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-rw-r--r--core/math/geometry.h281
1 files changed, 180 insertions, 101 deletions
diff --git a/core/math/geometry.h b/core/math/geometry.h
index b52b081016..a61bf20c4c 100644
--- a/core/math/geometry.h
+++ b/core/math/geometry.h
@@ -78,8 +78,9 @@ public:
// clamp to segment S1. Else pick arbitrary s (here 0).
if (denom != 0.0) {
s = CLAMP((b * f - c * e) / denom, 0.0, 1.0);
- } else
+ } else {
s = 0.0;
+ }
// Compute point on L2 closest to S1(s) using
// t = Dot((P1 + D1*s) - P2,D2) / Dot(D2,D2) = (b*s + f) / e
t = (b * s + f) / e;
@@ -110,14 +111,18 @@ public:
real_t mub = (d_of(p1, q1, q2, q1) + mua * d_of(q2, q1, p2, p1)) / d_of(q2, q1, q2, q1);
// Clip the value between [0..1] constraining the solution to lie on the original curves.
- if (mua < 0)
+ if (mua < 0) {
mua = 0;
- if (mub < 0)
+ }
+ if (mub < 0) {
mub = 0;
- if (mua > 1)
+ }
+ if (mua > 1) {
mua = 1;
- if (mub > 1)
+ }
+ if (mub > 1) {
mub = 1;
+ }
c1 = p1.lerp(p2, mua);
c2 = q1.lerp(q2, mub);
}
@@ -158,22 +163,22 @@ public:
if (tN < 0.0) { // tc < 0 => the t=0 edge is visible.
tN = 0.0;
// Recompute sc for this edge.
- if (-d < 0.0)
+ if (-d < 0.0) {
sN = 0.0;
- else if (-d > a)
+ } else if (-d > a) {
sN = sD;
- else {
+ } else {
sN = -d;
sD = a;
}
} else if (tN > tD) { // tc > 1 => the t=1 edge is visible.
tN = tD;
// Recompute sc for this edge.
- if ((-d + b) < 0.0)
+ if ((-d + b) < 0.0) {
sN = 0;
- else if ((-d + b) > a)
+ } else if ((-d + b) > a) {
sN = sD;
- else {
+ } else {
sN = (-d + b);
sD = a;
}
@@ -193,34 +198,39 @@ public:
Vector3 e2 = p_v2 - p_v0;
Vector3 h = p_dir.cross(e2);
real_t a = e1.dot(h);
- if (Math::is_zero_approx(a)) // Parallel test.
+ if (Math::is_zero_approx(a)) { // Parallel test.
return false;
+ }
real_t f = 1.0 / a;
Vector3 s = p_from - p_v0;
real_t u = f * s.dot(h);
- if (u < 0.0 || u > 1.0)
+ if (u < 0.0 || u > 1.0) {
return false;
+ }
Vector3 q = s.cross(e1);
real_t v = f * p_dir.dot(q);
- if (v < 0.0 || u + v > 1.0)
+ if (v < 0.0 || u + v > 1.0) {
return false;
+ }
// At this stage we can compute t to find out where
// the intersection point is on the line.
real_t t = f * e2.dot(q);
if (t > 0.00001) { // ray intersection
- if (r_res)
+ if (r_res) {
*r_res = p_from + p_dir * t;
+ }
return true;
- } else // This means that there is a line intersection but not a ray intersection.
+ } else { // This means that there is a line intersection but not a ray intersection.
return false;
+ }
}
static inline bool segment_intersects_triangle(const Vector3 &p_from, const Vector3 &p_to, const Vector3 &p_v0, const Vector3 &p_v1, const Vector3 &p_v2, Vector3 *r_res = nullptr) {
@@ -229,67 +239,78 @@ public:
Vector3 e2 = p_v2 - p_v0;
Vector3 h = rel.cross(e2);
real_t a = e1.dot(h);
- if (Math::is_zero_approx(a)) // Parallel test.
