internal static bool CirclesOverlap(ref fp2 aOrigin, ref fp aRadius, ref fp2 bOrigin,
ref fp bRadius)
{
var radsum = aRadius.value + bRadius.value;
return(DistanceSqr(ref aOrigin, ref bOrigin).value <= ((radsum * radsum) >> fixlut.PRECISION));
}
internal static fp RadiansSignedSkipNormalize(fp2 v1, fp2 v2)
{
var rad = RadiansSkipNormalize(v1, v2);
var sign = Sign(v1.x * v2.y - v1.y * v2.x);
return(rad * sign);
}
internal static void RectangleMinMax(fp2 center, fp2 size, out fp2 min, out fp2 max)
{
min.x = center.x - (size.x * fp.half);
min.y = center.y - (size.y * fp.half);
max.x = center.x + (size.x * fp.half);
max.y = center.y + (size.y * fp.half);
}
internal static void ClampMagnitude(ref fp2 value, ref fp length)
{
if (SqrMagnitude(value).value <= ((length.value * length.value) >> fixlut.PRECISION))
{
return;
}
value = Normalize(value) * length;
}
internal static fp2 Clamp(fp2 value, fp2 min, fp2 max)
{
fp2 r;
r.x = Clamp(value.x, min.x, max.x);
r.y = Clamp(value.y, min.y, max.y);
return(r);
}
internal static fp Distance(fp2 a, fp2 b)
{
fp2 v;
v.x.value = a.x.value - b.x.value;
v.y.value = a.y.value - b.y.value;
return(Magnitude(v));
}
internal static fp2 ClosestPointOnCicle(fp2 center, fp radius, fp2 point)
{
var v = fm.Normalize(point - center);
v *= radius;
v += center;
return(v);
}
//
// internal static bool linecast_collider_fast(fix3 point0, fix3 point1, ref collider2 collider) {
// fix3 intersection;
//
// switch (collider.type) {
// case collider2_types.circle: return linecast_circle_fast_nopoint(ref point0, ref point1, ref collider.circle.center, ref collider.circle.radius);
// case collider2_types.aabb: return linecast_aabb(new line { point0 = point0, point1 = point1 }, collider.aabb, out intersection);
// case collider2_types.oobb: return linecast_oobb(new line { point0 = point0, point1 = point1 }, collider.oobb, out intersection);
// }
//
// throw new NotImplementedException(collider.type.ToString());
// }
//
internal static bool linecast_circle_fast(ref fp2 point0, ref fp2 point1, ref fp2 circle_center,
ref fp circle_radius, out fp2 point)
{
fp2 v;
fp2 z;
fp2 z_normalized;
fp z_magnitude;
v.x.value = point0.x.value - circle_center.x.value;
v.y.value = point0.y.value - circle_center.y.value;
z.x.value = point1.x.value - point0.x.value;
z.y.value = point1.y.value - point0.y.value;
z_normalized = z;
z_magnitude = default(fp);
Normalize(ref z_normalized, ref z_magnitude);
var b = Dot(ref v, ref z_normalized).value;
var c = Dot(ref v, ref v).value - ((circle_radius.value * circle_radius.value) >> fixlut.PRECISION);
if (c > fp.RAW_ZERO && b > fp.RAW_ZERO)
{
goto MISS;
}
var d = ((b * b) >> fixlut.PRECISION) - c;
if (d < fp.RAW_ZERO)
{
goto MISS;
}
var distance = -b - Sqrt_Raw(d);
if (distance <= z_magnitude.value)
{
