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// This file is part of the 64k demo project.
// It provides shared vector, matrix and animation utilities, templatized and
// inlined.
#pragma once
#include <cmath>
// --- Configuration ---
#define USE_VEC2
#define USE_VEC3
#define USE_VEC4
#define USE_QUAT
#define USE_MAT4
#define USE_EASING
#define USE_SPRING
// --- Operator Macro ---
// T: Class Name (e.g., vec3)
// N: Number of active components for math (e.g., 3)
#define VEC_OPERATORS(T, N) \
float& operator[](int i) { return v[i]; } \
const float& operator[](int i) const { return v[i]; } \
T& operator+=(const T& r) { for(int i=0; i<N; ++i) v[i]+=r.v[i]; return *this; } \
T& operator-=(const T& r) { for(int i=0; i<N; ++i) v[i]-=r.v[i]; return *this; } \
T& operator*=(float s) { for(int i=0; i<N; ++i) v[i]*=s; return *this; } \
T operator+(const T& r) const { T res(*this); res += r; return res; } \
T operator-(const T& r) const { T res(*this); res -= r; return res; } \
T operator*(float s) const { T res(*this); res *= s; return res; } \
T operator-() const { T res; for(int i=0; i<N; ++i) res.v[i] = -v[i]; return res; } \
static float dot(const T& a, const T& b) { float s=0; for(int i=0; i<N; ++i) s+=a.v[i]*b.v[i]; return s; } \
float dot(const T& a) const { return dot(*this, a); } \
float norm() const { return std::sqrt(dot(*this, *this)); } \
float len() const { return norm(); } \
float inv_norm() const { float l2 = dot(*this, *this); return l2 > 0 ? 1.0f/std::sqrt(l2) : 0; } \
T normalize() const { return (*this) * inv_norm(); }
#ifdef USE_VEC2
struct vec2 {
union { struct { float x, y; }; float v[2]; };
vec2(float x=0, float y=0) : x(x), y(y) {}
VEC_OPERATORS(vec2, 2)
};
#endif
#ifdef USE_VEC3
struct vec3 {
union {
struct { float x, y, z; float _; }; // _ is padding for 16-byte alignment
float v[4]; // Size 4 to match alignment
};
vec3(float x=0, float y=0, float z=0) : x(x), y(y), z(z), _(0) {}
VEC_OPERATORS(vec3, 3) // Operators only touch x,y,z (indices 0,1,2)
static vec3 cross(vec3 a, vec3 b) { return {a.y*b.z-a.z*b.y, a.z*b.x-a.x*b.z, a.x*b.y-a.y*b.x}; }
};
#endif
#ifdef USE_VEC4
struct vec4 {
union { struct { float x, y, z, w; }; float v[4]; };
vec4(float x=0, float y=0, float z=0, float w=0) : x(x), y(y), z(z), w(w) {}
VEC_OPERATORS(vec4, 4)
};
#endif
#ifdef USE_MAT4
struct mat4 {
float m[16] = {1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1}; // Identity (Column-Major)
static mat4 perspective(float fov, float asp, float n, float f) {
mat4 r = {}; float t = 1.0f/std::tan(fov*0.5f);
r.m[0]=t/asp; r.m[5]=t; r.m[10]=f/(n-f); r.m[11]=-1; r.m[14]=(n*f)/(n-f);
return r;
}
static mat4 look_at(vec3 eye, vec3 center, vec3 up) {
vec3 f = (center - eye).normalize();
vec3 s = vec3::cross(f, up).normalize();
vec3 u = vec3::cross(s, f);
mat4 res;
res.m[0] = s.x; res.m[4] = s.y; res.m[8] = s.z;
res.m[1] = u.x; res.m[5] = u.y; res.m[9] = u.z;
res.m[2] =-f.x; res.m[6] =-f.y; res.m[10]=-f.z;
res.m[12]=-vec3::dot(s, eye); res.m[13]=-vec3::dot(u, eye); res.m[14]= vec3::dot(f, eye);
return res;
}
};
#endif
#ifdef USE_QUAT
struct quat {
union { struct { float x, y, z, w; }; float v[4]; };
