public void Intersects(ref BoundingCircle circle, out bool result)
{
float distSq;
Vectors2.DistanceSq(ref Center, ref circle.Center, out distSq);
result = distSq <= (Radius * Radius + circle.Radius * circle.Radius);
}
/// <summary>Returns current <see cref="Vector2" /> with absolute values.</summary>
/// <param name="current">The current <see cref="Vector2" />.</param>
/// <returns>Current <see cref="Vector2" /> with absolute values.</returns>
public static Vector2 Abs(this Vector2 current)
{
Vector2 result;
Vectors2.Abs(ref current, out result);
return(result);
}
public static void GetInertia(Vector2[] vertices, out float result)
{
Contract.Requires(vertices != null);
Contract.Requires(vertices.Length > 0);
if (vertices.Length == 1)
{
result = 0;
return;
}
float denom = 0;
float numer = 0;
var v1 = vertices[vertices.Length - 1];
Vector2 v2;
for (var index = 0; index < vertices.Length; index++, v1 = v2)
{
v2 = vertices[index];
float a, b, c, d;
Vector2.Dot(ref v2, ref v2, out a);
Vector2.Dot(ref v2, ref v1, out b);
Vector2.Dot(ref v1, ref v1, out c);
Vectors2.ZCross(ref v1, ref v2, out d);
d = Math.Abs(d);
numer += d;
denom += (a + b + c) * d;
}
result = denom / (numer * 6);
}
/// <summary>
/// Determines the current angle in radians of the current <see cref="Vector2" /> and returns it.
/// </summary>
/// <param name="current">The current <see cref="Vector2" />.</param>
/// <returns>The angle in radians of the current <see cref="Vector2" />.</returns>
public static float ToAngle(this Vector2 current)
{
float result;
Vectors2.Angle(ref current, out result);
return(result);
}
public static void GetDistanceSq(ref Vector2 vertex1, ref Vector2 vertex2, ref Vector2 point,
out float result)
{
float edgeLength;
Vector2 edge, local;
Vector2.Subtract(ref point, ref vertex2, out local);
Vector2.Subtract(ref vertex1, ref vertex2, out edge);
Vectors2.Normalize(ref edge, out edgeLength, out edge);
var nProj = local.Y * edge.X - local.X * edge.Y;
var tProj = local.X * edge.X + local.Y * edge.Y;
if (tProj < 0)
{
result = tProj * tProj + nProj * nProj;
}
else if (tProj > edgeLength)
{
tProj -= edgeLength;
result = tProj * tProj + nProj * nProj;
}
else
{
result = nProj * nProj;
}
}
public bool Equals(BoundingPolygon other)
{
if (ReferenceEquals(null, other))
{
return(false);
}
if (ReferenceEquals(this, other))
{
return(true);
}
if (Vertices == null || other.Vertices == null || Vertices.Length != other.Vertices.Length)
{
return(false);
}
for (var index = 0; index < Vertices.Length; index++)
{
var vertex1 = Vertices[index];
var vertex2 = other.Vertices[index];
if (!Vectors2.Equals(ref vertex1, ref vertex2))
{
return(false);
}
}
return(true);
}
public void Intersects(ref BoundingRectangle rect, out bool result)
{
// Find the closest point to the circle within the rectangle
Vector2 closest;
Vector2.Clamp(ref Center, ref rect.Min, ref rect.Max, out closest);
// Calculate the distance between the circle's center and this closest point
float distanceSquared;
Vectors2.DistanceSq(ref Center, ref closest, out distanceSquared);
// If the distance is less than the circle's radius, an intersection occurs
result = (distanceSquared < Radius * Radius);
}
/// <summary>
/// Calculates the area of a polygon.
