/// <summary>
/// Intersects a line segment with the shape and returns the intersection point closest to the beginning of the segment.
/// </summary>
/// <param name="segment">The line segment to intersect.</param>
/// <param name="scalar">A value between 0 and 1 indicating how far along the segment the intersection occurs.</param>
/// <param name="p">The point of the intersection closest to the beginning of the line segment.</param>
/// <returns>Returns a value indicating whether there is an intersection.</returns>
public bool Intersect(ref Segment seg, out float scalar, out Vector3 p)
{
p = Vector3.Zero;
scalar = float.NaN;
Vector3 s, d;
Vector3.Subtract(ref Center, ref seg.P1, out s);
Vector3.Subtract(ref seg.P2, ref seg.P1, out d);
float l2s = Vector3.Dot(s, s);
float r2 = Radius * Radius;
if (l2s <= r2)
{
p = seg.P1;
scalar = 0f;
return true;
}
float tc = Vector3.Dot(s, d) / Vector3.Dot(d, d);
float l2h = (r2 - l2s) / d.LengthSquared() + tc * tc;
if (l2h < 0f) return false;
scalar = tc - (float)Math.Sqrt(l2h);
Vector3.Multiply(ref d, scalar, out p);
Vector3.Add(ref seg.P1, ref p, out p);
return scalar >= 0f && scalar <= 1f;
}
/// <summary>
/// Intersects a line segment with the shape and returns the intersection point closest to the beginning of the segment.
/// </summary>
/// <param name="segment">The line segment to intersect.</param>
/// <param name="scalar">A value between 0 and 1 indicating how far along the segment the intersection occurs.</param>
/// <param name="p">The point of the intersection closest to the beginning of the line segment.</param>
/// <returns>Returns a value indicating whether there is an intersection.</returns>
public bool Intersect(ref Segment segment, out float scalar, out Vector3 p)
{
p = Vector3.Zero;
scalar = float.NaN;
float a, d, e;
Vector3 diff;
Vector3.Subtract(ref segment.P2, ref segment.P1, out diff);
Vector3.Dot(ref segment.P1, ref Normal, out a);
Vector3.Dot(ref P, ref Normal, out d);
Vector3.Dot(ref Normal, ref diff, out e);
if (Math.Abs(e) <= Constants.Epsilon) return false;
scalar = (d - a) / e;
Vector3.Multiply(ref diff, scalar, out p);
Vector3.Add(ref segment.P1, ref p, out p);
return scalar >= 0f && scalar <= 1f;
}
/// <summary>
/// Intersects two line segments.
/// </summary>
/// <param name="sa">The first line segment.</param>
/// <param name="sb">The second line segment.</param>
/// <param name="scalarA">Returns a value between 0 and 1 indicating the point of intersection on the first segment.</param>
/// <param name="scalarB">Returns a value between 0 and 1 indicating the point of intersection on the second segment.</param>
/// <param name="p">Returns the point of intersection, common to both segments.</param>
/// <returns>Returns a value indicating whether there was an intersection.</returns>
public static bool Intersect(ref Segment sa, ref Segment sb, out float scalarA, out float scalarB, out Vector3 p)
{
Vector3 pa;
float dist;
Segment.ClosestPoints(ref sa, ref sb, out scalarA, out pa, out scalarB, out p);
Vector3.DistanceSquared(ref pa, ref p, out dist);
return dist < Constants.Epsilon;
}
/// <summary>
/// Transform the segment using the specified transformation.
/// </summary>
/// <param name="s">The segment to transform.</param>
/// <param name="transform">the transform to apply.</param>
/// <param name="output">Returns the transformed segment.</param>
public static void Transform(ref Segment s, ref Transform transform, out Segment output)
{
Vector3.Transform(ref s.P1, ref transform.Combined, out output.P1);
Vector3.Transform(ref s.P2, ref transform.Combined, out output.P2);
}
/// <summary>
/// Gets the closest two points on two line segments.
/// </summary>
/// <remarks>
/// If the line segments are parallel and overlap in their common direction, then the midpoint of the overlapped portion of line segments
/// is returned.
