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Diffstat (limited to 'archive/src/maths/maths.h')
-rw-r--r-- | archive/src/maths/maths.h | 321 |
1 files changed, 321 insertions, 0 deletions
diff --git a/archive/src/maths/maths.h b/archive/src/maths/maths.h new file mode 100644 index 0000000..e77b81a --- /dev/null +++ b/archive/src/maths/maths.h @@ -0,0 +1,321 @@ +/** + * @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"); |