/// </summary>
/// <param name="vertices">The vertices of the polygon.</param>
/// <param name="result">the area.</param>
public static void GetArea(Vector2[] vertices, out float result)
{
Contract.Requires(vertices != null);
Contract.Requires(vertices.Length > 2);
float area = 0;
var v1 = vertices[vertices.Length - 1];
Vector2 v2;
for (var index = 0; index < vertices.Length; ++index, v1 = v2)
{
v2 = vertices[index];
float temp;
Vectors2.ZCross(ref v1, ref v2, out temp);
area += temp;
}
result = Math.Abs(area * .5f);
}
public static void FromVectors(Vector2[] vertices, out BoundingCircle result)
{
Contract.Requires(vertices != null);
Contract.Requires(vertices.Length > 2);
BoundingPolygon.GetCentroid(vertices, out result.Center);
result.Radius = -1;
for (var index = 0; index < vertices.Length; ++index)
{
float distSq;
Vectors2.DistanceSq(ref result.Center, ref vertices[index], out distSq);
if (result.Radius == -1 || (distSq < result.Radius))
{
result.Radius = distSq;
}
}
result.Radius = (float)Math.Sqrt(result.Radius);
}
public static bool Collide(BoundingCircle circle1, BoundingCircle circle2, out Vector2 contactPoint,
out float distance, out Vector2 normal)
{
Vector2.Subtract(ref circle2.Center, ref circle1.Center, out normal);
Vectors2.Normalize(ref normal, out distance, out normal);
distance = distance - (circle1.Radius + circle2.Radius);
bool collision = (distance <= 0);
if (collision)
{
contactPoint.X = circle2.Center.X - normal.X * circle2.Radius;
contactPoint.Y = circle2.Center.Y - normal.Y * circle2.Radius;
}
else
{
contactPoint = Vector2.Zero;
}
return(collision);
}
public static void Intersects(ref Vector2 vertex1, ref Vector2 vertex2, ref Ray2D ray, out float result,
float tolerance = 0.0001f)
{
Vector2 tangent, normal;
float edgeMagnitude;
Vector2.Subtract(ref vertex1, ref vertex2, out tangent);
Vectors2.Normalize(ref tangent, out edgeMagnitude, out tangent);
Vectors2.RightPerp(ref tangent, out normal);
float dir;
Vector2.Dot(ref normal, ref ray.Direction, out dir);
if (Math.Abs(dir) >= tolerance)
{
Vector2 originDiff;
Vector2.Subtract(ref ray.Origin, ref vertex2, out originDiff);
float actualDistance;
Vector2.Dot(ref normal, ref originDiff, out actualDistance);
var distanceFromOrigin = -(actualDistance / dir);
if (distanceFromOrigin >= 0)
{
Vector2 intersectPos;
Vector2.Multiply(ref ray.Direction, distanceFromOrigin, out intersectPos);
Vector2.Add(ref intersectPos, ref originDiff, out intersectPos);
float distanceFromSecond;
Vector2.Dot(ref intersectPos, ref tangent, out distanceFromSecond);
if (distanceFromSecond >= 0 && distanceFromSecond <= edgeMagnitude) // Hit!
{
result = distanceFromOrigin;
return;
}
}
}
// No hit.
result = -1;
}
/// <summary> Calculates the centroid of a polygon.</summary>
/// <param name="vertices">The vertices of the polygon.</param>
/// <param name="centroid">The centroid of a polygon.</param>
/// <remarks>This is also known as center of gravity/mass.</remarks>
public static void GetCentroid(Vector2[] vertices, out Vector2 centroid)
{
Contract.Requires(vertices != null);
Contract.Requires(vertices.Length > 2);
centroid = Vector2.Zero;
float temp;
float area = 0;
var v1 = vertices[vertices.Length - 1];
Vector2 v2;
for (var index = 0; index < vertices.Length; ++index, v1 = v2)
{
v2 = vertices[index];
Vectors2.ZCross(ref v1, ref v2, out temp);
area += temp;
centroid.X += ((v1.X + v2.X) * temp);
centroid.Y += ((v1.Y + v2.Y) * temp);
}
temp = 1 / (Math.Abs(area) * 3);
centroid.X *= temp;
centroid.Y *= temp;
}
public static bool Equals(ref BoundingRectangle rect1, ref BoundingRectangle rect2)
{
return(Vectors2.Equals(ref rect1.Min, ref rect2.Min) && Vectors2.Equals(ref rect1.Max, ref rect2.Max));
}
/// <summary>Clamps the specified point to be contained within the box.</summary>
/// <param name="target">The target point.</param>
/// <param name="clamped">The clamped point.</param>
public void Clamp(ref Vector2 target, out Vector2 clamped)
{
Vectors2.Clamp(ref target, ref Min, ref Max, out clamped);
}
public static bool Equals(ref LineSegment line1, ref LineSegment line2)
{
return(Vectors2.Equals(ref line1.Start, ref line2.Start) &&
Vectors2.Equals(ref line1.End, ref line2.End));
}
public static bool Equals(ref BoundingCircle circle1, ref BoundingCircle circle2)
{
return(Vectors2.Equals(ref circle1.Center, ref circle2.Center) &&
circle1.Radius.NearlyEquals(circle2.Radius));
}
public static bool Equals(ref Line line1, ref Line line2)
{
return(Vectors2.Equals(ref line1.Normal, ref line2.Normal) && line1.D.NearlyEquals(line2.D));
}
public static bool Equals(ref Ray2D ray1, ref Ray2D ray2)
{
return(Vectors2.Equals(ref ray1.Origin, ref ray2.Origin) &&
Vectors2.Equals(ref ray1.Direction, ref ray2.Direction));
}