/// </remarks>
/// <param name="sa">The first line segment.</param>
/// <param name="sb">The second line segment.</param>
/// <param name="scalarA">Returns a value between 0 and 1 indicating the position of the closest point on the first segment.</param>
/// <param name="pa">Returns the closest point on the first segment.</param>
/// <param name="scalarB">Returns a value between 0 and 1 indicating the position of the closest point on the second segment.</param>
/// <param name="pb">Returns the closest point on the second segment.</param>
public static void ClosestPoints(ref Segment sa, ref Segment sb,
out float scalarA, out Vector3 pa, out float scalarB, out Vector3 pb)
{
Vector3 d1, d2, r;
Vector3.Subtract(ref sa.P2, ref sa.P1, out d1);
Vector3.Subtract(ref sb.P2, ref sb.P1, out d2);
Vector3.Subtract(ref sa.P1, ref sb.P1, out r);
float a, e, f;
Vector3.Dot(ref d1, ref d1, out a);
Vector3.Dot(ref d2, ref d2, out e);
Vector3.Dot(ref d2, ref r, out f);
if (a < Constants.Epsilon && e < Constants.Epsilon)
{
// segment a and b are both points
scalarA = scalarB = 0f;
pa = sa.P1;
pb = sb.P1;
return;
}
if (a < Constants.Epsilon)
{
// segment a is a point
scalarA = 0f;
scalarB = MathHelper.Clamp(f / e, 0f, 1f);
}
else
{
float c;
Vector3.Dot(ref d1, ref r, out c);
if (e < Constants.Epsilon)
{
// segment b is a point
scalarB = 0f;
scalarA = MathHelper.Clamp(-c / a, 0f, 1f);
}
else
{
float b;
Vector3.Dot(ref d1, ref d2, out b);
float denom = a * e - b * b;
if (denom < Constants.Epsilon)
{
// segments are parallel
float a1, a2, b1, b2;
Vector3.Dot(ref d2, ref sa.P1, out a1);
Vector3.Dot(ref d2, ref sa.P2, out a2);
Vector3.Dot(ref d2, ref sb.P1, out b1);
Vector3.Dot(ref d2, ref sb.P2, out b2);
if (a1 <= b1 && a2 <= b1)
{
// segment A is completely "before" segment B
scalarA = a2 > a1 ? 1f : 0f;
scalarB = 0f;
}
else if (a1 >= b2 && a2 >= b2)
{
// segment B is completely "before" segment A
scalarA = a2 > a1 ? 0f : 1f;
scalarB = 1f;
}
else
{
// segments A and B overlap, use midpoint of shared length
if (a1 > a2) { f = a1; a1 = a2; a2 = f; }
f = (Math.Min(a2, b2) + Math.Max(a1, b1)) / 2f;
scalarB = (f - b1) / e;
Vector3.Multiply(ref d2, scalarB, out pb);
Vector3.Add(ref sb.P1, ref pb, out pb);
sa.ClosestPointTo(ref pb, out scalarA, out pa);
return;
}
}
else
{
// general case
scalarA = MathHelper.Clamp((b * f - c * e) / denom, 0f, 1f);
scalarB = (b * scalarA + f) / e;
if (scalarB < 0f)
{
scalarB = 0f;
scalarA = MathHelper.Clamp(-c / a, 0f, 1f);
}
else if (scalarB > 1f)
{
scalarB = 1f;
scalarA = MathHelper.Clamp((b - c) / a, 0f, 1f);
}
}
}
}
Vector3.Multiply(ref d1, scalarA, out d1);
Vector3.Multiply(ref d2, scalarB, out d2);
Vector3.Add(ref sa.P1, ref d1, out pa);
Vector3.Add(ref sb.P1, ref d2, out pb);
}
/// <summary>
/// Intersects a segment with this collision skin part and returns the intersection point that is nearest to the
/// beginning of the segment.
