path: root/src/maths/maths.h

/**
 * @file maths.h
 * @author your name (you@domain.com)
 * @brief
 * @version 0.1
 * @date 2024-02-24
 * @copyright Copyright (c) 2024
 */
#pragma once

#include <math.h>
#include <stdio.h>
#include "defines.h"
#include "maths_types.h"

// #undef c_static_inline
// #define c_static_inline static

// --- Helpers
#define deg_to_rad(x) (x * 3.14 / 180.0)
#define MIN(a, b) (a < b ? a : b)
#define MAX(a, b) (a > b ? a : b)

// --- Vector Implementations

// Dimension 3
PUB c_static_inline Vec3 vec3_create(f32 x, f32 y, f32 z);
#define vec3(x, y, z) ((Vec3){ x, y, z })
PUB c_static_inline Vec3 vec3_add(Vec3 a, Vec3 b);
PUB c_static_inline Vec3 vec3_sub(Vec3 a, Vec3 b);
PUB c_static_inline Vec3 vec3_mult(Vec3 a, f32 s);
PUB c_static_inline Vec3 vec3_div(Vec3 a, f32 s);

PUB c_static_inline f32 vec3_len_squared(Vec3 a);
PUB c_static_inline f32 vec3_len(Vec3 a);
PUB c_static_inline Vec3 vec3_negate(Vec3 a);
PUB c_static_inline Vec3 vec3_normalise(Vec3 a);

PUB c_static_inline f32 vec3_dot(Vec3 a, Vec3 b);
PUB c_static_inline Vec3 vec3_cross(Vec3 a, Vec3 b);

static const Vec3 VEC3_X = vec3(1.0, 0.0, 0.0);
static const Vec3 VEC3_NEG_X = vec3(-1.0, 0.0, 0.0);
static const Vec3 VEC3_Y = vec3(0.0, 1.0, 0.0);
static const Vec3 VEC3_NEG_Y = vec3(0.0, -1.0, 0.0);
static const Vec3 VEC3_Z = vec3(0.0, 0.0, 1.0);
static const Vec3 VEC3_NEG_Z = vec3(0.0, 0.0, -1.0);
static const Vec3 VEC3_ZERO = vec3(0.0, 0.0, 0.0);
static const Vec3 VEC3_ONES = vec3(1.0, 1.0, 1.0);

static void print_vec3(Vec3 v) {
  printf("{ x: %f, y: %f, z: %f )\n", (f64)v.x, (f64)v.y, (f64)v.z);
}

// TODO: Dimension 2
static Vec2 vec2_create(f32 x, f32 y) { return (Vec2){ x, y }; }
#define vec2(x, y) ((Vec2){ x, y })
static Vec2 vec2_div(Vec2 a, f32 s) { return (Vec2){ a.x / s, a.y / s }; }

// TODO: Dimension 4
static Vec4 vec4_create(f32 x, f32 y, f32 z, f32 w) { return (Vec4){ x, y, z, w }; }
#define vec4(x, y, z, w) (vec4_create(x, y, z, w))
#define VEC4_ZERO ((Vec4){ .x = 0.0, .y = 0.0, .z = 0.0, .w = 0.0 })

// --- Quaternion Implementations

static f32 quat_dot(Quat a, Quat b) { return a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w; }

static Quat quat_normalise(Quat a) {
  f32 length = sqrtf(quat_dot(a, a));  // same as len squared

  return (Quat){ a.x / length, a.y / length, a.z / length, a.w / length };
}

static Quat quat_ident() { return (Quat){ .x = 0.0, .y = 0.0, .z = 0.0, .w = 1.0 }; }

static Quat quat_from_axis_angle(Vec3 axis, f32 angle, bool normalize) {
  const f32 half_angle = 0.5f * angle;
  f32 s = sinf(half_angle);
  f32 c = cosf(half_angle);

  Quat q = (Quat){ s * axis.x, s * axis.y, s * axis.z, c };
  if (normalize) {
    return quat_normalise(q);
  }
  return q;
}

// TODO: grok this.
static Quat quat_slerp(Quat a, Quat b, f32 percentage) {
  Quat out_quaternion;

  Quat q0 = quat_normalise(a);
  Quat q1 = quat_normalise(b);

  // Compute the cosine of the angle between the two vectors.
  f32 dot = quat_dot(q0, q1);

  // If the dot product is negative, slerp won't take
  // the shorter path. Note that v1 and -v1 are equivalent when
  // the negation is applied to all four components. Fix by
  // reversing one quaternion.
  if (dot < 0.0f) {
    q1.x = -q1.x;
    q1.y = -q1.y;
    q1.z = -q1.z;
    q1.w = -q1.w;
    dot = -dot;
  }

  const f32 DOT_THRESHOLD = 0.9995f;
  if (dot > DOT_THRESHOLD) {
    // If the inputs are too close for comfort, linearly interpolate
    // and normalize the result.
    out_quaternion =
        (Quat){ q0.x + ((q1.x - q0.x) * percentage), q0.y + ((q1.y - q0.y) * percentage),
                q0.z + ((q1.z - q0.z) * percentage), q0.w + ((q1.w - q0.w) * percentage) };

    return quat_normalise(out_quaternion);
  }

  // TODO: Are there math functions that take floats instead of doubles?