quat(float x=0, float y=0, float z=0, float w=1) : x(x), y(y), z(z), w(w) {}
VEC_OPERATORS(quat, 4)
quat operator*(const quat& q) const {
return { w*q.x + x*q.w + y*q.z - z*q.y, w*q.y - x*q.z + y*q.w + z*q.x,
w*q.z + x*q.y - y*q.x + z*q.w, w*q.w - x*q.x - y*q.y - z*q.z };
}
static quat from_axis(vec3 a, float ang) {
float s = std::sin(ang*0.5f); return {a.x*s, a.y*s, a.z*s, std::cos(ang*0.5f)};
}
static quat from_to(vec3 a, vec3 b) {
float d = vec3::dot(a, b); vec3 axis = vec3::cross(a, b);
if (d < -0.9999f) return {0, 1, 0, 0};
float s = std::sqrt((1.0f + d) * 2.0f), inv_s = 1.0f/s;
return {axis.x*inv_s, axis.y*inv_s, axis.z*inv_s, s*0.5f};
}
static quat look_at(vec3 eye, vec3 target, vec3 up) {
vec3 f = (target - eye).normalize();
vec3 r = vec3::cross(f, up).normalize();
vec3 u = vec3::cross(r, f);
float m00 = r.x, m11 = u.y, m22 = -f.z, tr = m00 + m11 + m22;
if (tr > 0) {
float s = std::sqrt(tr + 1.0f) * 2.0f;
return { (u.z - (-f.y)) / s, ((-f.x) - r.z) / s, (r.y - u.x) / s, 0.25f * s };
} else if ((m00 > m11) && (m00 > m22)) {
float s = std::sqrt(1.0f + m00 - m11 - m22) * 2.0f;
return { 0.25f * s, (r.y + u.x) / s, ((-f.x) + r.z) / s, (u.z - (-f.y)) / s };
} else if (m11 > m22) {
float s = std::sqrt(1.0f + m11 - m00 - m22) * 2.0f;
return { (r.y + u.x) / s, 0.25f * s, (u.z + (-f.y)) / s, ((-f.x) - r.z) / s };
} else {
float s = std::sqrt(1.0f + m22 - m00 - m11) * 2.0f;
return { ((-f.x) + r.z) / s, (u.z + (-f.y)) / s, 0.25f * s, (r.y - u.x) / s };
}
}
vec3 rotate(vec3 v_in) const {
vec3 qv(x, y, z), t = vec3::cross(qv, v_in) * 2.0f;
return v_in + t * w + vec3::cross(qv, t);
}
mat4 to_mat() const {
mat4 r; float x2=x+x, y2=y+y, z2=z+z, xx=x*x2, xy=x*y2, xz=x*z2, yy=y*y2, yz=y*z2, zz=z*z2, wx=w*x2, wy=w*y2, wz=w*z2;
r.m[0]=1-(yy+zz); r.m[4]=xy-wz; r.m[8]=xz+wy; r.m[1]=xy+wz; r.m[5]=1-(xx+zz); r.m[9]=yz-wx; r.m[2]=xz-wy; r.m[6]=yz+wx; r.m[10]=1-(xx+yy);
return r;
}
};
inline quat slerp(quat a, quat b, float t) {
float d = a.x*b.x + a.y*b.y + a.z*b.z + a.w*b.w;
if (d < 0) { b = b * -1.0f; d = -d; }
if (d > 0.9995f) { // Linear fall-back
quat r; for(int i=0;i<4;++i) r.v[i] = a.v[i] + (b.v[i] - a.v[i])*t;
return r;
}
float th0 = std::acos(d), th = th0*t, s0 = std::sin(th0), s1 = std::sin(th)/s0, s2 = std::sin(th0-th)/s0;
return a * s2 + b * s1;
}
#endif
template<typename T>
inline T lerp(const T& a, const T& b, float t) { return a + (b - a) * t; }
#ifdef USE_EASING
namespace ease {
inline float out_cubic(float t) { return 1.0f - std::pow(1.0f - t, 3.0f); }
inline float in_out_quad(float t) { return t < 0.5f ? 2.0f*t*t : 1.0f - std::pow(-2.0f*t + 2.0f, 2.0f) / 2.0f; }
inline float out_expo(float t) { return t == 1.0f ? 1.0f : 1.0f - std::pow(2.0f, -10.0f * t); }
}
#endif
#ifdef USE_SPRING
namespace spring {
template<typename T>
void solve(T& current, T& velocity, const T& target, float smooth_time, float dt) {
float omega = 2.0f / smooth_time;
float x = omega * dt;
float exp = 1.0f / (1.0f + x + 0.48f*x*x + 0.235f*x*x*x);
T change = current - target;
T temp = (velocity + change * omega) * dt;
velocity = (velocity - temp * omega) * exp;
current = target + (change + temp) * exp;
}
}
#endif
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