
+
+/* |description|
+Calculates the length (magnitude) of the 2D integer vector `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 f32 vec2i_length(Vec2i a) {
+    return sqrtf(a[0] * a[0] + a[1] * a[1]);
+}
+
+/* |description|
+Normalizes the 2D integer vector `v` so that its length (magnitude) becomes 1, while retaining its direction
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2i_normalize(OUT Vec2i v) {
+    f32 mag = vec2i_length(v);
+    vec2i_div(v, mag);
+    return v;
+}
+
+/* |description|
+Sets the length (magnitude) of 2D integer vector `v`, while retaining its direction
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2i_set_magnitude(OUT Vec2i v, f32 mag) {
+    vec2i_normalize(v);
+    vec2i_mul(v, mag);
+    return v;
+}
+
+/* |description|
+Computes the dot product of the two 2D integer vectors `a` and `b`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 f32 vec2i_dot(Vec2i a, Vec2i b) {
+    return (f32) (a[0] * b[0] + a[1] * b[1]);
+}
+
+/* |description|
+Takes two 2D integer vectors `vecA` and `vecB`, multiplies them by `sclA` and `sclB` respectively, adds the scaled vectors together and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2i_combine(OUT Vec2i dest, Vec2i vecA, Vec2i vecB, f32 sclA, f32 sclB) {
+    dest[0] = vecA[0] * sclA + vecB[0] * sclB;
+    dest[1] = vecA[1] * sclA + vecB[1] * sclB;
+    return dest;
+}
+
+/* |description|
+Calculates the distance between two 2D integer vectors `v1` and `v2`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 f32 vec2i_dist(Vec2i v1, Vec2i v2) {
+    Vec2i diff;
+    vec2i_dif(diff, v1, v2);
+    return vec2i_length(diff);
+}
+
+/* |description|
+Returns `true` if all components of the 2D integer vector `v` are zero
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 bool vec2i_is_zero(Vec2i v) {
+    return memcmp(v, gVec2iZero, sizeof(Vec2i)) == 0;
+}
+
+/* |description|
+Converts a 2D integer vector `a` into a 2D floating-point vector and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2i_to_vec2f(OUT Vec2f dest, Vec2i a) {
+    dest[0] = a[0];
+    dest[1] = a[1];
+    return dest;
+}
+
+/* |description|
+Converts a 2D integer vector `a` into a 2D short integer vector and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2i_to_vec2s(OUT Vec2s dest, Vec2i a) {
+    dest[0] = a[0];
+    dest[1] = a[1];
+    return dest;
+}
diff --git a/src/engine/math_util_vec2s.inl b/src/engine/math_util_vec2s.inl
new file mode 100644
index 000000000..2dde2fdbd
--- /dev/null
+++ b/src/engine/math_util_vec2s.inl
@@ -0,0 +1,178 @@
+/* THIS FILE IS AUTO-GENERATED */
+/*   DO NOT EDIT IT MANUALLY   */
+
+#pragma once
+
+/* |description|
+Sets the components of the 2D short integer vector `v` to 0
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2s_zero(OUT Vec2s v) {
+    memset(v, 0, sizeof(Vec2s));
+    return v;
+}
+
+/* |description|
+Copies the contents of a 2D short integer vector (`src`) into another 2D short integer vector (`dest`)
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2s_copy(OUT Vec2s dest, Vec2s src) {
+    dest[0] = src[0];
+    dest[1] = src[1];
+    return dest;
+}
+
+/* |description|
+Sets the values of the 2D short integer vector `dest` to the given x and y values
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2s_set(OUT Vec2s dest, s16 x, s16 y) {
+    dest[0] = x;
+    dest[1] = y;
+    return dest;
+}
+
+/* |description|
