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3d_collision_helpers/src/sc_sacd.cpp
Stephen Seo de126aa150 Matrix/Vector multiplication and changes 
Change Mat3 values to column-major (I think?) order.

Add Matrix/Matrix multiplication and tweak Matrix/Vector multiplication.

Fix Matrix rotation values since Mat3 representation changed.

Added more UnitTest tests.
2024-04-29 13:23:47 +09:00

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#include "sc_sacd.h"
// Standard library includes.
#include <cmath>
#include <stdfloat>
#include <vector>
// =============================================================================
// Private Helpers BEGIN
// =============================================================================
constexpr float INV_SQRT2 = 0.70710678118654752440F;
SC_SACD_Vec3 operator+(const SC_SACD_Vec3 &a, const SC_SACD_Vec3 &b) {
return SC_SACD_Vec3{a.x + b.x, a.y + b.y, a.z + b.z};
}
SC_SACD_Vec3 operator-(const SC_SACD_Vec3 &a, const SC_SACD_Vec3 &b) {
return SC_SACD_Vec3{a.x - b.x, a.y - b.y, a.z - b.z};
}
SC_SACD_Vec3 operator*(const SC_SACD_Vec3 &a, float scalar) {
return SC_SACD_Vec3{a.x * scalar, a.y * scalar, a.z * scalar};
}
SC_SACD_Vec3 operator/(const SC_SACD_Vec3 &a, float scalar) {
return SC_SACD_Vec3{a.x / scalar, a.y / scalar, a.z / scalar};
}
SC_SACD_Mat3 operator*(const SC_SACD_Mat3 &a, const SC_SACD_Mat3 &b) {
SC_SACD_Mat3 mat;
mat.x0 = b.x0 * a.x0 + b.y0 * a.x1 + b.z0 * a.x2;
mat.y0 = b.x0 * a.y0 + b.y0 * a.y1 + b.z0 * a.y2;
mat.z0 = b.x0 * a.z0 + b.y0 * a.z1 + b.z0 * a.z2;
mat.x1 = b.x1 * a.x0 + b.y1 * a.x1 + b.z1 * a.x2;
mat.y1 = b.x1 * a.y0 + b.y1 * a.y1 + b.z1 * a.y2;
mat.z1 = b.x1 * a.z0 + b.y1 * a.z1 + b.z1 * a.z2;
mat.x2 = b.x2 * a.x0 + b.y2 * a.x1 + b.z2 * a.x2;
mat.y2 = b.x2 * a.y0 + b.y2 * a.y1 + b.z2 * a.y2;
mat.z2 = b.x2 * a.z0 + b.y2 * a.z1 + b.z2 * a.z2;
return mat;
}
SC_SACD_Vec3 operator*(const SC_SACD_Mat3 &mat, const SC_SACD_Vec3 &vec) {
return SC_SACD_Vec3{vec.x * mat.x0 + vec.y * mat.x1 + vec.z * mat.x2,
vec.x * mat.y0 + vec.y * mat.y1 + vec.z * mat.y2,
vec.x * mat.z0 + vec.y * mat.z1 + vec.z * mat.z2};
}
std::vector<SC_SACD_Vec3> SC_SACD_Get_Box_Normals(
const SC_SACD_Generic_Box *box) {
std::vector<SC_SACD_Vec3> normals;
normals.emplace_back(SC_SACD_Vec3{1.0F, 0.0F, 0.0F});
normals.back() = SC_SACD_Vec3_Rotate(normals.back(), box->x_radians,
box->y_radians, box->z_radians);
normals.emplace_back(SC_SACD_Vec3{0.0F, 1.0F, 0.0F});
normals.back() = SC_SACD_Vec3_Rotate(normals.back(), box->x_radians,
box->y_radians, box->z_radians);
normals.emplace_back(SC_SACD_Vec3{0.0F, 0.0F, 1.0F});
normals.back() = SC_SACD_Vec3_Rotate(normals.back(), box->x_radians,
box->y_radians, box->z_radians);
// Not normalizing the normals on purpose for optimization. It should already
// be normalized as each normal is a rotated unit vector.