  // Since dot is in range [0, DOT_THRESHOLD], acos is safe
  f64 theta_0 = cos((f64)dot);            // theta_0 = angle between input vectors
  f64 theta = theta_0 * (f64)percentage;  // theta = angle between v0 and result
  f64 sin_theta = sin((f64)theta);        // compute this value only once
  f64 sin_theta_0 = sin((f64)theta_0);    // compute this value only once

  f32 s0 =
      cos(theta) - (f64)dot * sin_theta / sin_theta_0;  // == sin(theta_0 - theta) / sin(theta_0)
  f32 s1 = sin_theta / sin_theta_0;

  return (Quat){ (q0.x * s0) + (q1.x * s1), (q0.y * s0) + (q1.y * s1), (q0.z * s0) + (q1.z * s1),
                 (q0.w * s0) + (q1.w * s1) };
}

// --- Matrix Implementations

Mat4 mat4_ident();

static Mat4 mat4_translation(Vec3 position) {
  Mat4 out_matrix = mat4_ident();
  out_matrix.data[12] = position.x;
  out_matrix.data[13] = position.y;
  out_matrix.data[14] = position.z;
  return out_matrix;
}

static Mat4 mat4_scale(Vec3 scale) {
  Mat4 out_matrix = mat4_ident();
  out_matrix.data[0] = scale.x;
  out_matrix.data[5] = scale.y;
  out_matrix.data[10] = scale.z;
  return out_matrix;
}

// TODO: double check this
static Mat4 mat4_rotation(Quat rotation) {
  Mat4 out_matrix = mat4_ident();
  Quat n = quat_normalise(rotation);

  out_matrix.data[0] = 1.0f - 2.0f * n.y * n.y - 2.0f * n.z * n.z;
  out_matrix.data[1] = 2.0f * n.x * n.y - 2.0f * n.z * n.w;
  out_matrix.data[2] = 2.0f * n.x * n.z + 2.0f * n.y * n.w;

  out_matrix.data[4] = 2.0f * n.x * n.y + 2.0f * n.z * n.w;
  out_matrix.data[5] = 1.0f - 2.0f * n.x * n.x - 2.0f * n.z * n.z;
  out_matrix.data[6] = 2.0f * n.y * n.z - 2.0f * n.x * n.w;

  out_matrix.data[8] = 2.0f * n.x * n.z - 2.0f * n.y * n.w;
  out_matrix.data[9] = 2.0f * n.y * n.z + 2.0f * n.x * n.w;
  out_matrix.data[10] = 1.0f - 2.0f * n.x * n.x - 2.0f * n.y * n.y;

  return out_matrix;
}

static Mat4 mat4_mult(Mat4 lhs, Mat4 rhs) {
  Mat4 out_matrix = mat4_ident();

  const f32* m1_ptr = lhs.data;
  const f32* m2_ptr = rhs.data;
  f32* dst_ptr = out_matrix.data;

  for (i32 i = 0; i < 4; ++i) {
    for (i32 j = 0; j < 4; ++j) {
      *dst_ptr = m1_ptr[0] * m2_ptr[0 + j] + m1_ptr[1] * m2_ptr[4 + j] + m1_ptr[2] * m2_ptr[8 + j] +
                 m1_ptr[3] * m2_ptr[12 + j];
      dst_ptr++;
    }
    m1_ptr += 4;
  }

  return out_matrix;
}

static Mat4 mat4_transposed(Mat4 matrix) {
  Mat4 out_matrix = mat4_ident();
  out_matrix.data[0] = matrix.data[0];
  out_matrix.data[1] = matrix.data[4];
  out_matrix.data[2] = matrix.data[8];
  out_matrix.data[3] = matrix.data[12];
  out_matrix.data[4] = matrix.data[1];
  out_matrix.data[5] = matrix.data[5];
  out_matrix.data[6] = matrix.data[9];
  out_matrix.data[7] = matrix.data[13];
  out_matrix.data[8] = matrix.data[2];
  out_matrix.data[9] = matrix.data[6];
  out_matrix.data[10] = matrix.data[10];
  out_matrix.data[11] = matrix.data[14];
  out_matrix.data[12] = matrix.data[3];
  out_matrix.data[13] = matrix.data[7];
  out_matrix.data[14] = matrix.data[11];
  out_matrix.data[15] = matrix.data[15];
  return out_matrix;
}