if (distance < fp.RAW_ZERO)
{
point = point0;
}
else
{
point = point0;
point.x.value += ((z_normalized.x.value * distance) >> fixlut.PRECISION);
point.y.value += ((z_normalized.y.value * distance) >> fixlut.PRECISION);
}
return(true);
}
MISS:
point = fp2.zero;
return(false);
}
internal static fp DistanceSqr(ref fp2 a, ref fp2 b)
{
var x = a.x.value - b.x.value;
var z = a.y.value - b.y.value;
fp r;
r.value = ((x * x) >> fixlut.PRECISION) + ((z * z) >> fixlut.PRECISION);
return(r);
}
internal static bool PointInTriangleFast(ref fp2 pt, ref fp2 p0, ref fp2 p1, ref fp2 p2)
{
bool b1, b2, b3;
b1 = Sign(ref pt, ref p0, ref p1) < fp.RAW_ZERO;
b2 = Sign(ref pt, ref p1, ref p2) < fp.RAW_ZERO;
b3 = Sign(ref pt, ref p2, ref p0) < fp.RAW_ZERO;
return((b1 == b2) && (b2 == b3));
}
internal static fp SqrMagnitude(ref fp2 v)
{
fp r;
r.value =
((v.x.value * v.x.value) >> fixlut.PRECISION) +
((v.y.value * v.y.value) >> fixlut.PRECISION);
return(r);
}
internal static fp2 Reflect(fp2 vector, fp2 normal)
{
fp dot = (vector.x * normal.x) + (vector.y * normal.y);
fp2 result;
result.x = vector.x - ((fp.two * dot) * normal.x);
result.y = vector.y - ((fp.two * dot) * normal.y);
return(result);
}
internal static fp Dot(ref fp2 a, ref fp2 b)
{
var x = ((a.x.value * b.x.value) >> fixlut.PRECISION);
var z = ((a.y.value * b.y.value) >> fixlut.PRECISION);
fp r;
r.value = x + z;
return(r);
}
internal static fp2 Rotate(fp2 vector, fp rotation)
{
var cs = fixmath.Cos(rotation);
var sn = fixmath.Sin(rotation);
var px = (vector.x * cs) - (vector.y * sn);
var pz = (vector.x * sn) + (vector.y * cs);
vector.x = px;
vector.y = pz;
return(vector);
}
public static bool AABBsIntersects(fp2 aMin, fp2 aMax, fp2 bMin, fp2 bMax)
{
if (aMax.x < bMin.x || aMin.x > bMax.x)
{
return(false);
}
if (aMax.y < bMin.y || aMin.y > bMax.y)
{
return(false);
}
return(true);
}
internal static void Normalize(ref fp2 v, ref fp m)
{
m = Magnitude(v);
if (m.value <= fp.epsilon.value)
{
v = default(fp2);
return;
}
v.x.value = ((v.x.value << fixlut.PRECISION) / m.value);
v.y.value = ((v.y.value << fixlut.PRECISION) / m.value);
}
internal static bool LinesIntersect(fp2 p, fp2 p2, fp2 q, fp2 q2, out fp2 intersection)
{
intersection = fp2.zero;
var r = p2 - p;
var s = q2 - q;
var rxs = Cross(r, s);
var qpxr = Cross(q - p, r);
// If r x s = 0 and (q - p) x r = 0, then the two lines are collinear.
if (rxs == fp.zero && qpxr == fp.zero)
{
// 1. If either 0 <= (q - p) * r <= r * r or 0 <= (p - q) * s <= * s
// then the two lines are overlapping,
//if (considerCollinearOverlapAsIntersect)
// if ((0 <= (q - p) * r && (q - p) * r <= r * r) || (0 <= (p - q) * s && (p - q) * s <= s * s))
// return true;
// 2. If neither 0 <= (q - p) * r = r * r nor 0 <= (p - q) * s <= s * s
// then the two lines are collinear but disjoint.