return normals;
}
std::vector<SC_SACD_Vec3> SC_SACD_Get_Box_Corners(
const SC_SACD_Generic_Box *box) {
std::vector<SC_SACD_Vec3> corners;
SC_SACD_Vec3 pos{box->x, box->y, box->z};
corners.push_back(
SC_SACD_Vec3_Rotate(SC_SACD_Vec3{-box->width / 2.0F, -box->height / 2.0F,
-box->depth / 2.0F},
box->x_radians, box->y_radians, box->z_radians) +
pos);
corners.push_back(
SC_SACD_Vec3_Rotate(SC_SACD_Vec3{box->width / 2.0F, -box->height / 2.0F,
-box->depth / 2.0F},
box->x_radians, box->y_radians, box->z_radians) +
pos);
corners.push_back(
SC_SACD_Vec3_Rotate(SC_SACD_Vec3{-box->width / 2.0F, box->height / 2.0F,
-box->depth / 2.0F},
box->x_radians, box->y_radians, box->z_radians) +
pos);
corners.push_back(
SC_SACD_Vec3_Rotate(SC_SACD_Vec3{box->width / 2.0F, box->height / 2.0F,
-box->depth / 2.0F},
box->x_radians, box->y_radians, box->z_radians) +
pos);
corners.push_back(
SC_SACD_Vec3_Rotate(SC_SACD_Vec3{-box->width / 2.0F, -box->height / 2.0F,
box->depth / 2.0F},
box->x_radians, box->y_radians, box->z_radians) +
pos);
corners.push_back(
SC_SACD_Vec3_Rotate(SC_SACD_Vec3{box->width / 2.0F, -box->height / 2.0F,
box->depth / 2.0F},
box->x_radians, box->y_radians, box->z_radians) +
pos);
corners.push_back(
SC_SACD_Vec3_Rotate(SC_SACD_Vec3{-box->width / 2.0F, box->height / 2.0F,
box->depth / 2.0F},
box->x_radians, box->y_radians, box->z_radians) +
pos);
corners.push_back(
SC_SACD_Vec3_Rotate(SC_SACD_Vec3{box->width / 2.0F, box->height / 2.0F,
box->depth / 2.0F},
box->x_radians, box->y_radians, box->z_radians) +
pos);
return corners;
}
struct SC_SACD_MinMax {
float min, max;
};
std::vector<SC_SACD_MinMax> SC_SACD_Get_Box_MinMax(
const SC_SACD_Generic_Box *box, const std::vector<SC_SACD_Vec3> &normals) {
std::vector<SC_SACD_MinMax> minmaxes;
std::vector<SC_SACD_Vec3> corners = SC_SACD_Get_Box_Corners(box);
// Assuming normals are not normalized, and will not normalize anyway.
// MinMax count should be same as normals count.
for (const auto &normal : normals) {
SC_SACD_MinMax minmax{INFINITY, -INFINITY};
for (const auto &corner : corners) {
float projected = SC_SACD_Dot_Product(corner, normal);
if (projected > minmax.max) {
minmax.max = projected;
}
if (projected < minmax.min) {
minmax.min = projected;
}
}
minmaxes.push_back(minmax);
}
return minmaxes;
}
// =============================================================================
// Private Helpers END
// =============================================================================
int SC_SACD_AABB_Box_Collision(const SC_SACD_AABB_Box *a,
const SC_SACD_AABB_Box *b) {
float ax_min = a->x - a->width / 2.0F;
float ax_max = a->x + a->width / 2.0F;
float ay_min = a->y - a->height / 2.0F;
float ay_max = a->y + a->height / 2.0F;
float az_min = a->z - a->depth / 2.0F;
float az_max = a->z + a->depth / 2.0F;
float bx_min = b->x - b->width / 2.0F;
float bx_max = b->x + b->width / 2.0F;
float by_min = b->y - b->height / 2.0F;
float by_max = b->y + b->height / 2.0F;
float bz_min = b->z - b->depth / 2.0F;
float bz_max = b->z + b->depth / 2.0F;
return (ax_min < bx_max && ax_max > bx_min && ay_min < by_max &&
ay_max > by_min && az_min < bz_max && az_max > bz_min)
? 1
: 0;
}
int SC_SACD_Generic_Box_Collision(const SC_SACD_Generic_Box *a,
const SC_SACD_Generic_Box *b) {
// Get all normals.
std::vector<SC_SACD_Vec3> normals = SC_SACD_Get_Box_Normals(a);
for (const auto &normal : SC_SACD_Get_Box_Normals(b)) {
normals.push_back(normal);
}
// Get all minmaxes.
std::vector<SC_SACD_MinMax> minmaxes_a = SC_SACD_Get_Box_MinMax(a, normals);
std::vector<SC_SACD_MinMax> minmaxes_b = SC_SACD_Get_Box_MinMax(b, normals);
// Check minmaxes.