#if defined(CEL_REND_BACKEND_VULKAN)
/** @brief Creates a perspective projection matrix compatible with Vulkan */
c_static_inline Mat4 mat4_perspective(f32 fov_radians, f32 aspect_ratio, f32 near_clip,
                                      f32 far_clip) {
  f32 half_tan_fov = tanf(fov_radians * 0.5f);
  Mat4 out_matrix = { .data = { 0 } };

  out_matrix.data[0] = 1.0f / (aspect_ratio * half_tan_fov);
  out_matrix.data[5] = -1.0f / half_tan_fov;  // Flip Y-axis for Vulkan
  out_matrix.data[10] = -((far_clip + near_clip) / (far_clip - near_clip));
  out_matrix.data[11] = -1.0f;
  out_matrix.data[14] = -((2.0f * far_clip * near_clip) / (far_clip - near_clip));

  return out_matrix;
}
#else
/** @brief Creates a perspective projection matrix */
static inline Mat4 mat4_perspective(f32 fov_radians, f32 aspect_ratio, f32 near_clip,
                                    f32 far_clip) {
  f32 half_tan_fov = tanf(fov_radians * 0.5f);
  Mat4 out_matrix = { .data = { 0 } };
  out_matrix.data[0] = 1.0f / (aspect_ratio * half_tan_fov);
  out_matrix.data[5] = 1.0f / half_tan_fov;
  out_matrix.data[10] = -((far_clip + near_clip) / (far_clip - near_clip));
  out_matrix.data[11] = -1.0f;
  out_matrix.data[14] = -((2.0f * far_clip * near_clip) / (far_clip - near_clip));
  return out_matrix;
}
#endif

/** @brief Creates an orthographic projection matrix */
static inline Mat4 mat4_orthographic(f32 left, f32 right, f32 bottom, f32 top, f32 near_clip,
                                     f32 far_clip) {
  // source: kohi game engine.
  Mat4 out_matrix = mat4_ident();

  f32 lr = 1.0f / (left - right);
  f32 bt = 1.0f / (bottom - top);
  f32 nf = 1.0f / (near_clip - far_clip);

  out_matrix.data[0] = -2.0f * lr;
  out_matrix.data[5] = -2.0f * bt;
  out_matrix.data[10] = 2.0f * nf;

  out_matrix.data[12] = (left + right) * lr;
  out_matrix.data[13] = (top + bottom) * bt;
  out_matrix.data[14] = (far_clip + near_clip) * nf;

  return out_matrix;
}

static inline Mat4 mat4_look_at(Vec3 position, Vec3 target, Vec3 up) {
  Mat4 out_matrix;
  Vec3 z_axis;
  z_axis.x = target.x - position.x;
  z_axis.y = target.y - position.y;
  z_axis.z = target.z - position.z;

  z_axis = vec3_normalise(z_axis);
  Vec3 x_axis = vec3_normalise(vec3_cross(z_axis, up));
  Vec3 y_axis = vec3_cross(x_axis, z_axis);

  out_matrix.data[0] = x_axis.x;
  out_matrix.data[1] = y_axis.x;
  out_matrix.data[2] = -z_axis.x;
  out_matrix.data[3] = 0;
  out_matrix.data[4] = x_axis.y;
  out_matrix.data[5] = y_axis.y;
  out_matrix.data[6] = -z_axis.y;
  out_matrix.data[7] = 0;
  out_matrix.data[8] = x_axis.z;
  out_matrix.data[9] = y_axis.z;
  out_matrix.data[10] = -z_axis.z;
  out_matrix.data[11] = 0;
  out_matrix.data[12] = -vec3_dot(x_axis, position);
  out_matrix.data[13] = -vec3_dot(y_axis, position);
  out_matrix.data[14] = vec3_dot(z_axis, position);
  out_matrix.data[15] = 1.0f;

  return out_matrix;
}

// ...

// --- Transform Implementations

#define TRANSFORM_DEFAULT                                                 \
  ((Transform){ .position = VEC3_ZERO,                                    \
                .rotation = (Quat){ .x = 0., .y = 0., .z = 0., .w = 1. }, \
                .scale = 1.0,                                             \
                .is_dirty = false })

static Transform transform_create(Vec3 pos, Quat rot, Vec3 scale) {
  return (Transform){ .position = pos, .rotation = rot, .scale = scale, .is_dirty = true };
}

Mat4 transform_to_mat(Transform* tf);

// --- Sizing asserts

_Static_assert(alignof(Vec3) == 4, "Vec3 is 4 byte aligned");
_Static_assert(sizeof(Vec3) == 12, "Vec3 is 12 bytes so has no padding");

_Static_assert(alignof(Vec4) == 4, "Vec4 is 4 byte aligned");