/// </summary>
/// <param name="segment">The segment to intersect with.</param>
/// <param name="scalar">Returns a value between 0 and 1 indicating where on the segment the first intersection occurs.</param>
/// <param name="point">Returns the point of the first intersection.</param>
/// <returns>Returns a value indicating whether the segment intersects with the part.</returns>
public override bool Intersect(ref Segment segment, out float scalar, out Vector3 point)
{
Segment bodySeg;
Segment.Transform(ref segment, ref TransformInverse, out bodySeg);
AlignedBox box;
AlignedBox.Fit(ref bodySeg.P1, ref bodySeg.P2, out box);
var tf = Functor;
tf.Segment = bodySeg;
tf.Scalar = float.MaxValue;
tf.Point = Vector3.Zero;
tf.BoundingBox = box;
_body.ProcessTriangles(tf);
scalar = tf.Scalar;
point = tf.Point;
Vector3.Transform(ref point, ref Transform.Combined, out point);
return scalar >= 0f && scalar <= 1f;
}
/// <summary>
/// Intersects a line segment with the shape and returns the intersection point closest to the beginning of the segment.
/// </summary>
/// <param name="segment">The line segment to intersect.</param>
/// <param name="scalar">A value between 0 and 1 indicating how far along the segment the intersection occurs.</param>
/// <param name="p">The point of the intersection closest to the beginning of the line segment.</param>
/// <returns>Returns a value indicating whether there is an intersection.</returns>
public bool Intersect(ref Segment segment, out float scalar, out Vector3 p)
{
Vector3 d, m, n;
float md, nd, dd;
Vector3.Subtract(ref P2, ref P1, out d);
Vector3.Subtract(ref segment.P1, ref P1, out m);
Vector3.Subtract(ref segment.P2, ref segment.P1, out n);
Vector3.Dot(ref d, ref m, out md);
Vector3.Dot(ref d, ref n, out nd);
Vector3.Dot(ref d, ref d, out dd);
if (!(md < 0f && md + nd < 0f) &&
!(md > dd && md + nd > dd))
{
float nn, mn, k;
Vector3.Dot(ref n, ref n, out nn);
Vector3.Dot(ref m, ref n, out mn);
float a = dd * nn - nd * nd;
Vector3.Dot(ref m, ref m, out k);
k -= Radius * Radius;
float c = dd * k - md * md;
if (Math.Abs(a) >= Constants.Epsilon)
{
float b = dd * mn - nd * md;
float discr = b * b - a * c;
if (discr >= 0f)
{
float t = (-b - (float)Math.Sqrt(discr)) / a;
if (t >= 0f && t <= 1f &&
md + t * nd >= 0f &&
md + t * nd <= dd)
{
scalar = t;
Vector3.Multiply(ref n, t, out p);
Vector3.Add(ref segment.P1, ref p, out p);
return true;
}
}
}
}
var cap = new Sphere(P1, Radius);
float s;
scalar = float.MaxValue;
p = Vector3.Zero;
Vector3 v;
if (cap.Intersect(ref segment, out s, out v))
{
scalar = s;
p = v;
}
cap.Center = P2;
if (cap.Intersect(ref segment, out s, out v) && s < scalar)
{
scalar = s;
p = v;
}
return scalar >= 0f && scalar <= 1f;
}
/// <summary>
/// Intersects a segment with this collision skin part and returns the intersection point that is nearest to the
/// beginning of the segment.
/// </summary>
/// <param name="segment">The segment to intersect with.</param>
/// <param name="scalar">Returns a value between 0 and 1 indicating where on the segment the first intersection occurs.</param>
/// <param name="point">Returns the point of the first intersection.</param>
/// <returns>Returns a value indicating whether the segment intersects with the part.</returns>
public override bool Intersect(ref Segment segment, out float scalar, out Vector3 point)
{
scalar = float.PositiveInfinity;
point = Vector3.Zero;
float scalar1;
Vector3 point1;
for (int i = 0; i < FaceCount; i++)
{
var face = Face(i);
Vector3 p0;
World(face[0], out p0);
var plane = new Plane(p0, _faceNormals[i]);
if (plane.Intersect(ref segment, out scalar1, out point1) &&
scalar1 < scalar && IsPointOnFace(i, ref point1, true))
{
scalar = scalar1;
point = point1;
}
}
return !float.IsPositiveInfinity(scalar);
}
/// <summary>
/// Gets the closest point on the triangle to the specified segment.
/// </summary>
/// <remarks>
/// The result can either be any of the vertices, on one of the edges, or another point within the interior of the triangle.
