core: fix bugs in mat4::lookat() and mat4::perspective(), and ensure these

function use degrees rather than radians.

src/matrix.cpp

@@ -12,6 +12,15 @@
 #   include "config.h"
 #endif
 
+#if defined WIN32 && !defined _XBOX
+#   define _USE_MATH_DEFINES /* for M_PI */
+#   define WIN32_LEAN_AND_MEAN
+#   include <windows.h>
+#   undef near /* Fuck Microsoft */
+#   undef far /* Fuck Microsoft again */
+#endif
+
+#include <cmath> /* for M_PI */
 #include <cstdlib> /* free() */
 #include <cstring> /* strdup() */
 
@@ -46,7 +55,7 @@ template<> vec3 cross(vec3 v1, vec3 v2)
 
 template<> vec2 normalize(vec2 v)
 {
-    float norm = v.sqlen();
+    float norm = v.len();
     if (!norm)
         return vec2(0);
     return v / norm;
@@ -54,7 +63,7 @@ template<> vec2 normalize(vec2 v)
 
 template<> vec3 normalize(vec3 v)
 {
-    float norm = v.sqlen();
+    float norm = v.len();
     if (!norm)
         return vec3(0);
     return v / norm;
@@ -62,7 +71,7 @@ template<> vec3 normalize(vec3 v)
 
 template<> vec4 normalize(vec4 v)
 {
-    float norm = v.sqlen();
+    float norm = v.len();
     if (!norm)
         return vec4(0);
     return v / norm;
@@ -188,42 +197,6 @@ template<> std::ostream &operator<<(std::ostream &stream, mat4 const &m)
 }
 #endif
 
-template<> mat4 mat4::ortho(float left, float right, float bottom,
-                            float top, float near, float far)
-{
-    float invrl = (right != left) ? 1.0f / (right - left) : 0.0f;
-    float invtb = (top != bottom) ? 1.0f / (top - bottom) : 0.0f;
-    float invfn = (far != near) ? 1.0f / (far - near) : 0.0f;
-
-    mat4 ret(0.0f);
-    ret[0][0] = 2.0f * invrl;
-    ret[1][1] = 2.0f * invtb;
-    ret[2][2] = -2.0f * invfn;
-    ret[3][0] = - (right + left) * invrl;
-    ret[3][1] = - (top + bottom) * invtb;
-    ret[3][2] = - (far + near) * invfn;
-    ret[3][3] = 1.0f;
-    return ret;
-}
-
-template<> mat4 mat4::frustum(float left, float right, float bottom,
-                              float top, float near, float far)
-{
-    float invrl = (right != left) ? 1.0f / (right - left) : 0.0f;
-    float invtb = (top != bottom) ? 1.0f / (top - bottom) : 0.0f;
-    float invfn = (far != near) ? 1.0f / (far - near) : 0.0f;
-
-    mat4 ret(0.0f);
-    ret[0][0] = 2.0f * near * invrl;
-    ret[1][1] = 2.0f * near * invtb;
-    ret[2][0] = (right + left) * invrl;
-    ret[2][1] = (top + bottom) * invtb;
-    ret[2][2] = - (far + near) * invfn;
-    ret[2][3] = -1.0f;
-    ret[3][2] = -2.0f * far * near * invfn;
-    return ret;
-}
-
 template<> mat4 mat4::translate(float x, float y, float z)
 {
     mat4 ret(1.0f);
@@ -238,39 +211,12 @@ template<> mat4 mat4::translate(vec3 v)
     return translate(v.x, v.y, v.z);
 }
 
-template<> mat4 mat4::lookat(vec3 eye, vec3 center, vec3 up)
-{
-    vec3 f = normalize(center - eye);
-    vec3 u = normalize(up);
-    vec3 s = normalize(cross(f, u));
-    u = cross(s, f);
-
-    mat4 ret(1.0f);
-    ret[0][0] = s.x;
-    ret[0][1] = s.y;
-    ret[0][2] = s.z;
-    ret[1][0] = u.x;
-    ret[1][1] = u.y;
-    ret[1][2] = u.z;
-    ret[2][0] =-f.x;
-    ret[2][1] =-f.y;
-    ret[2][2] =-f.z;
-    return ret * mat4::translate(-eye);
-}
-
-template<> mat4 mat4::perspective(float theta, float width,
-                                  float height, float near, float far)
+template<> mat4 mat4::rotate(float angle, float x, float y, float z)
 {
-    float t1 = tanf(theta * 0.5f);
-    float t2 = t1 * height / width;
-
-    return frustum(-near * t1, near * t1, -near * t2, near * t2, near, far);
-}
+    angle *= (M_PI / 180.0f);
 
-template<> mat4 mat4::rotate(float theta, float x, float y, float z)
-{
-    float st = sinf(theta);
-    float ct = cosf(theta);
+    float st = sinf(angle);
+    float ct = cosf(angle);
 
     float len = sqrtf(x * x + y * y + z * z);
     float invlen = len ? 1.0f / len : 0.0f;
@@ -299,9 +245,77 @@ template<> mat4 mat4::rotate(float theta, float x, float y, float z)
     return ret;
 }
 