+ if (Math::is_zero_approx(a)) { // Parallel test.
return false;
+ }
real_t f = 1.0 / a;
Vector3 s = p_from - p_v0;
real_t u = f * s.dot(h);
- if (u < 0.0 || u > 1.0)
+ if (u < 0.0 || u > 1.0) {
return false;
+ }
Vector3 q = s.cross(e1);
real_t v = f * rel.dot(q);
- if (v < 0.0 || u + v > 1.0)
+ if (v < 0.0 || u + v > 1.0) {
return false;
+ }
// At this stage we can compute t to find out where
// the intersection point is on the line.
real_t t = f * e2.dot(q);
if (t > CMP_EPSILON && t <= 1.0) { // Ray intersection.
- if (r_res)
+ if (r_res) {
*r_res = p_from + rel * t;
+ }
return true;
- } else // This means that there is a line intersection but not a ray intersection.
+ } else { // This means that there is a line intersection but not a ray intersection.
return false;
+ }
}
static inline bool segment_intersects_sphere(const Vector3 &p_from, const Vector3 &p_to, const Vector3 &p_sphere_pos, real_t p_sphere_radius, Vector3 *r_res = nullptr, Vector3 *r_norm = nullptr) {
Vector3 sphere_pos = p_sphere_pos - p_from;
Vector3 rel = (p_to - p_from);
real_t rel_l = rel.length();
- if (rel_l < CMP_EPSILON)
+ if (rel_l < CMP_EPSILON) {
return false; // Both points are the same.
+ }
Vector3 normal = rel / rel_l;
real_t sphere_d = normal.dot(sphere_pos);
real_t ray_distance = sphere_pos.distance_to(normal * sphere_d);
- if (ray_distance >= p_sphere_radius)
+ if (ray_distance >= p_sphere_radius) {
return false;
+ }
real_t inters_d2 = p_sphere_radius * p_sphere_radius - ray_distance * ray_distance;
real_t inters_d = sphere_d;
- if (inters_d2 >= CMP_EPSILON)
+ if (inters_d2 >= CMP_EPSILON) {
inters_d -= Math::sqrt(inters_d2);
+ }
// Check in segment.
- if (inters_d < 0 || inters_d > rel_l)
+ if (inters_d < 0 || inters_d > rel_l) {
return false;
+ }
Vector3 result = p_from + normal * inters_d;
- if (r_res)
+ if (r_res) {
*r_res = result;
- if (r_norm)
+ }
+ if (r_norm) {
*r_norm = (result - p_sphere_pos).normalized();
+ }
return true;
}
@@ -297,8 +318,9 @@ public:
static inline bool segment_intersects_cylinder(const Vector3 &p_from, const Vector3 &p_to, real_t p_height, real_t p_radius, Vector3 *r_res = nullptr, Vector3 *r_norm = nullptr) {
Vector3 rel = (p_to - p_from);
real_t rel_l = rel.length();
- if (rel_l < CMP_EPSILON)
+ if (rel_l < CMP_EPSILON) {
return false; // Both points are the same.
+ }
// First check if they are parallel.
Vector3 normal = (rel / rel_l);
@@ -315,13 +337,15 @@ public:
real_t dist = z_dir.dot(p_from);
- if (dist >= p_radius)
+ if (dist >= p_radius) {
return false; // Too far away.
+ }
// Convert to 2D.
real_t w2 = p_radius * p_radius - dist * dist;
- if (w2 < CMP_EPSILON)
+ if (w2 < CMP_EPSILON) {
return false; // Avoid numerical error.