/// </remarks>
/// <param name="seg">The segment against which to find the closest triangle point.</param>
/// <param name="segPoint">Returns the point on the segment that is closest.</param>
/// <param name="triPoint">Returns the point on the triangle that is closest.</param>
/// <returns>Returns a value indicating whether the closest point is in the interior of the triangle (not on any vertex or edge).</returns>
public bool ClosestPointTo(ref Segment seg, out float scalar, out Vector3 segPoint, out Vector3 triPoint)
{
// segment intersects triangle
if (this.Intersect(ref seg, out scalar, out triPoint))
{
segPoint = triPoint;
return true;
}
Vector3 v;
float minDist = float.MaxValue, dtri;
bool p1inside, p2inside;
segPoint = Vector3.Zero;
Vector3.Dot(ref Normal, ref V1, out dtri);
p1inside = this.Contains(ref seg.P1);
p2inside = this.Contains(ref seg.P2);
// both points inside triangle
if (p1inside && p2inside)
{
float d1, d2;
Vector3.Dot(ref Normal, ref seg.P1, out d1);
Vector3.Dot(ref Normal, ref seg.P2, out d2);
d1 -= dtri;
d2 -= dtri;
if (Math.Abs(d2 - d1) < Constants.Epsilon)
{
// segment is parallel to triangle
minDist = d1;
Vector3.Add(ref seg.P1, ref seg.P2, out segPoint);
Vector3.Multiply(ref segPoint, 0.5f, out segPoint);
}
else if (Math.Abs(d1) < Math.Abs(d2))
{
segPoint = seg.P1;
minDist = d1;
scalar = 0f;
}
else
{
segPoint = seg.P2;
minDist = d2;
scalar = 1f;
}
Vector3.Multiply(ref Normal, -minDist, out v);
Vector3.Add(ref segPoint, ref v, out triPoint);
return true;
}
else if (p1inside)
segPoint = seg.P1;
else if (p2inside)
segPoint = seg.P2;
// one point is inside triangle
if (p1inside || p2inside)
{
Vector3.Dot(ref Normal, ref segPoint, out minDist);
minDist -= dtri;
Vector3.Multiply(ref Normal, -minDist, out v);
Vector3.Add(ref segPoint, ref v, out triPoint);
minDist = Math.Abs(minDist);
minDist *= minDist;
scalar = p1inside ? 0f : 1f;
}
float sa, sb, dist;
Vector3 pa, pb;
// test edge 1
var edge = new Segment(V1, V2);
Segment.ClosestPoints(ref seg, ref edge, out sa, out pa, out sb, out pb);
Vector3.DistanceSquared(ref pa, ref pb, out dist);
if (dist < minDist)
{
minDist = dist;
scalar = sa;
segPoint = pa;
triPoint = pb;
}
// test edge 2
edge.P1 = V2;
edge.P2 = V3;
Segment.ClosestPoints(ref seg, ref edge, out sa, out pa, out sb, out pb);
Vector3.DistanceSquared(ref pa, ref pb, out dist);
if (dist < minDist)
{
minDist = dist;
scalar = sa;
segPoint = pa;
triPoint = pb;
}
// test edge 3
edge.P1 = V3;
edge.P2 = V1;
Segment.ClosestPoints(ref seg, ref edge, out sa, out pa, out sb, out pb);
Vector3.DistanceSquared(ref pa, ref pb, out dist);
if (dist < minDist)
{
minDist = dist;
scalar = sa;
segPoint = pa;
triPoint = pb;
}
return false;
}
/// <summary>
/// Intersects a line segment with the shape and returns the intersection point closest to the beginning of the segment.
