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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(); \
}
#if defined(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 /* defined(USE_VEC2) */
#if defined(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 /* defined(USE_VEC3) */
#if defined(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 /* defined(USE_VEC4) */
#if defined(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)
// Array access
float& operator[](int i) {
return m[i];
}
const float& operator[](int i) const {
return m[i];
}
// Matrix multiplication
mat4 operator*(const mat4& r) const {
mat4 res;
for (int col = 0; col < 4; ++col) {
for (int row = 0; row < 4; ++row) {
float sum = 0.0f;
for (int k = 0; k < 4; ++k) {
sum += m[k * 4 + row] * r.m[col * 4 + k];
}
res.m[col * 4 + row] = sum;
}
}
return res;
}
// Vector multiplication (Transform)
vec4 operator*(const vec4& v) const {
vec4 res;
for (int row = 0; row < 4; ++row) {
res.v[row] = m[row] * v.x + m[row + 4] * v.y + m[row + 8] * v.z +
m[row + 12] * v.w;
}
return res;
}
// Translation
static mat4 translate(vec3 t) {
mat4 r; // Identity
r.m[12] = t.x;
r.m[13] = t.y;
r.m[14] = t.z;
return r;
}
// Scaling
static mat4 scale(vec3 s) {
mat4 r; // Identity
r.m[0] = s.x;
r.m[5] = s.y;
r.m[10] = s.z;
return r;
}
// Rotation (Axis-Angle)
static mat4 rotate(vec3 axis, float angle) {
vec3 a = axis.normalize();
float s = std::sin(angle);
float c = std::cos(angle);
float oc = 1.0f - c;
mat4 r;
r.m[0] = oc * a.x * a.x + c;
r.m[1] = oc * a.x * a.y + a.z * s;
r.m[2] = oc * a.x * a.z - a.y * s;
r.m[4] = oc * a.x * a.y - a.z * s;
r.m[5] = oc * a.y * a.y + c;
r.m[6] = oc * a.y * a.z + a.x * s;
r.m[8] = oc * a.x * a.z + a.y * s;
r.m[9] = oc * a.y * a.z - a.x * s;
r.m[10] = oc * a.z * a.z + c;
return r;
}
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 /* defined(USE_MAT4) */
#if defined(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 /* defined(USE_QUAT) */
template <typename T> inline T lerp(const T& a, const T& b, float t) {
return a + (b - a) * t;
}
#if defined(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);
}
} // namespace ease
#endif /* defined(USE_EASING) */
#if defined(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;
}
} // namespace spring
#endif /* defined(USE_SPRING) */
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