+ }
Size2 size(Math::sqrt(w2), p_height * 0.5);
Vector3 x_dir = z_dir.cross(Vector3(0, 0, 1)).normalized();
@@ -341,15 +365,17 @@ public:
real_t cmin, cmax;
if (seg_from < seg_to) {
- if (seg_from > box_end || seg_to < box_begin)
+ if (seg_from > box_end || seg_to < box_begin) {
return false;
+ }
real_t length = seg_to - seg_from;
cmin = (seg_from < box_begin) ? ((box_begin - seg_from) / length) : 0;
cmax = (seg_to > box_end) ? ((box_end - seg_from) / length) : 1;
} else {
- if (seg_to > box_end || seg_from < box_begin)
+ if (seg_to > box_end || seg_from < box_begin) {
return false;
+ }
real_t length = seg_to - seg_from;
cmin = (seg_from > box_end) ? (box_end - seg_from) / length : 0;
cmax = (seg_to < box_begin) ? (box_begin - seg_from) / length : 1;
@@ -359,10 +385,12 @@ public:
min = cmin;
axis = i;
}
- if (cmax < max)
+ if (cmax < max) {
max = cmax;
- if (max < min)
+ }
+ if (max < min) {
return false;
+ }
}
// Convert to 3D again.
@@ -378,10 +406,12 @@ public:
res_normal.normalize();
- if (r_res)
+ if (r_res) {
*r_res = result;
- if (r_norm)
+ }
+ if (r_norm) {
*r_norm = res_normal;
+ }
return true;
}
@@ -392,8 +422,9 @@ public:
Vector3 rel = p_to - p_from;
real_t rel_l = rel.length();
- if (rel_l < CMP_EPSILON)
+ if (rel_l < CMP_EPSILON) {
return false;
+ }
Vector3 dir = rel / rel_l;
@@ -404,15 +435,17 @@ public:
real_t den = p.normal.dot(dir);
- if (Math::abs(den) <= CMP_EPSILON)
+ if (Math::abs(den) <= CMP_EPSILON) {
continue; // Ignore parallel plane.
+ }
real_t dist = -p.distance_to(p_from) / den;
if (den > 0) {
// Backwards facing plane.
- if (dist < max)
+ if (dist < max) {
max = dist;
+ }
} else {
// Front facing plane.
if (dist > min) {
@@ -422,13 +455,16 @@ public:
}
}
- if (max <= min || min < 0 || min > rel_l || min_index == -1) // Exit conditions.
+ if (max <= min || min < 0 || min > rel_l || min_index == -1) { // Exit conditions.
return false; // No intersection.
+ }
- if (p_res)
+ if (p_res) {
*p_res = p_from + dir * min;
- if (p_norm)
+ }
+ if (p_norm) {
*p_norm = p_planes[min_index].normal;
+ }
return true;
}
@@ -437,25 +473,28 @@ public:
Vector3 p = p_point - p_segment[0];
Vector3 n = p_segment[1] - p_segment[0];
real_t l2 = n.length_squared();
- if (l2 < 1e-20)
+ if (l2 < 1e-20) {
return p_segment[0]; // Both points are the same, just give any.
+ }
real_t d = n.dot(p) / l2;
- if (d <= 0.0)
+ if (d <= 0.0) {
return p_segment[0]; // Before first point.
- else if (d >= 1.0)
+ } else if (d >= 1.0) {
return p_segment[1]; // After first point.
- else
+ } else {
return p_segment[0] + n * d; // Inside.
+ }
}
static Vector3 get_closest_point_to_segment_uncapped(const Vector3 &p_point, const Vector3 *p_segment) {
Vector3 p = p_point - p_segment[0];
Vector3 n = p_segment[1] - p_segment[0];
real_t l2 = n.length_squared();
- if (l2 < 1e-20)
+ if (l2 < 1e-20) {
return p_segment[0]; // Both points are the same, just give any.
+ }
real_t d = n.dot(p) / l2;
@@ -466,17 +505,19 @@ public:
Vector2 p = p_point - p_segment[0];
Vector2 n = p_segment[1] - p_segment[0];
real_t l2 = n.length_squared();
- if (l2 < 1e-20)
+ if (l2 < 1e-20) {
return p_segment[0]; // Both points are the same, just give any.
+ }
real_t d = n.dot(p) / l2;
- if (d <= 0.0)
+ if (d <= 0.0) {
return p_segment[0]; // Before first point.
- else if (d >= 1.0)
+ } else if (d >= 1.0) {
return p_segment[1]; // After first point.
- else
+ } else {
return p_segment[0] + n * d; // Inside.
