public static bool RayCastCircle(ref Vector2 pos, GGame.Math.Fix64 radius, ref RayCastInput input, ref Transform transform, out RayCastOutput output)
{
// Collision Detection in Interactive 3D Environments by Gino van den Bergen
// From Section 3.1.2
// x = s + a * r
// norm(x) = radius
output = new RayCastOutput();
Vector2 position = transform.p + MathUtils.Mul(transform.q, pos);
Vector2 s = input.Point1 - position;
GGame.Math.Fix64 b = Vector2.Dot(s, s) - radius * radius;
// Solve quadratic equation.
Vector2 r = input.Point2 - input.Point1;
GGame.Math.Fix64 c = Vector2.Dot(s, r);
GGame.Math.Fix64 rr = Vector2.Dot(r, r);
GGame.Math.Fix64 sigma = c * c - rr * b;
// Check for negative discriminant and short segment.
if (sigma < 0.0f || rr < Settings.Epsilon)
{
return(false);
}
// Find the point of intersection of the line with the circle.
GGame.Math.Fix64 a = -(c + (GGame.Math.Fix64)Fix64.Sqrt(sigma));
// Is the intersection point on the segment?
if (0.0f <= a && a <= input.MaxFraction * rr)
{
a /= rr;
output.Fraction = a;
output.Normal = s + a * r;
output.Normal.Normalize();
return(true);
}
return(false);
}
public static bool RayCastPolygon(Vertices vertices, Vertices normals, ref RayCastInput input, ref Transform transform, out RayCastOutput output)
{
output = new RayCastOutput();
// Put the ray into the polygon's frame of reference.
Vector2 p1 = MathUtils.MulT(transform.q, input.Point1 - transform.p);
Vector2 p2 = MathUtils.MulT(transform.q, input.Point2 - transform.p);
Vector2 d = p2 - p1;
GGame.Math.Fix64 lower = 0.0f, upper = input.MaxFraction;
int index = -1;
for (int i = 0; i < vertices.Count; ++i)
{
// p = p1 + a * d
// dot(normal, p - v) = 0
// dot(normal, p1 - v) + a * dot(normal, d) = 0
GGame.Math.Fix64 numerator = Vector2.Dot(normals[i], vertices[i] - p1);
GGame.Math.Fix64 denominator = Vector2.Dot(normals[i], d);
if (denominator == 0.0f)
{
if (numerator < 0.0f)
{
return(false);
}
}
else
{
// Note: we want this predicate without division:
// lower < numerator / denominator, where denominator < 0
// Since denominator < 0, we have to flip the inequality:
// lower < numerator / denominator <==> denominator * lower > numerator.
if (denominator < 0.0f && numerator < lower * denominator)
{
// Increase lower.
// The segment enters this half-space.
lower = numerator / denominator;
index = i;
}
else if (denominator > 0.0f && numerator < upper * denominator)
{
// Decrease upper.
// The segment exits this half-space.
upper = numerator / denominator;
}
}
// The use of epsilon here causes the assert on lower to trip
// in some cases. Apparently the use of epsilon was to make edge
// shapes work, but now those are handled separately.
//if (upper < lower - b2_epsilon)
if (upper < lower)
{
return(false);
}
}
Debug.Assert(0.0f <= lower && lower <= input.MaxFraction);
if (index >= 0)
{
output.Fraction = lower;
output.Normal = MathUtils.Mul(transform.q, normals[index]);
return(true);
}
return(false);
}
public static bool RayCastEdge(ref Vector2 start, ref Vector2 end, ref RayCastInput input, ref Transform transform, out RayCastOutput output)
{
// p = p1 + t * d
// v = v1 + s * e
// p1 + t * d = v1 + s * e
// s * e - t * d = p1 - v1
output = new RayCastOutput();
// Put the ray into the edge's frame of reference.
Vector2 p1 = MathUtils.MulT(transform.q, input.Point1 - transform.p);
Vector2 p2 = MathUtils.MulT(transform.q, input.Point2 - transform.p);
Vector2 d = p2 - p1;
Vector2 v1 = start;
Vector2 v2 = end;
Vector2 e = v2 - v1;
Vector2 normal = new Vector2(e.Y, -e.X); //TODO: Could possibly cache the normal.
normal.Normalize();
// q = p1 + t * d
// dot(normal, q - v1) = 0
// dot(normal, p1 - v1) + t * dot(normal, d) = 0
GGame.Math.Fix64 numerator = Vector2.Dot(normal, v1 - p1);
GGame.Math.Fix64 denominator = Vector2.Dot(normal, d);
if (denominator == 0.0f)
{
return(false);
}
GGame.Math.Fix64 t = numerator / denominator;
if (t < 0.0f || input.MaxFraction < t)
{
return(false);
}
Vector2 q = p1 + t * d;
// q = v1 + s * r
// s = dot(q - v1, r) / dot(r, r)
Vector2 r = v2 - v1;
GGame.Math.Fix64 rr = Vector2.Dot(r, r);
if (rr == 0.0f)
{
return(false);
}
GGame.Math.Fix64 s = Vector2.Dot(q - v1, r) / rr;
if (s < 0.0f || 1.0f < s)
{
return(false);
}
output.Fraction = t;
if (numerator > 0.0f)
{
output.Normal = -MathUtils.MulT(transform.q, normal);
}
else
{
output.Normal = MathUtils.MulT(transform.q, normal);
}
return(true);
}