+Adds the components of the 2D short integer vector `a` to `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2s_add(OUT Vec2s dest, Vec2s a) {
+    dest[0] += a[0];
+    dest[1] += a[1];
+    return dest;
+}
+
+/* |description|
+Adds the components of two 2D short integer vectors `a` and `b` and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2s_sum(OUT Vec2s dest, Vec2s a, Vec2s b) {
+    dest[0] = a[0] + b[0];
+    dest[1] = a[1] + b[1];
+    return dest;
+}
+
+/* |description|
+Subtracts the components of the 2D short integer vector `a` from `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2s_sub(OUT Vec2s dest, Vec2s a) {
+    dest[0] -= a[0];
+    dest[1] -= a[1];
+    return dest;
+}
+
+/* |description|
+Subtracts the components of the 2D short integer vector `b` from the components of `a` and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2s_dif(OUT Vec2s dest, Vec2s a, Vec2s b) {
+    dest[0] = a[0] - b[0];
+    dest[1] = a[1] - b[1];
+    return dest;
+}
+
+/* |description|
+Multiplies each component of the 2D short integer vector `dest` by the scalar value `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2s_mul(OUT Vec2s dest, f32 a) {
+    dest[0] *= a;
+    dest[1] *= a;
+    return dest;
+}
+
+/* |description|
+Multiplies the components of the 2D short integer vector `dest` with the components of `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2s_mult(OUT Vec2s dest, Vec2s a) {
+    dest[0] *= a[0];
+    dest[1] *= a[1];
+    return dest;
+}
+
+/* |description|
+Multiplies the components of two 2D short integer vectors `a` and `b` and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2s_prod(OUT Vec2s dest, Vec2s a, Vec2s b) {
+    dest[0] = a[0] * b[0];
+    dest[1] = a[1] * b[1];
+    return dest;
+}
+
+/* |description|
+Divides each component of the 2D short integer vector `dest` by the scalar value `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2s_div(OUT Vec2s dest, f32 a) {
+    if (a == 0) { return dest; }
+    dest[0] /= a;
+    dest[1] /= a;
+    return dest;
+}
+
+/* |description|
+Calculates the length (magnitude) of the 2D short integer vector `a`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 f32 vec2s_length(Vec2s a) {
+    return sqrtf(a[0] * a[0] + a[1] * a[1]);
+}
+
+/* |description|
+Normalizes the 2D short integer vector `v` so that its length (magnitude) becomes 1, while retaining its direction
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2s_normalize(OUT Vec2s v) {
+    f32 mag = vec2s_length(v);
+    vec2s_div(v, mag);
+    return v;
+}
+
+/* |description|
+Sets the length (magnitude) of 2D short integer vector `v`, while retaining its direction
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2s_set_magnitude(OUT Vec2s v, f32 mag) {
+    vec2s_normalize(v);
+    vec2s_mul(v, mag);
+    return v;
+}
+
+/* |description|
+Computes the dot product of the two 2D short integer vectors `a` and `b`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 f32 vec2s_dot(Vec2s a, Vec2s b) {
+    return (f32) (a[0] * b[0] + a[1] * b[1]);
+}
+
+/* |description|
+Takes two 2D short integer vectors `vecA` and `vecB`, multiplies them by `sclA` and `sclB` respectively, adds the scaled vectors together and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2sp vec2s_combine(OUT Vec2s dest, Vec2s vecA, Vec2s vecB, f32 sclA, f32 sclB) {
+    dest[0] = vecA[0] * sclA + vecB[0] * sclB;