+ }
}
static bool is_point_in_triangle(const Vector2 &s, const Vector2 &a, const Vector2 &b, const Vector2 &c) {
@@ -486,8 +527,9 @@ public:
bool orientation = an.cross(bn) > 0;
- if ((bn.cross(cn) > 0) != orientation)
+ if ((bn.cross(cn) > 0) != orientation) {
return false;
+ }
return (cn.cross(an) > 0) == orientation;
}
@@ -496,8 +538,9 @@ public:
Vector2 p = p_point - p_segment[0];
Vector2 n = p_segment[1] - p_segment[0];
real_t l2 = n.length_squared();
- if (l2 < 1e-20)
+ if (l2 < 1e-20) {
return p_segment[0]; // Both points are the same, just give any.
+ }
real_t d = n.dot(p) / l2;
@@ -524,24 +567,28 @@ public:
Vector2 D = p_to_b - p_from_a;
real_t ABlen = B.dot(B);
- if (ABlen <= 0)
+ if (ABlen <= 0) {
return false;
+ }
Vector2 Bn = B / ABlen;
C = Vector2(C.x * Bn.x + C.y * Bn.y, C.y * Bn.x - C.x * Bn.y);
D = Vector2(D.x * Bn.x + D.y * Bn.y, D.y * Bn.x - D.x * Bn.y);
- if ((C.y < 0 && D.y < 0) || (C.y >= 0 && D.y >= 0))
+ if ((C.y < 0 && D.y < 0) || (C.y >= 0 && D.y >= 0)) {
return false;
+ }
real_t ABpos = D.x + (C.x - D.x) * D.y / (D.y - C.y);
// Fail if segment C-D crosses line A-B outside of segment A-B.
- if (ABpos < 0 || ABpos > 1.0)
+ if (ABpos < 0 || ABpos > 1.0) {
return false;
+ }
// (4) Apply the discovered position to line A-B in the original coordinate system.
- if (r_result)
+ if (r_result) {
*r_result = p_from_a + B * ABpos;
+ }
return true;
}
@@ -551,18 +598,21 @@ public:
Vector3 n1 = (p_point - p_v3).cross(p_point - p_v2);
- if (face_n.dot(n1) < 0)
+ if (face_n.dot(n1) < 0) {
return false;
+ }
Vector3 n2 = (p_v1 - p_v3).cross(p_v1 - p_point);
- if (face_n.dot(n2) < 0)
+ if (face_n.dot(n2) < 0) {
return false;
+ }
Vector3 n3 = (p_v1 - p_point).cross(p_v1 - p_v2);
- if (face_n.dot(n3) < 0)
+ if (face_n.dot(n3) < 0) {
return false;
+ }
return true;
}
@@ -570,8 +620,10 @@ public:
static inline bool triangle_sphere_intersection_test(const Vector3 *p_triangle, const Vector3 &p_normal, const Vector3 &p_sphere_pos, real_t p_sphere_radius, Vector3 &r_triangle_contact, Vector3 &r_sphere_contact) {
real_t d = p_normal.dot(p_sphere_pos) - p_normal.dot(p_triangle[0]);
- if (d > p_sphere_radius || d < -p_sphere_radius) // Not touching the plane of the face, return.
+ if (d > p_sphere_radius || d < -p_sphere_radius) {
+ // Not touching the plane of the face, return.
return false;
+ }
Vector3 contact = p_sphere_pos - (p_normal * d);
@@ -663,8 +715,9 @@ public:
// If the term we intend to square root is less than 0 then the answer won't be real,
// so it definitely won't be t in the range 0 to 1.
- if (sqrtterm < 0)
+ if (sqrtterm < 0) {
return -1;
+ }
// If we can assume that the line segment starts outside the circle (e.g. for continuous time collision detection)
// then the following can be skipped and we can just return the equivalent of res1.
