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+/**
+ * @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");