// No need to implement this expression, as it follows from the expression above.
return(false);
}
// 3. If r x s = 0 and (q - p) x r != 0, then the two lines are parallel and non-intersecting.
if (rxs == fp.zero && qpxr != fp.zero)
{
return(false);
}
// t = (q - p) x s / (r x s)
var t = Cross(q - p, s) / rxs;
// u = (q - p) x r / (r x s)
var u = Cross(q - p, r) / rxs;
// 4. If r x s != 0 and 0 <= t <= 1 and 0 <= u <= 1
// the two line segments meet at the point p + t r = q + u s.
if (rxs != fp.zero && (fp.zero <= t && t <= fp.one) && (fp.zero <= u && u <= fp.one))
{
// We can calculate the intersection point using either t or u.
intersection = p + t * r;
// An intersection was found.
return(true);
}
// 5. Otherwise, the two line segments are not parallel but do not intersect.
return(false);
}
internal static bool LinesIntersectFast(ref fp2 p, ref fp2 p2, ref fp2 q, ref fp2 q2)
{
// manually inlined fix3 subtract
var r = default(fp2);
r.x.value = p2.x.value - p.x.value;
r.y.value = p2.y.value - p.y.value;
// manually inlined fix3 subtract
var s = default(fp2);
s.x.value = q2.x.value - q.x.value;
s.y.value = q2.y.value - q.y.value;
// manually inlined fix3 subtract
var qp = default(fp2);
qp.x.value = q.x.value - p.x.value;
qp.y.value = q.y.value - p.y.value;
// r crossed with s
long r_x_s = CrossFast(ref r, ref s);
// qp crossed with r
long qp_x_r = CrossFast(ref qp, ref r);
// r x s = 0 and (q - p) x r = 0, lines are collinear
if (r_x_s == fp.RAW_ZERO && qp_x_r == fp.RAW_ZERO)
{
return(false);
}
// r x s = 0 and (q - p) x r != 0, lines are parallel
if (r_x_s == fp.RAW_ZERO && qp_x_r != fp.RAW_ZERO)
{
return(false);
}
// t = (q - p) x s / (r x s)
long t = (CrossFast(ref qp, ref s) << fixlut.PRECISION) / r_x_s;
// u = (q - p) x r / (r x s)
long u = (CrossFast(ref qp, ref r) << fixlut.PRECISION) / r_x_s;
// r x s != 0 and 0 <= t <= 1 and 0 <= u <= 1
return(r_x_s != fp.RAW_ZERO && (fp.RAW_ZERO <= t && t <= fp.RAW_ONE) &&
(fp.RAW_ZERO <= u && u <= fp.RAW_ONE));
}
internal static fp RadiansSkipNormalize(fp2 from, fp2 to)
{
var dot = Dot(from, to);
return(Acos(Clamp(dot, -fp.one, +fp.one)));
}
internal static fp2 Max(fp2 a, fp2 b)
{
return(new fp2(Max(a.x, b.x), Max(a.y, b.y)));
}
internal static fp Cross(fp2 a, fp2 b)
{
return((a.x * b.y) - (a.y * b.x));
}
internal static fp SqrMagnitude(fp2 v)
{
return(SqrMagnitude(ref v));
}
internal static fp Magnitude(fp2 value)
{
return(Sqrt(SqrMagnitude(value)));
}
internal static fp2 ClampMagnitude(fp2 value, fp length)
{
ClampMagnitude(ref value, ref length);
return(value);
}
internal static fp DistanceSqr(fp2 a, fp2 b)
{
return(DistanceSqr(ref a, ref b));
}
internal static fp2 Lerp(fp2 from, fp2 to, fp t)
{
t = Clamp01(t);
return(new fp2(from.x + (to.x - from.x) * t, from.y + (to.y - from.y) * t));
}
internal static fp2 TriangleCenter(fp2 v0, fp2 v1, fp2 v2)
{
return(Lerp(Lerp(v0, v1, fp.half), v2, fp.half));
}
internal static void Normalize(ref fp2 v)
{
fp m = default(fp);
Normalize(ref v, ref m);
}
internal static fp2 Normalize(fp2 v)
{
Normalize(ref v);
return(v);
}
internal static fp Angle(fp2 from, fp2 to)
{
return(Radians(from, to) * fp.rad2deg);
}