@@ -672,10 +725,12 @@ public:
real_t res1 = (-b - sqrtterm) / (2 * a);
real_t res2 = (-b + sqrtterm) / (2 * a);
- if (res1 >= 0 && res1 <= 1)
+ if (res1 >= 0 && res1 <= 1) {
return res1;
- if (res2 >= 0 && res2 <= 1)
+ }
+ if (res2 >= 0 && res2 <= 1) {
return res2;
+ }
return -1;
}
@@ -686,8 +741,9 @@ public:
LOC_OUTSIDE = -1
};
- if (polygon.size() == 0)
+ if (polygon.size() == 0) {
return polygon;
+ }
int *location_cache = (int *)alloca(sizeof(int) * polygon.size());
int inside_count = 0;
@@ -710,7 +766,6 @@ public:
if (outside_count == 0) {
return polygon; // No changes.
-
} else if (inside_count == 0) {
return Vector<Vector3>(); // Empty.
}
@@ -818,15 +873,17 @@ public:
static Vector<int> triangulate_polygon(const Vector<Vector2> &p_polygon) {
Vector<int> triangles;
- if (!Triangulate::triangulate(p_polygon, triangles))
+ if (!Triangulate::triangulate(p_polygon, triangles)) {
return Vector<int>(); //fail
+ }
return triangles;
}
static bool is_polygon_clockwise(const Vector<Vector2> &p_polygon) {
int c = p_polygon.size();
- if (c < 3)
+ if (c < 3) {
return false;
+ }
const Vector2 *p = p_polygon.ptr();
real_t sum = 0;
for (int i = 0; i < c; i++) {
@@ -841,8 +898,9 @@ public:
// Alternate implementation that should be faster.
static bool is_point_in_polygon(const Vector2 &p_point, const Vector<Vector2> &p_polygon) {
int c = p_polygon.size();
- if (c < 3)
+ if (c < 3) {
return false;
+ }
const Vector2 *p = p_polygon.ptr();
Vector2 further_away(-1e20, -1e20);
Vector2 further_away_opposite(1e20, 1e20);
@@ -914,25 +972,29 @@ public:
return (1 << 23) | (1 << 22) | (1 << 21) | (1 << 20);
} else {
int ret = 0;
- if ((p_idx % 8) == 0)
+ if ((p_idx % 8) == 0) {
ret |= (1 << (p_idx + 7));
- else
+ } else {
ret |= (1 << (p_idx - 1));
- if ((p_idx % 8) == 7)
+ }
+ if ((p_idx % 8) == 7) {
ret |= (1 << (p_idx - 7));
- else
+ } else {
ret |= (1 << (p_idx + 1));
+ }
int mask = ret | (1 << p_idx);
- if (p_idx < 8)
+ if (p_idx < 8) {
ret |= 24;
- else
+ } else {
ret |= mask >> 8;
+ }
- if (p_idx >= 16)
+ if (p_idx >= 16) {
ret |= 25;
- else
+ } else {
ret |= mask << 8;
+ }
return ret;
}
@@ -954,15 +1016,17 @@ public:
// Build lower hull.
for (int i = 0; i < n; ++i) {
- while (k >= 2 && vec2_cross(H[k - 2], H[k - 1], P[i]) <= 0)
+ while (k >= 2 && vec2_cross(H[k - 2], H[k - 1], P[i]) <= 0) {
k--;
+ }
H.write[k++] = P[i];
}
// Build upper hull.