/// </summary>
/// <param name="segment">The line segment to intersect.</param>
/// <param name="scalar">A value between 0 and 1 indicating how far along the segment the intersection occurs.</param>
/// <param name="p">The point of the intersection closest to the beginning of the line segment.</param>
/// <returns>Returns a value indicating whether there is an intersection.</returns>
public bool Intersect(ref Segment seg, out float scalar, out Vector3 p)
{
scalar = float.NaN;
p = Vector3.Zero;
bool switched = false;
Segment backup = seg;
Vector3 v12, v13, p21, v1p1, e, n;
float d, t, v, w;
Vector3.Subtract(ref V2, ref V1, out v12);
Vector3.Subtract(ref V3, ref V1, out v13);
Vector3.Subtract(ref seg.P1, ref seg.P2, out p21);
Vector3.Cross(ref v12, ref v13, out n);
Vector3.Dot(ref n, ref p21, out d);
if (Math.Abs(d) < Constants.Epsilon)
return false; // segment is parallel
else if (d < 0f)
{
backup = seg;
p = seg.P1;
seg.P1 = seg.P2;
seg.P2 = p;
switched = true;
Vector3.Subtract(ref seg.P1, ref seg.P2, out p21);
d = -d;
}
Vector3.Subtract(ref seg.P1, ref V1, out v1p1);
Vector3.Dot(ref n, ref v1p1, out t);
Vector3.Cross(ref p21, ref v1p1, out e);
Vector3.Dot(ref v13, ref e, out v);
if (v < 0f || v > d)
return false; // intersects outside triangle
Vector3.Dot(ref v12, ref e, out w);
w = -w;
if (w < 0f || v + w > d)
return false; // intersects outside triangle
d = 1f / d;
t *= d;
v *= d;
w *= d;
scalar = t;
// compute intersect point from barycentric coordinates
Vector3.Multiply(ref v12, v, out v12);
Vector3.Multiply(ref v13, w, out v13);
Vector3.Add(ref V1, ref v12, out p);
Vector3.Add(ref p, ref v13, out p);
if (switched)
{
seg = backup;
scalar = 1 - scalar;
}
return scalar >= 0f && scalar <= 1f;
}
/// <summary>
/// Gets a triangle edge.
/// </summary>
/// <param name="index">The index of the triangle edge, or the first vertex that makes up the edge: 1, 2 or 3.</param>
/// <param name="edge">Returns the edge line segment.</param>
public void Edge(int index, out Segment edge)
{
switch (index)
{
case 1:
edge.P1 = V1;
edge.P2 = V2;
break;
case 2:
edge.P1 = V2;
edge.P2 = V3;
break;
case 3:
edge.P1 = V3;
edge.P2 = V1;
break;
default:
throw new ArgumentException("Invalid triangle edge index.", "index");
}
}
/// <summary>
/// Intersects a segment with this collision skin part and returns the intersection point that is nearest to the
/// beginning of the segment.
/// </summary>
/// <param name="segment">The segment to intersect with.</param>
/// <param name="scalar">Returns a value between 0 and 1 indicating where on the segment the first intersection occurs.</param>
/// <param name="point">Returns the point of the first intersection.</param>
/// <returns>Returns a value indicating whether the segment intersects with the part.</returns>
public override bool Intersect(ref Segment segment, out float scalar, out Vector3 point)
{
return Plane.Intersect(ref segment, out scalar, out point);
}
public Segment fireBullet()
{
canFire = false;
this.bullets--;
//calculate innacuracy offset
Vector3 vOffset = new Vector3((float)random.NextDouble() - 0.5f, (float)random.NextDouble() - 0.5f, (float)random.NextDouble() - 0.5f);
vOffset *= fAccuracyCoefficient;
//calculate position bullet will be fired at
vFireAt_Position = this.Position;
vFireAt_Position += this.Forward * fBulletRange;
vFireAt_Position += vOffset;
drawBullet = true;
m_Timer.AddTimer("Aircraft Fire Cooldown", fRateOfFire, resetFire, false);
Segment Ray = new Segment(this.Position, vFireAt_Position);
SoundManager.Get().PlaySoundCue("PlaneMachineGun");
return Ray;
}
/// <summary> /// When overridden in a derived class, intersects a segment with the collision part, returning the intersection nearest /// to the beginning of the segment. /// </summary> /// <param name="segment">The segment to intersect with.</param> /// <param name="scalar">Returns a value between 0 and 1 indicating where on the segment the first intersection occurs.</param> /// <param name="point">Returns the point of the first intersection.</param> /// <returns>Returns a value indicating whether the segment intersects with the part.</returns> public abstract bool Intersect(ref Segment segment, out float scalar, out Vector3 point);
/// <summary>
/// Intersects a segment with all parts of the composition and returns the intersection point that is nearest to the
/// beginning of the segment.