for (unsigned int i = 0; i < normals.size(); ++i) {
if (minmaxes_a[i].max < minmaxes_b[i].min ||
minmaxes_b[i].max < minmaxes_a[i].min) {
return 0;
}
}
return 1;
}
int SC_SACD_AABB_Generic_Box_Collision(const SC_SACD_AABB_Box *a,
const SC_SACD_Generic_Box *b) {
SC_SACD_Generic_Box a_conv;
a_conv.x = a->x;
a_conv.y = a->y;
a_conv.z = a->z;
a_conv.width = a->width;
a_conv.height = a->height;
a_conv.depth = a->depth;
a_conv.x_radians = 0.0F;
a_conv.y_radians = 0.0F;
a_conv.z_radians = 0.0F;
return SC_SACD_Generic_Box_Collision(&a_conv, b);
}
int SC_SACD_Sphere_Collision(const SC_SACD_Sphere *a, const SC_SACD_Sphere *b) {
SC_SACD_Vec3 vec{a->x - b->x, a->y - b->y, a->z - b->z};
return (a->radius + b->radius) > std::sqrt(SC_SACD_Dot_Product(vec, vec)) ? 1
: 0;
}
int SC_SACD_Sphere_AABB_Box_Collision(const SC_SACD_Sphere *sphere,
const SC_SACD_AABB_Box *box) {
SC_SACD_Vec3 box_min{
box->x - box->width / 2.0F,
box->y - box->height / 2.0F,
box->z - box->depth / 2.0F,
};
SC_SACD_Vec3 box_max{
box->x + box->width / 2.0F,
box->y + box->height / 2.0F,
box->z + box->depth / 2.0F,
};
SC_SACD_Vec3 clamped{std::max(box_min.x, std::min(sphere->x, box_max.x)),
std::max(box_min.y, std::min(sphere->y, box_max.y)),
std::max(box_min.z, std::min(sphere->z, box_max.z))};
SC_SACD_Vec3 diff = clamped - SC_SACD_Vec3{sphere->x, sphere->y, sphere->z};
float dist = std::sqrt(SC_SACD_Dot_Product(diff, diff));
return dist < sphere->radius;
}
int SC_SACD_Sphere_Box_Collision(const SC_SACD_Sphere *sphere,
const SC_SACD_Generic_Box *box) {
// Adapted from Generic_Box/Generic_Box collision.
// First check plane where normal = box_pos - sphere_pos.
SC_SACD_Vec3 sphere_pos{sphere->x, sphere->y, sphere->z};
SC_SACD_Vec3 sphere_box_normal =
SC_SACD_Vec3{box->x, box->y, box->z} - sphere_pos;
sphere_box_normal =
sphere_box_normal /
std::sqrt(SC_SACD_Dot_Product(sphere_box_normal, sphere_box_normal));
std::vector<SC_SACD_Vec3> normals{sphere_box_normal};
std::vector<SC_SACD_MinMax> box_minmaxes =
SC_SACD_Get_Box_MinMax(box, normals);
float projected_0 = SC_SACD_Dot_Product(
sphere_box_normal, sphere_pos + sphere_box_normal * sphere->radius);
float projected_1 = SC_SACD_Dot_Product(
sphere_box_normal, sphere_pos - sphere_box_normal * sphere->radius);
if (projected_0 < projected_1) {
if (box_minmaxes[0].max < projected_0 ||
box_minmaxes[0].min > projected_1) {
return 0;
}
} else if (box_minmaxes[0].max < projected_1 ||
box_minmaxes[0].min > projected_0) {
return 0;
}
// Next check the planes for the 3 normals of the box.