+    dest[1] = vecA[1] * sclA + vecB[1] * sclB;
+    return dest;
+}
+
+/* |description|
+Calculates the distance between two 2D short integer vectors `v1` and `v2`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 f32 vec2s_dist(Vec2s v1, Vec2s v2) {
+    Vec2s diff;
+    vec2s_dif(diff, v1, v2);
+    return vec2s_length(diff);
+}
+
+/* |description|
+Returns `true` if all components of the 2D short integer vector `v` are zero
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 bool vec2s_is_zero(Vec2s v) {
+    return memcmp(v, gVec2sZero, sizeof(Vec2s)) == 0;
+}
+
+/* |description|
+Converts a 2D short integer vector `a` into a 2D floating-point vector and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2fp vec2s_to_vec2f(OUT Vec2f dest, Vec2s a) {
+    dest[0] = a[0];
+    dest[1] = a[1];
+    return dest;
+}
+
+/* |description|
+Converts a 2D short integer vector `a` into a 2D integer vector and stores the result in `dest`
+|descriptionEnd| */
+INLINE OPTIMIZE_O3 Vec2ip vec2s_to_vec2i(OUT Vec2i dest, Vec2s a) {
+    dest[0] = a[0];
+    dest[1] = a[1];
+    return dest;
+}
diff --git a/src/game/mario_misc.c b/src/game/mario_misc.c
index 2163116da..f2e742d69 100644
--- a/src/game/mario_misc.c
+++ b/src/game/mario_misc.c
@@ -788,8 +788,11 @@ static Gfx *geo_mario_create_player_colors_dl(s32 index, Gfx *capEnemyGfx, Gfx *
     if (gfx) {
         Gfx *gfxp = gfx;
         for (s32 part = 0; part != PLAYER_PART_MAX; ++part) {
-            gSPLight(gfxp++, &gNetworkPlayerColors[index].parts[part].l, (2 * (part + 1)) + 1);
-            gSPLight(gfxp++, &gNetworkPlayerColors[index].parts[part].a, (2 * (part + 1)) + 2);
+            Lights1 *light = alloc_display_list(sizeof(Lights1));
+            if (!light) { return NULL; }
+            *light = gNetworkPlayerColors[index].parts[part];
+            gSPLight(gfxp++, &light->l, (2 * (part + 1)) + 1);
+            gSPLight(gfxp++, &light->a, (2 * (part + 1)) + 2);
         }
         if (capEnemyGfx) { gSPDisplayList(gfxp++, capEnemyGfx); }
         if (capEnemyDecalGfx) { gSPDisplayList(gfxp++, capEnemyDecalGfx); }
diff --git a/src/pc/gfx/gfx_pc.c b/src/pc/gfx/gfx_pc.c
index 10cb2b500..9c1a6b62e 100644
--- a/src/pc/gfx/gfx_pc.c
+++ b/src/pc/gfx/gfx_pc.c
@@ -1028,6 +1028,11 @@ static void OPTIMIZE_O3 gfx_sp_tri1(uint8_t vtx1_idx, uint8_t vtx2_idx, uint8_t
             cross = -cross;
         }
 
+        // Invert culling: back becomes front and front becomes back
+        if (rsp.geometry_mode & G_CULL_INVERT_EXT) {
+            cross = -cross;
+        }
+
         switch (rsp.geometry_mode & G_CULL_BOTH) {
             case G_CULL_FRONT:
                 if (cross <= 0) return;
diff --git a/src/pc/lua/smlua_hooks.c b/src/pc/lua/smlua_hooks.c
index f08e156d3..0149e1711 100644
--- a/src/pc/lua/smlua_hooks.c
+++ b/src/pc/lua/smlua_hooks.c
@@ -41,10 +41,10 @@ struct LuaHookedEvent {
 static struct LuaHookedEvent sHookedEvents[HOOK_MAX] = { 0 };
 
 static const char* sLuaHookedEventTypeName[] = {
-#define SMLUA_EVENT_HOOK(hookEventType, ...) #hookEventType,
+#define SMLUA_EVENT_HOOK(hookEventType, ...) [hookEventType] = #hookEventType,
 #include "smlua_hook_events.inl"
 #undef SMLUA_EVENT_HOOK
-    "HOOK_MAX"
+    [HOOK_MAX] = "HOOK_MAX"
 };
 
 int smlua_call_hook(lua_State* L, int nargs, int nresults, int errfunc, struct Mod* activeMod, struct ModFile* activeModFile) {