/// </summary>
/// <param name="segment">The segment to intersect with.</param>
/// <param name="scalar">Returns a value between 0 and 1 indicating where on the segment the first intersection occurs.</param>
/// <param name="point">Returns the point of the first intersection.</param>
/// <returns>Returns a value indicating whether the segment intersects with any part of the composition.</returns>
public bool Intersect(ref Segment s, out float scalar, out Vector3 point)
{
scalar = float.PositiveInfinity;
point = Vector3.Zero;
float scalar1;
Vector3 point1;
for (int i = 0; i < _parts.Count; i++)
{
if (_parts[i].Intersect(ref s, out scalar1, out point1) && scalar1 < scalar)
{
scalar = scalar1;
point = point1;
}
}
return !float.IsPositiveInfinity(scalar);
}
public Segment FireBullet()
{
canFire = false;
drawBullet = true;
//calculate innacuracy offset
Vector3 vOffset = new Vector3((float)random.NextDouble() - 0.5f, (float)random.NextDouble() - 0.5f, (float)random.NextDouble() - 0.5f);
vOffset *= fAccuracyCoefficient;
vFireAt_Position = vTarget_Position + vOffset;
m_Timer.AddTimer("EnemyBoat Fire Cooldown", fRateOfFire, resetFire, false);
Segment Ray = new Segment(this.Position, vFireAt_Position);
GameState.Get().ParticlesManager.effectFlakBurst(vFireAt_Position + GameState.Get().Aircraft.Forward * 15.0f);
return Ray;
}
/// <summary>
/// Attempts to encapsulate a cloud of points within a capsule. This may not produce an optimal or exact fit. The results
/// are approximate.
/// </summary>
/// <param name="points">The list of points with which to build an enclosing capsule.</param>
/// <param name="capsule">Returns the capsule containing all points.</param>
public static void Fit(IList<Vector3> points, out Capsule capsule)
{
capsule = new Capsule();
Vector3 axis, axisNeg;
GeometryHelper.ComputeMaxSpreadAxis(points, out axis);
Vector3.Negate(ref axis, out axisNeg);
if (axis.LengthSquared() < Constants.Epsilon)
return;
GeometryHelper.ComputeExtremePoint(points, ref axis, out capsule.P2);
GeometryHelper.ComputeExtremePoint(points, ref axisNeg, out capsule.P1);
Segment s = new Segment(capsule.P1, capsule.P2);
for (int i = 0; i < points.Count; i++)
{
var p = points[i];
float x = s.DistanceSquaredTo(ref p);
if (x > capsule.Radius)
{
capsule.Radius = x;
}
}
capsule.Radius = (float)Math.Sqrt(capsule.Radius);
Vector3.Multiply(ref axis, capsule.Radius, out axis);
Vector3.Negate(ref axis, out axisNeg);
Vector3.Add(ref capsule.P1, ref axis, out capsule.P1);
Vector3.Add(ref capsule.P2, ref axisNeg, out capsule.P2);
}
/// <summary>
/// Determines whether the specified point, when projected onto the face plane of the polyhedron, is within the face.
/// </summary>
/// <param name="faceIndex">The index of the face in which to check containment.</param>
/// <param name="p">The point in world-space that is either inside or outside the face.</param>
/// <param name="inclusive">Indicates whether points on the edge or vertices of a face should be considered within the face.</param>
/// <returns>Returns a value indicating whether the point is contained within the face.</returns>
public bool IsPointOnFace(int faceIndex, ref Vector3 p, bool inclusive)
{
int[] face = Face(faceIndex);
int low = 0, high = face.Length;
Vector3 normal;
FaceNormal(faceIndex, out normal);
Segment s;
Vector3 p0;
World(face[0], out p0);
do
{
int mid = (low + high) / 2;
Vector3 p1;
World(face[mid], out p1);
s = new Segment(p0, p1);
if ((mid == face.Length - 1 || mid == 1) &&
s.DistanceSquaredTo(ref p) < Constants.Epsilon)
{
return inclusive;
}
if (GeometryHelper.IsTriangleCcw(ref normal, ref s.P1, ref s.P2, ref p))
{
low = mid;
}
else
{
high = mid;
}
}
while (low + 1 < high);
if (low == 0 || high == face.Length) return false;
World(face[low], out s.P1);
World(face[high], out s.P2);
return GeometryHelper.IsTriangleCcw(ref normal, ref s.P1, ref s.P2, ref p) ||
(inclusive && s.DistanceSquaredTo(ref p) < Constants.Epsilon);
}