normals = SC_SACD_Get_Box_Normals(box);
box_minmaxes = SC_SACD_Get_Box_MinMax(box, normals);
for (unsigned int i = 0; i < normals.size(); ++i) {
projected_0 = SC_SACD_Dot_Product(normals[i],
sphere_pos + normals[i] * sphere->radius);
projected_1 = SC_SACD_Dot_Product(normals[i],
sphere_pos - normals[i] * sphere->radius);
if (projected_0 < projected_1) {
if (box_minmaxes[i].max < projected_0 ||
box_minmaxes[i].min > projected_1) {
return 0;
}
} else if (box_minmaxes[i].max < projected_1 ||
box_minmaxes[i].min > projected_0) {
return 0;
}
}
return 1;
}
float SC_SACD_Dot_Product(const SC_SACD_Vec3 a, const SC_SACD_Vec3 b) {
return a.x * b.x + a.y * b.y + a.z * b.z;
}
SC_SACD_Vec3 SC_SACD_Cross_Product(const SC_SACD_Vec3 a, const SC_SACD_Vec3 b) {
return SC_SACD_Vec3{a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z,
a.x * b.y - a.y * b.x};
}
SC_SACD_Mat3 SC_SACD_Mat3_Identity(void) {
return SC_SACD_Mat3{1.0F, 0.0F, 0.0F, 0.0F, 1.0F, 0.0F, 0.0F, 0.0F, 1.0F};
}
SC_SACD_Mat3 SC_SACD_Mat3_Mult(const SC_SACD_Mat3 *a, const SC_SACD_Mat3 *b) {
return (*a) * (*b);
}
SC_SACD_Vec3 SC_SACD_Mat3_Vec3_Mult(const SC_SACD_Mat3 *mat,
const SC_SACD_Vec3 vec) {
return (*mat) * vec;
}
SC_SACD_Vec3 SC_SACD_Vec3_Rotate(const SC_SACD_Vec3 vec, float x_axis,
float y_axis, float z_axis) {
/*
* z_axis counter-clockwise affects x and y.
* [ cos, -sin, 0 ]
* [ sin, cos, 0 ]
* [ 0, 0, 1 ]
*
* x_axis counter-clockwise affects y and z.
* [ 1, 0, 0 ]
* [ 0, cos, -sin ]
* [ 0, sin, cos ]
*
* y_axis counter-clockwise affects x and z.
* [ cos, 0, sin ]
* [ 0, 1, 0 ]
* [ -sin, 0, cos ]
*/
SC_SACD_Mat3 mat;
SC_SACD_Vec3 result;
// About x_axis.
mat = SC_SACD_Rotation_Mat3_XAxis(x_axis);
result = SC_SACD_Mat3_Vec3_Mult(&mat, vec);
// About y_axis.
mat = SC_SACD_Rotation_Mat3_YAxis(y_axis);
result = SC_SACD_Mat3_Vec3_Mult(&mat, result);
// About z_axis.
mat = SC_SACD_Rotation_Mat3_ZAxis(z_axis);
return SC_SACD_Mat3_Vec3_Mult(&mat, result);
}
SC_SACD_Mat3 SC_SACD_Rotation_Mat3_XAxis(float x_radians) {
SC_SACD_Mat3 mat;
mat.x0 = 1.0F;
mat.x1 = 0.0F;
mat.x2 = 0.0F;
mat.y0 = 0.0F;
mat.y1 = std::cos(x_radians);
mat.y2 = -std::sin(x_radians);
mat.z0 = 0.0F;
mat.z1 = -mat.y2;
mat.z2 = mat.y1;
return mat;
}
SC_SACD_Mat3 SC_SACD_Rotation_Mat3_YAxis(float y_radians) {
SC_SACD_Mat3 mat;
mat.x0 = std::cos(y_radians);
mat.x1 = 0.0F;
mat.x2 = std::sin(y_radians);
mat.y0 = 0.0F;
mat.y1 = 1.0F;
mat.y2 = 0.0F;
mat.z0 = -mat.x2;
mat.z1 = 0.0F;
mat.z2 = mat.x0;
return mat;
}
SC_SACD_Mat3 SC_SACD_Rotation_Mat3_ZAxis(float z_radians) {
SC_SACD_Mat3 mat;
mat.x0 = std::cos(z_radians);
mat.x1 = -std::sin(z_radians);
mat.x2 = 0.0F;
mat.y0 = -mat.x1;
mat.y1 = mat.x0;
mat.y2 = 0.0F;
mat.z0 = 0.0F;
mat.z1 = 0.0F;
mat.z2 = 1.0F;
return mat;
}
SC_SACD_Vec3 SC_SACD_Closest_Point_Dir_Normalized(const SC_SACD_Vec3 *pos,
const SC_SACD_Vec3 *dir,
const SC_SACD_Vec3 *point) {
float alpha =
SC_SACD_Dot_Product(*dir, *point) - SC_SACD_Dot_Product(*dir, *pos);
return *pos + *dir * alpha;
}
SC_SACD_Vec3 SC_SACD_Closest_Point(const SC_SACD_Vec3 *pos,
const SC_SACD_Vec3 *dir,
const SC_SACD_Vec3 *point) {
float alpha =
(SC_SACD_Dot_Product(*dir, *point) - SC_SACD_Dot_Product(*dir, *pos)) /
SC_SACD_Dot_Product(*dir, *dir);
return *pos + *dir * alpha;
}
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