for (int i = n - 2, t = k + 1; i >= 0; i--) {
- while (k >= t && vec2_cross(H[k - 2], H[k - 1], P[i]) <= 0)
+ while (k >= t && vec2_cross(H[k - 2], H[k - 1], P[i]) <= 0) {
k--;
+ }
H.write[k++] = P[i];
}
@@ -983,14 +1047,18 @@ public:
#define FINDMINMAX(x0, x1, x2, min, max) \
min = max = x0; \
- if (x1 < min) \
+ if (x1 < min) { \
min = x1; \
- if (x1 > max) \
+ } \
+ if (x1 > max) { \
max = x1; \
- if (x2 < min) \
+ } \
+ if (x2 < min) { \
min = x2; \
- if (x2 > max) \
- max = x2;
+ } \
+ if (x2 > max) { \
+ max = x2; \
+ }
_FORCE_INLINE_ static bool planeBoxOverlap(Vector3 normal, float d, Vector3 maxbox) {
int q;
@@ -1004,10 +1072,12 @@ public:
vmax[q] = -maxbox[q];
}
}
- if (normal.dot(vmin) + d > 0.0f)
+ if (normal.dot(vmin) + d > 0.0f) {
return false;
- if (normal.dot(vmax) + d >= 0.0f)
+ }
+ if (normal.dot(vmax) + d >= 0.0f) {
return true;
+ }
return false;
}
@@ -1024,8 +1094,9 @@ public:
max = p0; \
} \
rad = fa * boxhalfsize.y + fb * boxhalfsize.z; \
- if (min > rad || max < -rad) \
- return false;
+ if (min > rad || max < -rad) { \
+ return false; \
+ }
#define AXISTEST_X2(a, b, fa, fb) \
p0 = a * v0.y - b * v0.z; \
@@ -1038,8 +1109,9 @@ public:
max = p0; \
} \
rad = fa * boxhalfsize.y + fb * boxhalfsize.z; \
- if (min > rad || max < -rad) \
- return false;
+ if (min > rad || max < -rad) { \
+ return false; \
+ }
/*======================== Y-tests ========================*/
#define AXISTEST_Y02(a, b, fa, fb) \
@@ -1053,8 +1125,9 @@ public:
max = p0; \
} \
rad = fa * boxhalfsize.x + fb * boxhalfsize.z; \
- if (min > rad || max < -rad) \
- return false;
+ if (min > rad || max < -rad) { \
+ return false; \
+ }
#define AXISTEST_Y1(a, b, fa, fb) \
p0 = -a * v0.x + b * v0.z; \
@@ -1067,8 +1140,9 @@ public:
max = p0; \
} \
rad = fa * boxhalfsize.x + fb * boxhalfsize.z; \
- if (min > rad || max < -rad) \
- return false;
+ if (min > rad || max < -rad) { \
+ return false; \
+ }
/*======================== Z-tests ========================*/
@@ -1083,8 +1157,9 @@ public:
max = p2; \
} \
rad = fa * boxhalfsize.x + fb * boxhalfsize.y; \
- if (min > rad || max < -rad) \
- return false;
+ if (min > rad || max < -rad) { \
+ return false; \
+ }
#define AXISTEST_Z0(a, b, fa, fb) \
p0 = a * v0.x - b * v0.y; \
@@ -1097,8 +1172,9 @@ public:
max = p0; \
} \
rad = fa * boxhalfsize.x + fb * boxhalfsize.y; \
- if (min > rad || max < -rad) \
- return false;
+ if (min > rad || max < -rad) { \
+ return false; \
+ }
_FORCE_INLINE_ static bool triangle_box_overlap(const Vector3 &boxcenter, const Vector3 boxhalfsize, const Vector3 *triverts) {
/* use separating axis theorem to test overlap between triangle and box */
@@ -1155,18 +1231,21 @@ public:
/* test in X-direction */
FINDMINMAX(v0.x, v1.x, v2.x, min, max);
- if (min > boxhalfsize.x || max < -boxhalfsize.x)
+ if (min > boxhalfsize.x || max < -boxhalfsize.x) {
return false;
+ }
/* test in Y-direction */
FINDMINMAX(v0.y, v1.y, v2.y, min, max);
- if (min > boxhalfsize.y || max < -boxhalfsize.y)
+ if (min > boxhalfsize.y || max < -boxhalfsize.y) {
return false;
+ }
/* test in Z-direction */
FINDMINMAX(v0.z, v1.z, v2.z, min, max);
- if (min > boxhalfsize.z || max < -boxhalfsize.z)
+ if (min > boxhalfsize.z || max < -boxhalfsize.z) {
return false;
+ }
/* Bullet 2: */
/* test if the box intersects the plane of the triangle */
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-22 00:46:38 +0000