-template<> mat4 mat4::rotate(float theta, vec3 v)
+template<> mat4 mat4::rotate(float angle, vec3 v)
+{
+    return rotate(angle, v.x, v.y, v.z);
+}
+
+template<> mat4 mat4::lookat(vec3 eye, vec3 center, vec3 up)
+{
+    vec3 v3 = normalize(eye - center);
+    vec3 v2 = normalize(up);
+    vec3 v1 = normalize(cross(v2, v3));
+    v2 = cross(v3, v1);
+
+    mat4 orient(1.0f);
+    orient[0][0] = v1.x;
+    orient[0][1] = v2.x;
+    orient[0][2] = v3.x;
+    orient[1][0] = v1.y;
+    orient[1][1] = v2.y;
+    orient[1][2] = v3.y;
+    orient[2][0] = v1.z;
+    orient[2][1] = v2.z;
+    orient[2][2] = v3.z;
+
+    return orient * mat4::translate(-eye);
+}
+
+template<> mat4 mat4::ortho(float left, float right, float bottom,
+                            float top, float near, float far)
+{
+    float invrl = (right != left) ? 1.0f / (right - left) : 0.0f;
+    float invtb = (top != bottom) ? 1.0f / (top - bottom) : 0.0f;
+    float invfn = (far != near) ? 1.0f / (far - near) : 0.0f;
+
+    mat4 ret(0.0f);
+    ret[0][0] = 2.0f * invrl;
+    ret[1][1] = 2.0f * invtb;
+    ret[2][2] = -2.0f * invfn;
+    ret[3][0] = - (right + left) * invrl;
+    ret[3][1] = - (top + bottom) * invtb;
+    ret[3][2] = - (far + near) * invfn;
+    ret[3][3] = 1.0f;
+    return ret;
+}
+
+template<> mat4 mat4::frustum(float left, float right, float bottom,
+                              float top, float near, float far)
+{
+    float invrl = (right != left) ? 1.0f / (right - left) : 0.0f;
+    float invtb = (top != bottom) ? 1.0f / (top - bottom) : 0.0f;
+    float invfn = (far != near) ? 1.0f / (far - near) : 0.0f;
+
+    mat4 ret(0.0f);
+    ret[0][0] = 2.0f * near * invrl;
+    ret[1][1] = 2.0f * near * invtb;
+    ret[2][0] = (right + left) * invrl;
+    ret[2][1] = (top + bottom) * invtb;
+    ret[2][2] = - (far + near) * invfn;
+    ret[2][3] = -1.0f;
+    ret[3][2] = -2.0f * far * near * invfn;
+    return ret;
+}
+
+template<> mat4 mat4::perspective(float fov_y, float width,
+                                  float height, float near, float far)
 {
-    return rotate(theta, v.x, v.y, v.z);
+    fov_y *= (M_PI / 180.0f);
+
+    float t2 = tanf(fov_y * 0.5f);
+    float t1 = t2 * width / height;
+
+    return frustum(-near * t1, near * t1, -near * t2, near * t2, near, far);
 }
 
 } /* namespace lol */

src/matrix.h

@@ -358,14 +358,29 @@ template <typename T> struct Mat4
     T det() const;
     Mat4<T> invert() const;
 
-    static Mat4<T> ortho(T left, T right, T bottom, T top, T near, T far);
-    static Mat4<T> frustum(T left, T right, T bottom, T top, T near, T far);
-    static Mat4<T> lookat(Vec3<T> eye, Vec3<T> center, Vec3<T> up);
-    static Mat4<T> perspective(T theta, T width, T height, T near, T far);
+    /* Helpers for transformation matrices */
     static Mat4<T> translate(T x, T y, T z);
     static Mat4<T> translate(Vec3<T> v);
-    static Mat4<T> rotate(T theta, T x, T y, T z);
-    static Mat4<T> rotate(T theta, Vec3<T> v);
+    static Mat4<T> rotate(T angle, T x, T y, T z);
+    static Mat4<T> rotate(T angle, Vec3<T> v);
+
+    static inline Mat4<T> translate(Mat4<T> mat, Vec3<T> v)
+    {
+        return translate(v) * mat;
+    }
+
+    static inline Mat4<T> rotate(Mat4<T> mat, T angle, Vec3<T> v)
+    {
+        return rotate(angle, v) * mat;
+    }
+
+    /* Helpers for view matrices */
+    static Mat4<T> lookat(Vec3<T> eye, Vec3<T> center, Vec3<T> up);
+
+    /* Helpers for projection matrices */
+    static Mat4<T> ortho(T left, T right, T bottom, T top, T near, T far);
+    static Mat4<T> frustum(T left, T right, T bottom, T top, T near, T far);
+    static Mat4<T> perspective(T fov_y, T width, T height, T near, T far);
 
     void printf() const;
 

src/scene.cpp

@@ -287,8 +287,8 @@ void Scene::Render() // XXX: rename to Blit()
 #if 0
     static float f = 0.0f;
     f += 0.01f;
-    data->model_matrix *= mat4::rotate(0.1f * sinf(f), 1.0f, 0.0f, 0.0f);
-    data->model_matrix *= mat4::rotate(0.3f * cosf(f), 0.0f, 0.0f, 1.0f);
+    data->model_matrix *= mat4::rotate(6.0f * sinf(f), 1.0f, 0.0f, 0.0f);
+    data->model_matrix *= mat4::rotate(17.0f * cosf(f), 0.0f, 0.0f, 1.0f);
 #endif
     data->model_matrix *= mat4::translate(-320.0f, -240.0f, 0.0f);
     // XXX: end of debug stuff

src/video.cpp

@@ -17,6 +17,8 @@
 #if defined _WIN32 && !defined _XBOX
 #   define WIN32_LEAN_AND_MEAN
 #   include <windows.h>
+#   undef near /* Fuck Microsoft */
+#   undef far /* Fuck Microsoft again */
 #endif
 
 #include "core.h"
@@ -79,8 +81,6 @@ void Video::Setup(ivec2 size)
 
 void Video::SetFov(float theta)
 {
-#undef near /* Fuck Microsoft */
-#undef far /* Fuck Microsoft again */
     vec2 size = GetSize();
     float near = -size.x - size.y;
     float far = size.x + size.y;